ABSTRACT
The Millstone
operated
Hill incoherent
since 1763 to perform
densities,
and electron
have been
conducted
digital
This report
Fi -regions).
from
These
to permit
which
computer
changes
By operating
include
the echo autocorrelation
and performing
of the reflected
coherently,
below 200 km (i.e.,
signals.
spaced
pairs
of echo
it has also been possible
clutter
signals
Samples
presented
of the results
from
timing
of pulses
can be determined
pairs
ex-
the E- and
to the radar
of close-spaced
function
( stronger)
are
electron
The se measurements
modifications
appropriately
tbe unwanted
these programs.
has been
made to the system in $969 to permit
to altitudes
changes
the radar
system
long pulses
analysis
the transmission
by processing
radar
study of F2 -region
single
and spectrum
of the measurements
equipment
a synoptic
by transmitting
describes
scatter
and ion temperatures.
sweep integration
tensions
(Thomson)
in the
samples.
to subtract
tbe ionospheric
echoes.
that can now be obtained
from
CONTENTS
iii
Abstract
Svbols
vi
and Abbreviations
4
1. INTRODUCTION
11. OPERATING
A.
5
MODES
5
General
5.
33. Mode E
5
C.
Mode F
D.
Mode G
E.
Mode H
F.
Model
G.
Observing
H.
Mode Modifications
io
10
io
m.
Iv
*3
program
ii
24
EQUIPMENT
Zi
A.
General
B.
Frequency
C.
Receiver
D.
Data Sampling
E.
Timing
Equipment
1.
2.
3.
4.
5.
6.
7.
8.
B.
c.
26
29
PROCEDURE
Timing
29
Control
Computer
Computer
Gene ral
Computer
comPuter
Computer
E
F
G
H
I
Output
@tput -Modes
Output –Mode
Output –Modes
E andl
F
G and H
iv
29
29
36
36
37
37
37
39
39
Operations
General
computer OperatiOns–
MOde
compute rOperatiOns–
MOde
Compute r Operations-Mode
Computer Operations –MOde
Computer Operations -MOde
Real-Time
4.
2.
3.
4.
25
Transmitter
Control –Mode
E
Transmitter
Control –Mode
F
Transmitter
Control–Mode
G
Transmitter
Control-Mode
H
Transmitter
Control–Mode
1
Transmitter
Modulator Control
Receiver
Control
Data-Sampling
ContrOl
Real-Time
i.
2.
3.
4.
5.
6.
?5
Equipment
OPERATING
A.
2+
Control
39
4t
44
46
47
47
48
48
48
49
49
V.
ANALYSIS
53
A.
General
53
B.
Power-Profile
1.
2.
3.
C.
2:
7.
8.
D.
E.
58
Analysis
General
Phase Analysis
Magnitude Analysis – Library
Search
Ion-Composition
Problem
Collisional
Region – h < i i 8 km
Temperature
Equality Region – 148< h < i30 km
Ion-Composition
Transition
Region – i 30< h < 225 km
(J+ Region – 225 km < h
Neutral-Atmosphere
Profile
1.
2.
3.
4.
53
55
56
Mode E – Routine Analysis
Mode E – RASEM Analysis
Mode 1
Correlation-Function
1.
2.
3.
4.
53
.inalysis
Deductions
and Ion-Composition
65
General
Tn, [0] Profile
Ion-Composition
Profile
Electron-Density-Profile
Debye-Length
5*
58
59
6i
63
63
65
65
Corrections
65
65
66
67
68
Corrections
Acknowledgments
69
References
70
APPENDIX
A - Systematic Distortions
Measurements
APPENDIX
B – Statistical Errors
Measurements
in Correlation-Function
in Correlation-Function
v
79
SYMBOLS
I
1
ABBREVIATIONS
A*
complex
A*B
convolution
JAI
magnitude
[A]
concentration
[A] ~
[A]
acf
autocorrelation
c
speed of light in free
f
frequency
fo
conjugate
radar
Im (A)
imaginary
k
Boltzmann’s
——-. .
density)
space
above the earth’s
part of complex
number
constant
mass
electron
Re (A)
real part of complex
S/N
signal-to-noise
T
pulse length
Te
electron
Ti
ion temperature
Tn
neutral
T.
exospheric
density
number
ratio
temperature
temperature
temperature
Tn at h = i20 krn
Vd
drift velocity
Ah
height resolution
wavelength
ion -neutral
collision
correlation
lag
vi
1
density.
frequency
Ne
v in
A
function
ion mass
radar
A
x in kilometers
mi
Tizo
number
(number
(height)
electron
number
of A and B
center
altitude
of complex
of complex
at altitude
h
‘e
,
AND
frequency
A
surface
A
Of gas species
A
INCOHERENT
SCATTER
DENSITY,
MEASUREMENTS
TEMPERATURES,
OF
AND
AT
E-
AND
COLLISION
MILLSTONE
F-REGION
FREQUENCY
HILL
1. 1NTRODUCTION
This report
the Millstone
(Thomson)
menced
is intended to complement
Hill,
West ford,
scatter
radar
system
tron and ion temperatures.z
listed
Lincoln
in Table
These
power
the measurements
studies
directed
of F-region
incoherent
These
electron
studies
density
com-
and elec -
1963 through i970 have been published
as in a number of journal
articles,
as
measurements
bythe
pulse length
Adequate
long pulses
together
The height resolution
T according
height resolution
T to a suitable
Te and Ti requires
value.
with echo-
Ah afforded
by
to
can be achieved
However,
a spectrum
on the pulse length that may be used.
is approximately
using single
computer.
(i)
by reducing
and ion temperatures
in a digital
cT/2
c is the speed of light.
constraints
during
as well
have been conducted
performed
is determined
Ah=
)
Reports
the manner in which
vertically
of the F2-region.
measurements
obtained
Technical
that described
74.5”W)
I.
F2-region
sweep integration
where
synoptic
The results
Laboratory
onei
(42.6oN,
is operated’ for studies
in 1963 and have provided
in earlier
an earlier
Massachusetts
for electron-density
the determination
analysis
of the signals,
The overall
doppler
of the electron
and this places
broadening
of the signals
3Afi (Ref. 9), where
(2)
is the doppler
speed,
shift produced
k is Boltzmannls
of the information
constant,
on the frequency
width of tbe pulse (-l/T)
broadening.
Thus,
As discussed
spectrum
in Ref.9,
this restriction
long-pulse
this useful range is approximately
and ion temperatures.
to extend the measurements
length (thereby
increasing
fully
23-cm-wavelength
possible
to achievea
tude range
130<
on the transition
the F-region,
the papers
Afi)
listed
andlor
radar
height resolution
between
in Table
to recover
dOppler
operated
the molecular
drifts
length limits
adequate
For the 68-cm-wavelength
250<
vertically
to lower
altitudes,
one may reduce
oblique
with the beam directed
Using this radar,
incidence.
obliquely,
information
NO+) in the E-regiOn
in the E- and F-regions;
the waveUsinga
it has heen
to cover
thealti-
has been obtained
and atOmic iOns (0+) in
these results
are published
II.
..
for
directed
h< 1000 km depending upon ionospheric
of 35 km and extend tbe measurements
ions (0~,
the range
height resolution
,
. .. ...-—=
most
that the spectral
Of the overall
use fulpulse
provide
make the measurementsat
h< 260 km approximately.
and on horizontal
to one-sixth
on the minimum
observations
radar
steerable
In order
it is necessary
(3)
of electron
In order
at its mean thermal
pulse length is
measurements
system,
wavelength.
of the returns,
to about one-fifth
acceptable
a radar
.
1
over which single
conditions.
i
and h is the radar
be restricted
the minimum
Tmin~2/Af.
of altitudes
by an ion of mass mi approaching
.
in
1TABLE I
PUBLICATIONS
CONCERNING
THE MILLSTONE
HILL UHF
(68-cm WAVELENGTH)
THOMSON
SCATTER RESULTS
Year
lv!entln Covered
March,
1963
July,
December,
August,
April,
Fublicotion
September
July,
November
February 1963 to January
1964
Ref. 3
Ref. 4
Technical
Repoti 374,
Lincoln lmbcdc.ry,
(22 Jonuary 1965),
M. I.T.
DDC AD-616607
Apil,
1964
July,
November
January fhrwgh
December
Ref. 5
Technical Relwt 430,
Lincoln Laboratory, M.I.
T.
(15 November 1967),
DDC AD-668.436
January,
1965
April,
Jmwarytkwgh
August
Ref. 6
December
Technical Report 474,
Lincoln Labcr.tory,
M.I.
(8 December 1969),
T.
DDC AD-707501
1964
January through December
Ref. 7;
Technical
Lincol.
Report 481,
Laboratory,
M. I.T.
(19 January 1971 ),
DDC AD-725742
1967
January through December
Ref. 7;
Technical
Reporf 482,
Lincoln Laboratory,
(22 July 1971),
M.I.
T.
DDC AD-735727
1968
January through December
Technical
Report 499,
Lincoln Laboratory,
(23 Ja”wy
1973),
M. I.T.
DDC AD-767251/2
1969
Jwwmythrough
December
Ref. 8;
Technical Report 513,
Lincoln Laboratory,
M.I.
(23 July 1974),
T.
DDC AD-AO+38505/O
1970
January thrwgh
December
Technical Report 522,
Lincoln Laboratory, M. I.T.
(11 I%y
!
,
1976)
TABLE II
PUBLICATIONS
CONCERNING
THE MILLSTONE
HILL L-BAND
(23-cm WAVELENGTH)
THOMSON
SCATTER RESULTS
Perbd Covered
Apri 1- November
October
Unfortunately,
incidence
time.
herent scatter
limitations
spacing
resolution
ber 1975.
Ref.
13
of the L -band radar
measurements,
system
by an interval
located
adequate
~ and measuring
Peru,
is routinely
resolution
between
employed
and at Arecibo,
can be set via Eq. (1) to any desired
The spectrum
employing
by transmitting
the correlation
This approach
at Jicamarca,
for oblique-
only during the day-
on the E- and Fi -regions
As outlined in Ref. 9, this may be achieved
stations
Puerto
the
pairs
of
pairs
of
at the incoRico?
Using
value subject only to
is set independently
by the
the pulses.
technique
program
is barely
and useful data can be gathered
has now been implemented
at altitudes
before.
as it etisted
hardware
This report
from
at Millstone
(addition
Hill,
describes
the Millstone
in November
of a hard-wired
program.
permitting
measure-
about 90 and 600 km with far better
its implementation
modification
to tbe 2-pulse
between
These
Hill 2 -pulse
inco-
4969 through Decemin January
correlator)
modifications
height
1976
will be the subject
of
report.
II of this report
radar
equipment
All Z-pulse
the various
and computer
to the data to derive
operations
are available
plots of tbe various
to the data o“ a routine
basis.
3
modes
performed
physical
on request
physical
of the 2 -pulse
In Sec. 111, the modifications
in the 2-pulse
timing
results
modes of operation
measurement.
needed for operation
applied
analysis
contour
not been applied
describes
for ionospheric
equipment
procedures
for producing
has
1969
and temperature
and their purpose6
analysis
September
some changes
Section
describes
1968-
by SIN considerations.
A major
necessitated
1-pulse
November
than could be achieved
scatter
a future
12
between
This 2-pulse
ments of density
herent
Ref.
the height resolution
imposed
maximum
11
1969
T separated
radar
Ref.
September
taken with the same separation.
this scheme,
10
1968-
radar.
of length
echo samples
1968
we have sought to obtain information
vertical-incidence
pulses
M.y
Ref.
September
scatter
Therefore,
1964
1965-
the sensitivity
Thomson
P.bl icotion
are presented
to outside users.
parameters
to the original
are discussed.
upon the received
results
(altitude-time
experiments
Section
signals.
IV
The
in Sec. V.
A program
contours),
exists
but it
11. OPERATING
A.
MODES
GENERAL
The goal of the 2-pulse
ionosphere,
where
heighi gradients
those encountered
H, and I–
experiments
at greater
range
ments,
and other characteristics
Modes
profiles.
experimental
and scale
heights
each designed
purposes.
TabIe
for these modes,
in the bottomside
smaller
compared
to probe
111lists
while
the altitude
Figs. i(a)
this table and the figures
Modes
efficiently
with
E, F,
G,
a specific
ranges,
through (c) give
are referenced
measure-
more
detailed
frequently
in
sections.
E and I are designed
Modes
frequencies,
F,
to study electron
G, and Hare
and composition;
tude of the acf yields
the phase provides
height resolution
designed
height resolution
A number of experiments-designated
on the acf measurements;
the following
larger
for this purpose,
altitude
information
for specific
become
heights.
have been devised
is to gain improved
deeigned
hence,
comparable
tudes where
collisions
clude a first
zero-crossing
collision
drift information.
to extend outtoa.t
to the local
least
smear
temperatures,
the acf of the scattered
frequency,
ionospheric
scale
height.
function).
of the function,
Theacf
of the function
from
scattered-power
motions,
power.
and composition
zero- crossing
the correlation
and minimum
they measure
Each mode bas been designed
thesecond
severely
hence,
to study ionospheric
they measure
the temperature,
plasma
density;
collision
The magni-
information
while
to probe with a
measurements
(except
are
atloweralti-
This is needed in order
which considerable
to in-
information
is derived.
All measurements
ground-cIutter
echoes,
antenna sidelobes.
digitally
below
which are reelections
Removal
those returns
enough for ionospheric
I
believe
scatter
length variations;
tests
The following
clutter
suggest
sections
neighboring
E
to yield
a complete
in practice
ionospheric
through the
by filtering
–a
time long
refractive
index.
We
owing to slight phase path
signal
E tbrough I in more
B.
Mode E is designed
milliseconds
the atmospheric
of the total clutter
these new Modes
entering
with
but short enough such that the clutter
is achieved
in which they have been used in experimental
I
mountains
of several
due tovarfationof
that 99 percent
are contaminated
and is accomplished
completely,
the manner
MODE
F, and I Modes)
for a period
subtraction
discuss
(E,
is necessary,
to decor relate
appreciably
tbat perfect
from
of these echoes
which are stationary
path length does notvary
do”ot
about i60 km altitude
is normally
removed.
detail,
and indicate
profile
of electron
program.
E- and F-region
density.
A fOO-psec
from
pulse is used,
6 km at the lower
than i5-km
spacing,
C.
F
MODE
altitudes
however,
Mode F is designed
vicinity
of the ionospheric
in tbe lower
imaginary
giving
a height resolution
to 15 km at the higher
Ab . 15 km.
altitudes
The sample
(Table
III);
interval
samples
varies
with less
are not independent.
to yield
profiles
E-region,
part of that region.
part of the correlation
of electron
and ion temperatures
and also a profile
of ion-neutral
Due to the need for clutter
function
is omitted
collision
subtraction,
to avoid doubling
Te and Ti in the
frequency
the calculation
the integration
Uin
of the
time.
All
TABLE
OPERATING
Altitude
Sample
Height
Range’
Interval
(km)
(km)
Resolution
(km)
Mcde
E
F
MODES
92 to 176
176 to 347
347 to 677
Ill
AND
THEIR
Meawrernent
6
15
9
15
15
15
Tots I power
65
Real part of
106 to 124
35
124to
166
6
167 to 317
15
6to
FUNCTIONS
Range of
step
Spacing*
Interval
(Ps:c)
(p~e;)
NA
NA
Clutter
Subtraction
Yes
No
No
12
corre Ioti on
Yes
o to 380
20
O to 380
20
No
o to 190
10
No
Yes
function
complex
m
G
15 to 27
correlot ion
function
Complex
H
215 to 515
I
56 to 140
‘Slightly
different
altitudes
in Mcde
fHeight
resolution
+Themaximum
30 to 42
30
1.5
3
altitude
rrmgesapply
E, -2kmin
Mcde
is.afunction
lagmeasured
5A d-km sample interval
G,
oflag-see
isafunction
and 6-to
Total power
for data collected
.nd Okm in Mcde
Fig.
prior to Decembsr
NA
1971:
NA
add 10km
Yes
to all
H.
1.
ofaltitude-see
12-km height
corre Iat i on
function
resolution
Fig.
1.
apply
for data taken before 30 Decembr
1970.
TIME-BASE CENTER
cm.AY. HE,GHT+
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AS ABOVE
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W~Ib38’h3..1.9..=u,sa
‘1=.
(a) Mode F.
Fig. i(a-c).
Diagrams showing time-base
delay t of first
for computing correlation
for different pulse spacings ?.
“:1
I
7
sample
of each pair
TEzE!_
j
,,
I
4
t s..T.bl.
111
W.dm
.l!ild.
AO!w”.
(b) Mode G.
Fig. i(a-c).
Continued.
-lEzL
I TIME-CASE
I CENTER
t
A’P
,..)
HE,
GHT
(km)
,,,-,
1,s3
1“”-1
II III lmiTTmTTTl
, 5,
I
0
I
I
1.55215
10 20
.
I
.
30 ] 40
I
.
I
.
50
I
.
60
I
m
I
80
I
90
I
lW
I .
110 120
.
..0...0
.
.
.
.
.
.
1,57
1
1
.tmmw@!
maIokm.!?Ime-bwd+, f+ T. Full,., 4 .m.-he delmp,,W, I,*W.6”. r d,.- i,I.t.ld ASABOVE,
(c) Mode H.
Fig. i (a-c).
Continued.
9
.
.
.
plasma-drift
information
difference
between
A 40.psec
the magnitude
pulse is used,
interval
sample
portion,
to a scheme
of averaging
(Fig. 1).
from
above
that covered
not expected
altitude,
results
from
adjacent
adjacent
(Table
III);
in the upper
lags due
Such averaging
6-km height =egions
but a shorter
im-
are no longer
maximum
lag applies
at the higher
is 20 Wsec.
T ~, and drift velocity
and its filtering
giving
degrades
Vd as a function of height in the
peak.
Ground-clutter
is not attempted.
with clutter,
echoes
(The lowest
and in very
adverse
were
Mode G
situations
of 200 km. )
Ah . 15 km, but averaging
of neighboring
this to 27 km at some correlation
i 5-km intervals
function
are not completely
is measured
a3titudes (Fig. i).
Therefore,
independent.
T = O to 380 psec,
from
time-base
lags (Fig. 4).
The spacing between
but a shorter
maximum
lag
lags is 20 vsec.
MODE R
to as high an aItitude
designed
Te,
results
Over
be studied
the increase
the acf is measured
(Fig. 1).
MODE
adjacent
region
in ionospheric
range of correlation
giving
with this mode.
temperature
only from
this to 42 km at some
30-km intervals
F-region,
This mode is also specifically
which useful nighttime
returns
of neighboring
correlation
are not completely
time-base
lags (Fig. i).
Ac-
independent
by Mode H, the echo power
and decrease
in comparison
is then reduced
spectrum widens owing to
9.
in ion mass;
this causes the interesting
with the Mode F and G values.
r . 0 to i9 O psec,
The spacing
ionospheric
at these times.
Ah = 30 km, but averaging
examined
to be reduced
in the topside
below the F2 peak from
F and G, degrades
from
the altitude
and Vd profiles
F and G may be omitted
pulse is used,
as in Modes
cordingly,
but a shorter
maximum
Accordingly,
lag applies
at the higher
to *IJ wee.
I
Mode 1 is designed
region
covered
values
using ionosonde
A 20-psec
extends
to yield
however,
an electron
density
upward into the lower
determinations
pulse is used,
giving
in the ionospheric
D-region.
to allow normalization
The
of the density
of foE.
Ah . 3 km.
The sample
are very
weak,
and below
the D-region
which are thought to be caused by aircraft.
the height region
profile
E-region
interval
is f. 5 km; adjacent
sam-
are not independent.
Mode I signals
observed
Ti,
as can usefully
so that Modes
A 200-psec
samples,
altitudes
to yield
to include enough of the region
are obtained
ples,
lags
to yield Ti,
pulse is used,
Mode H is designed
,
of Mode F, the
to $2 km at some correlation
by Mode F as high as the layer
as in Mode F,
applie S at the bigher
F.
are not independent
is often seen to be contaminated
The correlation
,,~
from
O to 380 psec,
has been seen out to ranges
A 100-~sec
samples,
., !.
portion
along the time base (Fig. i).
but results
to extend to these ranges,
however,
this clutter
I
samples
altitude
MODE G
region
.
In the lower
3-km samples
The spacing between
This mode is designed
,1
‘;!
the small
part of the acf.
Ah . 6 km.
neighboring
also neglects
independent.
altitudes
E.
of these data therefore
is 6 km, but Ah is degraded
of the acfrs,
The acf is measured
D.
and real
giving
interval
the statistics
completely
Analysis
is 3 km, but adjacent
the sample
proves
is thus lost.
that can be studied.
io
These
‘fledge*
weak clutter
essentially
returns
set a lower
limit
are
to
The D-region
Mode 1 observations
have been the subject
paper, 14 but are in-
of a separate
eluded here for completeness.
G.
OBSERVING
PROGRAM
The observing
program
in that any sequence
of modes
might use a repeated
during
Such a scheme
duration.
Operations
Besides
to-time.
of E-mgicm
These
A few operations
were
i 5 min.
EFFFFGH),
termed
consisting
to observe
The Mode I signals
Tables
W,
A typical
of 8 and 20 min..
observing
are very
of E Modes
achieved
sequence
a sequence
every
hour.
satellite.
disturbances
in these
496?.
time-
has been modiOccasional
One eclipse
run in rapid succession
ionospheric
of 30-min.
have been run from
the typical
completing
Respectively.
(e.g.,
has
2-rein.
with fine time resolu-
E NJOde (RASEM).
usually
i“ coordination
weak and require
with Wallops
long integration
Island rocket
times
(typically
by night).
V, and VI provide
November
programs
tides,
oPeratiOn
respectively,
sequence
the S/N differences
pass of a scientific
traveling
&Apid Sequence
by day and 30 min.
tained from
times
a complete
specialized
have been made during an overhead
have been conducted
launches.
i
on Mode F (e.g.,
more
atmospheric
Mode I bas been run only a few times,
4
with integration
of maintaining
may be used.
of 4, 10, 8, a“d 4 min.,
are made unequal to offset
observations,
been observed.
times
times
E, F, G, H, and I is flexible
such as this have he en run about once a month since November
these routine
fied to concentrate
of integration
EH sequence
times
using Modes
with integraticm
For observations
observations
runs),
and choice
sequence
has the merit
The integration
modes.
tion.
EFGH
the day and a repeated
at night.
‘,,;
that can be established
lists
of regular
1969 through December
2-pulse,
4975.
RASEM,
and Mode I operations
Some RASEM
results
ob-
have been presented
in Ref. 45.
H.
MODE
MODIFICATIONS
The evolution
to existing
modes
of the Z-pulse
that affect
their dates of implementation,
(i)
6 November
(Sec. IV-B
(2)
(3)
at Millstone
analysis,
and the locations
20 December
1970-
three
additional
lower
16 December
changes
3971-
These
modifications
modifications,
with them are given belOw:
was modified
XI).
Fig. l(a),
is written
of the data.
in the text dealing
added to Mode F (Sec. V-A,
but many comments
Hill has seem three major
and quality
1970 – the mamner of noise measurement
and Table
ment (Table
This report
program
collection,
timing
E-region
and Table
modified
altitudes
were
III).
the altitudes
of measure-
HI).
to apply specifically
have been included
to data collected
to cover
commencing
tbe operations
prior
i6 December
to that date.
i973,
TABLE
TWO-PULSE
UHF
IV
OBSERVATIONS
PRIOR
TO
1976
start
End
(GMT)
(GMT)
1440
1410
Modes F, G only
19-2U Decemlxx
0200
0200
Modes F, G,
H only
30 December
1445
2050
Mode,
F, G,
H Only
January
1350
1450
Mocks F, G,
H only
30 Ja”IMty
1420
2040
1420
1440
5 March
15C0
2250
Pre-eclip*
run
6 March
15C0
2215
Pre-eclipse
run
7 March
1350
2400
Eclipse olxervations
9 March
1415
1940
9 Apri I
1415
1940
1 May
1330
2050
2 July
1215
1900
July
1305
0225
August
125S
0140
25 Augtmt
2105
2240
Mcdes E, G,
H only
26 Augwt
a345
0510
Mcdes E, G,
H only
19 Septembsr
1130
232U
6 Novemter
14@l
21C0
30-3 I Decemter
2010
04w
Date
Comments
~9
28-29
Nc.vembar
1970
—
13-14
5-6
25-26
9-10
February
Low tmnsmitter
power
First Mcde F with correlation
fun.tio”s every 3 km (h <127
km)
I
I
*2
—--..,
--:.. . .
.-
TABLE
IV (Continued)
Start
End
(GMT)
(GMT)
6 January
1430
2100
January
0105
0200
8-9
February
2240
0400
23-24
Febru.wy
1625
I 650
25-26
March
1525
1540
13- /4 April
2135
2050
10-11
May
2015
2015
June
21@l
2100
Date
Comments
1971
—
29-30
3-4
July
2005
0900
27 July
1410
2010
28 Ju[y
0045
1415
26-27
I
,,
30-31
August
2045
2000
21-22
September
1610
1625
Mode F with 20-Psec
Modes E, G,
Only
pulse
H only
Mode E gced
Adder+
sudden cammencemenl
Adalert
magstorm
23-24
Octo!xm
1135
1120
16-17
November
I&Xl
1640
21-22
December
1535
1755
27 December
1415
2135
Modes E, F only (tidal
studies)
28 Decemker
1310
2115
Modes E, F only (tidal
studies)
29 Decemter
1330
I 900
Modes E, F only (tidal
studies)
30 December
1330
2045
Modes E, F only (tidal
studies)
TABLE
stat
IV
(Continued)
End
Comments
(GMT)
(GMT)
January
1710
1820
February
22C0
0500
1603
1700
March
16CiI
1640
3 Apri I
1300
2100
EFFFFGH
(tidal
studies)
4 April
1300
2330
EFFFFGH
(tidal
studies)
5 April
1505
2330
EFFFFGH
(tidal
studies)
6 April
1250
2100
EFFFFGH
(tidal
studies)
7 April
I 500
2320
EFFFFGH
(tidal
studies)
16 May
1025
2400
EFFFFGH
(m.agstmn alert)
17 May
I 020
2345
EFFFFGH
(rn.agstorm alert)
18 May
1010
2350
EFFFFGH
(magstorm alert)
DcIte
~
11-12
7-8
1-2 March
28-i9
.~
I
20-21
June
1515
1600
24-25
July
1810
2205
17-18
Augmt
1135
1615
20-21
September
1000
1340
21-22
September
1430
2330
EFF FGH (tidal
studies)
23 September
0955
2400
EFF FGH
(tidal
studies)
24 September
I 000
2300
EFFFGH
(tidal
studies)
October
1340
1550
21-22
November
1415
2205
1>13
Decem&r
1155
1200
13 Decernbsr
1215
2345
EFFFFGH
(tidal
studies)
14 December
I 2C0
2305
EFFFFGH
(tidal
studies)
24-25
TABLE IV (Continued)
start
End
(GMT)
(GMT)
January
1720
2145
March
2225
2235
April
1640
1940
8-9 MOy
1730
2320
10 May
1715
1955
AEROS
Date
C.mnments
1973
24-25
6-7
13-14
.:
and AEROS transit
transit
5-6
June
1835
2100
ISIS II transit
18-19
June
1450
2200
Magsiorm
a Iert
20 June
1145
2020
21 June
1150
2230
EFFFFGH
(tidal
st.dies)
22 June
1125
2230
EFFFFGH
(tidal
studies)
(tidal
studies)
23 June
1210
I91O
EFFFFGH
10 July
1805
1925
AEROS transit
AEROS
30-31
July
2005
2155
28-29
August
1530
2210
24-25
September
I 835
2315
26 September
1200
2230
EFFFFGH
(tidal
studies)
27 September
1150
2200
EFFFFGH
(tidal
studies)
28 September
1150
2210
EFFFF GH (tidal
studies)
25 October
12C0
2040
6 November
1915
2145
8 November
1955
2200
10 November
1915
2145
23 November
1225
2135
6 DecemEer
1135
1300
Decembsr
2030
2150
19 Decemker
1235
2145
20 December
1235
2130
21 December
1540
2120
17-18
I
#
Magstorm alert
i5
EFFFFGH
transit
(tidal
studies)
TABLE
IV (Continued)
start
End
(GMT)
(GMT)
3 January
1215
2235
4 Janmry
1225
2248
5 January
1205
2230
16 January
1115
2115
14 February
1545
1745
15 Febrvary
1540
1755
22 February
1135
2144
4 March
1225
1350
18 March
1110
2205
EFFFFGH
(tidal
studies)
19 March
1115
2240
EFFFFGH
(tidal
studies)
20 March
1105
2300
EFFFFGH
(tidal
studies)
19 Apri I
0220
0450
30 Apri I
1055
1915
EFFFFGH
(tidal
studies)
17 May
1450
1750
28 hby
1015
2340
EFFFFGH
(tidal
studies)
2 June
I 045
2355
EFFFFGH
(tidal
studies)
18 June
0940
2240
EFFFFGH
(tidal
studies)
19 June
loa5
0015
EFFFFGH
(tidal
studies)
1545
1715
0315
0?20
Modes E, Honly
1 August
1025
2350
EFFFFGH
(tidal
studies)
10 August
1130
2325
EFFFFGH
(tidal
studies)
11 AuguN
I 050
2245
EFFFFGH
(tidal
st”dies)
12 August
1040
0C05
EFFFFGH
(tid~l
studies)
13 August
1050
0015
EFFFFGH(tid.al
studies)
14 August
1105
CC05
EFFFFGH
(tidal
studies)
15 August
111o
2330
EFFFFGH
(tidal
studies)
17- I B September
I 040
2105
EFFFFGH
(tidal
st”dies)
30-31
October
1455
1535
12-13
Noveinber
I21O
2215
EFFFFGH
(tidal
studies)
10-11
Decembsr
1250
2150
EFFFFGH
(tidal
studies)
13-14
December
1205
2125
EFFFFGH
(tidal
st”dies)
Date
Comments
1974
—
,,..:,
29-30
June
2 July
EFFFF GH (tidal
studies)
EFFFFGH (tidal studies)
(unable to read data tape)
TABLE IV (Continued)
Date
start
End
(GMT)
(GMT)
Comments
1975
—
15-16
January
1330
1400
12-13
Fetxuary
1150
2305
21-22
March
1725
2040
15-16
April
1440
2150
2-4
May
2145
0230
7 May
2155
2400
May
2320
2345
10 June
1055
1I June
12 June
EFFFFGH
(tidal
studies)
2240
EFFFFGH
(tidal
studies)
1035
2305
EFFFFGH
(tidal
studies)
I 030
2245
EFFFFGH
(tidal
studies)
2130
2000
11 August
1125
2250
EFFFFGH
(tida I studies)
12 August
1103
1605
EFFFFGH
(tidal
studies)
2250
EFFFFGH
(tidal
studies)
23-24
‘:/
16-18
hly
13 August
1945
1215
1355
13 October
1110
2205
EFFFFGH
(tidal
studies)
14 October
1535
2130
EFFFFGH
(tidal
studies)
15 Octoter
1040
2140
EFFFFGH
(tidal
studies)
16 October
1210
1910
EFFFFGH
(tidal
studies)
17 October
I 040
2210
EFFFFGH
(tidal
studies)
November
22Ca
2400
13 December
1210
2310
EFFFFGH
(tidalstudies)
16 December
I21O
2120
EFF FFGH (tidal
24-25
21-22
Septembsr
studies)
TABLE
RASEM
Stati
OPERATIONS
V
PRIOR
TO
1976
End
(GMT)
(GMT)
13 March
1400
20Q0
interrupted
1448-1520;
10 April
1420
22C0
Interrupted
1430-1442
Date
Comments
~
8-9
May
1545
C4Ds
Interrupted
0000-CO02
15-16
May
1555
0330
Interrupted
1758-1 806;
1700-1B20
2052-21
and 0000-0014
22-23
&y
170Q
0400
Interrupted
0000-0241
28-29
May
1540
0320
Interrupted
ODOO-0002
1345
2400
1110
2330
8-9 August
26 September
1571
—
20-21
May
1730
0340
Interrupted
OLWO-0LY38
IC-11
June
2010
2020
interrupted
0000-WCG;
23C0
0400
30 Novemter
1 December
i
-
0041-0044
10;
.. .
TABLE
MCIDE
Date
VI
I OPERATIONS
start
End
(GMT)
(GMT)
PRIOR
TO
1976
Comment
~
27-28 )November
2110
2130
Operated
with separate
recovery
31 Decemt&
1600
channel
21CQ
1971
—
23-24
April:
1545
.0040.
1972
20 January
.1730
1800
Coordinated
rocket
with Wal 10ps Island
launches.
1715
~~~1900
15 knuary
1605
1810
Ccdinated
with Wallops
rocket “iaunches
16 January
1645
2000.
Cocmdincded with W.al 10ps Island
3 I January..
Ccbrdlnated with Wallops. Island ~~~
rocket icwnches”
1973
—
rocket
1974
15 January
4
1355
1850
launches
Island
III.
A.
EQUIPMENT
GENE RAL
The system
with a brief
parameters
description
Fig. 2, directs
of the 68-cm
of the apparatus;
a pencil
there
bills.
is a virtual
In normal
to ranges
absence
operations,
of the order
ter echoes
radar
ing regions.
Figure
come from
of natural screening
out to 200 km range.
display
of 8 nmi (14.8 km).
Nearly
a,re observed
The most distant
i 50 km being the White Mountains.
Smaller
short pulse:
appear
tbe clutter
side of the antenna.
a fence would need to be over
out on tbe basis
include
of cost.
observed
has been placed
solutions
Additional
(Fig. 2).
and are prob-
along each of the three legs a distance
i.e.,
the taper
to have decreased
so that more
such
choke round its edge.
despite
the increase
and strengthening
however.
the intensity
to come via re -
these,
absorbing
netting
?./4 from the inside
energy
is directed
over the aperture
face.
toward
has been increased
by adding to the feed horn an extension
The choke appears
with the result that the effective
One final step that may have contributed
been a reworking
Unfortunately,
are believed
to reduce
of approximately
of the illumination
This last change was accomplished
a quarter-wave
is the construction
have been attempted,
returns
In an effort
the size of tbe feed horn has been increased
of the reflector,
returns
skirt to the antenna feed horn to reduce
from the horizon.
feed support legs
of the feed horn,
appear
of a Large conical
directly
t O to 20 dB.
ficiency
those at
100 ft high and seve r-al hundred feet long and thus far has been ruled
A number of less -expensive
the addition
off the tripod
incorporated
in range and
to the south are not permanent
for combatting
from
de-
by aircraft.
of the northern
the center
with
with the main
to be extended
fence over a 60- sector
In addition,
clut -
of the offend-
in New Hampshire,
that has heen considered
flections
out
conditions,
on this display
One scheme
of echces
distant
and searching
in this manner,
of an anti-clutter
These
from
and directions
The range markers
with mountains
returns
reflections
i“ the antenna sidelobes
the ranges
returns
shown in
the radio star
During very’ adverse
obtained
of 0.2-.
together
Since the antenna is on a
By transmitting
all can be identified
allows
that would prevent
of returns
in Ref.1
The antenna,
purposes.
we have been able to locate
antenna at an elevation
here.
this slight offset
beam for calibration
3 shows a PPI
the north.
ably caused
this is not repeated
strong ground returns
antenna,
beam of the steerable
note intervals
have been presented
of $00 km, and again near i 50 km.
can be detected
the steerable
system
beam 20 south of the zenith;
Cygnus to pass through the radar
hill,
radar
collecting
to have improved
that
the ef-
area of the antenna does not
in beamwidth.l
to improving
of the surface
the radiation
that has reduced
pattern
of tbe antenna has
the rms surface
tolerance
to
about an inch (h/24).
B.
FREQUENCY
CONTROL
The modifications
point where,
makes
it possible
the ground
the radar
required
citer,
described
as a rule,
to consider
returns
be obtained
from
local
the echoes
a single
oscillator
coherent
to phase-sensitive
the intensity
the receiver
to be coherent.
so that phase coherence
that all the receiver
nals must be applied
saturate
removing
are expected
equipment
above have reduced
they no longer
from
modifications
of the ground returns
frequencies,
oscillator
24
Also,
linear
as
have been made to
will be preserved.
of a simple
This
in frequency,
as well as those generated
as shown in Fig. 4.
in place
to the
gain setting.
the data by filtering
Accordingly,
rectifiers
of the ground returns
at its normal
This has
in tbe ex-
the received
rectifier
Sig-
employed
Fig. 2. Millstone
Hill Field Station,
To left is 220-ft vertically
pointing
UHF antenna.
Tripod supports horn feed at focus.
Building to right contains transmitting
and receiving
equipment.
Larger,
fully steerable
antenna operates at L-band and has been employed for ionosphere studies at
Ohlio,,e
incidence.
Fig. 3. PPI display of ground-clutter
Range marks are 14.8 km apart.
returns
22
observable
from
Millstone.
I 18-9-6603 I
TRAN&TTER
FROM
TR SWITCH
440 -MHz
AMPLIFIER
440-MHz
PREAMPLIFIER
d
440
d
410
41 O-MHZ
AMPLIFIER
A
I
II AWL!%I
I
I
I
30
w%%.
I-1
II
1
I
1
.n
1
28.2-MHZ
SYNTHESIZER
4!0
X8
MULTIPLY
4
28.2
A
L
1
2-MHz
AMPLIFIER
2-MHZ
AMPLIFIER
2-MHz
AMPLIFIER
(I
n
52.5
51.25-MHz
SYNTHESIZER
%
1
2
1
LOW
PAss
LOW
PASS
1
TO sAMPE
LOW
PASS
LOW
PASS
1
1
-AND-HOLD
I
CIRCUITS
Fig. 4. Block diagram showing frequency control system
employed for measurements
described
in this report.
23
for radar
FROM LOW- PASS FILTERS
1
SAMP\;i:~}-HLID
1
I
__
SANpLE-ANO-HOLO
CIRCUIT
118-9-660+]
__
~PLE+M()-~u
1
__
~A~pL~+,/&H~~
CIRCUIT
CIRCUIT
Am
10- BIT
REGISTER
1O-BIT
REGISTER
20-/JsecCLCCK
PULSES
1-4
I
t
T
“ DATA
ACKNOWLEDGE”
PULSES
( 1.75-psec spacing]
10-~sec
%
CLOCK PULSES
(HI)
I
] CONTROLLER
“ TAKE
0
OATA” PULSE
“INTERRU=T
AND
OIRECT
MEMORY
ACCESS
“ DATA
REQUEST
ENAELE”
PULSE
“INTERRUPT 44”
77
f
XOS 9300 COMPUTER
Fig. 5. Block diagram
employed
to measm.e
computer.
I
showing data-sampling
and data-transfer
equipment
signal voltqes
(Fig. 4) ~d c.mmnu”icate
these to
24
40”
hitherto.
With these
changes
it is possible
turns and see that this does indeed vary
The new frequency
frequency
rapidly
C.
adjacent
of a single
to receive
been modified
spacing
30-MHz
These
switch S2.
moved.
the transmitter
the radar
frequency
to
to be performed
dur-
tuned to the correct
by ~ltering
frequencies,
frequencies
the setting
rectifie
M,
in turn,
channels
This is of particular
drive
low-pass
filters
the role played
in their
importance
Frequency
by the common
rectifiers
ope r-
having a time constant
rectifiers
can be reversed
by the two phase detectors
gain m- incomplete
in attempting
has
as shown in Fig. 4. The
of the 28.2 -MHz
a pair of phase -sensitive
of the phase -sensitive
due to differences
tbe receiver
in each channel,
phase separation
to determine
of
by
the ionospheric
can be re drift ve-
accurately.
In order
to minimize
the time over which the noise in the receiver
a wide receiver
bandwidth.
Thus,
tbe overall
set at 50 kH-z and the post-detector
bandwidth at f 00 kHz,
of the order
represents
of 45 kHz.
This value
bandwidth as narrow
as possible
and the need to limit
the distortion
width (see Appendix
In order
to improve
second
has been changed.
sion was ac cmnplished
by applying
and suppression
In this way,
DATA
tbe recover-y
additional
in the receiver)
of finite band-
modifications
the time interval
operating
receiver
time to approximately
employed
Finally,
vacuum tubes,
pentodes
A solid-state
diode gates between
to -iO
2 psec.
A
tube TR switch by one employing
switch bad a cleanup time of ZOO to
was about iOO Fsec.
time is reduced
the trans -
As originally
200 psec to tmm off the transmitter.
to short- s“pp~essor-base
by inserting
have
between
condition.
to nomnal in a few microseconds.
pulses
is, carried
the gating
and suppres-
in various
receiver
various
IF
is now em-
amplifier
stages.
psec.
out in the rna.rmer indicated
aPPearing
at the outputs of the low-pass
circuits.
0“
eratine
by a. receiver
to keep the
SAMPLING
Data sampling
sampled
abow
gas-discharge
The original
is achieved
i.e.,
the turn-off
tube in the older
The time constant for recovery
ployed,
time,
req”itwd
the original
The gas-discharge
100 km,
to its normal
to reduce
b“t the new switch is restored
of the receiver
stages.
recovery
modulator
has since been rebuilt
diodes.
300 psec,
below
of the receiver
change has been to replace
solid-state
we rail bandwidth
the desire
the mnvanted noise power
data produced
at altitudes
the receiver
the UHF transmitter
The modulator
an effective
between
it is nec -
bandwidth has been
A).
mitte r pulse and the restoration
designed,
of the spectral
is correlated,
pm-detector
yielding
a compromise
(and thus minimize
to make measurements
been necessary
command
for an interval
over
from
filters
of i 00 nsec,
a range of * 5 V assigns
in Fig, 5.
(Fig. 4) are applied
a clock pulse (normally
and this voltage
any applied
25
i_
permits
two experiments
m adjacent
channel drives
By commutating
effects
es sary to employ
i
of switching
must be kept to a value that can be accepted
Each receiver
The sine and cosine
throwing
‘1
permits
transmitted
may be varied
but the separation
any systematic
pulses
two IF channels
IF amplifier.
40 ps’?c.
locity
separately
the frequencies
ated in quadrature.
D.
re -
sweep of the radar.
to provide
between
synthesizer,
,.
the capability
This provision
and, in effect,
distant clutter
with time.
(Fig, 4) provides
switch Si.
pulses
the phase of the more
RECEIVER
In order
.1
only slowly
system
via the solid-state
be changed between
ing tbe course
control
to monitor
every
to four
20 psec),
is then stored.
voltage
The video
signal voltages
‘sample-and-hold
the applied
A digital
voltages
voltmeter
a sign and one of 512 levels.
m
are
0p-
The digital
words
representing
to the computer
format
register
i.e.,
Transfer
namely,
are required
(see Sees, IV-A-4
a“d -5).
instead
of every
TIMING
equipment
etc.,
operations.
modes
the computer
In order
of the data,
channel is employed
digital
at a time
samples
time is now 7 psec and is carried
is trans-
out eve~
B timer
version
equipment
provided
i O psec
pulse length
This timing
generator
in Ref. i (A timer),
for the four preset
of the B timer
allowed
operating
a variety
made in Mode
was
which provided
Modes
E,
F,
of pulse lengths,
I.
Subsequently,
unit.
was constructed
from
by push buttons,
the desired
system.
that described
for measurements
into a single
is provided
selects
employed
to cent ml the transmitter
to the radar
it from
Tbe
combined
to synchronize
a synchrcmizing
commercially
available
but can be transferred
operating
mode by loading
the data-acceptance
pulse ( ‘,Interrupt
on each sweep of the radar
data pulse n) is required
the remainder
logic
cards.
Selec-
to the computer.
an output register
coupler
100 K, allowing
In some
of the modes
In this
with an ap-
modes
and spacings,
operation
of tbe gates.
the required
modulator
any one modulator
gates
gene rater
Accordingly,
pulses
synchronizing
the noise level
yields
and connect
pulse can hold the excite r ON.
in Fig. 6.
26
( ,,Inte r-
pulse.
terminals
via a
in the receiver
supe rheterodyne
(diode)
ON and OFF
ON and OFF
to employ
these through
hy
RF
As shown in Fig. 4, the
system.
(Fig. 4) and tO the 51.25-MHz
separate
coincident
pulse
as many as four separate
out using solid-state
it is necessary
channel for
units.
which is an inverse
require
pulse (Wake-
40’1 synchronization
equipment,
op-
equipment
This pulse is transmitted
at the receiver
(temperature)
levels
interface
the alte mate
on each of two frequencies).
by an exciter
These
the timing
inserted
pulse raises
This
The gating is carried
Associates.
proper
pdse
at the 2- and 30-MHz
(not shown in Fig. 4).
A third
with the radar
synchronizing
from
‘of pulse spacings.
hy the new timing
are generated
samples
of the next ,tlnterrupt
measurement
to amplifiers
by Sanders
and -5).
ccmve rsion to absolute
provided
(2-pulse
RF pulses
Gating is applied
factured
IV-A-4
a noise -calibration
intensity
at the computer
H and I, a second
to accept
to the end of a cycle
at the end of each sweep.
signal
are required
transmitter
In Modes
200 ~sec in advance
E and I include
operations
40 ‘t) is tram mitted to the digital
the computer
(see Sec..
the computer
to the data interface
Modes
time base.
to alert
of the sweep
rupt 4481) alerts
erate
rate,
word.
erations,
as well
multiplica-
clock
to the presence
in
time is iO.5 wsec.
receiver
was const rutted
experimental
and was initially
The new timing
tion between
pulses
the computer
position
for immediate
out at the computer
only one pair of the available
the computer
to distinguish
A second,
all these units were
coaxial
by the computer
only a single
I“ this case,
and to synchronize
for single -pulse
case,
in a 10-bit word to first
is carried
to alert
one at a time
The function of the
EQUIPMENT
and spacing
propriate
(H, I),
and transferred
register.
20 psec.
known as the B timer
spacings,
position
so that the total transfer
The data transfer
New timing -gene rater
G, and H.
first
required
In order
modes
into the computer,
in registers
and a format
into tbe memory
(3.5 #see)
In two of the operating
ferred
are stored
(switch)
place it in the location
of the samples
one word per 1.75 psec.
two cycles
E.
voltages
multiplexer
is to move the sign bit from
a 24-bit word,
tion,
the sampled
via a digital
switches
triggers.
pulses
signal
leading
the trigger
manu-
For
to im-
pulses
to gen-
13
OR** gates in such a manner
This arrangement
is indicated
some
that
schematically
I
1
+5
INVERTER
Fig. 6. Block diagram
showing manner in which
exciler ON and OFF triggers
are mixed to control
Changes
timing
reverses
reverse
of the exciter
equipment
the frequenciess
arriving
at St;
by the receiver
to be averaged
but is retained
of the
switch which
it is under the cOntrOl Of the cOmPute r and is used ‘0
appear
channels
in the pulse train.
and thereby
out in the sweep integration
E, F, G, H, and I use this capability
useful purpose,
under control
Not shown in Fig. 4 is a ‘commutate”
in which the frequencies
tates the role played
Modes
are made during the train of pulses
via switch S, in Fig. 4.
the order
the two channels
frequency
separate
transmitter
RF pulses generated.
for simplicity
(E -Mode
of timer
27
allows
any gain difference
performed
frequency
operation).
This effectively
commubetween
by the computer.
commutation
accomplishs
All
no
,
OPERATING
IV.
A.
EQUIPMENT
1.
Transmitter
Mode
iOO-~sec
frequency.
transmitted
from
the second
pulses
(Fig.
2.
for 20 sweeps.
Figure
Frequency
from
from
the first
tbe first
vs altitude.
pulse are summed
between
The roles
in which the pulses
of the computer,
out.
and causes
together
irrespective
and/or differences
the transmitter.
in the
performs
b“t is retained
on receipt
a
and then returns
This commutation
by the computer
TWO
one m each radar
the order
for all other modes)
the relationship”
and Fig. 7(a).
pulse for 20 sweeps
will be averaged
.is pe=formed
VII
of the echo power
20 s-weeps by chazging
in the gains of the two channels
7(a) shows
Control
for simplicity
and: sync pulses
of the ?!Interrupt
4411
timing
pair),
pair is made
at a fixed interpulse
operating
at an inter’pulse
shown in Fig. 8(a).
period
period
These
appear
four pulses
displaced
by counting
the number
time-base
through the logic
from
* O sweeps.
of sweeps,
since
generator
(BI
genera$or
(BZ timer),
summing
the first
network
in time-base
timer)
two each successive
of sweeps
Thus.
and resets
the maximum
the two timers
the
sweep.
A pulse counter
the B2 counter
spacing
were
as
shown irr
length,
by 20 #see per sweep.
counts the number
with the B1 [ Fig. 8(a)] every
.(wide-spaced
the last two pulses. of the series
for each pair is made to increase
of
pair as shown in Fig. 7(b).
Owing to the difference
exciter.
20 psec further
T < 380@ec
by a time-base
generates
are passed
200<
the close-spaced
are com$rdked
A pair
of the time base – one pair for de -
of 8.0 O msec ....A second
on the output of the Bi timer
is set
each sweep
to surround
of. 8.02 msec,
the transmitter
3n this way, the spacing
into coincidence
are shown in .Tahle VII and Fig.7 (b).
the other for delays
that are trazzsmitted
operating
two pulses
characteristics
(close-spaced
The wide-spaced
to control
- Mode F
on each of two frequencies
firs.$ two pulses
pulses
Returns
commutation
is transmitted
operating
iII Table
of the time base,
5).
lays O < r < i 80 ~sec
Fig. 8(a)
shown
This is under control
at the two frequencies
Transmitter
second
estimates
to handle the returns
Mode F transmitter
The
yield
so that any differences
operation.
in Mode E.
pair).
separately
are
cm each sweep
function in the E Mode (it is essential
of timer
pulses
characteristics
transmitted
are Fevers ed every
channel
transmitted
no useful
are
at the two frequencies.
receiver
of frequency,
- Mode E
timing
pulses
channels
given
pulse
Control
These
of the receiver
powers
COXTROL
E transmitter
adjacent
are
TIMING
PROCEDURE
between
forced
into
coincidence.
At the instant the Bi and B2 timers
first
of the B2 pulses
coincide
(T = O).
are forced
200 wsec.
Thus,
on the first
sweep
the second
sweep
one obtains
the correlation
and 380 ~sec.
values
The B2 timer
of T are obtained
A complication
subtraction
coherent
procedure
from
into coincidence,
The wide-spaced
the correlation
is measured
at 20 and 220 psec,
is then desynchronized
the second
pair of pulses
of the Bi and
is then separated
at T .0
and T = 200 psec.
and this continues
to the Bi timer.
by
In this way.
COI
until T = 180
all possible
in i O sweeps.
is introduced
is basically
sweep-to-sweep.
by the need to remove
a simple
For
digital
this reason,
29
filter
clutter
echoes
that removes
it is necessary
(Sec. 111-A).
echoes
to repeat
The clutter
that appear
each sweep
to be
at least
mm
Mm”,,,,%
1
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PRF [0’I, WW”P1 40”)
0
COMMUTATE
I
FREQUENCIES
i“lntemurd 44”)
I
I
—.. —
f,
I
1
+mmse.
(every 2W
~we.P)
RF PULSE
_~
-Ioopsec
‘
.
+7.9 m8ec
0
12 RF PULSE
y
FREQUENCIES
COMMUTATED
y=:;
INTERRUPT
—.—
0
44”
—
+Ioopwc
TX MoDULATOR
PULSE
E.oop$ec
.._~
+7. T8m8ec
-220/I*ec
I
+ 380psec
.,,oF,w
/
+500@c
----~
I
!
RX SUPPRESSION PULSE
NOISE cALIBRATION
PULSE
\
~----
,,.om,en
“TAKE
+770
msec
DATA” PULSE
(not .sed )
————
+ 6.4 “WC
(a)
Fig. 7(a-d).
differs from
Mode
E.
Timing diagrams (not to scale) for Modes E, F, H, and 1. Mode G
Mode F only in that all four RF pulses are $00 psec in length.
31
PRF(” Interrupt 40”)
I
r
I
+8,0
0
mm
SET r = 0 [“Interrupt
4 4“)
COMMUTATE FREQUENCY
———
I
+7.0 nwec
[every 20th sweep)
f. RF PULSES
-1
‘“w
(r=
Q, 0,20,20,40,...,
----~
I
FREQUENCIES
COMMUTATED
180psecl
JG51-LJ:::::LJLGJ
(, = 2Q0,200,220,220,240,...,
TX MODUL4TOR
S00psee)
PULSE
_____~
-220/L1Oc
-220psec
+7.78 “s,,
+380p8eo
+7.78
+500Pse0
I
r-------~
RX SUPPRESSION
PULSE
“TAKE
_——~
+6.9 msec
(b)
Mode F.
Fig. 7(a-d).
Continued.
‘1
I
1
‘1
““,{
nwec
32
DATA” PULSE
[not used)
PRF [“ Interrupt 40”)
J~
L._._..
+8.0 msec
0
SET
T =O
(“ Inierrupt
44” )
_____–_~
+7,8 m$ec
(every 20th
tl(or
f2)RF
I }
(r=
200+
f2 (or fl) RF PULSE
FREQUENCY
PULSE
0
sweep]
w:i’’’’up’::~
1’ psec
O, 0,10, IO,2O,,I9OPW1
Tx MOOUL ATOR PULSE
600psec
-i_________~
+390 psec
-Zzopsec
-220+0.
+778
msec
+778 rose,
+700psec
r-------~
7
RX SUPPRESSION PULSE
“TAKE OP.TA’CPULSE
(change RX channel)
(c)
PRF [“ Interrupt
Mode
H.
40”1
+5.0 me..
0
f)(or
f2) RF PULSE
“}
FREOUENCY
Commutate
EVERY “INTERRUPT
PULSE
f2(w
f,) RF PULSE
40”
n
0
+5.Omsec
+20pse.
~
-Zoopsec
+20 /Lsoe
+4.8msec
-200
+400/L%ec
+4.8msee
fisec
I
RX SUPPRESSION PULSE
NOISE CALIBRATION
I
+4.3msec
PULSE
I
+4. srnsec
“ TAKE DATA” PULSE
(chmqe RX channel]
+3.9m$ec
(d)
Mode I.
Fig. 7 (a-d).
Continued.
33
Wm!!.L
LRFPULSEION
,
>
RF PULSE 1 oFF
PRF l/RF
B1
PULSE 2 ONICHANGE
-
RF PULSE 2 OFF
b
MODULATOR
~
MODULATOR PULSE OFF
FREQUENCY
PULSE ON/RX oFF
R&ii
i
RX ON
TIMER
*
NoISE
+
NOISE PULSE OFF
PULSE ON
\
1
~
i
+
“INTERRUPT
44”
w
“INTERRUPT
40”
1
i
TO COMPUTER
T
(PRF 2)
B2
—
TIMER
(a)
Original
scheme;
Block diagrams
Fig. 8(a-b).
with right spacing (Fig. 6).
RF PULSE 3 ON
.
RF PULSE 3 OFF
*
RF PULSE 4 ON/CHANGE
+
RF PULSE 4 oFF
spacing
incre%ses
showing
::1
1
34
after
TO RADAR
FREQUENCY
}
every
method of generating
sweep.
RF pulses
lo-p,,,
-i
-
CLOCK PULSES
m
RF PULSE 1 ON
RF PULSE 1 OFF
PRF 1/RF PULSE 2 ON/CH&NGE FREQUENC
RF PULSE 2 OFF
01
TO .
‘ RADAR
MODULATOR PUL2E ON/RX OFF
TIMER
MODULATOR PULSE OFF
RX ON
NOISE PULSE ON
NOISE PULSE
OFF
[Recycle)
[
j RESET
COUNTER
RESET
,?:
,~
“TAKE
DATA”
TO COMPUTER
‘“INTERRUPT 44”
“ INTERRUPT 40” 1
GATE
-F!
4
OR
L
-J
,.
I
9-%
—
PRF 1)
GATE
COMMUTATE
—
OR
‘IMER
-RF
E=
PULSE 30N]
4=F’E” ‘T”’’’”
RF F’”LSE 4 ON/CHANGE FREQUENCY
I
(b)
Final
scheme;
spacing
increases
Fig. 8(a-b).
after
Continued.
35
every
second
sweep.
once in order
to get an estimate
20,40, 40,...
psec for the close-spaced
for the wide-spaced
pair [Fig.
these two on alternate
scheme
sweeps
only on every
through all spacings.
spacings.
(Figs.
pair of pulses
[ Fig. 8(b)].
second
radar
Commutation
5, 7, and 8).
from
In Modes
being measured
and receiver
3.
Transmitter
gains,
of the frequencies
Control
Mode G transmitter
[Fig.
cm one frequency
pulse transmissions
simplicity
spacing
utilize
of timer
were
From
Figs.
is the reason
the longer
Control
timing
than the pulse length (2OO ~sec),
where
frequency
between
characteristics
maximum
the first
spacing
the two pulses
etc.,
frequency
pair of pulses
for
and
and to best
simply
obtained
is transmitted.
This
edge of the second pulse rather
This also explains
commutation
employed,
since
always
as outlined
the superflu-
in Sec. 7 below.
VII and Fig. 7(c).
only a single
the maximum
overlap,
is transmitted
the ionospheric
i.e.,
pair of pulses
spacing
a single
on successive
Owing to
(i 90 ~sec)
is
is less
pulse of length
time-base
sweeps
as
echoes
are taken in the other modes.
are expected
Accordingly,
to extend out to
the transmitter
on each sweep of the time base so that a pulse of a given length is trans -
may then be obtained by taking these from
on one frequency
channels
(A/D) converters
nels is initiated
is retained
and the pulse lengths
of different
at the leading
Actually,
first
between
COntrOl is
is needed in Mode G, the
but this repetition
are shown in Table
echoes
digital
subtraction
it can be seen that Mode E is very
mitted
over
pulses
Transmitter
of Fig. 7(c).
the noise samples
is altered
VII.
one conceived,
and phase-detector
Due to the long H Mode pulse lengths,
delays
This
transmitter
that the length of all four pulses
(as in the H and I Modes).
200, 200, 210, 210, 220, 220, . . . ~sec,
diagram
except
As no clutter
so that ody
per sweep of the time base.
shown in the timing
the close-spaced
lags on the other.
– Mode H
pulse length and reduced
transmitted
of
44” pulse
in the results.
as for the F Mode,
VII,
the B2 timer
commutation
Mode H transmitter
to
to step
available.
edge of the first
Transmitter
of an ‘tInterrupt
using different
are shown in Table
why the Mode E sync pulse is located
ous E Mode frequency
with respect
is now required
prevents
to be measured
Mode G was the first
7(a) and (b) and Table
than at the leading
4.
40 to i 00 psec.
then chosen to avoid overlap
Mode G by disabling
commutation
in all respects
need not be repeated
power
between
out at the end of each cycle
on receipt
and the wide-spaced
disparity
characteristics
control
operation.
the transmitter
from
timing
from
is carried
function
for the B2 timer
– Mode G
to Mode F transmitter
7(b)] is increased
are O, 0, 20,
generator
is made to retard
hy the computer
with an inevitable
by arranging
reset-pulse
and a total of 20 sweeps
F a“d G, this frequency
always
tie
Thus, the B2 timer
sweep,
would cause the two parts of the correlation
powers
employed
and 200, 200, 220, 220, 240, 240, . . . psec
of Fig. 8(a) is accomplished
As in Mode E, this is performed
identical
the actual spacings
a pulse at 8.oO and 8.02 rnsec and commutating
the B1 timer
lags
Thus,
7(b)].
This change to the basic
to provide
of the clutter.
and repeated
is accomplished
on the second frequency.
by controlling
(Fig. 5) is transmitted
by the radar
timer
the alternate
by means of the ‘Itake-datat!
free
channel.
which pair of words
to the computer.
36
Samples
receiver
from the analog-to-
The command
pulse.
of ionospheric
This change-
In effect,
to change chanthe radar
frequency
is switched
pulse of a given
back and forth in advance
frequency
of the sync pulse so that the delay between
and the correspo”di”g
“ois,e samples
is approximately
a
t 5 instead of
7 msec.
5.
Transmitter
Mode
Control
I transmitter
timing
surements
were
adjustment
of all transmitter
single
initially
number
wing
timing
in order
the problem
can be considered
allows
the original
completely
samples
of noise
frequency
of tbe B timer,
to minimize
the delay required
suppression.
steps.
In order
the interpulse
between
mea-
wbicb allowed
In this mode,
only a
the start of the
to compensate
period
These
for the reduced
is reduced
to 5 mSec.
This
in tbe H Mode that there is no place on the time base that
free
of echoes.
Accordingly,
the radar
frequency
is switched
by the ‘rtake -data!( pulse [ Fig. 7(d)] to tbe other channel.
to be gathered
(instead
version
VII and Fig. 7(d).
in the 10-psec
made per unit time,
encountered
a point along the time base defined
on a given
are shown in Table
parameters
and the end of the receiver
of measurements
introduces
characteristics
conducted
pulse is transmitted
transmission
- Mode I
apprwxinmtely
of 4 msec).
9 msec after
a pdse
In Mode L the “Interrupt
at
This
has been transmitted
44 ‘p pulse is not used by the
computer.
Transmitter
b.
Modulator
The beam current
penultimate
amplifier)
TabIe
In Modes
VII).
length
(6OO ~sec)
in the klystron
is controlled
E, F,
is also used to initiate
to 220 ysec
wasteful,
7.
Receiver
Table
above,
table.
from
the RF drive
modulator
VII).
of the receiver.
In the RASEM
is made to reduce
the timing
is suppressed
The receive=
Provision
a fixed
used (r =
the long (600 -psec)
pulse length is
modulator
pulse is
it to 320 psec.
sequence
are especially
pulse,
insofar
as it affects
at the time the modulator
is restored
to operation
is made for manual control
returns
The noise -calibration
in the H and I Modes
accepting
pulse waveform
In Mode 1, the modulator
mode,
pulse (Fig. 7,
pulse is maintained
the sync pulse by 22o psec and
strong,
employed
after
of the turn-on
causing
samples
of noise,
and marks
the receivers.
pulse is turned on.
time;
receiver
the position
This is true
given in the
this is useful when the near-
saturation.
only in the E and I Modes,
which in these modes
As noted
the sync pulse at delays
is placed
at the end of
The IItake -data!! pulse is em-
the time base and turned off at the same time as the receiver.
ployed
via a modulator
the widest
pulse precedes
(and in the klystron
Control
the receiver
ground clutter
of the transmitter
long enough to encompass
suppression
VIII summarizes
for all modes.
separately
The “modulator-on”
(Table
and provision
final amplifiers
G, and H, the transmitter
that is just
380 psec for the G Mode),
reduced
Control
on the time base where
are taken from
the computer
the (alternate)
starts
channel con-
taining noise only.
The sine and cosine
modes
receipt
except
F.
of every
80 sweeps
channels
Modes
For
second
of the phase detectors
Interrupt
44 pulse (i. e.,
for Mode H), and hence proceeds
E Mode commutation
performs
are commutated
E, G, and H this commutation
every
is carried
40 sweeps
(via S2 Of Fig. 4, in all
out (by the computer)
for Modes
at half the rate of the frequency
no useful purpose
37
but is implemented
because
E and G, every
commutation.
of the way in
on
TABLE Vlll
RECEIVER
TIMING
CHARACTERISTICS
M&e
Pammeter
I nterpu Ise Pericd
(n.aminal)
RX ON
“
.
F
G
H
I
8
8
8
8
5
500
500
600
700
40Q
220
220
220
220
200
NA
NA
NA
t4A
NA
NA
(N.:)
6.9
(msec)
(after sync) (Pse.)
RX OFF (before sync) (Psec)
Noise
E
Puke ON
7.0
4.3
(after sync) (msec)
Noise
Pu Ike OFF
“Take-Data”
(after
(r4)
(u)
Every 40 sweeps
NA
Every 40 sweeps
Commutation
_.A.. ...,.=..,
At Rx OFF
Pulse
sync) (rime.)
Phase Detector
At Rx OFF
---
... . .
Every 80 sweep
3.9
Every 8 sweeps
which it is obtained
mutated
every
by modifying
8 sweeps.
Mode G timing
In this instance,
only.
In Mode I, the phase detectors
the computer
counts Interrupt
are com-
40 pulses t.o control
commutation.
8.
Data-Sampling
Control
The !Isample -and-hold!!
voltages
continuously
frequency
is increased
computer
and format
words
@se,
register
made every
In Modes
controller
5).
sends
These
the sampled
20 psec,
These
at i. 75-Wee
cha””el
output register
(not shown in Fig. 5) used to commutate
controller
puter... .ln all modes,
The computer
In Modes
trati”of
delays. over
in Table
which the data samples
pulses
whi5h opens S3 whe”n th”e”cOrrect
pulses. so-that
the radar
ace
sent to the comvia S2..in Fig. 5.
a ‘rdata -
numb~r has been re-
pulse
time base is sampled over
obtaimed,.. together
via the same
and transmitting
‘take-data’!
into
governs...
and ttie phase detectors.
the train of samples
werds
is
i 0.5 psec.
are transferred
is accepted
of the computer
the frequencies
for the
thb digital
of the following
the “data-request”
40 pulse is used to initiate
H and I this pulse also arranges.
‘!data-~-questt!
and transfer
E, F, and G a request
pair. ~f words
the length of the train. by counting
request -enable 89pulse to tha: controller,
ceived.
to define
of
multiplexer
In Modes
and this is under control
(Fig. 5) serves
an Interrupt
determines
On receipt
intervals,
and only two words
of which
which receiver
The interface
the sample
are also sent to the
to take data.
during the course
intervals,
Choice
is being s.ampletl;
of the signal
In the H and I Modes,
for the computer
are transferred
7 ‘psec.
take samples
clock pulses
into the computer.
are at f O-psec
during the following
voltmeters
,,d?.ta-acknowle dge!l pulSeS to the digital
are spaced
voltages
and four words
H and I the requests
the computer
digital
E, F, and G.
as requests
the comPuter
(Fig.
representing
and associated
to iOO kHz (via S1 in Fig. 5).
via the interface
a t!da~ .reque~tu
circuits
at a 50 -kHz rate in Modes
to initiate
a second
two regions.
The
with the sample. spacings,.
are listed
~:
IX.
i
B.
REAL -’T2ME
COMPUTER
OPERATIONS
of operation,
the computers
)
1.
Gene ral
In all modes
almost
Accordingly,
continuously.
been separated.
in one section
The data samples
of the memory,
during the previous
are being written
‘,’.
,!
.,,.
.! ~
area.
period
tectors
l~(t)l
and stored
ina
Modes
of time (de finedin
program
different
is operating
section.
period
to take data samples
data samples
Table
have
IX) are stored
on the samples
In other words,
the previous
gathered
while data samples
set is being processed
is timed by the computer
E, F, G, H. and 1 uses twO frequencies
to a separate,
a pair of low-pass
and a pair of 10-bit
is to resolve
signal
sin a, where
and the arbitrary
physical
filters,
storage
the instantaneous
cos a and l~(t)l
the received
interval
the length of the integration
corresponding
phase detectors,
converters,
given
requests
and processing
in another
through count-
40 pulses.
Each Of the operating
frequency
fora
to answer
of storing
while the processing
into one area of the memory,
III each mode,
ing Interrupt
required
the functions
a pair of sample-and-hold
registers
receiver
(Figs.
cOmPlex
t is the time-base
phase-detector
in channel i as =(t) and in channel 2 as ~(t),
ith
transmitter
sweep is
Of transmissi0n8
data channel containing
4 and 5).
reference.
the information
39
circuits,
each
a pair of
a pair of A/D
The action of the phase de-
VOltage ~(t)
delay ad
an amplifier,
into orthogonal
components
a is the phase difference
Denoting
presented
the samples
he~een
obtained
tO the cOmPuter On the
TABLE IX
DATA-SAMPLING
ARRANGEMENTS
Mde
Parameter
Delay
E
.af First Data
Sample Accepted
COmputer (msec)
0.56
G
0.56
H
0.56
I
-
0.55
0.35
by
Spacing of Succeeding
Samples (psec)
20
Last Dcit.a Sample
Accepted
F
20
7.560
20
7.460
10
10
7.460
4.95
2.95
6.90
3.9
by the
Computer for This
Train OF Samples
(msec)
Delay
to First Data
NA
NA
NA
NA
NA
NA
NA
NA
NA
7.50
4.59
I
T
4
Sample in Seccmd
Wi ndc.w (rnse.)
Spacing of Succeeding
10
10
Samples (psec)
Last Data $ample
Accepted
by the
Computer
for This
Tmi.
of Samples (msec)
Number of Sweeps
Over Which Data
2
2
Are Gathered Before
Being Processed
w
All
delays are measured with respect to the Interrupt
40
40 pulse.
Xi(t)i
where
= ];(t)il
yi (t)i = I;(t)il
sin @i
x2(t)i
= l~(t)il
cos ei
y2(t)i
= l~(t)il
sin ei
(4)
@i and e i are the phase differences
and 2, respectively.
the designed
are used,
The choice
purposes
and Table
from
the phase-detector
of when to take samples
of the individual
X lists
uses to which the samples
modes.
are put.
The sections
that follow
are being received.
The altitudes
quoted below
for the various
(see Sec. II-H).
cated in Table
2.
Prior
Computer
III).
modes
describe
them depends
gathered
the computer
to modify
upon
in T#hle fx
is conducted
apply to data taken starting
it is necessary
1
and the
operations
i 6 Decem-
these a~titudes as indi-
III.
Operations
Mode E is employed
(Table
to that date,
on channels
and how to process
over which data processing
data samples
ber i97i
references
Not all the data samples
the delay intervals
out while
carried
]
Cos @i
– Mode E
to. determine
To determine
the echo power
the echo power
profile
over
as a function of delay,
the altitudes
the computer
92 to 677 km
squares
the in-
put samples
‘1
,
51 (t)i
= X:(t)i
+ Y:(t)i
= :(t)i
:*(t)i
= I=(t)il
2
Sz(t)i
= X:(t)i
+ Y;(t)i
= 7(t)i
T*(t)i
= .\F(t)il
2
The measured
unnormalized
Pm(t)
power vs delay Pm(t)
. ~ si(t)i
+ ~
i
]
where
–im
100 -psec
delay in reality
in the discussion
In general,
is then taken as the summation
(6)
wec)i
for the time separation
The frequencies
alternates
are actually
accordingly
between
commutated
between
channels.
every
the pulses
transmit-
20 sweeps,
and the
This complication
has been
in this section.
the total power
wanted noise power,
(5)
i
the shift in delay by i 00 psec allows
ted at the two frequencies.
ignored
52(t
.
Pm(t)
measured
and unwanted clutter
includes
echo power.
wanted ionospheric
Denoting
echo power,
un -
these by the subscripts
s, n,
and c, respectively,
Pm(t)
The signal
interval
of less
samples
= P~(t)
+ Pn(t)
are correlated
than i msec
over
correlated
over
an interval
the receiver
(45 kHz).
It follows
Ground-clutter
intervals
of the order
des crfbed
O< T < b~~f,
that the signal
echoes,
(7)
.
for tbe measurements
are likewise
sweep-to-sweep.
+ Pc(t)
where
and noise
of O <
T <
in this report.
samples
i.e.,
The noise
beff is the effective
over
correlated
an
samples
bandwidfi
are not correlated
cm the other hand, should be well
41
Af~*,
Of
from
over
an
TABLE X
COMPUTER
REAL-TJME
SAMPLES
Mode
Delay
Parameter
E
F
t.a First Echo
0.68
0.74
G
H
1.18
1,55
i
0.35
Sample (msec)
Sample Spacing
Delay
(psec)
40
to End of This
20
NA
NA
NA
1.24
0.86
NA
NA
NA
1.30
NA
NA
NA
NA
NA
NA
NA
NA
2.38
NA
NA
NA
NA
2.48
0.90
NA
NA
NA
Train (msec)
Delay
to First lnter-
mediate
(msec)
Echo Sample
Intermediate
Sample
60
Spacing (psec)
Delay
to End of
This Train
“i
:1
Delay
(msec)
tO Next
mediate
(msec)
l“ter-
Echo Sample
Sample Spacing
Delay
(psec)
to End of This
I 00
40
I 00
200
10
4.58
1.14
2.18
3.55
0.91
6.50
6.96
6.?6
6.95
4.00
Train (msec)
First Noise
Noise
S.ampie(msec)
Sample Spacing
40
20
20
10
10
(psec)
Last Noise
Sample (msec)
First Culibratim
6.82
7.14
7.18
7.09
4.14
7.20
NA
NA
NA
4.40
Pulse Sample (msec)
Calibration
Pulse
SOmple Sp.aciW
Last Noise
N@g
40
Pulse (msec)
Alldeloys
NA
NA
NA
NA
NA
NA
arem~s.red
7.40
with respect tothel.tem"pt
4Op"lse.
changes in these delays apply f.ard.at.a take” prim tO.]6
resulting in small shifts i.. Ititude -see Table Ill.
.,j
1
42
I
!
—.
10
(psec)
4.49
Slight
December
1971,
-
interval
as short as 8 msec,
puting the amount of power
p=(t)
= 2 ~
=(t)i
so that an estimate
that is correlated
~*(t)i+f
+ 2 ~
i
This expression
imaginary
of 2 allows
clutter
is purely
real
T(t
if the clutter
is not actually
can be obtained
by com-
sweez-tO-SWeep
- foo
+sec)i
The product ~(t)i
is per fectl;.
calculated,
for the fact that the clutter
i odd.
from
Pc(t)
v*(t
–100
wsec)i+i
(8)
.
i
part of Pc(t)
only for
of the echo power
is calculated
=*(t)i+i
correlated
from
but is assumed
sweep-to-sweep.
to be zero.
or.i? once fOr everY
can be expanded
in terms
Here,
The
the factor
Pair Of swee Ps, i.e.,
of signal,
nois$,
and
contributions
Ii(t)i:J* (t)i
H = [X, (t)i+ I“(t)i+ TC(t)il
. [;: (t)i+i
(t)i+l+ ;:(t)i+i1
+ ;;
= Y$(t)i:: (t)i+i+ ;n(t)iT:(t)i*
+ ;C(t)i;: (t)i+i+ cross
The terms
and hence
representing
cross
have an expected
are uncm-r-elated
from
products
sweep-to-sweep,
xG,(t)iq
echoes
i
(10)
.
are essentially
‘
identical,
i.e.,
clutter
subtraction
scheme
proposed
(MTI)
radar
here
represents
The advantages
to any desired
the signals
so that there
value,
(b) precise
by analog means,
is no possibility
described
Pm(t)
of the digital
–P=(t)
= ~
:(t)i
approach
timing
of the receiver
[T*(t)i
period
of the Sampling
and delayed
gain differing
out more
simply
implementation
reflections
to store
are (a) tbe freedOm
and (c) the current
above can be carried
a digital
method of c~celing
sweep.
The operation
Thus,
(ii)
which uses a delay line equal in length to the interpuke
identically
C=~c(t)i+i.
i
moving-target-indicator
period
=C(t)i
.
the previous
thao delaying
phase angles
and noise samples
out to zero
ary objects,
interpulse
have arbitrary
the signal
also average
-0
$=
standard
since
i
hand, the clutter
The simple
(9)
and clutter
Similarly,
these terms
x=(t)iIi”(t)i+i zIuc(t)il
of tie
noise,
.
xIin(t)i:: (t)i+l
(t)i+i=
i
On the other
of signal,
mean value of zero.
products
from
signals
station from
tO adjust the
is eaSier
to aCbieVe
samPles
are treated
fOr the twO.
as
–ti*(t)i+.il
1
+ ~
F(t –100
wec)i
[T*(t – 100 w=c)i
-~*(t
–~oo
wec)i+il
(i2)
i
but this has not been done.
Since the clutter
92 to i 76 km, it is not clem- that a. significant
subtraction
is performed
amcmnt of computer
43
only over
the height range
time would be saved.
The clutter
signal
subtraction
spectrum
scheme
described
above effectively
imposes
a weighting
of the applied
of the form
(i3)
H(f) = i – COS(2fif/fr)
where
f is the frequency
frequency
(425 Hz).
displacement
Thus,
from
the admitted
the radar
power will
If the echo power was distributed
in frequency
this filtering
echo power
would be to remove
Although
at 40-psec
vals,
data samples
arrive
intervals,
as listed
1.30<
in Table
X.
(- 3Afi)
at the computer
for the second pulse transmitted
●
mfr,
m is any integer.
to f=, the action of
as a function of frequency.
every
IX),
the range 0.68<
and 2.48<
[via
This occurs
than fr.
2.0 Wsec (Table
over
intervals,
is estimated
where
comparable
is much larger
are formed
t < 7..38 at 60-psec
The clutter
an interval
selectively
fo, and f= is the pulse repetition
at f.
be zero
over
in Mode I, but for Mode E the echo bandwidth
nal power
frequency
t <4.58
Eq. (8)] only over
products
of the sig-
t < 1.24 msec
at 100-psec
the first
only
inter-
of these
intervals.
To estimate
6.50<
level
t <6.82
the average
msec
spaced
in the receiver,
For
calibration
An important
covered
taining
data from
the result
error
echoes
the first
up and down i 5 km.
maximum
lag applies
Description
profile
This causes
assume
for the moment
the wide -spaced
the first
pulse transmitted,
t <7.40
msec
the same operations
was unfortunately
was,
in fact,
no problems
profile
operations
throughout
delay which should be applied
applied
an average
in regions
features.
to the other channel,
of the desired
of linear
This error
the 1969-i 975
to the channel conwith
measurement
power-profile
was not discovered
gradient,
in time
to
program.
to determine
the echo acf over
altitudes
operations
the range
O < T < 380 psec [a shorter
– see Fig. 1 (a)] for altitudes
is facilitated
that the close-spaced
pair in channel 2 (v channel).
acf can be calculated
7.20<
are taken
– Mode F
at higher
of computer
six samples
computer
power
Operations
A further
in the real-time
in the analysis
Mode F is employed
from
The i 00-psec
attempt
Computer
of t.
on the time base [Eqs. (6) and (8)].
near sharper
any correction
of these nine is taken as the mean noise
pulse Pn+cal (t) in the range
pulse transmitted
that the measured
at delays
fOO @see earlier
but could be important
3.
An average
for nine samples
of temperature.
existed
by this report.
is computed
to be independent
and noise -calibration
in terms
out but for samples
period
shifted
40 psec apart.
the channel containing
are carried
the power
and this is assumed
of the sum of the noise
for power
noise ~n(t),
by initially
ignoring
pulse pair is sampled
In this case,
i 06< h < i 66 km (Table III).
channel commutation,
i.e.,
in channel i (u channel)
and
the total unnormalized
measured
as
Pm(t, 7) = ~
[Xi(t)i
xi (t + T)i + Y, (t)i Y4(t + T)il
i
Pm(t, T) = ~ [Xz(t– 100 psec)i
x2(t + T – 100 w=)i
i
+ y2(t – 100 wsec)i
TIIUS, the acfvs computed
that the vertical
in Mode F are assumed
drift velocity
ZOO< T <380
y2(t + T – ioo wsec)il
for the altitudes
to be wholly
covered
44
real.
Vsec
.
(44)
This amounts to assuming
by this mode is negligibly
small.
Pm(t, T) includes
contributions
due to signal,
clutter.
Pm(t, 7) = P~(t, 7) + Pn(t, T) + Pc(t, T)
The clutter
component
is computed
and noise
.
via (see Sec. 2 above
(i5)
for
discussion
of clutter
subtraction
technique)
Pc(t,
T) = 2 ~ [Xi(t)i
Xi(t
+T)i+i
Pc(t,~) . 2 ~ [x2(t–400
psec)i
+Yi(t)i
Yi(t
+ 7)iti)
+ T –400
~sec)i+l
0< T<i80psec
i
xz(t
i
+ Yz(t – ~oo w=)i
That is, the first
factor
sample
on one sweep
of 2 in Eq. (16) allows
sweeps,
i.e.,
is multiplied
by the second
for the fact that the operation
sample
T< 380 psec
. (i6)
on the next sweep.
is only carried
out for every
The
pair of
only for odd i.
The noise
acf is measured
Only the channel
ficient
200<
Yz(t + T – 100 w=-)iAl
number
containing
of samples
i O independent
complete
and 5 per sweep
using samples
the close-spaced
is taken to form
pair samples
several
acf ,s are computed
for 100 G r < i 80 psec,
echo acf measurements
at the end of the sweep
(iO time-base
entire
per sweep
giving
at t . 6.96 msec.
is used fOr this measurement.
noise
acfts per sweep.
when the pulse
75 noise
starting
spacing
acf measurements
A suf-
To be specific,
is 0<
r < 80 psec
for each profile
of
sweeps).
m
Pn(~n)i
.
~
[xi (t + jA’rn)i
xi(t
+ jATn + Tn)i
j.o
+ Yi(t
Pn(Tn)
= 1/75 ~
+ jA7n)i
Yi (t + 3ATn + Tn)il
(17)
Pn(T”)i
i
with
m . 9 for O < T G 80 +sec and m = 4 for iOO < r < i 80 vsec,
ber.
Equation
(17) applies
and hence there
real.
accuracy
sible
the first
at these lags,
to achieve
others,
t and T employed
to the above
equation
amount of physical
sample
constructed
Psec, p“(r)
Pn(T)
-0,
to be
of the second
30 December
●
transmissions
does not lend itself
to height at these lags.
before
the values
to increase
While
more
An alternate
this is carried
i 970) for T > i 00 #sec.
to the wanted one.
of delay tabulated
it is POS-
often than the
to this.
In the F Mode,
3 km with respect
sample
may be obtained
fn order
are made near them.
spaciog
at Millstone
information
of the function.
multiplications
the desired
are for altitudes
The location
FOr T >100
(i 7) assumes
must be changed to O, 0, and i O
minimum
and first
by repeating
.
Equation
sweep num-
XI).
are shown in Fig. i (a) where
of any pair.
products.
which the greatest
with respect
computed
further
crossing
h > f30 km (and all altitudes
tional correlations
sample
1970 (Table
additional
equipment
iS to average
at altitudes
zero
this simply
the timing
approach
in forming
4, 9, and 75 applying
to 6 November
The lags of the acf from
are those near
for O < Tn < 100 psec and ATn ‘ 20 Wec
is no purpose
The numbers
for data prior
and i representing
out
The addiThe values
are for the first
is obtained by adding the vahe
of T to
TABLE XI
NUMBER
N OF
NOISE-CORRELATION
PER SWEEP IN
FUNCTIONS
MODES
F.
G,
AND
FORMED
H
Close-Spaced Pair Pulse
Spacing
O to 80
F
I
G
;
H
;
Note:
the corresponding
(6 km before
;
December
ber i970 in order
Figure
i (a) ignores
120 t.a 180
12 (1)
4(1)
I (1)
o to 40
50 to 90
15 (1)
10 (1)
i 06<
group,
to data taken
h < i 24 km,
Since the roles
of the frequency
for T .380
Computer
to reverse
Operations
Mode G is employed
maximum
lag applies
are obtained
and thence
is carried
every’
3 km
6 km over
30 Decem-
For the higher
to save some
of the first
every
out starting
of the measurements.
psec fn order
computer
time.
pulse for T ~ 200 #sec.
In
used to compute
the full,
in the imaginary
part.
information
part and magnitude
in this mode,
Aside
these basic
differences
it is evident
20 sweeps.
contaminated
correlation,
differences,
echoes.
221).
Accordingly,
computer
drift information
time is
contained
only for O < ~ < i 80 psec as the drift
small,
Also,
The difference
as no clutter
between
subtraction
the real
is needed
independently.
F and G Mode computer
being those of timing,
as given in Fig. i and Tables
psec.
b < 3i 7 km (Table
the available
to obtain the plasma
part is calculated
T <380
167<
by unwanted clutter
and, instead,
as tbe real part becomes
fm. 200<
the range O < T < 380 psec [a shorter
– see Fig, i (b)] for altitudes
a,cf in order
each sweep is processed
from
the remaining
calculated
clutter
This imaginary
is ignored
20 sweeps,
then in channel 2 for 20 sweeps;
of u and v in Eqs. (14) through (i 7) every
the echo acf over
altitudes
complex
content decreases
every
– Mode G
is not normally
is made to subtract
are commutated
in channel i for 20 sweeps,
the roles
to determim
at higher
This range of altitudes
no attempt
channels
pair will appear
it is necessary
4.
height averaging,
IX through XI.
,,I
46
,
‘1
functions
no beigbt averaging
the shift of i 00 psec in the location
that the close-spaced
:1
.]
350 (40)
5 (1)
the full height resolution
is not computed
104 (40)
llx)t0190
1 (a) shows that correlation
197 O) between
.
this is taken into account.
practice,
)
in
150 (40)
(1)
60t011Yl
Figure
to preserve
the correlation
>
o to 40
For the lower
group,
hence,
lo(l)
delay.
i 30 s h < i 66 km.
Total
20 Sweeps
100 to 180
Numbers i“ parentheses .pply
before 6 November 1970.
—
T
(ysec)
Mcde
operaticms
are largely
and number
the same,
of noise acfis
,.,
The
section)
full
acf
is calculated
(once
agafn
ignoring
channel
commutation
as in the previous
as
Fm(t,
T) = ~
;(t)i
li*(t
+ T)i
(i 8)
0< T< 180 psec
i
Pm(t, 7) = ~ Re [~(t
i.
Commutation
effect
of reversing
designed
the roles
F,
P“(T)
analysis
to be symmetric
A discusses
Computer
the effect
Operations
lag applies
(i9)
every
frequency
. (i9)
channels has the
20 sweeps.
function as the receiver
bandpass was
This has been found to be not completely
to cause an important
of ignoring
between
‘r< 380 #see
systematic
tbe imaginary
distortion
in Im [ ~m(t, r)].
part of the noise acf. upon the data
function
to determine
Computer
III).
major
differences
Thus,
the equation
=
~
and measurement
Pc(t)
.2
profile
III).
complex
cor-
G and H Mode
com-
height averaging,
IX through XI.
to retain
z
over
lines
arise
the range
55< h <140
of E Mode processing,
due to the transmission
of signal-plus
-noise
processing
in the computer
for Mode 1 corresponding
51 (t)i +
of alternate
and noise-only
of sweeps
km
but several
on op-
in groups
a pair of sweeps
of four
on each
to Eq. (6) for Mode E becomes
(20)
s2(t)i
i
even
to Eq. (8),
~ [:(t)i
psec.
being those of timing,
This necessitates
purposes
i
odd
and, corresponding
5i5 km (Table
and the full,
O < r < 190
along the general
sweep.
subtraction
Pm(t)
the echo power
follows
sweeps
on a given
lags
in Fig. i and Tables
Most of these differences
on alternate
2i 5< h<
at these altitudes,
all
the differences
as given
to determine
exist.
for
O < T 4 i90 psec [a shorter
for altitudes
- Mode 1
1 Mode processing
at a time for clutter
frequent y.
the same,
Operations
frequencies
Eq. (i8)l
acfts calculated
Mode I is employed
(Table
frequencies
[i. e.,
the range
- see Fig. l(c)]
need not be considered
are largely
of noise
the echo aci over
altitudes
is measured
puter operations
and number
– Mode H
at higher
As in Mode G, clutter
posite
and
real
frequency.
200<
psec)i
pulse pairs
to be a purely
about its center
exists
Mode H is employed
maximum
6.
+ 7 –iOO
results.
5.
relation
%t
of u and v in Eqs. (i8)
is assumed
Enough asymmetry
Appendix
psec).
of the C1OSe- and wide-spaced
As in Mode
true.
-100
:*
we have
(t)i+2
+ v(t)i+i
~“ (tIi+31
(i - i )/4 an integer
(21)
.
i
AS with Mode E, only the real
altitudes
calculated.
Clutter
is subtracted
at all
in the I Mode.
A separate
version
to a frequency
outside
Tbe integration
rately
part of Pc (t) is acma~y
from
of the Mode I program
the receiver
was allowed
the others.
passband
to proceed
In this way,
was developed
during four
as normal,
the recovery
47
except
in which tbe transmitter
consecutive
sweeps
that these sweeps
of the receiver
was switched
out of every
were
stored
could be monitored,
eight.
sepa-
albeit
at
a cost of half the integration
time.
the receiver
recovered;
had essentially
not attempt
c.
to monitor
REAL-TIME
1.
the receiver
COMPUTER
At the termination
are first
pose of providinga
computer
2.
and P “+Cal(t)
of the program,
these operations
that does
power
P,(t)
= Pm(t)
ismultipliedbyhz,
Error
integration-time
temperature
process,
Pn+cal(t)
P~(t)
a modest
form.
Also.
of the prfmary
the
results.
These
has determined
Pm(t),
data are saved on magnetic
only.
P“(t),
tape.
The mean receiver
noise
level
t.
as
(22)
.
(base 10) is then taken,
(Appendix
a height profile
B).
values
and the result
of tbe logarithm
are calculated
Signal temperature
temperature
from
T~(t),
T”arecalculated
is arbitrarily
of relative
scat-
signal-to-noise
and
noise-plus-clutter
from
the relationships
=PS(t)/Tn
[P”(t)
T “R(t)
over
c(t)
and noise (system)
T~(t)
X.
of these power
considerations
Tn& (t),
for the pur-
performs
t, and the mean noise plus calibration-pulse
value of 5 to yield
estimates
The”,
in
detail.
the computer
is then calculated
–Fn-P
andacf
is employed
meaningful
presentation
tonthe line printer
Pn(t) over
the logarithm
to a maxinmrn
power.
in more
t given in Table
by averaging
signal
are in binary.
the computer
visual
power
format
1
are now made foroutp”
is estimated
normalized
a real-time
Eand
the integrated
to an immediately
discuss
by averaging
period,
themselves
the information
of the integration
~“ is estimated
Ionospheric
tered
version
to.
BCD and binary
copy of these resdts,
provides
at delays
calculations
A mixed
display
Output –Modes
At the terminaticm
Several
printed
t.a reduce
sections
Computer
integration
tape.
is in BCD and the results
oscilloscope
The following
P~(t)
was reverted
of 60 km
OUTPUT
onto magnetic
real-time
amount of processing
Fn+ca,
it was found that by an altitude
the original
recovery,
of each experimental
written
which the data heading
level
hence,
General
results
Pc(t),
Using this program,
=
+Pc(t)l
T
n
(23)
Altitude
h is calculated
as
h=i50(t
where
T is the radar
-~)
pulse length and D is the delay introduced
t, T, and D are measured
of header
information
standard-deviatiori
(24)
km
in milliseconds
Tn. and lists
error
for this equation.
TS, and scatter
of h, TnW,
bounds (relative
logarithms)
1
48
vs t.
by the receiver
The line printer
power
(-0.03
listing
msec);
consists
plus its upper and lower
l%eos.illoacope
displays
Pm(t)
225
150
75
I
o~
>
POWER [ relative
(a)
and Pc(t)
3.
Several
power
T)
correlation
t and T listed
are then calculated
for instrumental
The line printer
and P=(t, 7)/P~(t,
directly
by Eq. (25). ]
printed.
This latter
measured
4.
Ife[~m(t.
HI and X.
listing
by averaging
of a
The best-fit
for
only.
Pn(t. r) over
in Appendix
A.
information
VS T.
(described
April
t.
The signal
theoretical
Altitude
tape.
noise
power
these tables,
in Appendix
t used.
h is computed
plus tables of P~(t, ~)/P~(t,
[For
Figure
the values
of unity,
h of P,(t,
O)/~n(0)
is
(S/N).
9(c) is an example
of a
function is also shown (see Sec. V).
G and H
process,
(Mode
the computer
G),
,These data are saved on magnetic
The mean receiver
49
and
tape.
Pn(t,
has determined
T) at delays
Several
noise pewer
of
A) and not as given
to a maximum
1974 by a list vs
O) vs T for each
T > 2oo wsec
only.
The mean receiver
(25)
of header
smearing
starting
of the integration
r)]
Pm(t, ‘r), Pn(t. 7),
data are saved on magnetic
T)
as discussed
consists
P~(t, 7)/P~(t,
for output on the line printer
,_
has determined
These
a list of h2P~(t, O) vs h, normalized
Output - Modes
At the termination
Tables
9(a) is an example
the computer
III and X.
– Pc(t,
smearing
list was replaced
Mode F acf.
T < ~90 psec,
of 5.
as
‘P”(T)
for instrumental
Finally,
displays
Computer
Mode I.
to a maximum
Figure
O) vs b and T, and a list of Pn(T)/Pn(0)
P~ are those corrected
The oscilloscope
vs h.
I.q)
Fig. 9(b) is a Mode I example.
process,
in Tables
is estimated
function ~n(r)
p~(t, 7) = Pm(t, 7)
via Eq. (24).
normalized
are now made for output on the line printer
functions
and corrected
10garithm)
by Mode E;
of the integration
at delays
calculations
correlation
obtained
power,
J
5
Output - Mode F
At the termination
and P=(t,
of scattered
pOwer (relative
profile
Computer
(b)
Logarithm
and scattered
scattered-power
‘POWER (relative
109)
Mode E.
Fig. 9(a-b).
(
4
!
.
50
2
~m(t,
t and
T) fOr
T given
in
calculations
are now made
correlation
function ~n(r)
O)
1
1
1
I
1
*
1
18 SEPTEM8ER 1974
1735-1747
UT
121 km ALTITUDE
Ti=404?16K
0.1
‘.
T, = TI ASSUMED
,1, = 0 ASSUMED
THEORETICAL
0.:
FIT
-a
r (F*..)
(c)
Mode F.
,
*
18 SEPTEMBER 1S74
1748-1756
UT
197 km ALTITUDE
T,=967f21K
T.= 14691
18 SEPTEMBER 197,
1756-1800 UT
395 km ALTITUDE
T,=1135*36K
1.0
T;= 1803* 40 K
. . -65+ 13m/, ec
0,s
19K
●
54% O“COMPOSITION
ASSUMED
MAGNITUDE
x PHASE
~ 0,6
g
●
THEORETICAL
MAGNITUDE
g
x PHASE
FIT
:0.4
5
q
LINEAR
g
FIT
50. ?
x
$
.
8
/
0
xx
.“
LINEAR
/
-0.2
“02L--...J
m
-
-0.4
b
0
,60
2+0
320
4oo
0
,
40
so
120
T (psecl
r (pee)
(d)
Fig. 9(c-e).
(e)
Mode G.
Measured
correlation
Mode H.
function and fitted theoretical
50.
FIT
function.
240
.
is estimated
power
_,_....,,. .
_,
by averaging
correlation
Pn(t, r) over
t.
The magnitude
function ~~ (t, ~) are calculated
M(t, T) = l~~(t,
,)1 = I ({w
[~m(t,
Im [~~(t,
T)l}z
+ (I~~m(t,
T)l)2)i’2
(26)
–~n(T)l
T)]
I
@(t, 7) . arctan
M(t, T) and phase @(t, T) of the signal
as
(27)
Re [~, (t, r)]
choosing
@ to lie in the quadrant *tr/2.
Im [~~(t,
velocity
~)] is assumed
at each altitude
to be zero
for T >200
~sec
(Mode
G).
@ is then interpreted
as a
via
(28)
where
dq/dr
center
of the remaining
is taken to be the slope
+6
points
z
of the line passing
through O(t) = O, T = O. and the weighted
TC)(T) Mz(r)
&+=r
(29)
x r2M2(r)
7
This equation
calculation
approximates
the uncertain
of q@ (Appendix
M is corrected
y in $ (u ~ ) by i/M
to avoid the complicated
rigOrOus
in Appendix
h is cal-
B).
for instrumental
smearing
as discussed
of header
information
A.
Altitude
culated via Eq. (24).
The line printer
fm [~~(t,
~)]/M(t,
listing
M used are those corrected
ized to a maximum
consists
O) vs h and T, plus a list of ~n(T)/~n(0)
for instrumental
of unity) vs h are printed.
liSt Of M(t, O)/~n(0) VS h (s/N).
acfts.
Fitted
theoretical
functions
Figures
effects.
plus tables
vi
r, where,
Finally,
This latter
lists
of M(t, ‘r)/M(t, O) and
again,
of
of v and hZM(t, O) (normal-
list was replaced
9(d) and (e) are examples
the values
in April
of measured
1974 by a
Mode
G and H
are also shown (see Sec. V).
54
L
——.
,..
- . . . ...-. ”.—
,-.. ..=-.
v.
A.
GENERAL
The real-time
and clutter
to analyze
sity Ne,
V&
magnetic
power
these
[Nz],
conce rni”g
atomic
munity.
oxygen
tape,
[0],
the neutral
and the neutral
and a library
The following
alyze
F Modes
(See, II-H).
analysis
fourth,
realized
containing
14 heights,
by averaging
that as the first
degree
7 heights
HI),
these
ventional
to the 2-pulse
altitudes
created
information.
(secOnd,
fOurth,
to an-
were
are created
heights
com-
data.
was written
mea-
in the
[second,
It should also be
F Mode are at 3-km intervals
altitudes
are saved
whereas
and sixth) have only
noise estimates,
not additional
measurements.
Mode E -
first
ANAI,YSIS
Routine Analysis
calctdates
the POwer PrOfile,
h vit112q. (24) and P~(h)via
via a radar
eq”aticm
which,
vertically
directed
p:tirabOlic antenna,
0.76 PtAI,cT
P8=————
i6n
1
I
same three
independent
and that due to independent
Mode E isusedtomeasum
related
additional
nitrogen
to the scientific
program
These
altitudes.
d rift
these a munbe.-
4970 only *I heights
missing
den-
vertical
of this analysik
applied
Tbe analysis
to 30 December
in the i4-height
from
for distribution
procedures
tbe three
the two neighboring
of independence,
POWER-PROFILE
program
but Prior
F MOdes,
and sixth in Fig. t (a)] do not yield
The results
is used
such as electron
the abundance of molecular
Tn.
the analysis
noise,
program
ions [0+] /Ne,
also calculates
is available
for completeness.
For the 1i -height
program
echo-signal
i.
describe
here
atomic
namely,
temperature
of such results
se ctiom
Ah = 6 km at best (Table
a small
atmosphere,
of signal,
A separate
of the ionosphere
percentage
The program
Vin.
consists
delays.
quantities
Te and Ti,
frequency
One note will be entered
sured
the physical
and ion temperature
collision
experiment
of time base and correlation
data to determine
and ion-neutral
on magnetic
outPut frOm a 2-Pulse
-t:kpe
as a function
electron
of parameters
B.
ANALYSIS
frOmwhich
Ne(h)
is deduced.
P~ and electron
Eq. (22).
in the case of a moncmtatic
radar
system
The analysis
density
Ne are
employing
a con-
maY be written9
N u
>
(30)
11*
where
j
Pt
.
peak tr:msrnitter
A . effectivv
As discussed
power,
antenna aperture,
L . waveguide
and other losses,
o . scattering
cross
in Ref.9,
provide, d Te/Ti
section
and
per election.
& 3.0, the scattering
cross
section
per electron
may be
written
a.
“e
(i+azl
(f
+Te/Ti+02)
(31)
(32)
53
De = 69~e
m
In Eq. (3i ), Oe is the radar cross
28
2
scattering,
is u= = i O
m (Ref. 9).
From
these expressions,
(33)
.
section
for a free
electron,
which,
in the case of back-
it may be seen that
Ne
(34)
P~ =
(4 + a2)
For typical
a 2<
IVe and Te,
(i + Te/Ti
De<
0.03 and may be ignored,
This approximation
variation
Equation
Mode E, ignoring
generally
reasonable
smoothing
Te/Ti
yields
The constant
profile
constant
from
values
simultaneous
is in megahertz.
vertical-incidence
ionosonde;
faulty local
readings. ‘7
through them.
terpolation
at the midpoint
Statistical
Te/Ti
From
uncertainty
applied
in determining
iza.ticm should be applied.
frequency
to derive
foF2
between
of the Te/Ti
the absolute
to determine
measurements
of the F2 -region
from
Ottawa,
at-e made using an on-site
Wallops
Island,
when available
and a curve
are read off at half-hour
values
this
(36)
have been considered
values
in the power
is used to normalize
measurements,
the still
Billerica
to correct
is drawn by hand
intervals.
Linear
in-
tbe E Mode Ne profile
This is resolved
profile
over the eight consecutive
vertex
of the parabola
larger
plus the use of discrete-height
the exact point on the umormalized
the peak and the ummrmalized
interpolation
Application
time.
to them,
marks
(the smooth-
via
are plotted vs time,
these half-hour
uncertainties
frequency
measurements
this smooth curve,
un-
a 2- or 3-point
m-’
(Massachusetts)
of its integration
corrections
critical
All these readings
in time between
Linear
It has been the practice
of the critical
X 1040
similar
(Mas sacbusetts ), and Maynard
- basically,
is used.
is
profile.
may be established
These
varia-
to remove
.wmmtbing is applied
program
of Ne mea~urement
measurements
= L24(foF2)2
profile
profile
data are edited
a smooth Ne profile.
demsity profile.
NmaxFZ
for Te/Ti
As the power
the temperature
of the analysis
data analysis.
F, G, and H following
in Eq. (35) must also be determined
from the unnormalized
through
foF2
density
profile
Modes
< 4) and some profile
to the heights
an ummrmalized
which the peal+ density
where
Te/Ti
of proportionality
N ~axF2
I
0.5<
the power
from
must then be made for the
2 -pulse
mode measurements.
profile,
has been used) to try to maintain
correction
‘!
between
than the Te/Ti
(requiring
and allowance
to correct
has changed during development
smoothed
density
altitudes,
data are obtained
the time difference
values
ing algorithm
tiese
temperature
much smoother
(35)
but Eq. (35) is used in the present
(35) shows that it is necessary
These
Thus at our wavelength
500 km
down at higher
of a (Ref. i),
tion to find Ne (h).
below about 500 km.
yielding
h<
breaks
“
i cm for heights
W*
altitude
+ a2)
heights
the desired
Ne value
by fitting
a parabola
““certainties
measurement
Ne profile
to which foF2 normal-
to the logi o Ne (unnOrmalized)
fo~ which the sum of these logarithms
point of normalization,
corresponding
54
in the
cause some
specifying
to the density
maximizes.
The
the height hmax of
Nmax F2.
Occasiomlly,
bad points (due to satellite
occasional
instances
At the higher
ground clutter,
of improperly
normalized
Mode E altitudes,
quite scattered.
profiles
the signal
could be more
accurately
this region.
A straight
to decrease
with altitude
decrease,
represented
line is fitted instead
height of measurement.
(decreasing
scale
Mode H altitude)
The lowest
altitude
in others,
of a parabola
able results.
casionally,
Efforts
or the parabola
No profile
vertex
is below
is applied
from
the real data profile
and not replaced
this high-altitude
f~r the data
just above highest
to the smoothed
fit,
but
by the fit.
smoothing
scheme
to yield
unreason-
successful,
md,
oc -
results.
to RASEM
jwt
described
except
for m rtai”
and normalization.
data,
run-to-run
by a weighted
i+n
.2
Mode E analysis
correction,
to reduce
P8 (b)i is replaced
~~(h)i
the maximum
fit is substituted
and 546 km (i. e.,
appears
fit also takes into account the data up to 50 km below
to the routine
temperature
smoothing
of the data i“
Analysis
in time is applied
power
smoothing
is identical
of data smoothing,
smoothing
signal
profile
Mode E - RASEM
analysis
versions
are retained
echo causes
increase
if the slope of the parabola
made to cull out these bad points have not been very
a distorted
RASEM
facets
a satellite
exponen-
high-altitude
fit to the logarithm
for which the parabola
smooth transition
data in this 50-km interval
Occasionally,
2.
The parabola
height to insure
the original
so weak that the data are
it has been felt that the trw
is set at i50 km above the F2 peak in some program
this lowest
becomes
by a parabola
height)
and
occur.
sometimes
ionosphere N , profile is expected to decrease nearly
h, with its scale height increasing
only slowly as temperatures
and mean ion mass and the pull of gravity
densities
etc. ) cause this method to go astray,
As the topside
with increasing
tially
echoes,
but becawe
fluctuations.
time average
the integration
time is short,
For the ith
run in time, the
~~ (b)i
WjP9 (h)i
. j=i-~+n
z
j.i-n
w.
J
Wj.2(n–lj–il)+l
i+n
2
This provides
a triangular
been employed.
possible
(37)
Wj=(”+p+nz
j.i-~
weighting
This smoothing
weighted
average
over
process
2n + 1 points.
truncates
that can be formed
Values
n = O, 1, 2, 5, and 10 have
the data series
is for
somewhat,
since the first
i . n + i and the last is for i = N – (n + 1)
for a total of N rons.
As no temperature
perature
data are gathered
dw-ing a ftASE M expe rinmnt,
correction
is modeled:
(a)
Te/Ti
= 1
(b)
Te/Ti
increases
linearly
to 2
(c)
Te/Ti
decreases
linearly
to i.2
h<
the density-profile
930km
i30<
300<
55
h <
300 km
h < 2000km
,
tem-
As in the regular
ization
to ionosonde
RASEM
Mode E analysis,
readings.
measurements
to determine
are made much more
I-”n-to-run.
Thus,
to maintain
fit determines
the ionosonde
the point for profile
readings
frequently
Nmax F2 [Eq. (36)] for each profile,
This should serve
dar.
a parabola
However,
(e g.,
are taken every
every
2 min.).
while
Rather than attemPt
we make use of the inherent
log, ~ NmaxF2
normal-
half-hour
stability
- log, ~ p~ (hmax ) approximately
of the ra-
constant
(38)
r . logi ~ Nmax F2 – logl ~ p~ (hmax)
is formed
for all the available
As the radar
line is fitted
electron
sensitivity
profile
values
a magnetic
to make the program
3.
the run (i.e.,
with time,
every
storm
a least-mean-square
the time variation
i+
(Te/Ti)
I
with the program
of this parameter
F(t).
The
(h)
(h
)
Inax I
These
(39)
+ ‘(:)
program.
when the FI -Iaye r has been pronounced
It is then possible
r and hmax.
-st raight .
using
+ 10gf O I + (Te/Ti)
in summer).
half-hour).
events
for tbe FI peak to be mis-
are sufficiently
infrequent
that at-
cope with them have not been made.
Mode I
The Mode I results
Mode E results,
density
profile
to an Ne profile
that it is assumed
to the E-region
usually
and magnitude
are converted
except
made with respect
contains
critical
frequency
making
the average
of power
and tbe normalization
in place of the F-region.
peak,
Accordingly,
as the value
in much the same mariner as the routine
that Te . Ti at all altitudes
no well-defined
of normalization.
125 and 135 km is employed
N
slowly
t is then obtained
have been encountered
following
throughout
b and t can be provided” by the processing
taken for the F2 both in obtaining
tempts
to drift
= 10gi OP~(h)
plots of “log, o Ne vs
Difficulties
(usually
of NmaxF2
of r to yield
at any time
logiONe(h)
Contour
values
is likely
to the available
density
from
the difference
it difficult
of the values
corresponding
is
The E-region
to decide
the location
of 10gl o p~ (h) between
to E -region
maximum
density
E.
max
The Ne profile
clutter
the center
wise,
results
subtraction
frequency
subtraction
high collision
carried
an appreciable
in the notch of the filter
the echo amplitude
frequency.
becomes
fraction
function
correlated
That is,
for the influence
H(f) [Eq. (43)].
over
the echo power
of the
of the echo power
intervals
lies at
Stated other-
as long as i O msec
PI remaining
after
clutter
becomes
PI . P~[i
where
i“ the case of Mode I, be corrected
This is because
and, hence,
at low altitudes
owing to the very
must,
scheme.
p (TC) is the correlation
out.
(40)
–p(TC)]
D. T. Farley
over
(private
tbe interval
(1 O msec)
communication)
autocorrelation
function in the collision-dominated
of the spectrum
equation
of Dougherty
and Farley
at which the clutter
has pointed
case,
subtraction
out that the expression
based on taking the Fourier
(Ref. i8 – see Sec. C IR1ow),
is
for the
transform
becomes
- T/*
P(, ) . e
Tn
=
(4i )
(42 )
r(2rAfi/A)
56
9 = vin/(2nAfi/X)
Adopting
k = 0.68 m, mi . 3i amu, yields
P(TC) . exp[-i820
In order
to use this result,
K(h) = i –
for model
U.S.
(43)
.
atmospheric
Standard
Ti/vin]
we have computed
(45)
conditions.
i962
Adopting
one computes
be employed
from
in Table
and [N2] (h) from
and the simple
the CI RA i965
expression
(Ref. i 9) and
Zi
of Wand and Perkins,
Vin and [Nz]
x iO-i5[N2]
K(h) as listed
by Banks differs
Ti(h)
(Ref. 20) models
hased on the work of Banks, 22 relating
.0.9
the function
p(Tc)h
Atmosphere
v in
(44)
.
(46 )
see-i
XII and plotted
that of Dougherty
and
in Eq, (44) is half that given
in Fig. 10.
Farley
by
The definition
a factor
of
2
so
that
of Vin employed
the value of vin to
by Eq. (46).
TABLE X11
COMPUTATION
OF THE EFFECT OF CLUTTER
ON THE MODE
I ELECTRON
DENSITY
Height
(km)
N(N2)
vi”
(m-3)
(s..-l)
Temperature
(K)
K(h)
Source
120
381
4.01
x
10’7
1.80
X 102
I .0
Ref.19
110
263
1.62
x
1018
7.23
X 102
I .0
Ref.19
100
213
8.18X
1018
3.68
X 103
I .0
ReF.19
90
186
4.96
X 1019
2.23
X 104
1.0
Ref.19
80
186
2.96
X 1020
1.33
x
105
0.92
Ref.19
70
219
I .41x
1021
6.35
X 105
0.47
Ref.20
60
243
4.95
10’1
2.22
x
0.18
Ref.20
The final electron
loglo
density
Ne(h)
profile
x
is therefore
= loglo[P~(h)l
obtained
~~ (h) is the aforementioned
average
106
from
the expression
– 10glo[~~(h)l
+ 10gl ~ Nmax E – logio
where
SUBTRACTION
PROFILE
value
over
(47 )
[K(h)]
the interval
i 25< h < 135 km.
57
—.. ..——...
..—.,-.---.-.,,-
--
-.
100
I
I
I
I
I
I
I
I
~
90 —
~
:.
80 -
+
$
y
70 -
60-
I
50
I
0.2
o
I
I
0.4
I
I
0.6
I
0.8
I
I
1.0
K (h]
Fig. i O. Altitude variation of fraction of echo power remaining
subtraction operation has been conducted in computer.
As discussed
in Ref. 34, the results
obtained using the Mode I program
doubt at altitudes
below about 75 to 80 km .cmdmay be in error
difficulty
to be the presence
appears
which may be clutter
returns
tudes causes
the Ne profile
as illustrated
in Fig. 9(b).
first
altitude
creased.
from
this is usually
of the filter
Each measured
the real
[Eqs. (25) through
mental
effects
analyzed
appears
the expected
plotting
larger
to be increasing
than a factor
at these low alti-
cw-ve
program
below about 80 km,
the plot is halted at the
as the altitude
to 80 km so that the correction
applied
is de-
to the results
of 2.
ANALYSIS
(27)].
independently
Phase
form.
are calculated
(Appendix
M by i/aO inEq.
estimate
phase estimate
The statistical
for purposes
of the datauncertainties
of weighting
program
forinstru-
see Sec. lV-C),
in these
and subsequent
first
and -4
but is
real parts,
temperature
is negative
is greater
(statistical
in error
to calculate
[Eqs.
(28) and (2,9)] to determine
aveloc
-
instead of the approximation
o
. i/M for weighting,
i.e.,
+
‘$
Lags are eliminated
from this fitting procedure
if the data
fluctuation
than half a radian
are systematically
failure
as in Sec. IV-C-4
of o
(29).
trum,
i.e.,
at this point in the analysis
printout
program
in Sees. IV-C-3
Analysis
using now the true estimate
variance
The analysis
B).
The phase @ of an acf is analyzed
replacing
of all other data.
and phase of an acf as described
M(T) is not corrected
in its uncorrected
and phases
calculations
2.
acf is analyzed
part or magnitude
(as was done to obtain a real-time
directly
magnitudes,
ity,
from
as yet unidentified,
observed
Gene ral
calculates
error
close
[Eq. (47)] is rarely
CORffELATION-FUNCTION
i.
progressively
in the 1 Mode profile
The cause of the
mechanism,
power
clutter
are open to serious
even higher.
scattering
The additional
below 80 km at which the density
In practice,
for the effect
c.
of an additional
aircraft.
to depart
Thus,
after
due to failure
due to near-zero
(unreasonable
signal-to-noise)
velocity).
The velocity
to account for the asymmetry
the imaginary
part of the noise acf.
58
or the
estimates
of the receiver
The effect
spec-
of this neglect
is examined
in Appendix
discussed.
Ffgu=es
3.
A,
where
the velocity
9(d) and (e) show examples
Magnitude
Analysis
The magnitude
- Library
part of the acf is not measured)
acf magnitudes.
has been felt that additional
Pin) library
general
The library
independent
is used at lower
A coarse-grid
library
search
for closer
by the fine search.
scrutiny
Table
XIII gives
given
values
The Te/Ti
of normalized
in Table
collision
are direct
Farleyi8
causes
Debye
error
plasma);
causes
occurs
other errors
made in order
These
functions
a very
in Te/Ti
rn by the coefficient
parabolic
or (Tf
slight
Tbe
of
abcmt the minimum
for each search
parameters
are tai -
for the coarse
The “in grid values
The
area
under investigation.
and
are stored
$ grid values
also are
acf!s
formulation
stores
-i.
for O;
4 percent
assumption
correlation
delay
was
grid point,
rn as de-
240 per acf
in steps of 0.05.
values;
the functions
are calibrated
To obtain the lags needed
smearing
smeared
by the equipment
(Appendix
between
such that the comparison
is addressed
9(c) through
The
for all ion species.
and increases
acfls
method
The lengths
are assumed
in Iag simply
for direct
by dividing
comparison
with the
in lag is used.
is mathematically
tYPe Of normalization
a simple
parameters.
for 0+ plasma,
ionospheric
The library
cases
assumption
This zero-electron-mass
would suffice
and
Tbe zero-electron-
in all determined
i87 points per acf for each Te/Ti
were
For each comparison
error
at zero
These
for the limiting
24 has developed
as a function of normalized
for reasonable
of r in Eq. (42).
interpolation
field
This zero -Debye -length
(-2 percent
rn in each case starts
lags are needed.
of a magnetic
of the acf (see Sec. E below).
than 1 percent.
are stored
acf magnitude is stored.
23
and by Dougherty
given by Farley
Moorcroft
systematic
with the data,
Figures
frOm the data.
space to find the proper
in Eq. (43).
ratio.
determination
To acccmnt for the instrumental
normalized
XIV.
Vin)] a theoretical
analysis
are not more
are sufficient
if greater
smeared
it
and the estimation
centered
grid
and step sizes
+ as defined
without the presence
after
The library
for each $ grid point;
of these
a libra~
altitudes.
and number of grid points wed
underestimated.
that one library
theoretical
fined in Eq. (42).
to be zero
search
of the physical
from the equations
plasma
of this error
mass assumption
greatest
.deduced
at higher
regression
tbe entire
are given in Table
length and electron-to-ion-mass
T= to be systematically
for correction
data,
Te/Ti)
calculations
for a monoionic
of small
library
library
limits
of variation
frequency
with
variables);
XIV.
At each grid point [(TV
functions
Te/Ti)
covers
step sizes,
grid values
comparison
B.
The grid
and ranges
psec in Mode G as
(two independent
by a fine-grid
search
the Ti g=id limits,
fine searches.
in terms
The coarse
through
could not be reliably
a (Tp
is followed
grid.
to the expected
parameters
in Appendix
point in the coarse
lored
is analyzed
the 2-parameter
is presented
F and for T >200
is 3-dimensional
altitudes,
method used fm. performing
by this technique
chirp is also
determinations.
M (set equal to the real part in Mode
of theoretical
errors
of velocity
frequency
Search
the imaginary
A (Td
bias due to transmitter
of the data,
by the computer
before
in the same manner
and a theoretical
closest
in Appendix
(e) show examples
acf,
comparison
in which the data
A).
a measured
yields
each library
acf,
fit in a weighted,
the data are multiplicatively
least-squares
sense.
B.
of theoretical
data.
59
acf magnitudes
fitted to measured
This
TABLE X111
Ti GRID
Fine Gridt
Altitudek
M&e
Came
Grid
(8 grid ~ints)
Lower Limit
106
lW
12
78
522
150
450
12
522
572
I 50
450
12
12
78
128
200
500
128
572
12
18
128
92
572
758
200
200
500
500
284
650
124
130
18
92
758
200
18
192
858
300
650
750
136
18
18
192
858
8CL9
30+3
250
70Q
858
3C0
750
350
400
450
800
850
900
121
142
Limit
Lower Limit
Upper
Limit
750
18
18
18
242
292
18
342
9m
958
1038
342
1(XJ8
1058
450
5C0
900
950
18
392
492
492
420
1158
1158
600
600
1050
18
30
1530
600
160
164
167
18
18
182
197
212
227
Upper
142
192
148
154
G
(13 grid ~ints)
Step Size
115
118
I
(K)
(km)
112
F
LIMITS
1Q50
242
30
420
1530
600
1350
1350
257
30
420
1530
60G
1350
272
287
302
30
30
420
42o
1530
1530
6043
6CiI
36
384
600
317
36
384
1716
1716
1350
1500
600
15C0
215
36
384
1716
245
36
384
1716
600
6W
1500
275
36
384
1716
6C0
1500
305
384
1716
600
1500
335
36
36
1716
600
15(XI
365
395
425
36
36
36
384
384
384
384
1716
1716
600
600
1500
1500
455
36
384
1716
1716
60il
600
1500
150U
1350
I
,!
H
●See
I
Table
tF1.e-grid
485
36
384
1716
600
15CXI
515
36
384
1716
600
1500
Ill regarding
altitude
search uses 13grid
toextendkyond
150Q
variations.
Wi.tscenterd
o"came~rid-s~rch
grid limits).
60
optim"m fit(ktnotall~wd
I
TABLE XIV
Te/Ti
AND
NORMALIZED
COLLISION
FREQUENCY
$
GRID
g
0.75
0.87
~
1.12
1.25
1.37
1.50
1.87
2.00
~
2.25
2.37
~
2.62
2.75
3.oiI
3.12
=5
3.37
3.50
~
POINTS
I .62
=5
+
0.00
—
0.05
0.10
~
0,20
0,25
~
0.35
0.40
0.45
0.50
0.55
Q&T
0.65
0.70
@
1.00
1.20
1.40
—
1.60
1.80
2.20
—
3.00
&
Ccarse-grid-se-srch
Fine-grid
points are under] ined.
search uses nine cc..sec.tive
search optimum Fit (but not allowed
Different
eters
altitude
expected
problems
Table
ranges
are analyzed
to be influential
in incoherent
XV is a summary
in different
in different
scatter
regions.
data analysis,
of the analysis
grid poi”fs centered
to extend
manners
Following
these
process
ob.o.t cowse-grid-
beyond grid I imits).
altitude
in different
according
to the physical
a discussion
regions
regions
param-
of ion-composition
are discussed
to be referred
in detail.
to in the next
few sections.
4.
Ion-Composition
The major
are 0+,
Problem
ions likely ’to be encountered
NO+,
o;,
H+, md occasionally
depends upon Ti and mi cmly as a ratio,
scatter
in ttie altitude
sporadic-E
range of these
metallic
im identification
ions.
2-pulse
is not possible
from
acf (e. g., 02+ at iOOO K and 0+ at 500 K would be indistinguishable).
could be a problem
in certain
day and NO+ and O;
outnumbered
species
circumstances,
hy night,
by tbe metallic
expected,
e.g.,
or in a sporadic-E
ions.
and tbe major
However,
near 200 km where
layer
in general.
a given
incoherent
we have mostly
0+ by
ions are well-
one knows the identities
of the relative
description
Such identification
in which the ambient
task is the determination
experiments
As plasma-wave
of the major
composition
if a mix-
ture is present.
When the plasma
contains
tions
f~om each species
ratio
is a factor
so closely
proached
entire
this profile
(e. g.,
of very
seen in the incohercmt
shape that essentially
from a given measured
Hill data,
of data simultanecmsly
type of analysis
different
In previous
spectrwn
mass
scatter
0+ - 02+ - NO+ or Fe+ - O;
the monoionic
detemnination
with Millstone
profile
can be easily
of 2 or less
approximates
composition
two ion species
(e. g., 0+, H+), contribu24
spectrmn.
If the mass
– NO+),
error-free
(m- acf).25
however,
data are required
This quality
data is diwwssed
in Sec. D below.
for
is not ap-
papers,~ i >i 2 we have shown bow znalysis
can be used to deduce this composition.
to tbe 2-pulse
the spectrum
Application
of an
of
TABLE XV
SUMMARY
OF ASSUMED
IN
Height
MEASURED
PARAMETERS
ANALYSIS
Range
(km)
106to
AND
THE DATA
Assume
118
Te=Ti=T
Measure
Ti,
n
V.
m
~=1)
I
l18t.a
130’
Te=Ti=T
Ti
n
~=o
v ;“ =“0
130to 166t
Ti=T
v
in
166t
to 225
n
from Eq.(48)
Te, p
from Eq.(48)
T=, P, Vd
=0
Ti=T
n
vi” =0
~=1
225 to 515
T=,
Ti,
vi “ =0
92 to <700
*See
text for discussion of special
tThisaltit”de
actwl
N
an.alpes
at these altitudes.
break corresponds tOthech.ngefrom
height wosa
little
higher
forsome
62
e
eorlydat~
Fto
GMcde;
(see Table
the
ill).
Vd
At the lowest
in the daytime,
similar
altitudes
except
covered
and unknown ~ priori,
uncertain
within a +3-percent
generally
the more
to errors
of +2/-5 percent,
Above
mass
spectrometer
i.e.,
possibly
NO+ and O;
region
conditions
rocket
determination
at even higher
of ion composition
too low for useful
ions takes place
creating
(giving
of usable
very
low Te/Ti
(> 40 percent)
nighttime
temperature
Collisional
In the lower
cases
of midlatitude
range
measurements
night) - a sufficient
number of
error
that extremely
in
unusual
ions to be more
important
Region
of transition
mixtures
ratios
exponentially
may well exist
in analysis,
from
is
to atomic
Both the rate of
as an ion descends
transition
in tbe volume
could cause significant
assuming
density
molecular
of the F2-layer.
The ion-composition
this occurrence
as tbe electron
from the
is, in fact,
so
responsible
distortion
a fixed composition),
for
of the
but this
for these data.
effects
in the acf’s
during the day, but may comprise
of the ion content near 500 km at night.
Its neglect
may cause
overestimates.
- h <148
km
by the influence
the shape of the incoherent scatter spectrum is significantly
affected
9 At the ~i~~~tone Hill radar wavelength these effects
of ion-neutral
collisions.
are consistently
seen below
sional effects
from
fore
6.
here precludes
in the li8-
to i30-km
reliable
Equality
is significantly
in the previous
region,
is a significant
Te-Ti
also,
- ii8
determinations.
higher
than Tr
i30 km,
colli-
Analysis
for h < i i 8 km there-
An ion mass of 30.5 amu is assumed.
determined
no consistent,
there is no evidence
find Ti with Te ,= Ti and Vin . 0, assuming
Above
130 km there is no evidence
from measured
data.
< h < i30 km
section,
difference
below
Ti and vin.
of Ti and vin values
Region
as high as i30 km, though the small-
in the region
and seeks to determine
t 1 shows an example
Temperature
consistent,
In addition,
Hill data that Te
Ti = Te,
As was mentioned
that there
’138 km and may be significant
are undetectable.
Millstone
assumes
Figure
I
i
ion
E-region,
ness of the effects
I
is
uncertainty.
from available
It is possible
the region
of 0+ decrease
returns;
portion
5.
data.
on the sharp underside
H+ does not seem to cause significant
serious
further
shows that the altituffe
200 km at night is moot,
sharp 0+ gradient.
has not been addressed
a sizable
to ca~~
) may cause molecular
At night,
region
and the lifetime
a very
altitude
spectrum
problem
however,
error.
This summary
scatter
below
sharp that a wide range of composition
the lowest
systematic
day) to 260 km (summer
Millstone
acf measurement.
in a narrow
diffusion
F 2 peak,
NO+,
is
are always
altitudes.
The question
ambipolar
composition
data in this region
within this range to cause a 3- to 100-percent
from incoherent
over
are so
of a mean mass of 30.5 may lead
of 0+ ions may appear
but that in its extreme
times
masses
the NO+ - O;
from
but assumption
a larger
molecular
a mean mass of 31 amu.
experiments.
i 30 km (winter
(e. g., trough passage
As
determined
and NO+ ions predominate
to 0+ ions has been studied by Oliver
is variable,
from
O;
These
be distinguished.
proportion
ions may exist at certain
temperature
cannot
range if one assumes
data from
the range extends
minor
layers.
abundant of these species,
from
of this transition
in sporadic-E
the temperatures
i 30 km, a sufficient
This transition
experiments,
occasionally
(3 O and 32 amu) that they
variable
by the 2-pulse
below
130 km.
from
reliable
Millstone
This altitude
an ion mass of 30.5 amu.
I
63
.in information
is obtained
27
Hill data9 or theory
range is analyzed
to
--EEL
c-w
-+’-
.
T; OR “in
X
T; FROM
(T;)
FIT AsSUMING
❑
11 FROM
(Ti,
T#l)
FIT ASSUMING
Vin = O
A
1.
(T;,
Tfl;)
FIT ASSUMING
Vin = 0
FROM
FROM
(Ti,”ln)
FIT ASSUMING
Te = 1:,
Te = T,
v;n
= Q
—
~
—
+
&
-’0-
+
—,
-+-
I
I
~
.500
TEMPERATURE
0
[K)
I
500
I
I
1500
I
I
I
3500
COLLISION FREQUENCY
(see-l)
++
k++{
,A*f~;,
,
Fig. 43.
Lower
F Mode results on 48 September
T,
T.
I
2500
1974,
4735-1747
UT.
T.
“+
2=
—
++
*+
,00
0
500
1000
1500
TEMPERATURE
2000
[K)
259Q
1
50
PERCENT
0+
Fig. 12. Profile
analysis
for data on 18 September i974, 1731-1800 UT.
Thermosphere
results yield:
T- . i052 * 17 K, s = 0.0262 * 0.0041 km-i;
T420 = 408 * i3 K; and [0]400 = (2.46 + 0.99) x i08 cm-3.
64
I
~500
1<
Some additional
assumptions
formed
calculations
7.
Te . Ti and Vin = O, i.e.,
i t shows results
Ion-Composition
Te and Ti differ
this region,
species
vi”)
Transition
ionosphere.
and a (Tp
proportions
Tbe temperature
this
estimate
to test the adequacy
Te/Ti)
search
8.
0+ Region
of the
has also heen per-
-225
Because
search
obtained
is thus performed.
from
analysis
are systematically
is obtained.
1“
znd atomic-ion
of a measured
under the assumption
too low,
Section
acf
of a puce 0+
but can be corD-2
below
explains
to Te and Ti are then applied.
significant
in this region,
amounts of mOleCUlar
beyond 26o km at night,
and a (Ti,
Te/Ti ) library
ions may on occasion
there
is the possibility
The H+ abmdance
search
exist up to 250 km
of underestimating
is also assumed
true at night and can cause the temperature
increasing
Figure
km
library
profile
to be important
in these height intervals.
is not always
data.
km < h
during the day and possibly
Ti and Te/Ti
so obtained
on measm.ed
amounts of both molecular-
range are analyzed
and bow corrections
Only 0+ ions are assumed
is performed.
Te/Ti)
cannot be reliably
values
performed
h <225
of significant
of the ion-composition
derived
fs
analyses
-430<
and a (Ti,
all acf, s in this altitude
when m estimate
the error
Region
in this region,
and, as their
rected
from these various
the ion content may consist
(Sec. 4 above),
This
a (Tr
on data in this region.
Figure
how
have been made for this region
to be negligible.
to be overestimated
above
400 km,
with altitude.
i 2 includes
some
sample
results
from this height region
from
an analysis
of mea-
sured data.
D.
NEUTRAL-ATMOSPHERE
i.
DEDUCTIONS
Althcmgh the incoherent
scatter
can be made concerning
properties
are equal.
as N2isthe
equal below
“in,
concerning
of data and invoking
2.
estimate
Tn,
Ba”er”~
[0]
&z’
measures
be assumed
additional
ionospheric
below
km,
i30
Also,
equal whenever
atmosphere
PROFILE
time-continuity
cases,
is essentially
Tiand
a number of
ionic and neutral
proportionalto
Tnaretbought
to be
Te is found to be eqwal to Tr
constraints.
constraints,
bas been obtained
can then be used to estimate
properties,
can be made by considering
profile-continuity
information
In some
atmosphere.
in this region.
the neutral
appropriate
by invoking
with these data. ) In this way,
Tn profile
constitutmt
200 km and can reliably
may be obtainable
technique
the neutral
which is measurable
predominant
Other deductions
profile
ION-COMPOSITION
General
deductions
[N2],
AND
(Further
in fm-matim
but this has not been done
on the [0] and Tn profiles.
the ion composition
an entire
This
in the F1-regiom
Profile
have shown how one may determine
where
the ion composition
t ion.
Their
analysis
Tn(h)
Tn from
incoherent
scatter
data in regions
is known and Te > Ti > Tn through use of the ion heat-balance
eq”a 29
profile shape above h . 420 km
assumes Tn to follow the Bates
.T~-(Ta
-Ti20)exp
[-s(h-i
65
ZO)]
and [0]
to be in diffusive
equilibrium
altitude
(usually
400 km) a“d Tn(h) then define
of Bauer Et ~,
specified
the parameters
above
s, and [0]400
T-,
and using a two-step
‘Odel
‘alue ‘0= Ti 20
from the data above 300 km
[0] ~oo value,
determined
For analysis
of Millstone
Hill Z-pulse
for simultaneowly.
data,
than
parameters
mmli”ear
20
mode130 and the remaining
the fit (e. g.,
at night),
retaining
than 75-percent
free parameters
cases,
is used.
Data
this lower-altitude
is that all four unknowns are solved
additional
of an initial
uncertainty,
remit
calculations
1s too great
procedure
set to their
are
or
(mmcon-
it is fixed using the Jaccbia
If no E-region
both TIZO and [0]400 are initially
asSUming a
determined
the just -determined
of the above analysis
are needed in tbe fitting
are sought.
were
scheme
225 km.
only a one -step procedure,
iterations
reference
analysis
from the data,
and [0]400
In some
held fixed if the uncertainty
If [0]400 has more
vergence).
Ti2w
A second difference
least-squares
T-
Then,
a variation
of O at some
In the original
determined
First,
from the data above
While this requires
made with certain
more
were
to 435 km are used and help to establish
range has been set at i 20 to i 30 km.
abundance
[0] (h).
altitude with s = 0.024 km-i.
and s were
li6
The
procedure.
T-
from
225 km.
i97 i
data are available
Jacchia
for
model values
before
solving
to find T ~ and ~ then, mtomatically,
the data are refitted with s additionally
held fixed
-i
to find ody T-.
at O.02 km
Only the results of the last fit made are preserved
on magnetic
tape,
although
all fitting
results
The need for nmltiple
the reliability
consistent
tests
and reascmable
have produced
Figure
3.
fitting
of the results.
are not thought to yield
are output onto the line printer.
ccmti”gencies
values
of this profile
discussed
in that region.
[Eq. (48)] is assumed
fitting procedure,
in the previous
For
is so nearly
analysis
complete,
lations
are given
in Table
assuming
an arbitrary
deduce
assuming
p . i,
XVI.
Shown here is A(p),
A similar
relation
these tabulated
accm-acy
due to the slight
is lost by choosing
(perhaps
values
a central
and F2-region
this Tn profile
meaestimate
temperatures
ambiguity can be solved.
li, i2
Because the
mapping
relations
ion composition.
of ion temperature
B(p) is shown for the Te/Ti
points is used in 2-pulse
differing
data,
E-
As the ion and neutral
simple
the ratio
(02+/NO+) ratio (see Sec. C-4 above).
obtain Table
Tn profile.
temperature
Moreover,
of Te/TV
member
one would
determination.
data analysis.
5 percent]
for the cor34
These re one would
p . [0+ ]/Ne to the ion temperature
uncertain
A and B for
2-pulse
to relative
molecular-im
for
although
Hill investigations.
to derive
temperatures
from
unambiguous
-composition
Millstone
ion composition
is derived
also.
of A(0) is somewhat
that little
uncertainty
there
is,
in E-region
in fact,
b“t each one is tightly
of each family.
Linear
The exact value
mean
a family
packed
such
This has been done to
XVI.
The Z-pulse
of p . 4, yielding
data i“ the i 30- to 225 -km region
profiles
of Ti(p
. i) and Te/Ti(p
66
I
Hill
ion-temperature
it is possible
ion and electron
deduce
of such relations
sinmltaneously,
showing the deduced
prevents
of Millstone
the Fi -region
of relative
between
secticm
of the Pi -region
has been used in some previous
mass
concerning
in determining
The [0 ]400 and s parameters
when determined
to $; valid through the F4 -region
are equal in this region,
interpolation
questions
Profile
The Tn(h) estimate
respondence
a“d Ti ~ o.
useful results
data as tbe .“kmmvn io” cmnpcxiticm
ambiguity
raises
good [0 ]400 re suits when s is fixed in the analysis.
i 2 is an example
This approach
analysis
is indeed often unsuccessful
of anything b“t T-
consistently
Ion-Composition
surement
for profile
The fitting procedure
are initially
. 1).
analyzed
under the assumption
Once the independent
Ti estimate
TABLE XVI
VALUES
OF A(p)
COMPOSITION
Ti(model)
simply
B(p) RELATING”
RELATIVE
1.937
1.000
0. I
1.744
1.065
0.2
1.570
1.123
0.3
1.427
1.165
0.4
1.308
1.188
0.5
1.218
1.192
0.6
1.146
1.177
0.7
1.W2
1.146
0.8
1.052
1.106
0.9
1.021
1.056
1.0
I. 000
I. 000
in this region
(see previous
fidence
interval
in p, there may be large
onto the p-axis
model
(A here denotes
systematic
Ti estimate.
Once
from the p- to the B-axis
On occasion,
the physical
and the temperatures
corresponding
Due to the possibility
the Ft-region,
O+).
of large
re.wits
with the exception
perhaps
even in the worst-case
situation.
To date,
procedure
In addition
yields
limit
(composition,
of Te/Ti
Te/Ti
The
. i)]
con-
to the statistical
necessary
mmpositim
in deriving
of Te/Ti
. B(p) (Te/Ti)
values
limit
by
(p . i).
outside
of
is assumed
are adopted.
in the independent
Ti ,estimate
Te) are also subject
to sizable
which is less than 20-percent
F4-region
. 1).
. 1) i ATi(p
the O or iOO-percent
uncei-ta.i”ties
these
. Ti(model)/Ti(p
one finds the final estimate
to this composition
the other F+-region
temat ic errors,
y).
then estimating
In such cases,
systematic
to A(p)
due to the assumptions
p is found,
estimation
(O - iOO-percent
one finds the ion composition
tbe Ti(model)/[Ti(p
Ti uncertain
errors
to find B(p),
this composition
range
section),
XVI corresponding
found by mapping
ION
TEMPERATURES
0.0
in p is similarly
the independent
FI-REGION
ELECTRON
B(p)
errors
mapping
RELATIVE
AND
A(p)
by finding the value of p in Table
error
ION
P
has been formed
statistical
I
AND
AND
results
in
sys -
uncertain
have not been extensively
used.
Figure
4.
i2 shows an example
Electron-Density-Profile
As explained
P~(h).
of the Te and composition
i“ Sec. B-i
The fim.1 estimate
evaluation
in this region
above,
(Te/Ti)(h)
of (Te/Ti)(h)
Sec. B-i
above.
Sec. 3 above],
may result
A large
is needed before
in the region
profile
the final estimate
measured
uncertainty
in ion composition
is grossly
Ne(h)
can be Calculated
data.
(Sec. 3 above),
determination.
from
(i30 to 225 km)
and thw
Ne(h)
Once this final esti-
of Ne(h) is made “ia the method explained
and thus to Ne(h) determination.
if ion composition
from
of unknown ion composition
is determined
must also await ion-composition
)(h) is made,
deduced
Corrections
cannot be made until the io”-imposition
mate of (Te/Ti
values
is not so detrimental
A maximum
in error.
67
to (Te/Ti)(h)
of iO- to 20-percent
i“
(see
em-cm in Ne(h)
E.
DEBYE-LENGTH
All
small
CORRECTIONS
acf analysis
employs
a library
De bye length (Sec. C-3 above).
results
appreciably
when Ne is very
mate is also low due to the Te/Ti
above ).
Moorcroft24
iterative
manner,
of theoretical
This assumptim
low,
calculated
is never
for the limiting
quite true,
in which case the Te estimate
correction
employed
has shown how one can correct
but this correction
acf!s
68
but cmly affects
the
is low and the Ne esti-
in its calculation
from P~ (Sec. B-i
these Te and Ne values
has not been applied
case of
to the Millstone
in a simple
Hill 2-pulse
but
data.
ACKNOWLEDGMENTS
In addition to the authors of this report,
several people have heen
instrumental
in the development
of the ‘two-pulse 81program
at
Millstone
Hill.
Wallace A. Reid has heen the engineer
in charge
of development,
modification,
and maintenance of the radar equipment.
Leonard B. Hanson has been the engineer in charge of the
development,
modification,
and maintenance of the radar-computer
interface and maintenance of the computer.
Glenn W. Armistead
was responsible
for much of the real-time
computer program development.
Richard A. Brockelman,
Tor Hagfors,
Robert
A.
Power,
John K. Upham, Arnold D. Kaminsky,
Alice R. Freeman,
John M. HoIt, Ralph F. Julian, and Gary A. Bullock provided programming and data analysis support.
69
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i.
J. V. Evans, R. F. Julian, and W .A. Reid, ‘tIncoherent Scatter Measurements
of F-Region
Density, Temperatures,
and Vertical
Velocity at Millstone Hill, at
Technical
Report 477, Lincoln Laboratory,
M. I. T,. (6 February
i970),
DDC AD-706863.
2.
J. V. Evans and M. Loewenthal,
3.
J.V.
Evans,
Planet.
Planet.
Space Sci. i3,
Space Sci. iZ,
1031 (1965),
4.
J. Geophys.
5.
Planet.
Space Sci. ~5, 3387 (1967).
6.
Planet.
Space Sci. i8,
i225 (1970),
7.
Planet.
Space Sci. 2J,
763 (i973),
8.
Planet.
Space Sci. 23, i46i
9.
Proc.
io.
Res. 7Q, i$75 (1965),
J. Geophys.
ii.
J.V.
Evans and L.P.
12.
L.P.
Cox and J.V.
Evans,
Res. ~,
DDC AD-616607.
DDC AD-6243 *O.
DDC AD-7i6056.
DDC AD-772 i37/6.
(1975),
IEEE ~7, 496 (1969),
915 (1964).
DDC AD-A024177/8.
DDC AD-694i92.
3343 (1967),
DDC AD-6589%2.
Cox,
J. Geophys.
Res. ~5, 159 (i970),
Evans,
J. Geophys.
Res.
DDC AD-703492.
75, 6271 (1970),
DDC AD-7229 ii.
13.
J.V.
14.
G.W. Armistead,
DDC AD-742616.
i5.
J. V. Evans, Editor, IfThe Millstone
FY 1970,. Technical Note 1970-20,
ber 1970), DDC AD-717156.
16.
J.V. Evans, R.A. Brockelman,
R. F. Julian,
Radio Sci. ~, 27 (i970), DDC AD-70463i.
i7.
J. V. Evans, ‘Millstone
Hill Thomson scatter Results for 1967, II Technical
Report 482. Lincoln Laboratory,
M.I.T.
(22 July 1971), DDC AD-735727.
J. Geophys.
Res. 77, 2341 (1972),
J. V. Eva”s,
i8.
J. P. Dougherty
19.
COSPAR
1965).
and D.T.
20.
U.S. Standard At mosp~
D. C., 1962).
21.
R.H.
22.
P.M.
International
Farley,
(U. S. Government
Perkios,
Banks,
Planet.
Space Sci. ~,
J. Geophys.
D.T.
Farley,
D.R.
Moorcroft,
25.
H. Carru,
26.
W.L.
Oliver,
J. Atmos.
27.
P.M.
Eanks,
Proc.
28.
P. Bauer,
R. Benoit,
Terr.
IEEE ~,
Proc.
W .A. Reid,
Res.
md L.A.
Carpenter,
6S, 5473 (1963),
(North-Holland,
Amsterdam,
Printing
Washington,
Res. ~,
Office,
6370 (i968).
4091 (i966).
~,
Res.
i53 (4972),
1105 (!966).
~,
and M. Petit,
P. Waldtetiel,
Bates,
J. Geophys.
Res.
J. Geophys.
Sci. ~,
Hill Propagation
Study: Progress
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Lincoln Laboratory,
M.1.T. (2 Decem-
Atmosp&e
Wand a“d F.W.
24.
Radio
J. Geophys.
Reference
23.
DDC AD-752948.
and W .A. Reid,
955 (i964).
LaNature,
Phys.
No. 3330, 422 (1962).
37, 1065 (i975).
258 (i969).
and D. Alcayde,
Roy. Sot.
~,
4825 (1970).
D.R.
30.
L. G. Jacchia,
‘Revised
Static Models of the Thermosphere
and Exosphere
with Empirical
Temperature
Profiles, n Smithsonian Astrophysical
Observatory Special Report 332 (1971).
31.
P. Waldteufel,
Res.
&,
~,
Res.
29.
J. Geophys.
(London)
J. Geophys.
451 (1959).
6995 (i971).
70
.—..
—.
APPENDIX
SYSTEMATIC
The techniques
cause a number
DISTORTIONS
employed
at Millstone
of systematic
into two categories.
incoherent
scatter
transmitter
calibrations,
and errors
in the analysis
undistorted
theoretical
distortions
1.
scatter
scatter
trum.
by D.T.
function
of the impulse
noise passed
where
t
receiver
passband
and
is of great
in comparison
measurements.
De flnition
may
improper
for these distortions
function
between
Calculation
and evaluation
of
of these
function
(or,
~IP(T)Pw(T)l
expected
fortbe
is that the ionospheric
of the transmitter
plasma
waveform,
at correlation
density
incoherent
fluctuations,
and the
bandpass
time delay
spec~, P(T)
pw(~)be
the auto-
and pn(~) be the autocorrelation
function
equivalently,
the autocorrelation
result
general
inco-
autOCOrrelatiOn
by the receiver
measured
waveform,
then Farley!s
gating upon ionospheric
have been considered
is then multiplied
of the ionospheric
GATING
and transmitter
function
signal
of the receiver
TRANSMITTER
remit
hytheautocorrelation
through the receiver),
~ > denotes
His basic
backscattered
<Pm(T)>
distortions
to any monostatic,
by inaccuracies,
consists
is possible.
AND
measurements
of the gated transmitter
response
Allowance
and the distorted
bandpass
be the autocorrelation
be the autocorrelation
correlation
receiver
Farley.
multiplied
If we let pm(T)
introduced
Such analysis
comparison
PASSBAND
correlation-function
of the resulting
These
intrinsic
function
of this appendix.
of finite-width
is first
spectrum
functions
before
RECEIVER
experiment
function
by the hardware.
correlation
correlation
those due to use of a finite-width
of the measurements.
are the objects
The effects
herent
introduced
the ionospheric
in the measurements.
we have those distortions
is thus required
FINITE-WIDTH
to appear
MEASUREMENTS
there are those distortions
-namely,
Second,
importance
the distortion
First,
experiment
gating.
Hill to measure
distortions
be grouped
A
IN CORRELATION-FUNCTION
function
of white
in the time domain can be written
* P“(T)
value,
and * denotes
convolution.
pm(r)
and
Pn(r)
are
known func -
tions for a given experiment.
Analysis
of measured
functions
pm(~)
at
Millstone
Hill uses a library
of theoretical
functions
Pt(T) cOvering the range Of fUnCtiOns over which P(T) may reasonably be expected to vary.
TO
be able to compare the measurements
pm(~) with the theory pt(~), we must follow one of twO
approaches:
(a)
Correction
approach
then compare
(b)
Convolution
Pt(T)
P(T) andpt(r)
approach
-apply
Eq. (A-l)fOr
P(T)
in terms
of pm(r),
and
directly.
the convolution
effects
of Eq. (A-i)
to
as
Ptc(7) =[Pt(T)
tD. T. Farley,
–solve
Radio
Sci.4,
Pw(d]
* Pn(T)
935 (i969).
(A-2)
and then compare
Pm(T) and Ptc( r) directly.
etone Hill 2 -pulse
data analysis;
A.
Correction
by T. Hagfors
A necessary
Implementation
we attempt
to solve
at Millstone
Hill;
assumption
to solve
Eq. (A-i)
a brief
Eq.
P(T-x)=
P(T)
in which case we may write
Pm(r)
=
is discussed
P(T)
+~
Eq.
[PW(T)
:
for
p(i).
description
below.
of Eq.
(A-i)
was originally
is given here.
is
well
con-
approximated
by
as
(-x)+*+2
(A-1)
This problem
of his approach
for P(T) is that <pm(T)>
(A-i)
The next step is to expand P(7 -x)
Pm(r).
of these methods
of Mill-
Approach
In this approach,
sidered
Each method has been used for some facet
+
(A-3)
. . .
as
Pn(T)]
+
Pw(d
*,
{PW(T)
~
* [-TPn(T)]}
~pn(T)
+...
II
~z
c? p( ,)
+ ----#
I
(A-4)
or
Pm(r)
= P(T)
Fk(,)
=
PW(7)
Fe(,)
‘k
+ ~
only three
terms
forms
Eq.
of the expansion
used in the Millstone
terms
for p(~).
of Eq.
estimate
p
isderived
from
by the derivatives
ference
IIOiSy
ptc(~)
between
data.
~gnitudes
An iterative
estimate
calculated
Fn(r),
F, ( T).
-.
and
F,(T)
for pn(T) and the actual transmitter
of p(r)
procedure
is calculated
wave-
is then used to solve
ignoring
the derivative
of P(T) is estinratedas
(T)
.~
dp. ~(T)
d~
measured
noisy data is undesirable,
functions
HagfOrs
waveform
Hill experiments.
Tbe first-iteration
pi(T)= *
Pi(r)
being retained.
Gaussian
(A-5)
The ith-iteration
from
(A-5)
0,1,2
1
using an appropriate
(A-5)
F2(T)
k=
P“(,)
#
[
analytically
2
+ &
Fi(T)
of aparabcda
d2p. 4(T)
+
FO(r)
the derivatives
fit to five
plots of pt(~) and pi(~).
noisy.
req”iredin
points inthe
5 iterations
F’2(T)
—.
As the calculation
Eq. (A-6)
neighborhood
were
A somewhat
(A-6)
FO(r)
d?
data and is therefore
for pm(~) show that i.
The procedure
Fi(T)
—_
required
larger
does not break down upon addition
of derivatives
are replaced
of ~.
toyield
Tests
with noiseless
animperceptible
number of iterations
of random
in practice
dif -
is required
noise to P(T);
for
noise
Of UP to P(0)/5 have been tested.
72
.—..—.————-
This
tortions
correction
approach
is used in Millstone
data cm the real-time
to the finite-width
Hill 2-pulse
computer
receiver
data analysis
printout;
it is not applied
netic tape,
nor Is it used in the final data analysis
tives
noisy data necessitate ed by Eq.
from
problem
can be entirely
apprOach
B.
we perform
this calculation.
The first
of these
functions,
leaving
ET represents
convolution
Eq.
time)
espbciall
y as the
by use of the convolution
TWO methods
the two methods
(A-2)
‘:
have bee”. used to
are small.
directly
through numerical
function
normalized
integration
to unity at zero
using
lag,
i.e.,
(A-7)
Pn(x)
of the waveform
W(T),
which,
in general,
quite time consuming,
hy the simple
may vary
with . . These
and to speed up the calculation
approximation
(A-8)
than the sum of T (the width of the transmitted
Calculations
have shown this approximation
<00, and 200 psec for Modes
most of the convolutions
performed
(A-2).
= Pt(d
all must still be performed
were
PW(T)(X)]
been replaced
such that ~ is greater
allows
Eq.
correlation
are intrinsically
Ptc(T)
Tn
[Pt(X)
in Practice,
30 psec and T .40,
of Eq.
between
calculates
tbe energy
half -width of pn( T)].
tbe calculation
the resulting
= Er
calculation
(A ‘7) has.
at lags
reliable,
of computer
on magof deriva-
= f,(7)/fo(o)
f~(x)
Eq.
data stored
it is felt that the calculation
is not sufficiently
at the expense
Discrepancies
methcds
Pte(T)
where
(A-6)
to the real-time
since
gating dis -
look at the corrected
Approach
In this approach,
sampled
(albeit
and transmitter
to tbe problem.
Convolution
perform
avoided
passband
to obtain an initial
to be avoided
F,
pulse)
to be quite good.
G, and H, respectively,
in Modes
T <
In practice,
out through +00 ~sec for Mode F and i50 psec for Mode G.
With ~n m
we see that ~ > T +
F and G, for which O<
for Mode H, for which O< r < 190 psec.
and ~“ [the
380 ~sec,
but
the convolutions
Approximation
of
(A-7)
by Eq. (A-8) for these longer lags produced errors
of about +i K in ion temperature
Ti
-’t
and +iO sec
m collision
freq”e”cy
Vin for Mode F, and O K in Ti and +10 K in electron temperature Te for Mode G.
These
The actual implementation
tunately,
did not greatly
Ptc(T)
i.e.,
a different
=
errors
of this convolution
factor
and +5 K in T= for Mode H.
These
each lag instead
In October
was applied
for each lag.
however,
errors
computations
time.
Sec. A above [Eqs. (A-3)
a small
error
was erroneously
The errors
have also been ignored
was that a different
normalization
constant actually
which,
for-
calculated
as
resulting
were
about
in the data analysis.
factor
needed;
K in Ti
The main
had to be calculated
this essentially
for
doubled the
required.
i 976, a second method for performing
to save computation
contained
(A-7)
fm. Mode F, +6 K in Ti and –5 K in Te for Mode G, and –iO
of tbe one normalization
number of convolution
calculation
fr(T)/fr(0)
normalizing
-i
m .in
of this error,
in the data analysis.
Equation
affect’ the final results.
O K in Ti and +2 sec
effect
have been ignored
the convolution
This method uses the results
through (A-5)]
to write
Eq. (A-2)
73
of fIagfors
as
of Eq. (A-2)
1 calculations
was instituted
as described
in
dpt(,)
Ptc(T) =
Whereas
Hagfors
Pt(T)
originally
of pn(T) and PW(T),
I?O(T)
approach
the measured
tions;
(A-9)
w.
data before
is presently
with the measured
data.
functions
instead
of noisy,
data with theoretical
used to convolve
The functions
2 -pulse
passed
Adoption
j
I
of Eq.
from
(A-9)
Fi[~),
to approximate
A-1.
Of course,
distortion
Receiver
(A-9)
in Sec. Iahove
design.
number
are discussed
for the Millstone
Hill
used for data
Of a parabola
tbe rmmber of computations
to
and 4 mdtiplicatioms
Ptc(0)
=
per lag –
t).
function
of finite
is valid
receiver
bandwidth
for any receiver
between
and
and pulse
the hardware
implemen
discrepancies
for the 2-pulse
experiments
miscalibrations,
and errors,
and have been
of instances.
Those
cases
-
for whicb important
here.
to be symmetric
Receiver
of receiver
tilt i“ the
from
through the receiver.
This bias can be mea-
data passed
but the fear
of receiver
Sucha
asymmetries,
an average
data taking produced
discovery
nwnber
74
in the next para-
(see
Sec. I above)
output from
profile
A-%.
de-
the receiver
of ionospheric
of such measurements
pn in Table
variatio”witb
in data interpretation,
spectrum
of the noise
each time an altitude
the adopted f”nction
bad changed
of bandwidth
could be important
function
a bias to
dubious wortb.
of the iommpheric
of a large
asymmetries
with time is presented
data tobeof
variation
Smearing
experiments
that receiver
variation
rift
The correlation
is measwed;
b“t important
of data
of applying
been made.
during the 2-pdse
that there was a small
a fixed
six years
This tilt has tbe effect
characteristics
bandwidth.
andtobave
until some
of the spectrum.
hese2 -pulsed
to the discovery
frequency
was not evaluated
It was tben”oticed
oconsidert
receiver
about its center
asymmetry
since the amount of instrumental
tion functions
unmodified
as the derivatives
discrepancies
These
pendsupon
days of 2-pulse
original
smooth. -theoretical
are presently
has decreased
for the effects
ina
calculated
time has also recently
is measured
and (A-9)
to b additions
correlation
for in the data analysis,
(evidence
In addition
(A-2)
impm’tance
results
at the center
drifts
hasledw.t
Eq.
inaccuracies,
been collected.
sured and allowed
with time
comparison
Hagfors’
of the original,
functions
are calculated
there are always
was designed
spectrum
all ionospheric
from
func -
of ,.
in hardware
of some 45 kHz.
had already
receiver
for direct
to
Inaccuracies
The receiver
bandwidth
of Eqs. (A-5)
than O. 00i (relative
experimental
Hill consist
found to be of significant
A.
functions
correlation
method has over
comparison
These
and i4 multiplications,
presented
tation and the proposed
measurement
was in an attempt
ionospheric
are now calculated
and F2(T)
by Eq.
gating upon the ionospheric
employed.
at Millstone
Of actual measurements
INACCURACIES
The development
graph)
(A-9)
In general,
in Table
ACCW.aCy is better
11. HARDWARE
scheme
!
data.
required
6 additions
savings.
transmitter
I
the theoretical
representations
is highly desirable.
are tabulated
The derivatives
functions
that the present
by Eq.
analytical
use of Eq. (A-9)
with theoretical
through three points i“ the neighborhood
necessary
a large
measured
Pn(~) and FO(~),
experiments
analysis.
required
calculations
original
comparison
The only advantage
method is that the derivatives
(A-9)
F,,,,
has used sampled
Hag forsl
of pn( T) and pw( r) for this calculation.
deconvolve
+ -
FO( T), Fi ( T), and F2 ( T) from
calculated
the present
F,(T)
+ ~
from
correlatbe earlier
Mm-e recent
TABLE A-1
Pn AND
THE FUNCTIONS
Fo,
F,,
AND
F2 FOR MODES
F,
G,
AND
H
—
,. .,.
J-fKme
r.
Mcde
G
Delay
(yse.)
P
n
o
1 .M
10
0.4s
20
0.0s
30
0.01
40
O.oc
Fo
—
.00(
F1
O.OQ(
Mode h
.
F2
—
Fo
F1
F2
—
Fo
F1
30.6
.003
0.00(
38.7
1 .Ooc
O.ooc
.193
-2.623
50.2
.067
.158
-1.680
48.5
.068
-0.920
46.0
.003
-0.077
31.8
.C6a
-0.920
46.0
30.6
.06a
-0.920
46.0
.068
-0.920
46.o
,001
–0.030
39.2
-0.89C
45.6
F2
41:0
1.028
-0.330
43.2
1.032
-0.430
44.3
1.033
-0.4-45
44.5
50
60
70
80
.000
O.ow
90
100
110
120
130
140
,000
O. COO
38.7
150
160
170
180
190
200
—
—
‘o is dimensi.an less; F1 has dimensions of microseconds;
4 column of pericds means that the hnction
node.
continues
75
F2 has dimensions of @see)
unchanged
thrwgh
the maximum delay
for the
measurements
have shown that the receiver
value changfng from
lyzed
with tbe Pn of Table A-i
tinue to analyze
deduced from
before
has narrowed
this time variation
all data with this same
several
in time,
years
been ana-
it was decided
The effects
in the adopted
the pn ( iO -ysec)
had already
was discovered,
Pn for consistency.
the data due to these inaccuracies
are probably
B.
spectrum
Since much data from
0.48 to O. 54.
to con-
upon the temperatures
p“ have not been evaluated,
but
small.
FulSe -Shape Distortions
The pulse waveforms
tangular
and flat.
employed
Rise
power
capacitor-bank
time.
In addition,
discharge
significant
enter into the calculation
for calculation
in the 2-pulse
and fall times
during pdse
are,
are designed
of course,
trammission
pulse timing errors
of the correlation
of the effects
experiments
in the equipment
causes
the pdse
have been identified.
function
shapes to droop with
pw of Eq.
upon measurement
rec-
and the znain -
All these factors
of the pulse waveform
of instrmnenta.1 smearing
to be perfectly
finite,
directly
(A-i)
needed
of the ionospheric
corre-
lation function.
The droop in the pulse waveforms
transmission
schemes.
well described
as dP/P
1s the longest
cant.
,
shape,
correction
which sbmld
transmission
accounted
for this effect
scheme
for.
should be multiplied
P is power
should rigorously
this distortion
for power
variation
factor
is small,
pulse pairs
waveform
it was decided
the slight distortion
In making this correction,
cm different
is that tbe measured
all
droop is
Since 0.4 msec
drooping
however,
vs time and ignore
effect.
for the droop correction
by the correction
affects
is small but signifi-
be made by using the true,
Since the correction
be a second-order
discharge
has show” that this power
and t is time in milliseconds.
experiments,
using close - and wide-spaced
Tbe result
capacitor-bank
with tbe equipment
in the 2-pulse
the true pw of Eq. (A-i).
make the simple
form
. dt/15, where
pulse transmitted
Correction
to calculate
d“e to main-power
Experimentation
to
i“ v..ave -
the real
pulse-
frequencies
nmst be
autocorrelation
function
f
i90 psec
f . i + 7/45000
T<
f = i + (, –200)/i5000
r > 200 ~sec
for lag T in microseconds.
The finite
rise
slopes
and fall times
of the leading
cause of the shortness
short compared
cially
apparent.
portance.
effect
“’
and trailing
of the pulse-generating
of the F-Mode
with tbe 40 -psec
Were
of leading-edge
rcm”ding
pulse.
F-Mode
a21 F-Mode
Tbe 20- and 40-psec
edges
of the transmitted
equipmcmt,
seem
The rise
and fall times
pulse Ie”gth;
pulses
a rounding
of the same length,
lag waveforms,
is relatively
however,
different
pulses,
to be important
due to the finite
ody
for Mode F be -
cannot be considered
of tbe leading
this rounding
very
edge is espe -
would be of small
use 60- and 80-psec
for these lags compared
pulses,
im-
and the
with other lag
waveforms.
Investigation
mode which were
of the leading-edge
pulse rounding
nmch more
tba” the pulse edge-rounding.
pulse length was discovered
since pw of Eq. (A-i)
seriow
to be 39 psec instead.
is easily
modified
sistently.
Measurements
a 59-~sec,
pulse is used for the 20-psec
gap are used instead
of waveforms
of two 39-psec
for Mode F uncovered
This difference,
to account for it were
for other lags,
lag,
pulses
bmvever,
separated
76
by a i-psec
errors
the basic
in itself,
this basic
and that two 36-psec
timing
First,
in this
40 -psec
is not detrimental
pulse length used con-
have show” that a 58 -psec,
pulses
separated
not
by a 6-psec
gap for the 40-psec
lag.
Furthermore,
this 6-psec
to the shortness
crepancies
gap appears
of the pulses,
in the F-Mode
in the measured
the waveforms
to be more
pulse waveforms
autocorrelation
functions,
was not successful
and even correction
in sufficiently
complexities,
uncertainties,
and discrepancies
and distortions
of the transmitted
ignored
Transmitter
c.
Although
single
from
electron
F-Mode
all the frequencies
These
removing
for the major
observed
encountered
timing errors
discrepancies.
i“ accounting
waveforms,
diseffects
and correcting
the 20- and 40 -psec
standard,
that expected
is open to direct
for
lags have been
in the transmitte~
the RF phase difference
due to transmitter
klystrcm
experimental
approximation,
chirp.
and receiver
between
This arises
a.mplifiep
changes
are derived
a pair of transmitter
because
the transit
during the course
i“vesti.gat ion, or may be calculated
the voltage
Vt applied
from
to the klystron
from
varies
energy
It is klystron
in reality,
and C is the capacity
Equation
this is not precisely
(A-i O) assumes
true.
where
time of the
first
during the pu18e as
shift between
condenser
achieve
that stores
ccmstamt during the pulse,
in the beam are accelerated
Vt, and thereby
a“d mass of an electron,
(2)”2
If d is the distance
This
principles.
between
the
though,
the
a speed Ve given in
. Vte
e and Me axe the charge
‘e’
of the high-voltage
that It remains
The electrons
cathode and ring anode by the potential
$ NfeV~
pulses
(A-iO)
current,
for the pdse.
a
of the pulse.
dVt
—
= – It/c
dt
where
in
Due to the
data.
employed
beam in the transmitter
To a first
in shape and, due
slanted.
Chirp
stable frequency
differs
effect
in analyzing
than rectangular
to be significantly
have berm seen to produce “quite detrimental
these errors
completely
triangular
the pulse edges appear
respectively.
It follows
that
~
between
the input and o“tp”t
cavities
in the klystrcm,
there will be a phase
the two of
~=_?#d
radian
=-’”:d(+s’z
where
f is the radar
frequemy.
The change in Vt during tbe pulse produces
a rate
M
$$
= 2rfd
r
Me
‘ -Tfd
It
z>
r
d~t
i
~e$~dt
c
“
t
I
I
77
L
a change in @ at
This,
in turn, leads to a frequency
= -~
fd
r
M
e
~ev3
t
shift in the transmitted
$
(A-ii)
c
For the case of the Millstone
Hill UHF transmitter
C = 24 HF so that Eq. (A-ii)
reduces
In practice,
& is typically
shift which,
unless
-8 m/see.
To compensate
from
G and H.
Modes
corrected,
(employing
Eimax
x626 klystrons),
d . i 08 cm,
to
of the order
of –23 Hz.
will he interpreted
for this,
pulse of
a correction
78
This corresponds
as a plasma
drift
must be applied
to an apparent
away from
the radar
to any drift velocities
doppler
of
obtained
APPENDIX
STATISTICAL
I.
EXPRESSIONS
FOR
The correlation
(sine and.osine
ERRORS
UNNORMALIZED
functions
channels).
during the same sweep,
our purposes,
CORRELATION
are estimated
In practice,
from
digital
separated
MEASUREMENTS
FUNCTIONS
samples
p“lsetransmission
and the returns
this maybe
B
IN CORRELATION-FUNCTION
into two pairs
taken as being equivalent
oforthogonal
may bemadeon
receiver
of orthogonal
to two separate
sweeps
outputs
two frequencies
outputs.
For
and one orthogonal
receiver.
Samples
from
sweep
i at time
t (meamn’edf romthec
noted by Yi(t)
for the sine output and Ui(t) for the cosine
to distinguish
samples
taken in the noise region
in the signal-plus-noise
scatter
over
signal,
region.
the computer
fn calculating
forms
certain
ommencementof
output.
of the sweep
Primes
are de-
are used (i. e., Y~,U~)
(near the end) from
theautocorrelation
products
the sweep)
samples
taken
function of the incoherent
of the samples
in real time and averages
a number of sweeps.
In general,
is calculated
the unnormalized
according
K
AR(T)
real part of the autocorrelation
function AR(T)
for time
lag r
to the expression
. &
s.
s
M-t
~
~
l=i
j.O
[Yi(t
+jc)
Yi(t
+7
+jc)
+Ui(t
+jc)
Ui(t +7 +jc)]
Kn
——
Zin
,2 [y;(t)
1.1
K~/2
- &
E
i=i
unnormalized
K
AI(T)
= &
s
,Z
1.1
U;(t + T)]
M-t
~
[yzi.i(t
j=O
+U2i-i(t
The corresponding
y~(t + T) + u;(t)
+j=)
Y2i(t
+~ + K)
+ jc) U2i(t +T + jc)]
imaginary
.
(B-i)
part of the autocorrelaticm
function AI(T)
is given hy
M-%
Z
j.O
[Yi(t
+ j<) Ui(t +7
+ jc)-Yi(t
+T
+ j.) Ui(t
+ jc)l
(B-2)
79
fn Eqs. (B-i)
and (B-2),
plus-noise
region,
and cosine
samples
the separation
separated
terms
noise,
in Eqs. (B-1)
and possibly
from
tion of the transmitted
subscripts
ensemble
average
of r.
There
products
from
from
noise contribution.
It is assumed,
of sine
U M # 1,
●.
incoherent
scatter
and airplanes.
signal,
The purpose
Each pair of noise-region
sweeps
however,
M pairs
and third terms.
distant hills
be taken in different
<Y~Y~ > = (Y:>
or sweeps
that noise samples
<Y~> for i =# j.
samp-
where the separa-
The brackets
with-different
<>
denote an
terms
are only
value.
in Eqa. (B-i)
in F- Mode calculations,
used fn forming
term
i.e.,
or expected
The third terms
present
pulses is T.
are uncorrelated,
the first
contain contributions
returns
the system
in this term may not necessarily
are taken in the signal-
taken in the noise region.
the next is taken to be a constant,
and (B-2)
also clutter
of the second term is to subtract
les
for which samples
pairs
by T are used to calculate
of one pair of samples
Tbe first
system
KS is the number of sweeps
Kn is the number of sample
and (B-2)
effect
a clutter
but are included
in these terms
here for generality.
is taken from
are only half as many products
subtraction.
consecutive
used in calculating
These
Each pair of samples
sweeps
with a pulse spacing
term three
as compared
with
one.
11.
EVALUATION
In order
assumption
variance
to evaluate
istaken
tohavea
T)> .–<ui(t)Yi(t+
samples
andp+~)
of terms
in Eqs. (B-i)
+T)],
normal
are defined
+7))
variables
Yi(t
and (B-2),
with zero
[Yi(t),
Ui(t +T)],
distribution.
the basic
mean and
[Ui(t),
The correlation
by
.UZPR(T)
T)> .U%l(T)
Xi(t) of the receiver
.
(B- 3)
output are written
.Yi(t)--Iui(t)
x;(t+
(B-4)
correlation
T)>
represent
function
is given by
.2 U2[PR(T)+IP1(T)]
tbe real
and imaginary
output in the signal-plus-noise
an odd function of r,
SAMPLES
are normal
bivariate
for these distributions
The complex
of the receiver
Adopting
+T)]
<Yi(t)ui(t+
<xi(t)
pR(T)
and Ui(t)
T)> . <ui(t)ui(t
xi(t)
I . ~.
and variance
Yi(t)
<Yi(t)Yi(t+
notation,
RECEWER
each pair ofvariables[Yi(t),
Yi(t
pR(.r) andpl(r)
In complex
Thus,
INVOLVING
the expectation
Furthermore,
and [Ui(t),
coefficients
where
PRODUCTS
is made that the samples
92.
Ui(t +T)],
OF
and wehavep
region.
R(0) . 1, PI(0)
.2 U2P(T)
.
(B-5)
parts
of thecomplex
correk.tion
function
PR(T)
iS an eVen fUnCtiOn Of r, PI(T)
is
. 0.
the notation
Zi.
we may summarize
Yi(t
+7)
the following
,
Vi.
ui(t
properties
+7)
of samples
80
(B-6)
in the signal-plus-noise
region
<Yi>
= <Zi>
<Y;>
More
= (2:)
= (vi)
= <u:>
<Yi.zi>
= <uiVi>
<Yivi>
= –<uizi>
complicated
be evaluated
= <Ui>
relationships
= o
= <v:>
= 02
= U20R(T)
=
UZP1(T)
involving
(B-7)
.
the expectation
value of products
of four samples
may
using the theorem,
<X,X2X3X4>
which applies
= <X1X2>
when Xi,
<X3X4>
+< X1X3>
Xz, X3, and X4 are jointly
<Xzx’t>
normal
+<xix4>
(B-8)
<X2X3>
random variables
with zero
mean.
For example.
I
<Yiziuivi>
<Yfz;>
In the noise
denoted by u;
region,
= u4[i
and pn for
relationships
to-sweep.
term
AR(T)
In evaluating
no correlation
and AI(T),
clutter
function of the receiver
output are
(B-ii)
the primed
samples
subtracts
the variant es of AR(T)
from
sweep-to-sweep,
as in Eq. (B-7)
by substituting
o:
<Yj(t2)>
= o
<Ui(tl)
uj(t2)>
= <Ui(ti)>
<Uj(tz)>
= o
e of the clutter
term
but it does affect
OF
variances
manner
TBE
We may now proceed
and AI(T)
‘ii’
their
in an empirical
UNNORMALIZED
the assumpticm
does not affect
of the variant
= ‘l’t
+ ‘<)
‘
Cij
‘ ‘ijzij
+ ‘fjvij
Eij
. YijVij
– ZijUij
c~ = Y~z: + u;v~,
is,
values
The effect
of
of non-
A.
CORRELATION
and (B-2).
‘ii
is made that there
the expected
and so must tie retained.
in Appendix
with the computation
,
sweep-
(B-i2)
defined
‘!(L +]’)
from
.
COMPLEX
in Eqs. (B-i)
that exists
for i ~ j
= <Yi(t,)>
the present
any correlation
and AI(T),
i.e.,
Yj(t2)>
is evaluated
AR(T)
and (B-2)
<Yi(ti)
111. VARIANCES
functiom
correlation
Defining
v; = U;(t + 7)
between
in Eqs. (B-i)
Under this assumption,
zero
,
(B- iO)
u and p.
The clutter
in fact,
+ 7)
.
and complex
= ,onR(7 ) + rPd(T).
z; = Y;(t
we obtain similar
+ 2P:(T)]
the variance
and P*(T)
(B-9)
– P:(T)]
= 04 [I@)
FUNCTIONS
es of the unmmmalized
Adopting
correlation
the notation
Zij = Yi(t +. + j.)
“iJ
>
= “J
‘2i,j
‘zi,
+’
+j<)
= ‘2i-4,jz2i.j
j = ‘2i.4,
+ ‘2i.
jvzi,>
E: = Y;V~- Z~U:
8i
%,jvZi,j
– ‘Z1, ju*l.
j,j
(B-i3)
we may write,
(B-14)
The complex
correlation
to as the measured
related
correlation
to the correlation
Appendix
function after
function
system
noise
i.e.,
pm(r),
function of the incoherent
and clutter
<AR(T)>
scatter
subtraction
- I<AI(T)>
signal
will tie referred
= U~Pm(T).
Pm(T)
(see Sec. VII below,
A).
Taking
expected
values
<AR(T)>
The variance
of AR(T),
in Eqs. (B-i4)
and (B-45),
= C72PR(T) – fJ:PnR(7)
<AI(T)>
=
U2P1(T)
–
the variant
U:Pnl(T)
= U:PmR(T)
=
e of AI(T),
U:PmI(T)
(B-16)
.
and tie covariance
of AR(T)
and AI(T)
are given by
u:(T)= <A:(T)>– <AR(T)>2
q%)
To calculate
and then subtract
three variables
of Cij variables,
i (sweep
0:(7)
=
+T)
OR
script
is
and also
o:,
<42(7)>
we square
(B-48)
<A1(T)>2
AI(T)> – <AR(T)>
= <AR(T)
<AR> 2.
Cif
-
the right-hand
is correlated.
is different.
Also,
I
+ *
terms
take expected
disappear
because
there is no correlation
values.
no pair of the
between
any pair
or any pair of D
variables
for which the sub21, j
With these simplifications,
u:(r) may be written
M-i
<C;>
s
(B-i9)
.
side of Eq. (B-i 4) for AR,
21, j
or any pair of Cl variables,
. &
<-41(T)>
A great many of the resulting
Cl, and D
number)
(B-17)
– <Cij>2
+ ~
~
(M -k)
[< CijCi,j+k>
-
<Cij>
I
k=i
[<C;2>
<Ci,j+k>l
- <C; >2]
n
M-1
I
<D~i j> _ <D2i,j>2
x [<
D2i,jD2i,j+k>
+ &
–
82
z
k=l
(M–k)
<D2i,j> <D2i,j+k>]
I
‘
(B-2o)
The expressions
in terms
in Eq. (B-20)
involving
of the autocorrelation
rmise region
(PW
PI,
the variables
functions
. 2U%R(T)
,
<c:>
<Cijci,j+k> = 2U4[2P:(T)+p:(kc)
XPR(T
<c;)
= 20:pnR(T)
<D2i,j>
= O
<Dzi jD~i,j+k>
The general
,
<D;i
= 2U4 [p~(k~)
result
for u;(T)
iv+ ;
Ph,
= 2U4 [i + 3P:(T)
+P1(T
,
(pRn,
+ pf(kc)
-k)
C;,
and D
may readilybe
evaluated
21,3
of the receiver
outnut in the sienal-&m-.
and va~iances
and U2) and in the “noise region
<Cij>
Cij,
<C;2>
+ OR(T
+k~)
o:).
These
results
are
-P:(7)]
+ ke)
P1(T–k~)]
= 20:
j> = 204
and
[1 + 3P:R(T)
– P:I(T)]
,
+ p~(kf)]
(B-21)
.
is then
i
~
(M
–
k) [Sp;(kc)
+ Sp12(ke) +PR(T
+ kc) PR(7 –k~)
k=l
–
PI(7
+
Aim
‘n
+ —
~4
where
S . 1 if no clutter
used.
The summation
k,)
PI(T
–
k.)]
+P;R(T)–P;l(T)]
—--= [i
Kn
(B-22)
I
s“bt~ action
is used in calculating
term must be omitted
and S . 3 if a clutter
AR(T),
if M . 1, i.e.,
if only one product
term
is formed
is
per
sweep.
The calculation
variance
of the variance
of AR(T).
tuted for Cij,
The
of AI(T)
follows
U12(T) is given by Eq. (B-20)
along similar
if the variables
lines to the calculation
Eij,
., and C;, respectively.
21,J
general
reswlt for ai2(r) is
q%)
D
=
&
*
F
21,j’
of the
and E; are substi-
s + P:(r) - +)
M-1
+ ~
~
(M-k)
[S&(kd
+Sp:(kc
)-j@
+kc)
OR(T
-k,
)
k= 1
+ PI(T
+ kc)
PI(T
-
k-)]
(B-23)
83
i
An equation for the covariance
of AR(T)
AI(T)
may be derived
in a similar
maoner
as Eq. (B-ZO),
M-$
OR@
.
&
<CijEij>
- <Cij>
<Eij>
+ ~
~
s
(M -k)
k=i
X [ <CijEi,j+k>
+
EijCi,j+k>
_ <Cij>
– <Eij>
++[
c;E;)
<Ei,j~>
I
<Ci,jw>
- <C:>
1
<E\>]
n
M-i
+ *
F ,?i,J> -<D2ij> ,
‘D2i,j
<F2ij>,
+4
I
x I< D2i,jF2i,jw>
+ ‘F2i,j
The terms
D
21,j+k
to evaluate
<CijEij>
= 8U4P1(T) PR(T)
and the result
<F2i,jtk>
<D2i,j+k>]
.
(B-24)
this are
= <EijCi,j+k>
x [PI(7
‘D2i,j
(M-k)
I
+ [OR(7 + k~) + PR(T – k~)l
= a4 (4pR(T) PI(T)
<C;E;>
– <D2i,j>
> – <F2i,j>
required
<CijEi,j+k>
~
k=i
+@)
=
+ kc)
+ PI(7
-
k~)})
PnR(T)
F..
>=(F
21,j+k
~i jD2i,j+k>
,
of substituting
these terms
= O
(B-25)
into Eq. (B-24)
is
M-i
4
OR *(T) = &
2PR(T) @
+ ~
s [
(M-k)
k=i
x [PI(T
‘n
‘~
~
+k~)
–k~)l
+P1(T
4 2MK~
_
PnR(T) Pn1(7)
Kn
84
.
I
[P#
+ kc)
+PR(T
-
k)]
Iv.
MAGNITUDE
OF NOISE
The last terms
tem noise
terms.
in Eqs. (B-22),
subtraction,
The values
SUBTRACTION
This term
TERM
(B-2 3), and (B-26)
is of order
(for u:,
u;,
K -4 compared
of M and the ratio Kn/ KS f~r Modes
and OR ~) reSUR from
with order
F,
the SYs-
(MK~)- 1 for the other
G, and H are given in Table
B-i.
TAB LE B-l
VALUES
OF
K#,
AND
K~K~
Mcde
F
I
* Numbers
that U2 & a;
at least
52(20)
I
1,3,0,5
75 (20)
I
l,3,0r5
in parentheses apply
6 November
mOin text.
is always
10,3
I I
H
1970.
to dalu taken prior tO
See also Fig.
and using the values
in Table
an order-of-magnitude
MODES
M
75 (20)”
G
Noting
M FOR THE 2-PULSE
smaller
I and Table Xl in
B-i,
it is seen that the noise
than the other terms
subtraction
term
and may he safely
neglected.
v.
CORRELATION
OF
Theunnormalized
correlation
lated using signal-plus
are still
from
correlated
ESTIMATES
-noise
estimates
LAGS
at different
different
the noise subtraction
lags [i. e., AR(’ri),
AR(T2)]
(and bence independent)
terms
in Eqs. (B-1)
sweeps,
and (B-2)
arecalcuhuttbey
use samples
for all lags.
Thecovarianceof
AR(7i),
AR(T2)
is
Kn
~RR(Tf,72)
DIFFERENT
sa.mples from
because
the same sweeps
AT
=-&
which may he evaluated
[(
-Cc’(’))(:ic+
x
n
to
Kn
i= t
C;(T,)Z
C;(T,)
i. i
)
(B-27)
4
‘n
‘RR(T4JTZ)
= ~
[P~#~-T~)
‘pnR(Ti)
85
PnR(T2)-Pn1(T4)
Pn1(T2)]
.
(B-28)
Similarly,
the covarianceof
AR(ri),
A1(T2) is
4
OR1(T,, T2) = $
[Pn1(T2–
Ti)
+PnR(T,)Pn1(T2)l
+PnR(T2)PnL(Ti)
(B-29)
.
n
The covarianceof
the estimates at different lags is of order K~i,
-i
(MK~)
. In the noise subtraction method used, Knis always
of order
larger
vI.
than MK~ (Table
B-i),
and the covariance
VARfANCE
IN THE AMPLITUDE
CORRELATION
FUNCTION
Theunnormalized
subtraction
amplitude
[Eqs. (B-1),
B(T)
We wish to derive
=[A~(,
xz)>
‘J:= <Ax,
#x2)>
i/2
correlation
without serious
COMPLEX
function after
noise and clutter
(B-30)
for evaluating
of B(r)
and its variance
the expectation
and variance
u~(r)
for later
of a general
2
u ,,
and X2.
u;,
Xi, xz are
$=f(<xf>,
(B-3i)
<X2>)
–<f(x,
ent applications,
mations
are,
and u
Thepartial
2(:)2‘2”
#xz)>z=ri
,3X
i$z(~)
(%)
(B-32)
are adequate
The expectation
<B(T)>
u:(T)
neglects
+P&(T)l~’z
. <B(T) >-2 [<AR(T)>2
U12,
‘d
X2 =<X2>.
Since KS is large,
in the pres -
these approxi-
(B-33)
.
+P:l(T)l-~
2
‘R, I
aregiven
u:(T)
+ <Ar(T)>2
u~(T)
+ 2<AR(T)>
OR ~(7)]
[P:
+2 PmR(T)Pm1(T)
u;,
K~2.
Of xi
of B(r)
=[P;R(7)
where
of the order
at xi = <xi>,
+<A1(T)>21i/2
x <AI(T)>
i
terms
of Xi and X2 and the covariance
are evaluated
of B(T) is then
=[<AR(T)>2
The variance
the variances
coefficients
for our purposes.
=U:[P:R(T)
I
respectively,
~~$ferential
Eq. (B-31)
use.
function
‘“:(%Y
where
error.
.
.
of the expectation
X2) of two randOm variables
<f> = <f(x*,
be neglected
UNNORMALIZED
B(T) of thecomplex
) +Af(?)]
expressions
THE
are
is
an estimate
Approximate
f(x,,
(B-2)]
OF
may always
while the variances
an order-of-magnitude
R(T)
a:(,
)+
P:l(T)
u:(T)
(B-34)
UR,l(T)I
in Eqs. (B-22),
86
(B-23),
and (B-26).
VII.
RELATION
BETWEEN
MEASURED
CORRELATION
FUNCTIONS
Theunnormalized
tractions
complex
AND
correlation
INCOHERENT
SCATTER
function ohtained after
system
noise and clutter
sub-
denoted byu~pm(’r).
U:Pm(T)
= (AR(T)>
o:Pm(r)
=
+I<A1(T)>
(B-35)
.
Using Eq. (B-16),
a*
P(T)
As both the signal-plus-noise
are Hermitian,
statistics
–m:Pn(T)
correlation
in the signal-plus-noise
maybe
(Appendix
A)
written
region
in terms
where
{[ Pw(T)P~(T)]
W. is the transmitter
the transmitter
PW(T)
V(T)
=
For the experiments
the measured
correlation
correlation
function p5(r)
func -
exp[luor]
* Pn(T)
(B-37)
The weighting
function pw(r)
is theautocorrelaticmof
* V*(–T)
(B-38)
’xv*(–T)]T=o
.
being considered,
length are transmitted
It is desirable
scatter
function pn(r)
noise has the same
V(t)
[V(T)
of the basic
as in the noise region,
correlation
thesystem
*Pn(T)}7=~
frequency.
waveform
andthenoise
Assuming
of the incoherent
P~(T)l
[PW(T)
‘m(T)=
function p(r)
i.e., pm (T) =P%(–T).
so also is pm(r),
tion pm(r)
(B-36)
.
to express
thevarianceum
This basic
(r . O).
thevarianceu2
m
forother
2.
M only estimated
single-pulse
variance
pulse transmissions
when single
is denoted
in terms
pulses
byu~.
of u;
2
2
‘m ‘ ‘rob
(B- 39)
where
[v,(t)
* V:(-t)}=o
(B-40)
aT=
[Vo(t)*V;(-t)]t=o
Vo(t)
being the transmitted
waveform
form
when lag T is measured.
when lag zero
is measured,
and VT(t) the transmitted
a7 is just the ratio of the total transmitted
energy
wave-
for the two
wav ef 0 rms.
It is adequate
convolution.
Defining
for our error
More
calculation
complicated
a new weighting
we may now express
procedures
Eq. (B-38)
areused
bytakingp~(r)
in practice
outside the
(Appendix).
function P!W(T) by
PW(T)
PL(T)
to simplify
deconvolution
= [P
w
(T)*
* Pn(T)
(B-4i)
Pn(T)]T=o
the incoherent
scatter
correlation
function intemns
of the
estimates
AR(T)
and AI(7),
<AR(T)>
+I<A1(T)>
(B-42)
P~(T) =
&(T)
87
—...
with
8(T)
Because
erable
(B-43)
.
our aim is to estimate
to use
PS(?)
and covariances
rather
the incoherent
scatter
place of the signal-plus-noise
in
for the variances
quantity o;
C17P’W(T)
=
of AR(T)
and AI(T).
than U2 which is not directly
correlation
correlation
function P*(T),
It is also preferable
The required
est~ated.
it is pref-
function p (?) in the expressions
to use tbe estimated
substitutions
are
(B-44)
o:Pm(T)
p(r)
.
2
the basic -pulse
noise-to-
x = 0:/0:
Some additional
because
the lag
signal
(B-45)
is x,
.
(B-46)
..
simplifications
may be made in relation
T at which AR(T)
the pulse separation.
ratio
+ W*(7)
a~+x
+.;
‘m
where
@(T) p~m
+ u: Pn(T)
=
and AI(T)
2n this case,
[Eqs. (B-i)
and assuming
to F,
and (B-2)1
perfect
G, and H Mode experiments
are
rectangular
measured
pulses
is the
same
as
and no transmitter
chirp,
(B-47)
PW(T) = i/ar
and
a7 . i + T/TB
for T < 7B
. 2
where
Tn is the basic pulse length.
calculations,
is P’W(T) s
(B-48)
for 7> TB
A further
Thus,
PW(T).
simplification,
which should be adequate
!3(7) ~ 1 and Eq. (B-45)
for error
becomes
P~(T) + XP*(T)
p(T)
VIII.
SUMMARY
The results
AI(T)
rized.
[Eqs. (B-1)
=
OF RESULTS
FOR
for the expectation
and (B-2)],
The noise subtracted
<AR(T)>
(B-49)
a~+x
UNNORM.ALIZED
and variance
of tbe u~Ormalized
and the unnormalized
term
is neglected
FUNCTIONS
amplitude
and p(r)
cOrrelatiOn
B(’r) [Eq. (B-34)]
functiOns AR(T).
are now summa-
is taken as unity.
(B- 50)
= U;P,R(T)
M-i
U;(T)
= ~
0;
S(CIT + X)2 + p2(T) – q2(7) + ~
s I
+ Sq2(k@
~
(M–
k) [Spz(kc)
k=i
+ p(T + kc) p(T –kc)
- q(7 +kc)
(B-5i)
q(7 –k<)]
88
-..-..-—-——
.m.=—
<AI(T)>
O:(T)
=
(B-52)
@:P,I(T)
M-i
~
= ~MK~
S(a7 +
X)2
+
q2(T)
+ P2(7) + ~
~
,(M,-k)
[:qz(kc)
k=l
+ Sp2(k@ +
q(7
+
kc) q(’f – kc) –
p(T
(B-53)
kc) p(7 -kc)]
+
1,
M-i
4
U;,l(T)
= ~
‘b
ZP(r)
q(7) + ;
~
s
.x[q(7
<B(T)>
0:(7)
=
(M –k)
[p(T + kc) + p(T - k~)]
k=i
+kc)
+q(r–
(B-54)
kc)]
I
U: [P:R(T)
+P:l(T)]’/2
‘[ P:R(T)
=
U:(T)
+P.&)
(B-55)
C:(T)
+ 2P~1(7)
P~R(T)
mR, r(T)]
(B-56)
[P&&)
)1
+P:l(T
where
P(T) = P ,R(7)
q(r)
The various
= P&)
+ X/InR(T)
+ xPnl(T)
quantities
appearing
PJT)
= P~R(T)
+ IP~l(T)
Pn(T)
= P“R(T)
+
IPnl(T)
(B- 57)
.
in these expressions
The incoherent
The system
and pn(T)
P:(-T),
x
scatter
correlation
noise correlation
are both Her-mitian,
Pn(T)
Noise-to-signal
altitude
are:
function
function.
i.e.,
PS(T )
p~(~)
.
= P:(-T)
power
at the measurement
using the basic pulse length TB
[Eq. (B-46)]
%
s
Ratio of total transmitted
energy
when lag
T is measured
to the total transmitted
ergy when lag
O is measured
Clutter
subtraction
constant;
clutter
subtraction
term
S . 1 when no clutter
(Modes
89
G and H)
[see
en-
Eq. (B”-48)]
S = 3 when a
is used (Mode
subtraction
F),
is made
I
TABLE B-2
VALUES
OF TB,
S,
AND
C.
FOR THE 2-PULSE
MODES
I
F
c
‘B
(pee)
Mode
40
F
(s.;)
s
0. OB
3
G
IN
0,08
1
H
200
0.16
1
TABLE B-3
VALUES
OF M AND
e VS ALTITUDE
AND
LAG
FCf
THE 2-PULSE
MODES
Center
Altitu&*
Mcde
F
(:=;
(km)
IM
(N/A)
130 (lo6)t0
All
to 124 (N/A)
0 to
16.5
Oto
All
BO
40
120 to 380
Al I
o to
50 to
lootolw
1
3
6ot0100
H
(p:.)
1
loot03Bo
130 (104) to 165
G
M
1
3
20
5
20
40
1
%3
3
20
5
20
*Numbers in parentheses apply to daiu COI Iected prim to 30 December 1970.
note i“ Table Ill OF rnai” text regarding alti~de
charges prior to 16 December
see also F;g. 1 ond Table Ill ;“ main text,
1
)
,
4
,
90
20
See
1971;
M
Number
of prod.cte
for a particular
Time
G
formed
sweep
lag and altitude
shift between
a particular
in &
successive
products
lag and altitude,
for
only defined
ifM>i
Number
KS
of sweeps
for which lag
sured KS = t~/C~,
where
? is mea-
t~ is the integra-
tion time in 6 econds and C~ is a constant
d
Variance
(power)
of incoherent
nal at the measurement
altitude
scatter
sig-
for the basic
pulse transmission
Table .B-2 gives
functions
of altitude
To evaluate
TB, S, and c~ for Modes. F; G, and H, while” Table
and lag for. Modes
the variances
know these functions
are the required
AnR(T)/’AnR(0)
exactly,.
M“ sfid” ~ as
F, G, and H.
we need to.have
values of
P6(T),
and x.
Pn(r),
tbe best that can. be done is to use quantities
Thus,
values.
B-3 gives
we mayuse
for OnR(~ ), Anl(T)/AtiR(0)
AR(’r)/AR(.O)
forp~R(7),
Sirice we do not
whose expectations
A1(:)/A~(0)
for PiI{T”)”, and ARn(0)/[ AR(0) -. ARn(o)l
fOr P~1(7),
~~~
fOr X, where
Kn
AnR(T).=
~
~ [Y\(r)
n i=+
K
AnI(T)
=
+
Y\(t + T) + U;(T)
U~(t +.T)]
n.
[Y\(7) ”U~(t + T) – Y:(t
~
+ T) U;(t)]
.
(B- 58)
How ever,.
o~. drops
n. 1,4.
AR(0)
could be used for the. remaining
sions for
the variances
cwant.i.ty,u~.
of tbe nm-maliz ed mm-relation function
out of the exPres -
(see next section)
and this substi-
tution is not required.
1X. NORMALIZATION
Final
estimates
tained by dividing
Two methods
u: “
measurement,
or
B(T)
AR(Tf)
A.
of the amplitude
the unnormalized
of deriving
and AR(T2)
depending
F only tbe real
correlation-function
estimate
8catter
correlation
function may be ob-
Eqs. (B- 50), (B- 5.3), Or (B-55)
incoherent
scatter
by an estimate
Of
one method uses the zerO lag
correlation
on the mode of tbe experiment.
as discussed
function.
Either
Tbe covariances
AR(T)
of
~ Sec. V Of this append~.
Lag
real part of the measured
and may be used to normalize
Normalization
ESTIMATES
of u; are considered;
and A1(T2) are ignored,
Using Zero
the unnormalized
of u:
In Mode
estimates
an estimate
and of AR(Ti)
Normalization
1,
of the incoherent
the other uses a theoretical
has to be normalized,
AR(0),
estimate
OF CORRELATION-FUNCTION
the estimates
of Real Part of Correlation
correlation
correlation
function AR(T)
function
at zero
lag,
is an
at all other lags.
Function
is measured.
ad
the incoherent
scatter
is 8R(T) where
I
,-
+&)
.
PR(T) = ~“
(B- 59)
The mean and variance
covariance
of AR(T)
of 2R(T)
are calculated
using Eqs. (B-3i)
and (B-32),
ignoring
the
and AR(0).
<AR(,)>
<bR(T)>
=
—
<AR(0)>
P~R(T)
—+—
z“[
= <aR(T)>
<AR(0)>Z
‘R
=
Note
that as p~l(T)
and u:(O)
In Modes
and PnI(T)
scatter
PA(T)
correlation
(T)]
andvarianceof$A(T)
correlations
Normalization
B(r)
=qiij
{0:(,
+
Al(?)
+P:l(T)]
1
u;(O)}
(B-64)
.
Function
that a theoretical
to playa
O;(T)
<B(T)>2
incoherent
when searching
to find the one which is the best fit to the measured
of AR(T),
(B-62)
.
.
+[P:R(T)
a Theoretical
This would be the situation
VAJeS
using
(B- 63)
<AR(0)>2
we assume
and the amplitude
are measured,
+P~I(T)l
=
~sing
Is Measured
i]z
‘[P:R(T)
. .&
Function
are
PA
s“red
in the expressions
i/2
AR(0)
(T)
In this case,
we may take them as zero
Correlation
u,? <8A(T)>2—+)
available.
(B-61)
function may be estimated
+A;
=
<6A(T)>
B.
I
.
are not estimated.
When Complex
[.A&)
A
The .expectation
z
[Eq. (B-51)].
G and H both real and imaginary
of the incoherent
<AR(T)>
0;4[+) +P:R(T)
0:(01
Normalization
z.
o;(r)
+0)
0/?(7)
for o:(T)
(B-60)
.
scatter
correlation
through alihraryof
function.
part in determining
function pt(r)
theoretical
This approach
the estimate
of o;
is
functions
allows
all the mea-
rather
than just
AR(0),
Thetheoretical
rectly
for F-Mode
be zero.
function pt(r)
analysis,
For G- and H-Mode
the amplitude
is for zero
since imagina~y
analysis,
doppler
shift and is wholly
correlations
thecomplete
is [pt(T)\ and phase is ~(~).
‘?2
real.
are not calculated
theoretical
function
pt(r)
isuseddi-
and are assumed
is /pt[T)/eiO(T),
to
where
,,,,
,,
1.
Normalization
The estimate
of o;
~
When Only Real Part of Correlation
is taken as the value
Wi [AR(Ti)
-
Function
11
a!t which minimizes
Is Measured
the sum
apt(Ti)12
o
(B-65)
i
The sum is over
It is convenient
all measured
values
of Ti,
of Ob because
a~(ri)
and the weights
Wi are proportional
to U~2(Ti).
to use
4
‘h
~,=T
1
‘R(Ti)
which makes
VIi independent
0b4. Solving
for ‘va;’
(B-66)
“
Z ‘ipf(Ti)
value of a is given by
-0
when
:
Thus,
a term
‘R(7i)
~ . ~ ‘iPt(Ti)
The expected
contains
a is an unbiased
estimate
Pt(Ti)
of al
-
PSR(Ti)
(B-67)
.
if the theoretical
function Pt is close
tO the true functiOn
as will be assumed.
pSR,
The variance
of a is o:
Z ‘fPf(Ti)‘~(7i)
- [2 wiP:(Ti)]’
~: _
4
‘b
x
Since
a is an estimate
“
PR(Ti)
Expressions
(B- 68)
wiP;(Ti)
of o;,
=
“
the normalized
‘R(ri)
~
for the expectation
<Y~(Ti)>
=P~~(Ti)
A
autocorrelation
function ~R(Ti)
may be defined
as
(B-69)
.
and varianCe
of ~R(Ti)
are
(B-70)
0:
(Ti)
=
P:R(Ti)
Upo:(,i) t–
o:(Ti)
‘R
z
P&(Tj)
(B-71)
u;%j)
1
j
The method of normalization
a small
eters
correlation
(such as ion or electron
ize the best -fit theoretical
ances).
Directly
Typically,
using a theoretical
between the statistical
temperature
comparing
the covariances
<6R(Ti)
- P~R(Ti)>
<&(Tj)
<~R(Ti)
<YR(Tj)
– P~R(ri)>
function has an advantage
of different
or ion-neutral
function are more
the RHS of Eq. (B-72)
Ieast-squares
errors
collision
accurately
- P, R(Tj)>
-
.
3.:(0)
P~R(Tj)>
is about 20, clearly
frequency)
determined
for the estimates
in that it produces
This means that the param-
lags.
which character-
(i. e., have Smalley
Vari-
$R and ~R gives
~
p:Ro;%i)
.
(B-72)
1
making it more
desirable
to use &R(r) in
fitting than $R(r).
Complete
2.
Correlation
The method used is similar
The estimate
of o;
~
Function
Measured
to that just described,
is the value which minimizes
Wi
[B(Ti)
-
b[pt(7i)
except that B(T) is used instead of AR(T).
the sum
(B-73)
1]2
i
with
.i=—“:
(B-74)
u:(Ti)
As before,
~
Wi
lpt(Ti
) [B(Ti)
b=
~
\vipt2(Ti)
and
<b> =Su:
Tbe normalized
v
PA(Ti)
<YA+(Ti)>
.
amplitude
(B-75)
~A(Ti)
iS defined
as
B(ri)
=
(B-76)
~
= P~A(Ti)
= [P~~(Ti)
(B-77)
+ Pjl(Ti)li’2
P:A(Ti)
U:
‘A
(Ti)
=
U;4U&i)
i
[
–
u;(Ti)
z
P~A(Tj)
94
oB2(Tj)
1
(B-78)
—-
For the same reason as discussed in the .laet section.
A
PA when deri vmg the best-fit theoretical
function.
x.
ERROR
IN PHASE
OF CORRELATION
The phase of the complex
correlation
it is desirable
to use %A instead of
FUNCTION
function measured
in Modes
G and H is
$(T)[1
.arc
(B-79)
tan ~
R
The expectation
and variance
of O(T) are derived
using theapproxhnate
Eqs. (B-3i)
apd
(B-32),
[.$
1
.:(,)
=-, 1[
-)+-) .p~:~’y(,,]
. arc tan
<$(.)>
[
s
s
i-l
XI.
ERROR
IN DRIFT
The plasma
(B-80)
13JT)2“2
P~R(T)
(B-8i)
“
VELOCITY
drift velocityvd
is related
tothephase
$(r) of the ~coherent
scatter
cOrrelatiOn
function by
(B-82)
where
A is the transmitted
@(Ti) atanumbe~of
lags ~ifromwhich
The estimate
weighted
wavelength.
ofd@/dT
least-squares
vd maybe
is the slope
sense,
i.e.,
The G- and Ii-Mode
experiments
yield
phase values
estimated.
S of a straight
line fitted to the measured
phases in a
S is chosen to minimize
(B-83)
~ Wi [@(Ti) - sTi]2
i
with Wi . U~2(Ti).
The solution
for
S is
(B-84)
‘=
‘~wi,:
1
and its vm’iance
v:
is
(B-85)
95
The drift velocity
1
is estimated
using
(B-86)
I
and its variance
c;
is given by
(B-87)
!
X11. ERRORS IN ACCURACY
OF PARAMETERS
DETERMINED
REGRESS1ON ON A MEASURED
CORRELATION
FUNCTION
Themagnitude
i
parameters
–Ti
tion estimates
obtained
1
I
{
eters
and vininthe
the errors
in the library
discrete
values
lower
f(x, y,zi)
In searching
data d(zi)
variable
(theoretical
are squared,
according
Zi (lagri)
incoherent
are given
correlation
correlation
of x and y, thedeviations
weighted,
and summed to yield
two physical
other altitudes.
This secvalues
in terms
function)
through comparison
scatter
.
to the goodness-of-fit
the derivations
(measured
LIBRARY
to determine
and Ti and Te/Tiat
parameters
For generality,
from
for the best estimates
functions
function is analyzed
E-region,
regression.
of the independent
functions
library
correlation
in these physical
x and y to be determined
retical
/
of a measured
FROM
of param-
measured
with a library
at
of theo-
functions),
between
the measured
and
the residual
4
1
6(X, y) = ~
j
Wi[f(x,
(B-88)
y,zi)–ad(zi)J2
i
I
where
the weights
Wi and normalization
constant
a are given in Sec. IX of this appendix,
Next,
a function of tbe form
:1
i
~
!
~*:
:::
q(x, y)=
is fitted
in a least-mean-squares
of x and y are the values
reasonable
,?
Ax2+By2+Cxy+Dx
assumptions,
of the coefficients
We assume
f(x, y,zi)
A,
+Ey+F
sense to the values
~ and ? which produce
to estimate
it is possible
by m amount b(zi)
mean.
j
that the probability
6(x, y).
The least-mean-squares
a minimum
in the function 6(x, y).
the statistical
uncertainty
estimates
By making
in $ and $ in terms
B, and C in Eq. (B-89).
that if x and y are given,
,1
(B-89)
We also assume
a measm’ed
which is normally
tbat the error
of observi”ga
point d(zi)
distributed
is independent
given value d(zi)
will deviate
with standard
oftbe
fore
errors
from the true value
deviation
in adjacent
O(zi) and zero
points.
It follows
x and y is
+zi)
P[d(zi)lx,
The joint probability
product
y] .P[8(zi)lx,
of observing
of these individual
P[d(z)lx,
y] aexp
a complete
probabilities,
y]c
—
Zuz(zi)
(autocorrelation)
(B-90)
functional(z)
given
x and y is the
viz:-
exp –~62(zi)/2u2(zi)
[
[1
i
96
I
.
(B-91)
ff we make various
ing probabilities
P [x, y] d(z)],
tion d(z).
hypotheses
of obtaining
regarding
the resdt
which is the probability
d(z).
the values
of x and y, Eq. (B-9i)
However,
what we really
that x, y are the correct
values
gives
the result-
want is the function
given the observed
func-
We have
P [x, yld(z)]
= m
P [d(z)
lx, y]
(B-92)
.
The .—
a priori probability
P(x, y) is essentially
unknown, and the best that cm be done is to
consider all hypotheses as to the true values of x, y to be equally likely.
P [d(z)] is a constant,
independent
of x, y.
Thus,
P [x, yld(z)]
where
~ K e
-6(x, y)/2
(B-93)
K is a constant.
From
Eq. (B-93),
also maximize
we see that the least-squares
P [x, y Id(z)].
Thus,
estimates
?, ~ are identical
~ and $ which minimize
to the maximum-likelihood
6(x, y)
eStimateS
Of
x and y.
The eXact form
of the function P [x, y Id(z)]
tion is made that it is a bivariate
A
as ~ and Y, the variances as u:
is difficult
to determine,
so the simple
assump-
normal distribution in the variables
x, y. The means are taken
2
and the correlation
coefficient
as u*y.
and o
Thus,
Y’
p[xyld(”)lm’’pl-2(,:.2
J(+++(+$z”xy(x:;:(y(B-94)
XY
and, from
Eq. (B-93),
(X–$)2
6(x, y) =
+
(i – U:y) u:
From
the fit [Eq. (B-89)]
‘y’
(,A~#2
_
–c.
:,
that
.
OF THE ERROR 2NTRODUCED
INTO THE
FUNCTIONS
BY CLUTTER
ECHOES
F-MODE
lntroducticm
Clutter
Sees.11-A,
practice,
subtraction
returns
III-A,
are removed
IV-B,
through digital
and IV-C
autocorrelation
algorithm.
ffitering,
andasindicated
that points tlrat exhibit alarge
the expected
as explained
by Eqs. (i6)
clutter-to-signal
it seems
appropriate
and (25).
inthe
main text in
Ithas
ratio often depart
function by an am.mmt not explained
Accordingly,
97
.
(B-95)
.
(i – U;y) Oxuy
dzm
EST1MATION
CORRELATION
A.
it follows
(xi%)i”
‘y
XIII.
to 6(x, y),
(y –9)
t constant
(i – U:y) u; -
“x’
0
20X (X-Q)
(Y - ?)2
been found,
considerably
by the statistics
in
frmn
of the clutter
to give these points less weight than
._.,
.,,,
F’
)
I
0.12
1
L(r)=
+,:,
[p(r,
t8,p -
P [T
t
p(r)
I
0.08
ALL
PO INTS, WEIGHTS=
llu,~,o,
X P (T)th,Or
SUPPRESSING
20-,
40-
0
SUPPRESSING
20-,
40-vsec
p
(T),heo,
1
h
VS LAG
AUTOCORRELATION
p iT),h,Or
●
I
I
I
I
Psec.LAGS,
WEIGHTS = I/w;heO,
LAGS, WEIGHTS=
1/02
●
-0,04
t
I
-O,oe
.
o
.
..lz~
o
40
sO
120
160
200
240
2S0
320
360
400
T (L!S,C)
Fig. B-1.
theoretical
0.14
Comparison
of experimental
autocorrelation
function and its best-fit
function –average
difference
vs lag; i4 April 1971, c/s <0.5.
I
-E&L
I
o
A ,m, [T) =
0,12
● USING
0.10
1
1
.
ALL
x
SUppreSSing
0
SUPPRESS
+!
,.,
1
1
[p(ri)e,p -p(ril,ha.,
I
I
]z
POINTS
LAGs, wEIGHTs=
20-,40-wc
lNG20-,40-pSeC
LAGS,
WEIGHTS
l/w~haO,
=l/C2
0
●
xx
0.0s
v
0
~
a
0.06’
i?
f
●
0.04
,
G
e
.- ———+~—8—
-.-/”
r’*—r—*-—
—A
888
0.02
0
!
1
1
1
40
80
12o
160
I
200
I
240
I
280
I
I
320
360
r [ we.)
Fig. B-2.
theoretical
Comparison
of experimental
autocorrelation
function – rms different e vs lag; i 4 April
function and its best-fit
197i, c/s <0.5.
98
4
d
—- . .
.,
,.
,...
one would otherwise
This section
B,
assign to them when matching
outlines
Experimental
In order
studied
proper
functions
in some detail.
Statistical
weights
in Mode
rived
self-clutter,
in this way,
the threshold
Figure
and a d-c clutter
contribution
ratio
c/s of >0.5 were
were
examined
deviations
estimated
accordtig
between
theoretically
to Eq. (B- 51).
Using theoretical
tbe theoretical
including
taking
However,
fun~tions
de-
and experimental
those for which c/s exceeded
value of 0.5.
B-1 shows the mean deviation
Only points where
that at ‘r . 40 pew
pec
A).
the theoretical
~ec
points as a
square
fit eliminating
that major
An aver-age
is probably
pulse assumed,
the 20- and 40- @ec
less than O.Oi, indicating
fit.
a“d particularly
for this discrepancy
the perfect
that
especially
points shows an
systematic
errors
have
for the case when c/s < 0.5.
The rms difference
Arms
between
the experimental
and theoretical
tions is shown in Fig. B-2 for the same data as in Fig. B-i.
c/s were
and experimental
wsed in tbe least- sqwares
The reason
from
A revised
that is gemxally
now heen removed
too low.
pulse shape departs
(see Appendix
deviation
between
c/s c 0.5 were
It is evident that the point at T .20
am systematically
the actual transmitted
small
days in f 97 i were
below i25 km.
were
ignored.
for all points,
to experimental
on four sample
to altitudes
functiom
of 120 points was used at each lag.
average
was limited
the random and systematic
f“nctiom
function of time lag.
for T .40
functions.
are established.
fit of theoretical
correlations
F autocorrelation
all points with a clutter-to-signal
autocorrelation
for the least- squares
F, the obsewed
The analysis
em-m-s in Mode
account of noise,
to theoretical
weights
Study
to derive
autocorrelation
the observations
the manner in which the appropriate
used,
Arms
is close
to the expected
autoc orrelation
func -
Since only points with relatively
value @theOr, at least for lags shorter
than
300 psec.
The effects
autocorrelation
c/&
of clutter
The latter
0.6, 0.6to
c/s >2.
were
functions.
parameter
0.8, 0.8 to i,
Thus,
was quantized
linear
relationship
model
will suffice
of systematic
the fit.
Arms
is seen to exist between
to estimate
errors
The rms deviation
As expected,
Arms
the additional
in the measured
2
‘c
= A:ms
as a function
of
0.2 to 0.4, 0.4 to
deviation
with c/s >2
for c/s >2
is apparent
at
is about 2 per-cent of
could be removed
by elim-
as a function of c/s is shown in Fig. B-4
is close
and c/s,
statistical
O to 0,2,
A systematic
to Ctheor for small
indicating
error
c/s.
that a simple
introduced
autocom. elation points due to clutter
– ot~eor
Four days of measurements
A roughly
empirical
by clutter.
were
O:(T)
= 0.0i3
as
(B-96)
used in deriving
the empirical
is defined
.
B-5 shows the data points on each day,
fitted to the data gives
the empirical
and the average
relationship
over
all days.
between
u: and c/s.
The straight
line
relationship
(c/s)
.
(B-97)
99
.
ranges:
and theoretical
calculated
Results
The variance
Figore
in the following
the number of samples
the effects
with Utbeor.
the experimental
deviation
i to 1.5, 1.5 to 2, 2.5 to 3, >3.
inating all these points from
and is compared
by comparing
B-3 shows the average
For the four days studied,
the total points.
c.
then obtained
Figure
0.12
!
1
I
I
I
-FmmL
J
0.08
8*
.
.
rZ[CA)
=
+,:l[PICA!T
)exp-
p (r,
l,,..,
]
i
t
20-,
0,04
40-M,.c
LAGS
.
wEIGHTS
0
WEIGHTS=
SUPPRESSED
= \/o,&O,
I/vz
[
●
io
e
-0,04
-0,08
0
●
[
1
-0.12
0
0,s
I
I
I
I
1.0
1.5
2.0
I
28,
I
I
I
I
I
1.?6
66
43
59
2)
NUMBER
Fig. B-3.
Comparison
of experimental
best -fit theoretical
function – average
0.30
1
1
I
3,0
2.5
,/s
I
,8,1
d
0
1
la
I
35
OF SAMPLES
autocorrelation
function and its
cliff erence vs c/s, f 4 April i 97 i.
I
I
1
1
118-9-665$ t
Arm, (C/S I =
0.23
20-,
40-
WEIGHTS
~,~,
“,,.
[pi./.,
LAGS
rllO.O -p (T( ),h,.r
12
SUPPRESSED
= l/u:heO,
a20
35
!8
21
~.
z
0.15
59
)46 z
——
0.10
43
281
—
951
~-————
0.05
0
——
———————
rm. r
—————
—————-
————————
i
I
I
I
1
1
0.9
1,0
1,5
2.0
2.5
3,0
C,A
Fig. B-4.
Comparison
of experimental
autocorrelation
best-fit theoretical
function – rms difference
vs c/s,
i 00
function and its
i4 April i971.
1
1
u: - A:.,
20-,
0.0s
40-
I
I
~
- U,:W
“s,,
LAGS
S“PP~SSED
o
25 M4RCH
1971
.
21 W2H4BER
!971
A
13 APRIL
1971
.
~,
1$71
DECEMBER
0,04
.
0
~b”
~,o,
0
/
0,02
x
0
x
0.01
1
0
,.0
0.5
1.5
2.0
2.5
m
,/s
Fig. B-5.. Comparison of experimental
best-fit theoretical
function - variance
Thus,
the total error
in the autocmn-elation
U*(T) = ut:mr(T)
where
o~eor
1/02 (T) instead
The elimination
.,.!
I
I
and u:
it was decided
of l/ut~eor (r).
function as a fumtion
of lag is given hy
+ 0:(7)
is given by Eq. (B-51)
Based on the foregoing,
autocorrelation
function and its
increase vs c/s.
Also,
of points c/s >2,
(+-98)
is given by Eq. (B-97).
to weight the F-Mode
correlation
the 20- and 40- psec lags were
while probably
desirable,
omitted
function points by
from
was not implemented.
consideration.
3lBLlOGRAPHlC DATA
SHEET
3. Recipient’s Accession No.
I. Title and Subtitle
5. Report Date
23 February 1979
Incoherent Scatter Measurements of E- and F-Region Density,
Temperatures, and Collision Frequency at Millstone Hill
7. Author(s)
Joseph E. Salah
John V. Evans
William L. Oliver
Ronald H. Wand
). Performing Organiiation Name and Address
Lincoln Laboratory, M. I. T.
P.O. Box 73
Lexington, MA 02173
6.
8. Performing Organization Rept.
No. Technical Report 531
10. Project/Task/Work Unit No.
11. Contract/Grant No.
ATM 75-22193
12. Sponsoring Organization Name and Address
National Science Foundation
Atmospheric Science Section
Washington, DC 20550
13. Type of Report 8r Period
Covered
Technical Report
14.
15. Supplementary Notes
16. Abstracts
The Millstone Hill incoherent (Thomson) scatter radar system has been operated since 1963
to perform a synoptic study of F2-region electron densities, and electron and ion temperatures.
These measurements have been conducted by transmitting single long pulses and performing
digital sweep integration and spectrum analysis of the reflected signals. This report describes
changes made to the system in 1969 to permit extensions of the measurements to altitudes below
200 km (i.e., the E- and Fl-regions). These changes include modifications to the radar timing
equipment to permit the transmission of close-spaced pairs of pulses from which the echo
autocorrelation function can be determined in the computer by processing appropriately spaced
pairs of echo samples. By operating the radar coherently, it has also been possible to subtract
the unwanted (stronger) clutter signals from the ionospheric echoes. Samples are presented of
the results that can now be obtained from these programs.
17. Key Words and Document Analysis.
Millstone radar
E-region
F-region
diurnal variations
electron density
ionospheric scatter
seasonal variations
temperature effects
spectrum analyzers
17a. Descriptors
7b. Identifiers/Open-Ended Terms
17~. COSATI Field/Group
19.. Security Class (This
18. Availability Statement
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(REV.
10-73)
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Report j
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21. No. of Pages
108
22. Price
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