484
IEEE TRANSACTIONS ON COMMUNICATIONS, VOL. COM-31, NO. 4, APRIL 1983
A Self-organizing Random Array Communications Relay
Abstract-A sparse random array with self-organizing propertiesis
proposed as a communications relay. The relay consists
of N randomly
deployed, low-power transmitlreceive elements with capabilities for
phasingtheirretransmissionstoarrivecoherentlyat
the ultimate
destination. Signal-to-noise ratio results for conventional modulation
schemes corrupted with additive noise are given, together with possiblesystemblockdiagrams.Itisconcludedthat,
in spite of the
complexity, practical systems can be built with extremely
low electromagnetic radiation densities with point-to-point characteristics at
least as good as withconventionalsystemsemployinghighpower
relays. The novel characteristics make the proposed system particularlysuitablefortacticalmilitarycommunication,andvariants
thereof may find application in urban communication.
\\
-.___.'
a
.
I. INTRODUCTION
I
Fig. 1. Schematic model of the random array relay system.
L
ARGE, lowdensity, nonuniformlyspacedsensorarrays
preciably. The scheme thus potentially offers space diversity,
have long been applied to radio direction finding and, parreliability, and signal obscurity, the latter being a consequence
ticularly in the field of astronomy, to high resolution imaging.
of the low powers and the dispersion of the retransmitting reThe large size is associatedwith high resolutionornarrow
lay elements. Potential applications may be found in military
beamwidth, the limited number of elements with economy,
communication,whereemittingsourcesmustbeconcealed,
and the nonuniformity with ambiguity resolution in direction
and the concept of a distributed emitter-receiver array
may
finders, or more generally, with the suppression of the lobing
also find application in urban communication for its diversity
phenomenon associated with lowdensity periodic arrays (low
potential.
densityimpliesmorethanhalf-wavelength
spacing between
Theschemedescribedhereinutilizesfrequencyinvariant
elements) [ 11 .
phase control only at the array elements. The constancy of the
Herewedealwithanarrayof
widely dispersed,sparse,
phase shift with frequency imposes a bandwidth limitation on
transmit-receive elements used as a two-way radio relay (see the signals to be handled by the array [8]. The use of phase
Fig. 1). The elements may be viewed as randomly scattered or
shift only also means that maximum signal-to-noise ratio will
deliberatelydeployednonuniformly
over somearea.Inuse,
be obtained at the ultimate receiver only if the signal-to-noise
thearrayelements will each receive a signal fromadistant
ratios delivered by each element to the final receiver are equal
transmitter and retransmit it so that the emissions from all ele- and if there is no incoming interference to the array. When
ments converge coherently on a distant receiver. This is accom- these conditions are not satisfied, complex (phase and ampliplished by phase control of the signal transmitted by each of
tude) element weighting, as opposed to simple phase shifting,
the elements, the phase information being obtained with the
is essential. Extensions to overcome these limitations are subcooperation,ofthedistantcommunicators.Thecommunijects of continuing study and are not pursued here.
cators using the relay take advantage of the array gain to opIn the next section we present results on the system properate at low power. Furthermore, the relay acting as a distrib- erties of the array relay along with a numerical example using
uted radiator will require low power from each of its elements.typical parameters to illustrate the advantages gained. This is
If a small number of elements fail or are not mutually visible followed by details of a possible system implementation. The
to the communicators, the channel quality will not suffer ap- essence of the method described here is also found in [2] and
Paper approvedby,the Editor forCommunication Systems
Disciplines
of the IEEE Communications Society for
publication after presentation
at.the 22nd Midwest Symposium on Circuits and Systems, Philadelphia,
PA, June1979.
Manuscript received December 21,1981;
revised
August 3, 1982.
J. B. Vespoli is with the Satellite Communications Division, Harris
Corporation, Argentina.
F. Haber and R. S. Berkowitz are with the Department of Systems
Engineering,Moore School ofElectrical Engineering, University of
Pennsylvania, Philadelphia, PA 19104.
D. Yavuz is with the Communications Division, Shape Technical
Centre, The Hague, The Netherlands.
ingreaterdetail,including
scheme, in [3].
an alternative implementation
11. SYSTEM ANALYSIS
In this section, we will determine the signal-to-noise ratio
propertiesofasystemforpoint-to-pointcommunication
through a widely dispersed random relay. The scheme is depicted schematically in Fig. l . We will present results for the
idealized, but reasonable, situation in which the noise sources
are independentateachreceptorand
wherepropagation
0090-6778/83/0400-0484$01.OO 0 1983 IEEE
485
VESPOLI er al.: SELF-ORGANIZING RANDOM ARRAY RELAY
lossses are purely inverse square. We will also assume that the
array, B in Fig. 1 , is somehow focused on the users. That is,
each element of the arraybj contains a phase shifter whichean
be set to make the signals emanating from the individual elements in phase on arrival at the destination receiver. We will
elaborate on this importantfocusing problem in Section111.
Referring to Fig. 1 , we denote by K b and K c the average
free space propagation losses for transmission from communication center A to array B , and from array to mobile station
C,respectively. For the purposes intended in this section we
assume no significantdifferencesamong
the individual distances between A and the array elements and between C and
the array elements. Thus, d and D will be viewed as distances
from A to each element of B and C to each element ofB, respectively.
When station A is transmitting, denote by Pt, the equivalent isotropic power radiation from its antenna. Each element
of the array bj isotropically receives powerPrbj which we will
assume is equal for all elements. Hence, we
have
sumgd neghgible, the SNR at C would be equal to N times the
SNR at an array element. Solving( 5 ) for Gb we obtain
Since Gb must be positive and finite we have the following inequality :
Using (l), (2), and ( 6 ) we may write an equality relationship
between the SNR’s at B and C:
The largest SNR improvement from B to C is N and occurs
when G b m. At this point it is convenient to define an equivalent system gain G , as the ratio of the power that would be
necessary to transmit from A to C withoutthe arrayfora
where
= number Of array
and K b = x2/(4.rr4)2 ;
given SNR at C to the power to attain the same SNR at C but
similarly,K C = x2/(4nD)2 for the path between and Contransmission through the array B . The formeris given by
sider first the case in whichA transmits through the array and
C receives. Eachelement bj receives a signal from A with
KaPm ‘
power Prb andretransmitsanoisyversion
withtotal power
(SNR),o = (9)
Ptb and signal-to-noise
ra,tio
(SNR)b.
is, That
NC
--f
where Pra’ is the power radiated fromA , and K , = X’ /(4.rrDac)2,
(2) D,, being the distance from A to C. Equating (9) to (5) and
letting Pta’/Pta= G, we obtain
where N b is the equivalent noise power at the input ofeach arrayelementand
Gb is thetotal poweramplification of each
array
element
(including
antenna
gain). Assuming that
the N
elements of the array are focused at C, the power received at C
becomes
Prc =N2K,Gd’rb -I- N K , G f l b .
(3)
G, =
N2KbGbKc/Ka .
NKcGb(NbINc)
Our aim is to maximize G,. However,thisoccurswhen
00, as in Fig. 2 . Denoting by r,,0 < r < 1, the practical fraction of the maximum attainable
value of G,, and calling this
value G,, the acceptable gain, we have
Gb
-f
Clearly, the first term in (3) is the power of the signal component at the input of C; it is proportional to fl as a consequence of coherent
the addition
of
signals from
the
N eleG, =r N k )
(1 1 )
ments. The second term in (3)
is
the
noise
power
transmitted
. .
from the array to C;it is proportional to N since the noise acG, max is given by (1 1) when I = 1 . Array element gain corcumulates noncoherently. The total noise at Cis that received
responding to G,, may be expressed in terms of r as
from B plus that generated in C and is given by
(2).
where N c is the equivalent noise power due to the receiver at
C. The signal-to-noise ratio at C,denoted by (SNR),, may thus
be written as
(5)
This result is obtained by setting (10) equal to (1 l), and solving for G b .
In terms of the parameter r, we may rewrite the previous
expressions relating SNR and transmitted powers. Putting(12)
into (8) we get
1
486
IEEE TRANSACTIONS ON COMMUNICATIONS, VOL. COM-31, NO. 4, APRIL 1983
6%
Knowing (SNR),,N,, and Kb, we obtain-thepower to be radiatedfrom A using (14) as Pt, = 6.30 mW. From (15), the
r G, m o x
power to be transmitted by each array element is P t b = 27.50
mW. From (1 1)) the system gain is G,, = 8000 (39 dB). Therefore, the necessary power transmitted by station A has been
reduced by 39 dB. Furthermore, since broadcasting fromA is
no longerneeded, wesee from Fig. 1 that adirectionalanGbo
Gb
tenna at A , focused toward the array area, could be used. An
Fig. 2. Equivalentsystempower gainas a function of theamplification in relay elements.
antenna gain of 15 dB is a reasonable value for this particular
case. If this is done, the required transmitted power at A beUsing (1) and (2) with (1 3) we get
comes P,, = 0.20 mW. To evaluate the power to be radiated
by C, when C transmits through the array and A receives, we
can make use ofthe sameequations by interchanging the
values of K b and K c . We then obtainp,, = 0.63 w. Similarly,
the power to be radiated from each array element
to A becomes
Ptb
=
0.27
mw.
Or,
when
using
a
15
dB
gain
antenna
at
Using (l), (2), and (14) with Gb taken from (12)we get
A , we have P t b = 0.01 mW. The necessary power transmitted
by C has been reduced by a factor equal to rN = 80 (19 dB)
and the power transmitted by A with the 15 dB gain antenna
has been reduced by a factor equal to 250 000 (54 dB).
A summary of the most relevant results of this example is
shown in Table I.
Expressions (14) and (15), together with the bound for N
It is interesting to note thatwhen A transmits to C through
given in (7), specify completely the array relay system we have the array, the totalpower of the main source of radiation (arhypothesized.
ray) amounts to NPtb = 2.70 W, this power being distributed
To this point we have assumed that A was transmitting to over a large area.
C through the array B . Due to the obvious symmetry of the
Originally, the system wasconceived to protect the comsystem, the results for the case when C transmits through the municationcenterormaininstallations
( A ) frombeingdearray to A couldbeobtained
easily by interchanging sub- tected and located. As we saw in the example, the mobile stascripts A and C.
tions (C) are also protected since their radiated power
is decreased by a factor of 80 (19 dB). We therefore conclude that
A Numerical Example
by using the array relay system we obtain a number of significant advantages: a great reduction in the powers transmitted
We will now give numerical results for a system with the by A and C, wide dispersion of the actual source of radiation,
following parameters.
anda conceivable improvementinthe
transmissionquality
0 Number of active elements in the array:
N = 100.
under adverse propagation conditions since the radio link does
0 Signal-to-noise ratio required at A and C: 1000 (30 dB).
not depend on a single path.
0 Distance from A to B : 5 km.
Distance from A to C: 50 km.
111. SYSTEM IMPLEMENTATION AND OPERATION
0 Array area: I k m 2 .
To this point the assumption was made that array elements
Requiredpowertransmitteddirectlyfrom
A to C to are, somehow, focused on the users. We will now elaborate on
achieve the required SNR: 50 W.
this matter. As a basis for discussion,ahalf-duplexrequireFrom the data we first estimate a value for the noise power ment will be assumed and a system for achieving focus to users
that will be present at the front end of receivers A , B, and C at both ends will be proposed. In Fig. 1 we assume that the
assuming that all three receivershave the samenoisefigure.
mobile station at C will receive and transmit at frequency f
Consistent with the signal power transmitted without the ar- and thatthecommunicationcenterat
A will receive and
ray, the distance. from A to C, and the SNR assumed at C, we transmit at frequency f' = f fro. The array elementswill upget'
convert signals from C t o A by an increment in frequency fro
G, m o x
+
and will downconvert signals from A to C by an equal increment.The arrayelements will be given the oscillatorreferencethroughaseparateorder-wirechannelfrom
A operatFrom (13), taking r = 0.8 (note that this value of r gives a sys- ing at a frequency fo. That is, cos q O twill be generated at
tem gain loss of only 1 dB with respect to maximum attainA , be broadcast to all elements at B , and hereceived at eacheleable G, and results in a reasonable GbO), we have
ment bi as cos(wl0t ~ j ) j, = 1 , 2, .*.,N. The -yj depend on
the distancesfrom A to eachelement(andonpropagation
(SNR)I, = 12.50 (1 1 dB).
conditions) and are not a priori known.
To focus the transmissions from, say, C to A requires that
1 The noise level obtained is perhaps two or three orders of magni- the up-conversion at each element be accompanied by a phase
tude higher thanone would ordinarily expect. The example is arbitrary.
shiftwhich will maketheseparateretransmissionsfromthe
+
487
VESPOLI et al.: SELF-ORGANIZING RANDOM ARRAY RELAY
Converting as shown in Fig.4(b), the received signal will be
TABLE I
POWER REQUIREMENTS FOR EXAMPLE SYSTEM USING A N
ARRAY RELAY COMPARED WITH A CONVENTIONAL
SYSTEM. 30 dB SNR ASSUMED REQUIRED AT
TERMINALSA AND C.
Array Relay System
15 dB antenna
at A
Conventional
0 dB antenna
at A
50 W
54 W
6.30 mW
0.63 W
system
Parameter
Pta
ptc
0.20 mW
0.63 W
Phose added of bl
B
Frequency f
Focal
Region
OD, + w'd,
again independent of the index j . Equations (16a) and (16b)
require knowledge of the phases y i . If these are available, one
can shft the local oscillators so that they are all cophased to,
say, y1 in which case (16a) and (16b) become identica1:'In this
case up and down conversion at each element would be carried
out as shown in Fig.5.
Estimation of the phases yi may be carried out as now described. Recall that the local oscillator waveform cos wlot is
generated at A and broadcast to all elements at B . For the purpose of this measurement an instruction is sent from A t o B
(throughtheorder
wirechannel)requestingonly
b , to respond. It shifts the received waveform at frequency o to frequency w ' with the phase of its local oscillator. Thisis now received back at A , is mixed at A with the originating waveform,
and forms the difference frequency term
Fig. 3.
Diagram showing paths for point-to-point
communication
through the array relay with relevant focusing parameters inqicated.
yi = oscillator phase at elementbp @i= focusing phase shift injected
at element bi.
bi arrive in phase at A . Such a process is indicated in Fig. 3 ,
showing two branches with phase shifts
and @i introduced
at the two elements for focusing. Branch 1 will be treated as
the referencebranchand
will be setequal to zero. For
branch j to be coherent with.branch 1 atA requires that'
@,
@,
c
The phase shfts involved are shown in Fig. 6 . Next, in a similar manner, A transmits to bl at frequency a'= w + wIo and
receives the shifted waveform at frequency w . Again, the returned waveform is compared with the orginating one and a
difference frequency term
(0
+ o')d,
C
which is independentoftheindex
transmitting fromA toC requires
j . Coherentcombining
Then, (18) and (19) are applied through a mixer retaining the
low frequencyterm, which is
(Al,'Al,~lf=cos 2Yl.
2 Quantities such as wDi/f represent the phase delay associated with
the transmission path. Equatlons (16a) and (16b) are written assuming
a single ray path. In multipath the phase delay would not depend on
the line-of-sight distances Di and di alone. The approach to be described
applies in the more general case, provlded the phase delays are the same
regardless of the direction of transmission, A to C or C to A. In Fig. 4
the phasedelays are denoted 9.i.
and are thereequated to -wDi/c
and -w'dj/c, respectively, for he-of-sight nonmultipath conditions.
- Yl]
(20)
Equations (1 8) and (1 9) are received waveforms resulting from
nonsimultaneous transmissions. To compare them will require
stretching the first one at the receiver 96 that the second will
overlap it. This is readily accomplished:in a circuit of sufficiently narrow bandwidth. Although
y1 obtained with (20) is
not unique, the ambiguity can be resolved by testing each of
the possible solutions using (18) and (19). The correct y1 used
to phase shift (18) downward and (19) upward
will produce
cophased sinusoids.
In a step-by-step manner, each of the local oscillator phases
is similarly determined. Feeding the measured y j , j = 1 , 2 , .-,
488
IEEE TRANSACTIONS ON COMMUNICATIONS, VOL. COM-31, NO. 4, APRIL 1983
CosIW~t.vC,.via.Yj
.VI)
IUSEI
Local oscillator
(b)
Fig. 4. Array element frequency andphasetranslation.Under
single
path propagation @a.= @iu
= - w ' d j / c and GCj = @jic = - w D . / c , where
w' = w + wlo,. (a) Gp-coqverting for transmission from
to A . @)
Down-converting for transmission from A to C.
CC
FROM Clf)
TO C l f l
7 7 T O A lf'l
7r
Y
Y
TRANSMITTER
CONJUGATOR
PHASE
SHIFTER
vi
TRANSMITTER
!. .
cos l wt ot
RECEIVER
If1
If')
Downconvertermixer
Fig. 5 . Basic operation of an array element. (f): signal is centered on
frequencyf: (f'):signal is centered on frequency f' = f + .,-lf
b y C through the array will arrive at A with less than maxi-
mum amplitude, The scheme involves comparison of thephase
of the total arriving signal at A with the phase of the signal
from each element in turn, and shifting the latter to conform
with that of the total signal. The scheme to be described deals
with the separation of the two phase angles for measurement
and the correction obtained with each step.
l - h cd , . y , l
Consider Fig. 7 where the conditions are shown relating to
Fig. 6. One step in scheme for determining the common phase referthe measurement of the present value of &. A signal from C is
ence for the array elements.
assumed t o be transmitted through B t o A ; we identify it on
N to the appropriate elements the local oscillator outputs in arrival at A by its carrier only, cos w't. A low frequency waveeach are shifted to put them all in phase. If the propagation form cos wmt is generated at A and transmitted on the orderpaths betweep A and the elements of B are fixed, one N-ele- wirechannel to all arrayelements. By instructionfrom A
ment scan will suffice to keep the local oscillators cophased
transmitted on the order-wirechannel,eachelement
will, in
for the system lifetime.
turn, amplitude modulate its signal from C with the low freWith all the yi = yl, (16a) and (16b), the phases to be in- quency waveform cos wmt. Since information may be present
jected at element bi for focusing in both directions of trans- on the signal coming from C, om is chosen outside the signal
mission, are identical depending only on the distances. While band so thatthemodulated
waveformcomingfrom
the
A and B are apt to be fixed in position, the communicators at element will have a spectrum as suggested by Fig. 7(a). Fig.
C are mobile and the distances Dj are not fixed. A scheme will 7(b) indicates the total signal environment when element bj is
be described for dynamically determining the required phases the one carrying the additional modulation. The totalreceived
allowing for communication even while C is in motion. A limit signal at A is
to the velocity, which depends on the size of the focal region
N
and the speed with which the phases can be tracked, is to exrA ( t ) =
cos ('d't e i ) cos ( a mt - aj)
pected; these matters aresubjects of other research.
i= 1
Assume the array is initially defocused with phase angles @
arbitrary (they may all be set initially to zero). A signal sent
COS (oft+ ei)
C O S I W( 0
+ +
-
489
JAL
V-fm
CHANNEL
1’
f’. 1,
f
(b)
(a)
Fig. 8.
Determination and correction of thejth element phase.
compared
in
phase
correction
aand
Aej = 0,- B j is applied to
bj through the order-wire channel. This increment of phase has
the effect of illcreasing the magnitude of the resultant
given by
(22) as suggested by the phasor diagram, Fig. 8, and as will be
shown subsequently. Element-by-element correction of phase
in this way, going through the array several times, will result
(b)
in convergence to coherence.
Fig. 7. Method of determiningfocusing phase angles. (a) Phase relaTo show the increasein the magnitude o f the resultant with
tionshipsamong signals involved. @) Spectrum of transmitted signal fromjth array element.
the correction, we write the phasors representing the separate
arrivals exp(jOi), i = 1 , 2 , -, N . The resultant phqor at A is
N ELEMENTS
COS
w,t
x
where, to avoid unnecessary complication, we assume all comN
ponents arriving to beofequalmagnitude. In (21) the phases O i ,
=
exp (ioi) = exp (io,).
i = 1, 2, -, N account for the phase delays in the path CBA
i= 1
plus the added phase shifts @iat each element, and aj represents the phase delay intheroundtrippath
A b / ( q = Aftercorrection is applied to bi, theresultant is
2wrndj/c).
The
two
components
of (21) being
nonoverlapping
in
freN
quency
are
separated
appropriate
in
filters.
The
first
term
is
4 = exp ( j e i ) - exp ( i q ) exp (io,)
i= 1
denoted
N
rA l(t) =
2 cos (w’t + ei) = R cos (w‘t + e,).
i= 1
(24)
(25)
where we have assumed that the original phasor expOej) has
simply been shifted in phase t o form exp(j0,). Denoting by
(22) R and R ’ the magnitude of r and r ’ , we find
The second term is mixed with the original waveform cos w, t
generated at A and the component at frequencyw ’ is retained;
that is, form
R
1 - exp [ @ j - e,)l
R
/ >1.
(26)
This ratio is unity if andonly if B i = e,, and greater otherwise.,
Thus, convergence is assured.
The focusingschemedescribed
is onein w h c h element
phases are adjusted in two steps: one to put all element local
where NBF stands for narrow band filtering around frequency oscillators to the same phase and the second to correct for the
w c r .We point out that the form(23) depends on having ident- different path lengths through the elements. If we were only
ical sidebands on the double sideballd modulated signal; devi- concerned with transmission along the path CBA, the first step
ations from the condition will cause an error in the phase of would not be needed. In this case the phase correction process
the local
the time-varying sinusoid. Provided laii < n/2, the phase of just described wouldalso account for deviations among
(23) is 0, regardless of the value of ai. We can ensure a result oscillator phases. The firststep is required only because wewant
the bidirective property whereby the same phase shifts f3i can
such as (23) with phase independent of aj by rep.bcingcos
wmt on the left of (23) with cos(o,t - 6) where & is a close be used in either direction of transmission through the array.
estimate of ai. For 6 we may have 2wmd/c where d is the Should it be possible to add circuitry to the equipment at C to
mean of the distances fromA to thearray dements. The latter assist in arrayorganization,thelocaloscillatorswouldnot
is known, at least approximately. With this change made, the have to be cophased and two sets of values B j would be used
right side of (23) has cos aj replaced by cos(aj - 6). Now if depending on the direction of thetransmission.
Observe that the phase organization or focusing scheme deJ ( q - &)I = 2w, i(dj - a l / c < 77/2 the output phase of the
use of the system;it
narrow band is independent of a,. If, for instance,fm = 15 scribed does not interfere with the normal
use continuously to compensatefor
kHz, the maximum Idj - dl is 2.5 km. We envision an array of maythereforebein
diameter approximately 1 km to operate at VHF so that the changes in the propagation characteristics and for movement
of the mobile stations
C.
maximum condition is satisfied.
The organizationscheme describedis robust in the sense
With the phase in (23) not affected by aj,(22) and (23) are
490
PHASE
DET.
E-
CARRIER
rfm
I I i ; : & E[ORDER
tiCY
WIRE
I,
CHANNEL1
OSC.
Fig. 9.
MOD
RF
AMP
A possible functional block diagram of array organizer situated at A .
that errors in the determination of the various phases will not switch controller SD to open the circuit in one direction when
affect
system
performance
catastrophically.
Furthermore, transmission is in the other direction.Switches S3 and S4 consince the focusing system will be operating continuously, ertrol the local oscillator inputs to the mixers in each element,
rors in successive scans of the array elements will tend to aver- admitting cos (ozot y j ) initially for measurement'of y j , then
age out. Another important fact
related to arrayfocusing is admitting cos (olot @ j ) for cohering the multiple arrivals at
that the accuracy requirements of the organizational circuitry the destination.
are not stringent. This is so because in an array with a
large
IV. DISCUSSION AND CONCLUSION
number of elements, if the focusing phases have random independenterrorsof
iess then1/2 rad rms, the resulting exThe intent in t h s paper was to show the feasibility and the
pected loss in gain of the array 'with respect to perfect focus value of the array relay concept.Thescheme
devisedwas
is only about 1 dB [ l , p. 3071 . In obtaining this result, use is based on the assumed requirement of compatibility with current mobile transceivers. No hardware was therefore added to
madeofthefactthatthe
phase errorsarenormallydistributed.
the mobile equipment, and the systemwas designed to operate
Possible implementationsforthearrayorganizer(located
in a half-duplex mode. Also, the scheme deals only with pointaccess communication.Extenat A ) and the array elements are given in the block diagrams, to-pointratherthanmultiple
Figs. 9 and 10, respectively. In Fig. 9, the subcarrier oscillator sions to satisfy other requirements can be imagined and the deis a low frequency oscillator used to form the sidebands at fre- tails of a system to fit different requirements will be different.
R F sources as ameansfor
quency 9, for determining the phase corrections O j and to Yet the ideaofdistributingthe
formthe LO signal at frequency azo. Circuitsarehere in- reducing the spatial power density, and as a diversity measure,
cluded for obtaining estimates of the LO phases yi [see (17)- is applicable generally. Among possible extensions we see no
achieving full duplexoperation,
(20) and accompanying discussion] and the correction phases fundamentalproblemsin
8, - bj [obtained by copparing (22) and (23)] . Note the in- simultaneous communication between communication center
clusion of the estimated phase & as discussed below (23). The and multiple mobile users', and even communication 'between
microprocessor control is programmed to instruct the elements mobile units through the array with the aid of the communicaon when to respond and which measuring waveforms are
to tion center.
The scheme described utilizes phase control only to coherbe transmitted from the array
ongaqizer. The transmitter on
the array organizer functions only when the yi are being deter- ently combine the arriving signals from the different array elemined. Instructions and subcarrier information are sent on the ments. When signals of equal magnitude arrive at the receiving
end, and when thenoise sources are not directional, phase conorder-wirechannel at frequency fo, differentfromthefretrol alone is adequate to achieve maximum output signal-toquencies 7 and f' used for information transmission and for
measuring the LQ phases,at the elements. The array elements noise ratio (SNR). More likely, thesignals relayed through difcontain circuits for separating the signals arriving on the order- ferent elements encounter different conditions of propagation
wire channel into' the control phase correction, and subcarrier and arrive with different'magnitudes relative to noise. In such
components. The' elements also contain the sideband adding cases, amplitude and phase (complex) weighting at the array
circuit iqed in'the Oj - 8 , measuring circuit, the phase shifters elements is required to achieve maximum SNR. The weighting
for equalizing the LO phases and for injecting the correct @ j , required is similar to thatfoundin maximalratiodiversity
and the phase conjugation circuit which makes transmission
combining [4],the differences arising fromthe two-legged
in both directions possible. The switches S1 and S2 are con- journeytakenbythe
signal whereitencounterstwo
noise
trolled bp the microprocessor in the array organizer via the sources in two receivers. With directional noise (interference)
+
+
49 1
VESPOLI e t al.: SELF-ORGANIZING RANDOM ARRAY RELAY
T,O
CA1FREQUENCY
f
TO A AT FREQUENCY 1.1’
RF
AMP.
COS %
t,,
,
Note: Y i s treated
araisl e r e n cien
this
d i a g r a m a n d i s set
t o zero.
TO S3 AND SL
cos IwLet.yl
I
FREQUEYCY=frn
TIMER
DRIVER g
STORAGE
TO S3’S‘
S I N U S O I D AT
FREQUENCY = 1,
RF
If,)
CODE
D ET.
Fig. 10.
A possible functional block diagram of an array element bf
also present, optimization of SNR requires further adjustment
in the complex weights at the array elements. Adaptive sidelobe cancelling schemes abound [SI -[7] and variants of some
of these may lendthemselves to thearray relay.
The frequency range and spatial focal region over which the
array remains in focus is reported elsewhere [8] and is not
dealt with here. Beamwidth
and depth of field of focus are
very nearly the usual functions of the aperture size measured
i n the plane of the arriving wavefront. The bandwidth is close
to the inverse of the travel timeofthe
arriving wavefront
through the array.
The scheme as described requires estimation of two sets of
phase differences, one set to equalize the initial phases of the
local oscillators at the array elements, thesecond set to correct
for path length differences through the elements. It was not
our purpose here to deal with the parameters of the estimation process such as estimation time and power forgiven noise
levels. We should point out, though, that the cophasing procedureinwhichthe
angles @j areadjusted begins withlow
SNR signals. Recall that the signal froma single element is
initiallycompared in phase with a signal from all elements
combined noncoherently. The SNR at the output of each element is.not high (in the numerical example of SectionI1 it was
11 dB, but lower valuesof SNR are not unreasonable). This
will impact the convergence time to achieve focus since both
components being compared are noisy, and it will also affect
the tracking rate since one of the components is still noisy in
this mode.
We have here described theconceptofthe
arrayrelay,
showing it to behavelikea lens systemcontrolled to focus
emissions in one region toward a receiver in another region.
Power requirements at each element are indeed low and may
be decreased at the expense of increased numbers of elements.
Individual elements in the shade ofsome obstacle, or not functioning, will not significantly alter the behavior of the system.
The gain provided by the array also lowers the power requirements of the remote users and, because of the path diversity,
increases reliability of communication.
Finally,weremarkthatthe
systemimplementationdescribed here is intended mainly as a demonstration of possibility. The functions to be carried out are not extraordinary,
although circuit realization, with all the imperfections which
attend practical devices, may require effort.
REFERENCES
[I]
[2]
[3]
[4]
[5]
[6]
[7]
[8]
B . Steinberg, Principles of ApertureandArraySystemDesign.
New York: Wiley, 1976.
J. B . Vespoli, F. Haber, R . S . Berkowitz, and D. Yavuz, “A
self-organizing randomarraycommunications
relay,” in Proc.
22nd Midwest Symp. Circuits Syst., Philadelphia, PA, June 1979,
pp. 452-460.
J . B. Vespoli, “The widely dispersedrandomarrayas
a radio
relay,” M.Sc. thesis, Moore School Elec. Eng. Sci., Univ. Pennsylvania, Philadelphia, June 1979; also in Valley Forge Res. Cen.
Quart. Progress Rep.. no. 28, pp.46-63, Feb. 1979, and no. 29,
pp. 35-48, May 1979.
F. Haber, “Element gain setting formaximum receiver SNR,”
ValleyForgeRes.Cen.Quart.ProgressRep.,
no.31,Univ.
Pennsylvania, Philadelphia, pp. 21-24, Nov. 1979.
S . P. Applebaum, “Adaptive arrays,” IEEE Trans.
Antennas
Propagat.. vol. AP-24, pp. 585-598, Sept. 1976.
R. T. Compton, Jr.,“An adaptive array inspread-spectrum communication,” Proc. IEEE, vol. 66, pp. 289-298, Mar. 1978.
W. F. Gabriel, “Spectral analysis and adaptive array superresolution techniques,” Proc.IEEE, vol. 68, pp. 654-666, June
1980.
D. Yavuz, “Frequency response and focal region characteristics of
random arrays,” Valley Forge Res. Cen. Quart. Progress Rep.,
no.
31, Univ. Pennsylvania, Philadelphia, pp. 15-20, Nov: 1979; also
no. 29, pp. 49-60, and no. 30, pp. 27-33.
492
IEEE TRANSACTIONS ON COMMUNICATIONS, VOL. COM-31, NO. 4, APRIL 1983
Jorge B. Vespoli (A’78)wasborn in Mar del
Plata, Argentina, in 1951.He received the Engineer Diploma from the University of Mar del
Plata in 1975, andthe M.S.E.E. and M.S.S.E.
degrees from the University of Pennsylvania,
Philadelphia, in 1978 and 1979,respectively.
From 1972 to 1982, he was with the National
Telephone Administration of Argentina, ENTEL,
where hewas engaged in the area of satellite
communications. From 1975 to 1982,he worked
as part-time Professor in the Department of Electrical Engineering at the University ofMar del Plata, instructing in
electromagnetics, communication theory, and electronic measurements.
From 1977 to 1979,he pursued graduate studies at the Moore School of
ElectricalEngineering, University of Pennsylvania, under a Fulbright
Scholarship. In October 1982, he joined the Satellite Communications
Division of Harris Corporation, where he currently works as a Systems
Engineer in the implementation of the National Satellite Communication
Network of Argentina.
*
Fred
Haber
(S’44-A’49-M’55-SM’68-F’78)
was born in New York, NY, on July 1, 1921.He
received the B.S.E.E. degree from Pennsylvania
State University, University Park, in 1948, and
the M.S.E.E. and Ph.D. degrees from the University of Pennsylvania, Philadelphia, in 1953
and 1960,respectively.
He was employed byRCA Corporation from
1948 to 1951 and has been associated for short
intervals with the Anna Corporation, General
Precision Inc., the U.S. Navy Underwater SystemCenter,
andthe
Aerospace Corporation. During 1968-1969, he
was a Visiting Professor at Pahlavi University, Shiraz, Iran. Since 195 1,
he has been at the University of Pennsylvania, where he is now Professor
of Systems Engineering. He teaches courses in communication theory and
relatedareas, and his current research deals with adaptive arrays for
communication and signal location.