Near-field Error Correction on RFSS for
Applications
Jing MA #1, Dong CHEN*2,Jindong FEI3
#13
Science and Technology on Space Simulation Laboratory,
Beijing,China
1
2*
phd.jingma@gmail.com
Institute of Telecommunication Satellites,
Beijing,China
Address Including Country Name
2
phd.DChen@gmail.com
Abstract— According to the applications for current RFSS(Radio
Frequency Simulation System) developing, this paper proposes a
near-field error correction method using mono-pulse amplitude
comparison. This method produces two tables which are used to
correct near-field error by adjusting the amplitudes on triad of
antenna from the gradation direction to make the error of
DOA(Direction-Of-Arrival) approaching zero. Meanwhile, this
method focuses on the model of mono-pulse amplitudecomparison for seeker setting with a circular slot array of wave
guide. Based on the character of symmetry for the slot array, the
process of forming the SUM signal and MINUS signal is
simplified. The precision of the tables for near-field error
correction by our method satisfies the demands of RFSS with the
deflection of 3×10-3 degree for azimuth and 2×10-3 degree for
elevation. The simplified method also meets the demand of RFSS
and reduces the running time by 55%.
I. INTRODUCTION
In order to realize high precision RFSS, synthesized target
position on array should be adjusted exactly to simulate
relative position between tested radar leader and target in real
flight condition. Simulation method is choosing certain triadof-antenna (ToA) to radiate signal by controlling amplitudes
and phases on triad-of-antenna according to glint equation of
radiation center. If caliber of antenna is too small to be taken as
a point when spherical wave radiates, ToA controlled by glint
equation can produce the expected target position. However, if
more than one radiation exist, or the caliber can not be
neglected, synthesized radiation from triad-of-antenna is no
longer spherical wave but aberration, glint equation isn’t
correct for controlling triad-of-antenna. This aberration is the
reason of Near-field Error Correction (NFEC). With NFEC
phenomenon, the real target position needs to be corrected [1].
NFEC is the permission of guarantee simulation precision
and VVA(Variable valve actuation). Nowadays, many scholars
have achieved some researches on these issues [2]-[4].
Recently, a new generation is promoted by homing guidance
tested radar leader’s rapid developing. Researchers are
studying the high precision RF guidance simulation system.
Therefore, NFEC is a hot study topic for the new generation
RF guidance simulation system.
______________________________________
978-1-4673-1800-6/12/$31.00 ©2012 IEEE
II. MODELLING OF NFEC IN RFSS
A. The HWIL modelling of NFEC
Figure 1 The HWIL system with NFEC
Figure 1 shows the consistent of RFSS with NFEC module.
It consists of the tested radar seeker, DOA measured device,
target antenna array, control system of array electronic feed
system. The angle positions simulated by RFSS are corrected
by NFEC module. The method in the paper considers on
symmetrical circular slot array for radar seeker and quadrupleridged circular horn antenna for target array in NFEC.
B. The Mathematics modelling of NFEC
Based on Electromagnetic Reciprocity Theorem and
electromagnetism field distribution on the face of radar seeker,
the direction diagrams of SUM signal and MINUS signal for
antenna on seeker can be deducted. The error of DOA
calculated by mono-pulse amplitude-comparison method is
adjusted approaching to zero through the amplitudes on ToA.
The amplitudes when the error value of DOA equals zero are
the true values for NFEC. The position of target (X,Y) can be
calculated accurately by equation (1), so the NFEC value
( 'X F , 'YF ) equals equation (2), where ( X F , YF ) is the
expectation position for target.
468
E2
­
E3
°X
2
®
°¯Y E2
(1)
­'X F X X F
®
¯'YF Y YF
Every node in NFEC table obtained by the above method is
saved into a form in computer, with ( X F , YF ) as the input and
( 'X F , 'YF ) as the result. If ( X F , YF ) is not a node in
NFEC table, it is obtained by two dimensional linear
interpolation. Therefore, the simulated target position is found
in table as
­ X X F 'X F
®
¯Y YF 'YF
(3)
where,
I
^
§ ' (t ) ·
real ¨
¸ ˜ cos(I )
© 6(t ) ¹
0,7KH'2$DQGUHIHUHQFHVLJQDOLVVDPHGLUHFWLRQ
S,7KH'2$DQGUHIHUHQFHVLJQDOLVRSSRVHGGLUHFWLRQ
' ¦
(6)
in
³³
Sj
f j ( x, z ) Fi. j ( x, y, z )dxdz
(7)
S j ( j 1, 2,3, 4) presents the jth area on the face
³³
Sj
means getting the sum or integral of all cells
S j . f j ( x, z ) is field distribution on seeker’s antenna. T is
azimuth and \ is elevation.
The direction diagrams of SUM signal, azimuth MINUS
signal and elevation MINUS signal are
SUM i
Fi ,1 Fi ,2 Fi ,3 Fi ,4
DAZ i
Fi ,1 Fi ,4 Fi ,2 Fi ,3
DELi
Fi ,1 Fi ,2 Fi ,3 Fi ,4
(8)
(9)
(10)
According to mono-pulse amplitude comparison method,
DOA of azimuth and elevation are
DT
§ DAZ1 E1 DAZ 2 E2 DAZ 3 E3 ·
real ¨
¸
© SUM 1 E1 SUM 2 E2 SUM 3 E3 ¹
§ DEL1 E1 DEL2 E2 DEL3 E3 ·
real ¨
¸
© SUM 1 E1 SUM 2 E2 SUM 3 E3 ¹
(11)
(12)
(2) Mono-pulse Amplitude-comparison Method for Slot
Array Antenna
'
Figure 3 Mono-pulse Amplitude-comparison Method for Slot Array Antenna
Figure 2 SUM signal and MINUS signal
According to Electromagnetic Reciprocity Theorem, the
field strength of ToA on the ith cell to jth cell is
Fi , j ( x, y, z )
where,
D\
means getting real part.
e jkRi
u u Mi u n
4S Ri
Fi , j (\ , T )
˄4˅
, real()
A
where, A is a constant, Mi is the inspired field of ith cell. u
is unit vector from source field to inspired field. n is unit vector
of direction on the face of the horn.
Therefore, synthesized field on one quadrant of seeker is
of antenna.
C. Mono-pulse Amplitude-comparison method
(1) Application of Mono-pulse Amplitude Comparison
Method in the Detection of Radar Seeker
One angle plane contents two overlapped beams receiving
at same time, which are processed into SUM signal(™) and
MINUS signal(Ƹ). MINUS signal is the DOA signal in this
angle plane as Figure 2 shown. Mono-pulse amplitude
comparison method compares two beams with same phase but
different direction to obtain target position. When target leaves
the center of the beam, the magnitude and polarity sign of
receiving normalized MINUS signal(Ƹ/™) present the position
which the target locates. DOA is
H
Fi
(2)
Fi f j
(5)
f j is the field strength of cell x, y, z on seeker to the
jth cell on triad of antenna;
Fi is the field strength of the ith cell on ToA to the cell
In RFSS, seeker’s antenna adopts symmetrical circular slot
array, which contents four subarrays marked 1,2,3 and 4 as
Figure 3 shown.
Construct coordinates for slot array antenna, subarrays
locate in four quadrants respectively. Then, DOAs of azimuth
and elevation can be obtained by equation (11) and (12).
When SUM signal and MINUS signal are generated on the
face of seeker’s antenna, the direction diagrams are
SUM (\ ,T ) GSUM (\ Ri , T Ri ) Eslot (rRi ,T Ri ,\ Ri ) (13)
DAZ (\ ,T ) GDAZ (\ Ri ,T Ri ) Eslot (rRi , T Ri ,\ Ri )
x, y, z on seeker. It presents as
469
(14)
DEL(\ ,T ) GDEL (\ Ri ,T Ri ) Eslot (rRi ,T Ri ,\ Ri )
(15)
where, ( rR , T R ,\ R ) is the coordinate of the ith cell of
ToA relative to seeker’s antenna;
GSUM (\ Ri ,T Ri ) ǃ GDAZ (\ Ri ,T Ri ) ǃ GDEL (\ Ri ,T Ri ) are
cell genes for SUM signal, azimuth MINUS signal and
elevation MINUS signal of seeker’s antenna respectively.
A slot on seeker’s antenna is presented by
Eslot (rRi ,T Ri ,\ Ri ) ,which expresses as
i
i
i
AR to present this amplitude. Equation(17) can be simplified
to
g Sj1,k (a, b) g Sj2,k (a, b) g Sj3, k (a, b) g Sj4, k (a, b)
4
AR ¦ e j ( al
R
blR )
l 1
4
AR ¦ cos(alR blR ) j sin(alR blR )
§S
·
cos ¨ sin T Ri cos\ Ri ¸
V
©2
¹
j m
i
2 i
2
S 1 sin T R cos \ R
Eslot (rRi ,T Ri ,\ Ri )
Build coordinates on the face of slot array antenna, cells on
j ,k
the same radius possess the same amplitude ASi , so make
l 1
(23)
Equation (23) is expanded by trigonometric function
R
R
R
R
R
R
R
R
satisfying a1 a2 a3 a4 and b1 b4 b2 b3 .
The cell gene is simplified to be calculated in a subarray
avoiding complex operation, which is
i
&
& e jkRR
˜(sin\ e cos T Ri cos\ Ri e\ ) i
RR
i
R T
3
n
m
¦¦¦
(16)
(24)
GSUM (\ Ri , T Ri )
ASji, k cos(a ) cos(b)
If each subarray on slot array antenna contents n u m cells,
i 1 j 1 k 1
cell genes of SUM signal, azimuth MINUS signal and
Similarly, the cell gene of azimuth MINUS signal and
elevation MINUS signal can be decomposed to each slot, elevation MINUS signal are
modeling as
3
n m
GSUM (\Ri ,TRi )
3
n
m
¦¦¦ g
j ,k
S1
i 1 j 1 k 1
GDAZ (\ Ri , T Ri )
(a,b) gSj,k (a,b) gSj,k (a,b) gSj,k (a,b)
2
3
i 1 j 1 k 1
4
(17)
GDAZ (\ ,T )
i
R
i
R
3
n
m
¦¦¦ g
j ,k
S1
i 1 j 1 k 1
j,k
S2
j,k
S3
GDEL (\Ri ,TRi )
n
m
¦¦¦ g
i1 j 1 k1
j,k
S1
(a,b) gSj,k (a,b) gSj,k (a,b) gSj,k (a,b)
2
3
4
(19)
j ,k
where, g Si ( a, b) is cell gene for the cell on ith row and
kth column in subarray
ASji,k e j ( a b )
n
m
¦¦¦ A
j ,k
Si
cos(a ) sin(b)
(25)
sin(a ) cos(b)
(26)
D. Precision Target Position adjusting by Gradient method in
NFEC
E2
Si , presenting as
g Sji,k (a, b)
3
j ,k
Si
Compared with equation (17),(18) and (19), operations of
SUM and MINUS signals are simplified to deal with slots in
only one subarray with avoiding complex operation,
overlapped multiplications and additions.
(18)
3
GDEL (\ Ri , T Ri )
i 1 j 1 k 1
(a,b) g (a,b) g (a,b) g (a,b)
j ,k
S4
¦¦¦ A
(20)
ASji, k is radiation amplitude of this cell.
E1
a and b are phase difference on X direction and Y direction
in this cell’s coordinate respectively, presenting as
a Z sin(T ) cos(\ )[( j 1)dx x0 ]
(21)
b Z sin(T ) cos(\ )[(k 1)dy y0 ]
(22)
\ and T are azimuth and elevation; dx and dy are
spaces between each slot cell on X and Y direction. x0 is
distance from origin to closest cell on X direction, so as y0 .
Making use of symmetry relation in slot array antenna
between four sunarray, equation (17),(18) and (19) about SUM
signal, azimuth MINUS signal and elevation MINUS signal
can be simplified in order to minimize the complexity of
NFEC’s arithmetic and improve running time.
E3
Figure 4 Control method for target in RFSS
The RFSS with target array adopts electron control unit to
realize the angle simulation of target movement. The target
position can be controlled exactly through adjusting the signals,
attenuator of amplitude and transposer for phase, on the ToA
as Figure 4 shown.
Reference [4] used Newton iterative algorithm to solve
linear equations, equation (11) and equation (12) equaling to
zero. However, because Newton iterative algorithm has slow
convergence speed, this paper abandons linear equation solvent
but adopts adjusting amplitudes of ToA on the gradient
directions of azimuth and elevation to make the error of DOA
calculated by mono-pulse amplitude comparison method
approaching to zero, Gradient method in NFEC namely.
Convergence speed of the Gradient method precedes which of
Newton iterative algorithm.
470
Therefore, take the gradient direction of azimuth and
elevation on amplitudes of ToA Ei ,
operation such as overlapped multiplications and additions, as
well as improving running time. Table III enumerates precision
and improvement for this simplification.
3 wD
From overall, the precision of simplification can be
\
G Ei grad ( Ei )
(27) guaranteed by 4×10-4 difference on azimuth and difference on
u G Ei
i 1 wEi
5×10-4 elevation. Nevertheless, the running time is improved to
Appending the condition E1 E2 E3 1 , Ei is adjusted 55% on average.
TABEL III
iteratively to make DOA of azimuth and elevation approaching
Precision and Improvement for Simplification
to zero. When the precision is satisfied, the controlled
Normalized
DOA of azimuth
DOA of elevation
Running
Amplitudes
Time(ms)
amplitudes on ToA are obtained by iteration end. The position
on triad-ofTRUTH SIMPLIF TRUTH SIMPLIF TRUT SIMPL
corrected by NFEC algorithm can be taken by equation (28).
antenna
¦
­
°\
®
°¯T
E2
E3
2
E2
(28)
III. THE RESULT OF NEAR-FIELD ERROR CORRECTION ON RFSS
A. The table of near-field error correction
Tables are needed to calculated for NFEC. According to
above-mentioned method, two tables are obtained for azimuth
and elevation. A triad of antenna can be divided into two
symmetrical right angles. Therefore, the tables are formed for
half data. The tables of azimuth and elevation are shown in
Table I and Table II separately.
TABLE I
NFEC FOR AZIMUTH
XF
YF
0
0.1
0.3
0.5
0.7
0.9
'X
0.05
0.15
0.25
0.35
0.45
0
0.0128
0.0154
0.0256
0.0273
0.0166
0.026
0.027
0.0199
0
0.0186
0.0191
0.0149
0.0036
-0.017
0.0066
0.0067
0.0054
0.0017
-0.005
-0.0159
[1]
[2]
0
0.1
0.3
0.5
0.7
0.9
0.05
0.15
0.25
0.35
0.45
0
0
0.0239
0
0.0157
0.0257
0
0.01
0.0096
0
0
0.0065
0
0.0171
0.0254
0
0.0048
-0.0052
-0.0255
0.25
0.3
0.35
0.4
0.45
0.0082
0.0118
0.0147
0.0102
0.0157
Y
0.0086
0.0120
0.0143
0.0109
0.0152
0.0209
0.0192
0.0120
0.0071
0.0201
Y
0.0201
0.0195
0.0114
0.0074
0.0206
H
45
43
42
42
41
IFY
17
20
21
19
20
REFERENCES
'Y
0
0.75
0.7
0.65
0.6
0.55
IV. CONCLUSION
According to the applications for current RFSS developing,
this paper proposes a near-field error correction method using
mono-pulse amplitude-comparison. This method produces two
tables of near-field error correction by adjusting the amplitudes
on ToA on the gradation direction to make the error of
DOA(Direction-Of-Arrival) which is measured by mono-pulse
amplitude comparison method approaching zero. Meanwhile,
this method focuses on the model of mono-pulse amplitude
comparison for seeker setting a circular slot array of wave
guide. Based on the character of symmetry for the slot array,
the process of forming the SUM signal and MINUS signal is
simplified. The precision of proposed method in this paper can
satisfy the required application of RFSS, as reducing the
running time.
0
TABLE II III
NFEC FOR ELEVATION
XF
YF
0
0
0
0
0
[3]
[4]
-0.0386
[5]
-0.0237
[6]
B. Simplification accuracy of mono-pulse amplitude
comparison for circular slot array antenna
Mono-pulse amplitude comparison method for slot array
antenna is introduced in Section II.C, where contains the
simplification for SUM and MINUS signal, avoiding complex
[7]
[8]
471
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