Optimum Amplitude and Phase Control for an Adaptive Linear
Array Using a Genetic Algorithm
You Chung Chung *
youchung@unr.edu
Electrical Eng. Dept.
University of Nevada
Reno,NV 89557
Tel : (775) 784-6921
Fax : (775) 784-6627
Randy L. Haupt
haupt@ee.unr.edu
Electrical Eng. Dept.
University of Nevada
Reno,NV 89557
Tel : (775) 184-6927
Fax : (775) 784-6621
1. INTRODUCTION
Phase-only adaptive nulling cannot generate nulls at symmetric locations about the main beam,
and it has a slower convergence rate than amplitude & phase adaptive nulling [I - 31. Phase-only
nulling places a null at one angle, and it causes the sidelobe at the symmetric location to go up [l,
31. The amplitude & phase adaptive nulling with a GA overcomes these problems. The
performance of amplitude & phase adaptive nulling with a GA will be compared with that of
phase-only adaptive nulling with a GA. In addition, the best bit setup of amplitude & phase
adaptive nulling with a GA will be found in terms of convergence speed and null depths when the
interference is incident at various locations-single, adjacent, symmetric and nonsymmetric about
the main beam. The 32 element half wavelength spaced linear array is used and simulated, and the
power of symmetric, non-symmetric and adjacent interference are symmetric.
2. ARRAYS AND GENETIC ALGORITHM
An amplitude & phase adaptive h e a r array with a genetic algonthm I S shown m figure 1, and the
linear a m y pattern is given by [I, 21
(1)
“=I
a,, = m a y weight at element n, Y = kdu ,
k = 27rlL,
= wavelength,
d = spacmg between elements,
9 = angle in degree,
= nullmg phase,
An=beam-steenng phase,
~ n amplitudes
z
are even symmetnc, and the phase is odd symmetnc [1,2,4]
incident
ficld
clemrms
Figure 1 Diagram of an amplitude and phase adaptive h e a r m a y
0-7803-5639-W99/$3000 01999 IEEE
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The GA controls the least significant bits of the phase shifter bits and amplitude weight bits, and
minimizes output power while it maintains the main beam direction and gain. The least
significant bits of phase shifter-3,4 and 5-bits are used for phase-only adaptive array, and the
least significant bits of amplitude weight and phase shifter-combination of 3,4 and 5 bits--are
used for amplitude & phase adaptive array. Since controlling more phase shifter bits gives higher
main beam reduction, the phase shifter bits for control should be limited. The results of each bit
for control are averaged over 30 runs after 25 generations when a single and multiple-adjacent,
symmetric and non-symmetric-interference is incident on amplitude & phase and on phase-only
adaptive array with a GA, and the results are compared. The array pattern of half wavelength
spaced 32 element linear array with initial -3OdB Chebyshev amplitude taper and possible
interference locations are shown in Figure 2.
n
-1J
cg -20
G
I
:
la-30
4
3
-
2 -40
-50
-60
1
180
20
40
60
80
100
120
140
160
theta in degree
Figure 2. Initial array pattern with possible interference locations.
3. RESULTS AND CONCLUSION
Figures 3 to 6 show that the resuts of some of the best bit setup of amplitude & phase adaptive
nulling are compared with those of 3, 4 and 5 bits setup phase-only adaptive nulling. Those
results are averaged over 30 runs after 25 generations on each bit setup of amplitude & phase and
phase-only. The 5 bits amplitude weight with 3 bits phase shifter [5, 3 bits] control adaptive
nulling with a GA outperforms any other bits control phase-only and amplitude & phase adaptive
nulling with a GA when interference is incident at single, adjacent, symmetric and non-symmetric
locations. Especially, in figure 5, the convergence speed of [5, 3 bits] amplitude & phase
adaptive nulling is faster than any other bits for control when interference is incident at symmetric
locations about main beam at [50 and 1301 degrees.
Adaptive nulling with a GA generates nulls quickly, and the amplitude & phase adaptive nulling
with a GA outperforms any phase-only adaptive nulling with a GA. The best adaptive nulling
uses a 5 bit amplitude weight with 3 bit phase shifter [5,3 bit] control adaptive nulling with a GA,
and it is strongly recommended for an adaptive nulling when any interference-single, adjacent,
symmetric and non-symmetric-is incident on an adaptive array.
4. REFERENCES
[l]. R. L. Haupt, “Phase-only adaptive nulling with a genetic algorithm,” IEEE Trans. Antennu
Propagut., vol. AP-45, pp. 1009-1015,June 1997.
[2]. Y.C. Chung, and R. L. Haupt, “Amplitude and phase adaptive nulling with a genetic algorithm ”
USNCNRSI National Radio Science Digest, pp. 225, Atlanta, Ga., June 1998. .
[3]. R. L. Haupt, “Comparison between genetic and gradient-basedoptimization algorithms for
solving electcomagnetics problems,” IEEE Trans. Mugnetics, vol. 3 1, pp. 1932-1935, May
1995.
[4]. Y.C. Chung, and R. L. Haupt, “OptimizingGenetic Algorithm Parameters for Adaptive
Nulling,” accepted to the 15“ Annual Review of Progress in Applied Computational
Electromagnetics, Monterey, Ca., March 1999.
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Generation
Figure 3. Null depth of Amplitude & phase vs. null depth of phase-only when a single
interferenceis incident on 141 degrees.
-30
-35
-40
0
E -45
..,
z
-50
-55
_-_
Amp & Ph Bits = [4 31
- Amp &Ph Bits = [5 31
1
i
-6C
Figure 4. Null depth of Amplitude & phase vs. null depth of phase-only when adjacent interference
are incident on [130and 1351 degrees.
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_ . . . . . _ _ _ _ . _ . . . _....................
_......
-60
-65
5
10
15
20
25
Generation
Figure 5. Null depth of Amplitude & phase vs. null depth of phase-only at symmetric interference
are incident on [50 and 1301 degrees.
0
+
0
--
5
10
15
Generation
Phase Bits = [3]
Phase Bits = [4]
Phase Bits = [5]
Amp & Ph Bits = [3 31
Amp&PhBts=[43]
Amp & Ph Bits = [531
Amp & Ph Bits = [5 41
20
25
Figure 6. Null depth of Amplitude & phase vs. null depth of phase-only when non-symmetric
interference are incident at [59 and 1301degrees.
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