Adaptive Nulling with Spherical Arrays Using a
Genetic Algorithm
You Chung Chung *
Randy L. Haupt
haupt@ee.unr.edu
Electrical Eng. Dept
University of Nevada
Reno,NV 89557
Tel : (775) 784-6927
Fax : (775) 784-6621
youchung@unr.edu
Electrical Eng. Dept.
University of Nevada
Reno, NV 89557
Tel : (775) 784-6921
Fax : (775) 784-6627
1. INTRODUCTION
Spherical arrays are arrays that conform to the surface of a sphere. One approach to a spherical
array layout is to mold a planar array to the surface of a sphere (spherical-planar array). Another
approach is to create circular arrays about the spherical surface (spherical-circular array). This
paper presents an approach to adaptive nulling with either type of spherical array using a genetic
algorithm.
Amplitude and phase adaptive nulling with a genetic algorithm generates deeper and faster nulls
than phase-only nulling [I-31. A genetic algorithm is used to place a null at the sidelobe of two
types of spherical arrays. The 16x16 element, 256 elements, rectangular grid half wavelength
spaced spherical planar array, and the spherical circular array with same number of elements as
spherical-planar a m y are simulated and compared.
2. SPHERICAL ARRAYS AND GENETIC ALGORITHM
An amplitude & phase adaptive linear array with a genetic algorithm is described in [1-4]. A
spherical array pattern is given by [5-61
R = radius of sphere;
A. = array weight at element n;
f&I$)= element pattern;
eo=angle of main beam;
e.=
angle of element n;
k2dk
e = angle;
C=angle of main beam;
&=angle of element n;
h= wavelength;
I$ =angle;
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 shifier4ombination of 3 , 4 and 5 bits out of 8 possible bits--are used for
amplitude & phase control spherical adaptive arrays.
A 16x16 element spherical-planararray and spherical-circular array are shown in Figures 1 and 2.
The null depths in dB of spherical-planar and of spherical-circular arrays are compared when a
jammer is incident on a sidelobe of both spherical arrays. The initial low sidelobe amplitude
tapers are used for both arrays.
0-7803-5639-X/99/$10.00 Q1999 IEEE.
2000
Figure 1. Spherical-Planar Array.
... _...
j.
I . . .
-20
-20
Figure 2. Spherical-Circular Array.
2001
3. RESULTS AND CONCLUSION
The nulled patterns are superimposedon the quiescent patterns for both spherical arrays in Figures
3 and 4. The null depths of both arrays are close to the Same depth.
The quiescent sidelobe of the spherical-planar array is about -3OdB below the peak of the main
beam, and the quiescent sidelobe of the spherical-circular array is about -2OdB below the peak of
its main beam.
The spherical-circular array has slower convergence speed than spherical-planar since a
chromosome of 16x16 spherical-planar array is shorter than that of spherical-circular. The GA of
the spherical-planar controls only 32 elements instead of 255 elements due to the symmetric
amplitude and phase. Thus, the search space for placing the null in the spherical planar array is
much smaller than the search space for the spherical circular array. The spherical-planar array
converges faster than the spherical-circular due to the less number of controlling elements, and it
only required 5 amplitude and 3 phase bits for control.
Therefore, the spherical-planar array using an adaptive GA generates nulls faster than the
spherical-circularand has more controllability of low initial sidelobe levels. In addition, this paper
shows that a GA generates nulls on two m e s of spherical arrays, and it is proved that GA can
optimize any antenna arrays quickly without any geomeaical limitation of antenna array.
4. REFERENCES
[I]. R. L. Haupt, “Phase-only adaptive nulling with a genetic algoritlun,” IEEE Tram.Antenna
Propagat., vol. AP-45, pp. 1009-1015, June 1997.
121. Y. C. Chung,and R L. Haupt, “Amplitude and phase adaptive nulling with a genetic algorithm, ”
USNC/URSINationalRadio Science Digest, pp. 225, Atlanta, Ga., June 1998. .
[3]. Y. C. Chung,and R L. Haupt, “Optimiziiggenetic algorithm parameters for adaptive
nulling,” accepted to the 15‘AnnualReview ofprogress in Applied Computational
Electromagnetics, Monterey, Ca.,March 1999.
[4]. M. Hoffman, “Conventions for the analysis of spherical Array,” IEEE Trans. Antennas
Propagat., vol. AP-11, pp. 390-393, July 1963.
[5]. E. A. Wolff,AntennaAM[ysis.Norivood, MA: Artech House,1988.
2002
Angle in degree
Figure 3. Array pattern of spherical-planar array.
2003