Modified GA-FFT for Synthesizing Shaped Pattern of Unequally Spaced Array in Presence of Mutual Coupling
YOU Pengfei① LIU Yanhui① HUANG Xin① ZHU Chunhui① LIU Qinghuo②
①(Department of Electronic Science, Xiamen University, Xiamen 361005, China) ②(Department of Electrical and Computer Engineering, Duke University, Durham 27708, USA)
A new Virtual Least-Square Active Element Pattern Expansion (VLS-AEPE) method is presented in this paper, which considers each active element pattern of an unequally spaced array as the one radiated by some of equally spaced elements of a virtual array. Using the help of this method, the pattern of an unequally spaced array including mutual coupling can be efficiently calculated by FFT. In addition, this method is combined with the Genetic Algorithm (GA) to deal with the shaped pattern synthesis problem for unequally spaced linear arrays. Two synthesis experiments including the synthesis of flat-top pattern for an unequally spaced dipole array and the synthesis of cosec-squared pattern for an unequally spaced microstrip array are conducted to verify the effectiveness and advantages of the proposed algorithm.
WANG X, ABOUTANIOS E, and AMIN M G. Thinned array beampattern synthesis by iterative soft-thresholding- based optimization algorithms[J]. IEEE Transactions on Antennas and Propagation, 2014, 62(12): 6102-6113. doi: 10. 1002/MOP.10823.
ZHAO Y N, ZHANG T, LI F C, et al. Optimal waveform design for MIMO radar via alternating projection[J]. Journal of Electronics & Information Technology, 2014, 36(6): 1368-1373. doi: 10.3724/SP.J.1146.2013.01198.
YU B, CHEN K S, ZHU P, et al. An optimum method of sparse concentric rings array based on dimensionality reduction[J]. Journal of Electronics & Information Technology, 2014, 36(2): 476-481. doi: 10.3724/SP.J.1146. 2013.00526.
[4]
WANG L L, FANG D G, and SHENG W X. Combination of Genetic Algorithm(GA) and Fast Fourier Transform(FFT) for synthesis of arrays[J]. Microwave and Optical Technology Letters, 2003, 37(1): 56-79. doi: 10.1002/MOP.10823.
[5]
LIU Q H and NGUYEN N. An accurate algorithm for NonUniform Fast Fourier Transforms (NUFFT,s)[J]. IEEE Microwave and Guided Wave Letters, 1998, 8(1): 18-20. doi: 10.1109/75.650975.
[6]
YANG K, ZHAO Z Q, and LIU Q H. Fast pencil beam pattern synthesis of large unequally spaced antenna arrays[J]. IEEE Transactions on Antennas and Propagation, 2013, 61(2): 627-634. doi: 10.1109/TAP.2012.2220319.
[7]
LIU J Z, ZHAO Z Q, YANG K, et al. A hybrid optimization for pattern synthesis of large antenna arrays[J]. Progress In Electromagnetics Research, 2014, 145: 81-91. doi: 10.2528/ PIER13121606.
[8]
JIANG M L, CHEN R S, ZHOU L, et al. Synthesis of arrays with Genetic Algorithm(GA) and Nonuniform Fast Fourier Transform (NFFT)[C]. Asia-Pacific Microwave Conference Proceedings(APMC), Suzhou, China, 2005, 4: 2. doi: 10. 1109/APMC.2005.1606885.
[9]
POZAR D M. The active element pattern[J]. IEEE Transactions on Antennas Propagation, 1994, 42(8): 1176-1178. doi: 10.1109/8.310010.
[10]
POZAR D M. A relation between the active input impedance and the active element pattern of a phased array[J]. IEEE Transactions on Antennas and Propagation, 2003, 51(9): 2486-2489. doi: 10.1109/TAP.2003.816302.
[11]
KELLY D F and STUTZMAN W L. Array antenna pattern modeling methods that include mutual coupling effects[J]. IEEE Transactions on Antennas and Propagation, 1993, 41(12): 1625-1632. doi: 10.1109/8.273305.
[12]
STEYSKAL H and HERD J S. Mutual coupling compensation in small array antennas[J]. IEEE Transactions on Antennas and Propagation, 1990, 38(12): 1971-1975. doi: 10.1109/8.60990.
[13]
YOU P F, LIU Y H, HUANG X, et al. Efficient phase-only linear array synthesis including coupling effect by GA-FFT based on least-square active element pattern expansion method[J]. Electronics Letters, 2015, 51(10): 791-792. doi: 10.1049/EL.2015.0431.
[14]
LIU Y H, NIE Z P, and LIU Q H. A new method for the synthesis of non-uniform linear arrays with shaped power patterns[J]. Progress In Electromagnetics Research, 2010, 107: 349-363. doi: 10.2528/PIER10060912.
[15]
WANG F, BALAKRISHNAN V, ZHOU P Y, et al. Optimal array pattern synthesis using semidefinite programming[J]. IEEE Transactions on Signal Processing, 2003, 51(5): 1172-1183. doi: 10.1109/TSP.2003.810308.
[16]
FUCHS B. Synthesis of sparse arrays with focused or shaped beampattern via sequential convex optimizations[J]. IEEE Transactions on Antennas and Propagation, 2012, 60(7): 3499-3503. doi: 10.1109/TAP.2012.2196951.
