Phase-only Beamforming via Iterative Majorization Minimization
WU Kai SU Tao LI Qiang
(National Laboratory of Radar Signal Processing, Xidian University, Xi’an 710071, China)
(Collaborative Innovation Center of Information Sensing and Understanding, Xidian University, Xi’an 710071, China)
To improve the interference and noise suppression ability of Phase-Only Beamforming (POB) and the real-time performance to obtain the optimal weight of the uon-convex POB, a phase-only Minimum Variance Distortion-less Response Beamformer (MVDRB) via the Iterative Majorization Minimization (IMM) algorithm is designed. The distortion-less response constraint is transformed into maximizing array response in the desired direction. The upper bound function of the objective function in quadratic form is derived which generates the IMM-POB model. The optimal weight in closed-form for each iteration is further deduced. Simulation analysis illustrates that the proposed IMM-POB can obtain better signal to interference and noise ratio improvement compared with the existing iterative POB algorithms and the optimal MVDRB; its interference suppression ability approximates the optimal MVDRB with better noise suppression ability; it is much less sensitive to the number of array taps compared with the optimal MVDRB; it has strong real-time performance and can be applied to large-scale array.
WU Kai and SU Tao. Design of generalised sidelobe canceller-based adaptive wideband beamformer without pre-steering delays[J]. Electronics Letters, 2016, 52(3): 177-179. doi: 10.1049/el.2015.3488.
WU Kai, SU Tao, JIN Biao, et al. Design of adaptive broadband beamformer with fixed feedback weights[J]. Journal of Jilin University (Engineering and Technology Edition), 2016, 46(1): 303-310. doi: 10.13229/j.cnki. jdxbgxb201601046.
[3]
FUCHS Benjamin. Application of convex relaxation to array synthesis problems[J]. IEEE Transactions on Antennas and Propagation, 2013, 62(2): 634-640. doi: 10.1109/TAP. 2013.2290797.
WANG Xuebin, LI Huiyong, and HE Zishu. Wide null steering based on genetic algorithm by controlling only the current phase[J]. Journal of China Academy of Electronics and Information Technology, 2011, 6(6): 634-638.
LU Chengjun, SHENG Weixing, HAN Yubing, et al. Phase-only beamforming based on iterative second-order cone[J]. Journal of Electronics & Information Technology, 2014, 36 (2): 266-270. doi: 10.3724/SP.J.1146.2013.00593.
[6]
KAJENSKI P J. Phase only antenna pattern notching via semidefinite programming relaxation[J]. IEEE Transactions on Antennas and Propagation, 2012, 60(5): 2562-2565. doi: 10.1109/TAP.2012.2189709.
[7]
SCHOLNIK D P. A parameterized pattern-error objective for large-scale phase-only array pattern design[J]. IEEE Transactions on Antennas and Propagation, 2016, 64(1): 89-98. doi: 10.1109/TAP.2015.2500239.
[8]
NAYERI P, YANG F, and ELSHERBENI A. Design of single-feed reflect array antennas with asymmetric multiple beams using the particle swarm optimization method[J]. IEEE Transactions on Antennas and Propagation, 2013, 61(9): 4598-4605. doi: 10.1109/TAP.2013.2268243.
[9]
SHORE R A. The use of nonlinear programming techniques for phase-only[C]. Antennas and Propagation Society International Symposium, Houston, TX, USA, 1983, 21: 23-26. doi: 10.1109/APS. 1983.1149075.
[10]
KHZMALYAN A D and KONDRAT’YEV A S. Fast iterative methods for phase-only synthesis of antenna array pattern nulls[J]. Electronics letters, 1995, 31(8): 601-602. doi: 10.1049/el:19950432.
[11]
MISMAR M J, ISMAIL T H, and ABU-AL-NADI D I. Analytical array polynomial method for linear antenna arrays with phase-only control[J]. AEU-International Journal of Electronics and Communications, 2007, 61(7): 485-492. doi: 10.1016/j.aeue.2006.06.009.
[12]
SMITH S T. Optimum phase-only adaptive nulling[J]. IEEE Transactions on Signal Processing, 1999, 47(7): 1835-1843. doi: 10.1109/78.771033.
[13]
CHOI W S and SARKAR T K. Phase-only adaptive processing based on a direct data domain least squares approach using the conjugate gradient method[J]. IEEE Transactions on Antennas and Propagation, 2004, 52(12): 3265-3272. doi: 10.1109/TAP.2004.836410.
[14]
STEYAKAL H. Simple method for pattern nulling by phase perturbation[J]. IEEE Transactions on Antennas and Propagation, 1983, 31(1): 163-166. doi: 10.1109/TAP.1983. 1142994.
[15]
BAIRD C A and RASSWEILER G G. Adaptive sidelobe nulling using digital controlled phase-shifters[J]. IEEE Transactions on Antennas and Propagation, 1976, 24(5): 638-649. doi: 10.1109/TAP.1976.1141415.
[16]
SHORE R A. Nulling at symmetric pattern location with phase only weight control[J]. IEEE Transactions on Antennas and Propagation, 1984, 32(5): 530-533. doi: 10.1109/TAP. 1984.1143360.
[17]
GIUSTO R and VINCENT P D. Phase-only optimization for the generation of wide deterministic nulls in the radiation pattern of phased arrays[J]. IEEE Transactions on Antennas and Propagation, 1983, 31(5): 814-817. doi: 10.1109/TAP. 1983.1143137.
WU Meng, LIU Hongwei, and WANG Xu. A cyclic iterative method for MIMO radar transmit beampattern design[J]. Journal of Electronics & Information Technology, 2015, 37(2): 322-327. doi: 10.11999/JEIT141043.
[19]
HUNTER D R and LANGE K. A tutorial on MM algorithms [J]. The American Statistician, 2004, 58(1): 30-37. doi: 10.1198/0003130042836.
FENG Can, XIAO Liang, and WEI Zhihui. ISAR compressive imaging based on majorization-minimization of total variation[J]. Journal of Terahertz Science and Electronic Information Technology, 2013, 11(5): 775-781. doi: 10.11805/ TKYDA201305.0775.