×

Robust adaptive phase-only beamforming algorithm for interference suppression. (English) Zbl 1330.93096

Summary: The adaptive phase-only beamforming technique is very important for suppressing interferences in phased array radar. However, similar to the conventional beamforming technique, which features variable magnitudes and phases, the performance of phase-only beamforming is severely degraded by steering direction and array geometry errors. No studies on this problem are available. In this paper, the problem of adequate robustness for adaptive phase-only beamformers is investigated, and a robust phase-only beamforming algorithm based on semidefinite relaxation is proposed. This algorithm can suppress interferences by minimizing the array output power and maintain the desired signal without distortion. Robust adaptive phase-only weighting is first converted into a non-convex quadratic optimization problem and then into a convex optimization problem by the semidefinite relaxation technique, which can be solved easily. Experimental results demonstrate that the new robust adaptive phase-only beamforming algorithm can significantly reduce performance degradation caused by various array errors.

MSC:

93B40 Computational methods in systems theory (MSC2010)
93B35 Sensitivity (robustness)
93C40 Adaptive control/observation systems
93C20 Control/observation systems governed by partial differential equations
93C25 Control/observation systems in abstract spaces

Software:

CVX
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Leavitt, A phase adaptation algorithm, IEEE Transactions on Antennas and Propagation 24 (5) pp 754– (1976) · Zbl 0352.16001 · doi:10.1109/TAP.1976.1141404
[2] Shore, The use of nonlinear programming techniques for phase-only null synthesis, IEEE Antennas and Propagation Society International Symposium 21 pp 207– (1983)
[3] Shore, A proof of the odd-symmetry of the phases for minimum weight perturbation phase-only null synthesis, IEEE Transactions on Antennas and Propagation 32 (5) pp 528– (1984) · doi:10.1109/TAP.1984.1143351
[4] Steyskal, Simple method for pattern nulling by phase perturbation, IEEE Transactions on Antennas and Propagation 31 (1) pp 163– (1983) · doi:10.1109/TAP.1983.1142994
[5] Baird, Adaptive sidelobe nulling using digital controlled phase-shifters, IEEE Transactions on Antennas and Propagation 24 (5) pp 638– (1976) · doi:10.1109/TAP.1976.1141415
[6] Shore, Nulling at symmetric pattern location with phase-only weight control, IEEE Transactions on Antennas and Propagation 32 (5) pp 530– (1984) · doi:10.1109/TAP.1984.1143360
[7] Giusto, Phase-only optimization for the generation of wide deterministic nulls in the radiation pattern of phased arrays, IEEE Transactions on Antennas and Propagation 31 (5) pp 814– (1983) · doi:10.1109/TAP.1983.1143137
[8] Khzmalyan, Fast iterative methods for phase-only synthesis of antenna array pattern nulls, Electronic Letter 31 (8) pp 601– (1995) · doi:10.1049/el:19950432
[9] Hirasawa, The application of a biquadratic programming method to phase-only optimization of antenna arrays, IEEE Transactions on Antennas and Propagation 36 (11) pp 1545– (1988) · doi:10.1109/8.9703
[10] Haupt, Phase-only adaptive nulling with a genetic algorithm, IEEE Transactions on Antennas and Propagation 45 (6) pp 1009– (1997) · doi:10.1109/8.585749
[11] Guney, Interference suppression of linear antenna arrays by phase-only control using a clonal selection algorithm, Journal of the Franklin Institute 345 (3) pp 254– (2008) · Zbl 1167.93311 · doi:10.1016/j.jfranklin.2007.09.002
[12] Guney, Bees algorithm for interference suppression of linear antenna arrays by controlling the phase-only and both the amplitude and phase, Expert systems with Applications 37 (4) pp 3129– (2010) · doi:10.1016/j.eswa.2009.09.072
[13] Guney, Optimal synthesis of linear antenna arrays using a harmony search algorithm, Expert Systems with Applications 38 (12) pp 15455– (2011) · doi:10.1016/j.eswa.2011.06.015
[14] Davis, Phase-only LMS and perturbation adaptive algorithms, IEEE Transactions on Antennas and Propagation 34 (1) pp 169– (1998)
[15] Khzmalyan, The phase-only shaping and adaptive nulling of an amplitude pattern, IEEE Transactions on Antennas and Propagation 51 (2) pp 264– (2003) · doi:10.1109/TAP.2003.809060
[16] Thompson, Adaptation by direct phase-shift adjustment in narrow-band adaptive antenna systems, IEEE Transactions on Antennas and Propagation 24 (5) pp 756– (1976) · doi:10.1109/TAP.1976.1141405
[17] Smith, Optimum phase-only adaptive nulling, IEEE Transactions on Signal Processing 47 (7) pp 1835– (1999) · doi:10.1109/78.771033
[18] Choi, Phase-only adaptive processing based on a direct data domain least squares approach using the conjugate gradient method, IEEE Transactions on Antennas and Propagation 52 (12) pp 3265– (2004) · doi:10.1109/TAP.2004.836410
[19] Mismar, Analytical array polynomial method for linear antenna arrays with phase-only control, AEU-International Journal of Electronics and Communications 61 (7) pp 485– (2007) · doi:10.1016/j.aeue.2006.06.009
[20] Kajenski, Phase only antenna pattern notching via a semidefinite programming relaxation, IEEE Transactions on Antennas and Propagation 60 (5) pp 2562– (2012) · Zbl 1369.78450 · doi:10.1109/TAP.2012.2189709
[21] Vural, Effects of perturbation on the performance of optimum adaptive arrays, IEEE Transactions on Aerospace and Electronic Systems 15 (1) pp 76– (1979) · doi:10.1109/TAES.1979.308798
[22] Er, Derivative constraints for broad-band element space antenna array processors, IEEE Transactions on Acoustics, Speech and Signal Processing 31 (6) pp 1378– (1983) · doi:10.1109/TASSP.1983.1164219
[23] Zhang, Robust presteering derivative constraints for broadband antenna arrays, IEEE Transactions on Signal Processing 50 (1) pp 1– (2002) · doi:10.1109/78.972477
[24] Guerci, Theory and applications of covariance matrix tapers for robust adaptive beamforming, IEEE Transactions on Signal Processing 47 (4) pp 977– (1999) · doi:10.1109/78.752596
[25] Gu, Robust beamforming based on variable loading, Electronics Letters 41 (2) pp 55– (2005) · doi:10.1049/el:20057279
[26] Tian, A recursive least squares implementation for LCMP beamforming under quadratic constraint, IEEE Transactions on Signal Processing 49 (6) pp 1138– (2001) · doi:10.1109/78.923296
[27] Li, Doubly constrained robust Capon beamformer, IEEE Transactions on Signal Processing 52 (9) pp 2407– (2004) · doi:10.1109/TSP.2004.831998
[28] Liu, Robust Capon beamformer under norm constraint, Signal Processing 90 (5) pp 1573– (2010) · Zbl 1194.94110 · doi:10.1016/j.sigpro.2009.10.027
[29] Robust adaptive beamforming (2006) · Zbl 1172.94421
[30] Vorobyov, Robust adaptive beamforming using worst-case performance optimization: a solution to the signal mismatch problem, IEEE Transactions on Signal Processing 51 (2) pp 313– (2003) · doi:10.1109/TSP.2002.806865
[31] Shahbazpanahi, Robust adaptive beamforming for general-rank signal models, IEEE Transactions on Signal Processing 51 (9) pp 2257– (2003) · doi:10.1109/TSP.2003.815395
[32] Hassanien, Robust adaptive beamforming using sequential quadratic programming: an iterative solution to the mismatch problem, IEEE Signal Processing Letters 15 pp 733– (2008) · doi:10.1109/LSP.2008.2001115
[33] Luo, Semidefinite relaxation of quadratic optimization problems, IEEE Signal Processing Magazine 27 (3) pp 20– (2010) · doi:10.1109/MSP.2010.936019
[34] Grant M Boyd S CVX users’guide for CVX version 1.21 2010
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.