OPARC: Optimal and Precise Array Response Control Algorithm—Part II: Multi-Points and Applications

In this paper, the optimal and precise array response control (OPARC) algorithm proposed in Part I of this two paper series is extended from single point to multi-points. Two computationally attractive parameter determination approaches are provided to maximize the array gain under certain constraints. In addition, the applications of the multi-point OPARC algorithm to array signal processing are studied. It is applied to realize array pattern synthesis (including the general array case and the large array case), multi-constraint adaptive beamforming, and quiescent pattern control, where an innovative concept of normalized covariance matrix loading is proposed. Finally, simulation results are presented to validate the effectiveness and good performance of the multi-point OPARC algorithm.

[1]  R. T. Compton,et al.  A numerical pattern synthesis algorithm for arrays , 1990 .

[2]  P. P. Vaidyanathan,et al.  Quadratically Constrained Beamforming Robust Against Direction-of-Arrival Mismatch , 2007, IEEE Transactions on Signal Processing.

[3]  Fan Wang,et al.  Optimal array pattern synthesis using semidefinite programming , 2001, 2001 IEEE International Conference on Acoustics, Speech, and Signal Processing. Proceedings (Cat. No.01CH37221).

[4]  Zishu He,et al.  Pattern Synthesis for Arbitrary Arrays via Weight Vector Orthogonal Decomposition , 2018, IEEE Transactions on Signal Processing.

[5]  Zhi-Quan Luo,et al.  A Unified Algorithmic Framework for Block-Structured Optimization Involving Big Data: With applications in machine learning and signal processing , 2015, IEEE Signal Processing Magazine.

[6]  Xiang-Gen Xia,et al.  OPARC: Optimal and Precise Array Response Control Algorithm—Part I: Fundamentals , 2019, IEEE Transactions on Signal Processing.

[7]  L. J. Griffiths,et al.  A unified approach to the design of linear constraints in minimum variance adaptive beamformers , 1992 .

[8]  O. L. Frost,et al.  An algorithm for linearly constrained adaptive array processing , 1972 .

[9]  Gene H. Golub,et al.  Matrix computations , 1983 .

[10]  Guisheng Liao,et al.  An Eigenstructure Method for Estimating DOA and Sensor Gain-Phase Errors , 2011, IEEE Transactions on Signal Processing.

[11]  Kesong Chen,et al.  Synthesis of Sparse Planar Arrays Using Modified Real Genetic Algorithm , 2007, IEEE Transactions on Antennas and Propagation.

[12]  Lloyd J. Griffiths,et al.  Quiescent pattern control in linearly constrained adaptive arrays , 1987, IEEE Trans. Acoust. Speech Signal Process..

[13]  D.H. Werner,et al.  Particle swarm optimization versus genetic algorithms for phased array synthesis , 2004, IEEE Transactions on Antennas and Propagation.

[14]  Vittorio Murino,et al.  Synthesis of unequally spaced arrays by simulated annealing , 1996, IEEE Trans. Signal Process..

[15]  Stephen P. Boyd,et al.  Antenna array pattern synthesis via convex optimization , 1997, IEEE Trans. Signal Process..

[16]  Jian Li,et al.  On robust Capon beamforming and diagonal loading , 2003, 2003 IEEE International Conference on Acoustics, Speech, and Signal Processing, 2003. Proceedings. (ICASSP '03)..

[17]  Fan Wang,et al.  Optimal array pattern synthesis using semidefinite programming , 2003, IEEE Trans. Signal Process..

[18]  Henry Cox,et al.  Robust adaptive beamforming , 2005, IEEE Trans. Acoust. Speech Signal Process..

[19]  B. Carlson Covariance matrix estimation errors and diagonal loading in adaptive arrays , 1988 .

[20]  Barry D. Van Veen Optimization of quiescent response in partially adaptive beamformers , 1990, IEEE Trans. Acoust. Speech Signal Process..

[21]  Paul Tseng,et al.  A coordinate gradient descent method for nonsmooth separable minimization , 2008, Math. Program..

[22]  L. J. Griffiths,et al.  A simple algorithm to achieve desired patterns for arbitrary arrays , 1992, IEEE Trans. Signal Process..

[23]  B. Fuchs Application of Convex Relaxation to Array Synthesis Problems , 2014, IEEE Transactions on Antennas and Propagation.

[24]  Lei Huang,et al.  Response Vector Constrained Robust LCMV Beamforming Based on Semidefinite Programming , 2015, IEEE Transactions on Signal Processing.

[25]  Nikos D. Sidiropoulos,et al.  Consensus-ADMM for General Quadratically Constrained Quadratic Programming , 2016, IEEE Transactions on Signal Processing.

[26]  Z. Yu,et al.  Beampattern Synthesis for Linear and Planar Arrays With Antenna Selection by Convex Optimization , 2010, IEEE Transactions on Antennas and Propagation.

[27]  Stephen P. Boyd,et al.  Distributed Optimization and Statistical Learning via the Alternating Direction Method of Multipliers , 2011, Found. Trends Mach. Learn..

[28]  Q. Liu,et al.  Fast Pencil Beam Pattern Synthesis of Large Unequally Spaced Antenna Arrays , 2013, IEEE Transactions on Antennas and Propagation.

[30]  C.L. Dolph,et al.  A Current Distribution for Broadside Arrays Which Optimizes the Relationship between Beam Width and Side-Lobe Level , 1946, Proceedings of the IRE.

[31]  Zishu He,et al.  Pattern Synthesis With Multipoint Accurate Array Response Control , 2017, IEEE Transactions on Antennas and Propagation.

[32]  M. A. Ingram,et al.  Pattern Synthesis for Arbitrary Arrays Using an Adaptive Array Method , 1999 .

[33]  Stephen P. Boyd,et al.  General Heuristics for Nonconvex Quadratically Constrained Quadratic Programming , 2017, 1703.07870.