Robust Least Squares Constant Modulus Algorithm to Signal Steering Vector Mismatches

The linearly constrained least squares constant modulus algorithm (LSCMA) may suffer significant performance degradation and lack robustness in the presence of the slight mismatches between the actual and assumed signal steering vectors, which can cause the serious problem of desired signal cancellation. To account for the mismatches, we propose a doubly constrained robust LSCMA based on explicit modeling of uncertainty in the desired signal array response and data covariance matrix, which provides robustness against pointing errors and random perturbations in detector parameters. Our algorithm optimizes the worst-case performance by minimizing the output SINR while maintaining a distortionless response for the worst-case signal steering vector. The weight vector can be optimized by the partial Taylor-series expansion and Lagrange multiplier method, and the optimal value of the Lagrange multiplier is iteratively derived based on the known level of uncertainty in the signal DOA. The proposed implementation based on iterative minimization eliminates the covariance matrix inversion estimation at a comparable cost with that of the existing LSCMA. We present a theoretical analysis of our proposed algorithm in terms of convergence, SINR performance, array beampattern gain, and complexity cost in the presence of random steering vector mismatches. In contrast to the linearly constrained LSCMA, the proposed algorithm provides excellent robustness against the signal steering vector mismatches, yields improved signal capture performance, has superior performance on SINR improvement, and enhances the array system performance under random perturbations in sensor parameters. The on-line implementation and significant SINR enhancement support the practicability of the proposed algorithm. The numerical experiments have been carried out to demonstrate the superiority of the proposed algorithm on beampattern control and output SINR enhancement compared with linearly constrained LSCMA.