Robust Recursive Algorithm under Uncertainties via Worst-Case SINR Maximization

The performance of traditional constrained-LMS (CLMS) algorithm is known to degrade seriously in the presence of small training data size and mismatches between the assumed array response and the true array response. In this paper, we develop a robust constrained-LMS (RCLMS) algorithm based on worst-case SINR maximization. Our algorithm belongs to the class of diagonal loading techniques, in which the diagonal loading factor is obtained in a simple form and it decreases the computation cost. The updated weight vector is derived by the descent gradient method and Lagrange multiplier method. It demonstrates that our proposed recursive algorithm provides excellent robustness against signal steering vector mismatches and the small training data size and, has fast convergence rate, and makes the mean output array signal-to-interference-plus-noise ratio (SINR) consistently close to the optimal one. Some simulation results are presented to compare the performance of our robust algorithm with the traditional CLMS algorithm.

Doubly Constrained Robust Blind Beamforming Algorithm

We propose doubly constrained robust least-squares constant modulus algorithm (LSCMA) to solve the problem of signal steering vector mismatches via the Bayesian method and worst-case performance optimization, which is based on the mismatches between the actual and presumed steering vectors. The weight vector is iteratively updated with penalty for the worst-case signal steering vector by the partial Taylor-series expansion and Lagrange multiplier method, in which the Lagrange multipliers can be optimally derived and incorporated at each step. A theoretical analysis for our proposed algorithm in terms of complexity cost, convergence performance, and SINR performance is presented in this paper. In contrast to the linearly constrained LSCMA, the proposed algorithm provides better robustness against the signal steering vector mismatches, yields higher signal captive performance, improves greater array output SINR, and has a lower computational cost. The simulation results confirm the superiority of the proposed algorithm on beampattern control and output SINR enhancement.

Efficient Robust Blind Beamforming Algorithm

Because blind adaptive beamforming algorithms do not depend on any reference signal, they have found numerous important applications in signal processing. However, the conventional constrained constant modulus algorithm (CMA) may suffer significant performance degradation in the presence of the slight mismatches between the actual and assumed signal steering vectors. In this paper, to combat the mismatches, a novel robust constrained CMA is proposed for implementing double constraints with recursive method updating, which is based on explicit modeling of uncertainties in the desired signal array response. The proposed robust constrained CMA provides an improved robustness against the signal steering vector mismatches, enhances the array system performance under random perturbations in sensor parameters and makes the mean output array SINR consistently close to the optimal one. The performance of the proposed algorithm is compared with that of linear constrained CMA algorithm by computer simulations, the results of which demonstrate a marked improvement in the robustness against signal steering vector mismatches.