Robust Block Sparse Beamforming for Strictly Non-Circular Signals and Unknown Array Mutual Coupling

Widely linear beamformers (WLBs) can greatly outperform the traditional adaptive beamformers. However, the performance of WLBs is extremely susceptible to the unknown mutual coupling (MC) effects caused by the imperfectly calibrated antennas array. In this brief, we propose a block sparse representation scheme and design a robust WLB for strictly non-circular (SNC) signals to mitigate the unknown MC mismatch. We use the structural characteristics of the steering vector under MC, and derive a new augmented formulation for the observed signals which takes into account the MC mismatches. We solve a block sparse optimization problem in order to estimate the directions of illuminating signals allowing us to reconstruct the augmented interference-plus-noise covariance matrix (AINCM). We then propose to estimate the augmented desired signal steering vector using the augmented subspace projection method. Our proposed robust WLB not only avoids estimating the MC coefficients, but also prevents the signal cancellation phenomenon from reconstructing the AINCM. Our simulation results demonstrate that the proposed WLB is effective for the SNC signals, outperforms the existing methods, and is robust against unknown MC and look direction mismatches.