Robust Adaptive Beamforming in Partly Calibrated Sparse Sensor Arrays

Two new approaches to adaptive beamforming in sparse subarray-based partly calibrated sensor arrays are developed. Each subarray is assumed to be well calibrated, so that the steering vectors of all subarrays are exactly known. However, the intersubarray gain and/or phase mismatches are known imperfectly or remain completely unknown. Our first approach is based on a worst-case beamformer design which, in contrast to the existing worst-case designs, exploits a specific structured ellipsoidal uncertainty model for the signal steering vector rather than the commonly used unstructured uncertainty models. Our second approach is based on estimating the unknown intersubarray parameters by maximizing the output power of the minimum variance beamformer subject to a proper constraint that helps to avoid trivial solution of the resulting optimization problem. Different modifications of the second approach are developed for the cases of gain-and-phase and phase-only intersubarray distortions.