Robust adaptive beamforming based on sparse representation technique

The problem of robust adaptive beamforming is addressed within the sparse representation framework. The basic idea of the proposed method is to calculate the adaptive beamformer (BF) with the combination of some easily obtained basic BFs, i.e. the conventional data-independent BFs and the loaded sample matrix inversion BFs. Through using the prior information of the spatial angular sector in which the signal of interest is located, a set of basic BFs pointed at this angular sector are calculated firstly. Then based on the observation that an adaptive BF with favourable performance can be obtained by the combination of only several basic BFs, a new sparse representation-based optimisation model is proposed to search for the adaptive BF. However, the initial optimisation model involves a non-convex constraint which makes the problem intractable. The authors show that the non-convex constraint can be relaxed properly and replaced with a convex one, and the resulting problem can be solved effectively with the interior point method. The obtained BF is robust against model mismatch caused by look direction error, imperfect array calibration etc. The effectiveness and robustness of the proposed method are demonstrated through extensive numerical experiments.