Robust beamforming for coherent signals based on the spatial-smoothing technique

Spatial-smoothing provides an elegant solution for both beamforming and direction of arrival (DOA) estimation in a coherent signal environment. However, this technique is based on special array structures such as uniform linear arrays (ULAs) and its performance will degrade when the special structure is destroyed by all kinds of array errors in practice. In this paper, the robust beamforming problem for coherent signals is addressed and a forward-only (FO) beamformer is proposed first based on worst-case optimization by considering both the steering vector and the correlation matrix errors. By treating the steering vector error differently, two solutions are derived, which are then extended to the forward–backward (FB) case with improved performance. By introducing a preprocessing matrix, real-valued closed-form solutions are then presented with the same performance as in the FB case, but with much lower computational complexity.