Signal-to-interference plus noise ratio loss constrained robust adaptive beamformer inpsired by random matrix theory

The optimal adaptive beamformer (ABF) maximizing output signal-to-interference plus noise ratio (SINR) has filter weights that depend on the data covariance and signal array response vector. The effectiveness of practical application of this optimal beamformer, however, is limited by (i) data stationarity (needed for covariance estimation), and (ii) knowledge of the true signal array response vector. Robust ABF attempts to address these two critical issues via a slight reformulation of the ABF problem, and often result in some form of diagonal loading yielding a hybrid beamformer that engages the tradespace between conventional beamforming (CBF) and ABF. The joint distribution of a CBF power spectral estimate and an ABF estimate based on the same data covariance reveals that estimates have a statistical coupling governed by the geometric cosine between their filter weights, i.e., the SINR loss between CBF and ABF. Thus, a robust ABF algorithm is proposed that constrains the SINR loss to an acceptable level while minimizing beamformer sensitivity to signal array response errors. This is practically appealing since this allows the user to specify the minimum SINR loss tolerable, and the resulting robust ABF solution uses the available degrees of freedom to reduce sensitivity to signal array response errors.