Minimum Dispersion Beamforming for Non-Gaussian Signals

Most of the existing beamforming methods are based on the Minimum Variance (MV) criterion. The MV approach is statistically optimal only when the signal, interferences and the noise are Gaussian-distributed. However, non-Gaussian signals arise in a variety of practical applications. In this paper, Minimum Dispersion Distortionless Response (MDDR) beamforming, which minimizes the $\ell_p$-norm of the output while constraining the desired signal response to be unity, is devised for non-Gaussian signals. It is shown that the MDDR beamformer, which implicitly exploits non-Gaussianity, can improve the performance significantly if $p > 2$ for sub-Gaussian signals or $p < 2$ for super-Gaussian signals. Three efficient algorithms, the Iteratively Reweighted Minimum Variance Distortionless Response (IR-MVDR), complex-valued full Newton's and partial Newton's methods, are developed to solve the resulting $\ell_p$-norm minimization with a linear constraint. Furthermore, the MDDR beamformer with a single constraint is generalized to the Linearly Constrained Minimum Dispersion (LCMD) beamformer with multiple linear constraints, which exhibits robustness against steering vector mismatch. The LCMD beamformer yields significant performance improvement over the conventional Linearly Constrained Minimum Variance (LCMV) beamformer. Simulation results are provided to demonstrate the superior performance of the proposed minimum dispersion beamforming approaches.