A Full Second-Order Analysis of the Widely Linear MVDR Beamformer for Noncircular Signals

TL;DR

This paper provides a comprehensive second-order statistical analysis of the widely linear MVDR beamformer for noncircular signals, revealing detailed insights into its performance advantages over traditional methods.

Contribution

It introduces a full second-order performance analysis framework for the WL MVDR beamformer, explicitly accounting for complementary second-order statistics and separating SINR gains along I and Q channels.

Findings

The WL MVDR outperforms the Capon beamformer for noncircular signals.

Performance gains are more significant with higher noncircularity of interferences.

The analysis offers detailed distribution of SINR gains in I and Q channels.

Abstract

A full performance analysis of the widely linear (WL) minimum variance distortionless response (MVDR) beamformer is introduced. While the WL MVDR is known to outperform its strictly linear counterpart, the Capon beamformer, for noncircular complex signals, the existing approaches provide limited physical insights, since they explicitly or implicitly omit the complementary second-order (SO) statistics of the output interferences and noise (IN). To this end, we exploit the full SO statistics of the output IN to introduce a full SO performance analysis framework for the WL MVDR beamformer. This makes it possible to separate the overall signal-to-interference plus noise ratio (SINR) gain of the WL MVDR beamformer w.r.t. the Capon one into the individual contributions along the in-phase (I) and quadrature (Q) channels. Next, by considering the reception of the unknown signal of interest (SOI) corrupted by an arbitrary number of orthogonal noncircular interferences, we further unveil the distribution of SINR gains in both the I and Q channels, and show that in almost all the spatial cases, these performance advantages are more pronounced when the SO noncircularity rate of the interferences increases. Illustrative numerical simulations are provided to support the theoretical results.