Performance Analysis of the Matrix Pair Beamformer with Matrix Mismatch

TL;DR

This paper analyzes the performance of the matrix pair beamformer under matrix mismatch conditions, revealing a threshold effect and conditions leading to unbounded interference, supported by theoretical analysis and simulations.

Contribution

It introduces a general framework for MPB with matrix mismatch, derives normalized output SINR, and explains the threshold effect caused by steering vector competition.

Findings

Matrix mismatch causes a threshold effect in MPB performance.

Infinite generalized eigenvalues lead to unbounded threshold increase.

Simulations verify the theoretical analysis.

Abstract

Matrix pair beamformer (MPB) is a blind beamformer. It exploits the temporal structure of the signal of interest (SOI) and applies generalized eigen-decomposition to a covariance matrix pair. Unlike other blind algorithms, it only uses the second order statistics. A key assumption in the previous work is that the two matrices have the same interference statistics. However, this assumption may be invalid in the presence of multipath propagations or certain "smart" jammers, and we call it as matrix mismatch. This paper analyzes the performance of MPB with matrix mismatch. First, we propose a general framework that covers the existing schemes. Then, we derive its normalized output SINR. It reveals that the matrix mismatch leads to a threshold effect caused by "steering vector competition". Second, using matrix perturbation theory, we find that, if there are generalized eigenvalues that are infinite, the threshold will increase unboundedly with the interference power. This is highly probable when there are multiple periodical interferers. Finally, we present simulation results to verify our analysis.