Random Matrix Theory Model for Mean Notch Depth of the Diagonally Loaded MVDR Beamformer for a Single Interferer Case

TL;DR

This paper develops a random matrix theory-based model to predict the mean notch depth of a diagonally loaded MVDR beamformer in single interferer scenarios, aiding in understanding and optimizing interference suppression.

Contribution

It introduces a novel analytical model for the mean notch depth of diagonally loaded MVDR beamformers using random matrix theory, validated by simulations.

Findings

Model accurately predicts mean notch depth across various conditions

Close agreement between theoretical predictions and simulations

Provides insights into the impact of system parameters on notch depth

Abstract

Adaptive beamformers (ABFs) suppress interferers by placing a notch in the beampattern at the interferer direction. This suppres- sion improves detection of a weaker signals in the presence of strong interferers. Hence the notch depth plays a crucial role in determining the adaptive gain obtained from using ABF over conventional beam- forming. This research derives models for the mean notch depth of a diagonally loaded MVDR ABF for a single interferer case. The model describes the mean notch depth as a function of number of snapshots, the number of sensors in the array, the interferer to noise ratio (INR) level, the interferer direction and the diagonal loading level. The derivation uses random matrix theory results on the be- havior of the eigenvectors of sample covariance matrix. The notch depth predicted by the model is shown to be in close agreement with simulation results over a range of INRs and snapshots.