Beamforming design for minimizing the signal power estimation error

TL;DR

This paper introduces the Capon$^+$ beamformer, which improves signal power estimation accuracy by minimizing mean squared error through a scaling approach, outperforming traditional Capon and MMSE beamformers.

Contribution

The paper proposes a novel scaled version of the Capon beamformer that reduces bias and improves power estimation accuracy in array signal processing.

Findings

Capon$^+$ beamformer reduces bias compared to traditional methods.

It achieves lower mean squared error in signal power estimation.

The bias approaches zero as sample size increases.

Abstract

We study the properties of beamformers in their ability to either maintain or estimate the true signal power of the signal of interest (SOI). Our focus is particularly on the Capon beamformer and the minimum mean squared error (MMSE) beamformer. The Capon beamformer, also known as the minimum power distortionless response (MPDR) or the minimum variance distortionless response (MVDR) beamformer, is a widely used method in array signal processing. A curious feature of both the Capon and the MMSE beamformers is their tendency to either overestimate or underestimate the signal power. That is, they are not asymptotically unbiased (as the sample size approaches infinity). To address this issue, we propose to shrink the Capon beamformer by finding a scaling factor that minimizes the mean squared error (MSE) of the signal power estimate. The new beamformer, referred to as the Capon$^+$ beamformer, is evaluated against the Capon and MMSE beamformers in terms of bias, signal power MSE, and signal waveform MSE. The Capon$^+$ beamformer strikes a better balance between signal power and waveform estimation while also exhibiting minimal bias, which approaches zero as the sample size increases.