Approach to Beamforming Minimizing the Signal Power Estimation Error

We study the properties of beamformers, particularly Capon and MMSE beamformers, in their ability to obtain the true signal power of the signal of interest (SOI). A curious feature of these beamformers is their tendency to either overestimate or underestimate the signal power. Consequently, they are not asymptotically unbiased (as the sample size approaches to 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 <tex>${ }^{+}$</tex> beamformer, is evaluated against the Capon and MMSE beamformers in terms of bias, signal power MSE, and signal waveform MSE. The Capon <tex>${ }^{+}$</tex>beamformer demonstrates a superior balance in both signal power and waveform estimation while exhibiting minimal bias, which approaches zero as the sample size increases.