MMSE Channel Estimation in Fading MIMO Gaussian Channels With Blockage: A Novel Lower Bound via Poincar\'e Inequality

TL;DR

This paper introduces a new lower bound for MSE in MIMO channel estimation with blockage, using Poincaré inequality, addressing limitations of traditional bounds like BCRB for complex channel distributions.

Contribution

A novel lower bound based on Poincaré inequality is proposed for MSE in fading MIMO channels with blockage, applicable to discrete and mixed distributions.

Findings

The new bound is applicable where BCRB fails.

The behavior of the bound at high SNR is characterized.

The bound provides tighter estimates for channel estimation error.

Abstract

Integrated sensing and communication is regarded as a key enabler for next-generation wireless networks. To optimize the transmitted waveform for both sensing and communication, various performance metrics must be considered. This work focuses on sensing, and specifically on the mean square error (MSE) of channel estimation. Given the complexity of deriving the MSE, the Bayesian Cramer-Rao Bound (BCRB) is commonly recognized as a lower bound on the minimum MSE. However, the BCRB is not applicable to channels with discrete or mixed distributions. To address this limitation, a new lower bound based on a Poincar\'e inequality is proposed and applied to fading MIMO AWGN channels with blockage probability, and the behavior of the lower bound at high SNR is precisely characterized.