Mismatched Estimation in Large Linear Systems

TL;DR

This paper analyzes the excess mean square error in large linear systems when the posterior mean estimator uses a mismatched prior, deriving relationships and approximations validated by numerical examples.

Contribution

It provides a novel analysis linking EMSE in large systems to scalar channels and offers closed-form approximations validated by numerical results.

Findings

Derived relationship between EMSE in large systems and scalar channels

Provided accurate closed-form approximations for EMSE

Validated approximations with numerical examples

Abstract

We study the excess mean square error (EMSE) above the minimum mean square error (MMSE) in large linear systems where the posterior mean estimator (PME) is evaluated with a postulated prior that differs from the true prior of the input signal. We focus on large linear systems where the measurements are acquired via an independent and identically distributed random matrix, and are corrupted by additive white Gaussian noise (AWGN). The relationship between the EMSE in large linear systems and EMSE in scalar channels is derived, and closed form approximations are provided. Our analysis is based on the decoupling principle, which links scalar channels to large linear system analyses. Numerical examples demonstrate that our closed form approximations are accurate.