Analytical Derivation of the Inverse Moments of One-sided Correlated Gram Matrices with Applications

TL;DR

This paper derives analytical formulas for the inverse moments of one-sided correlated Gram matrices, aiding in the approximation of performance metrics in signal processing and wireless communications.

Contribution

It provides the first closed-form expressions for inverse moments of such matrices, enabling improved performance analysis in related applications.

Findings

Closed-form expressions for inverse moments derived

Approximate performance metrics like estimation error shown to be feasible

Results applicable to signal processing and wireless communication scenarios

Abstract

This paper addresses the development of analytical tools for the computation of the moments of random Gram matrices with one side correlation. Such a question is mainly driven by applications in signal processing and wireless communications wherein such matrices naturally arise. In particular, we derive closed-form expressions for the inverse moments and show that the obtained results can help approximate several performance metrics such as the average estimation error corresponding to the Best Linear Unbiased Estimator (BLUE) and the Linear Minimum Mean Square Error LMMSE or also other loss functions used to measure the accuracy of covariance matrix estimates.