Channel Capacity Estimation using Free Probability Theory

TL;DR

This paper introduces free probability theory to estimate the capacity of MIMO channels accurately, even with limited measurements and in the presence of phase and frequency impairments, providing new unbiased estimators.

Contribution

It presents the first asymptotically unbiased capacity estimators for MIMO channels using free probability and Gaussian matrix mean methods, effective with phase offset and frequency drift.

Findings

The estimators are asymptotically unbiased as the number of transmit antennas increases.

Both estimators perform well with limited samples and antennas.

Simulations confirm the estimators' effectiveness in practical scenarios.

Abstract

In many channel measurement applications, one needs to estimate some characteristics of the channels based on a limited set of measurements. This is mainly due to the highly time varying characteristics of the channel. In this contribution, it will be shown how free probability can be used for channel capacity estimation in MIMO systems. Free probability has already been applied in various application fields such as digital communications, nuclear physics and mathematical finance, and has been shown to be an invaluable tool for describing the asymptotic behaviour of many large-dimensional systems. In particular, using the concept of free deconvolution, we provide an asymptotically (w.r.t. the number of observations) unbiased capacity estimator for MIMO channels impaired with noise called the free probability based estimator. Another estimator, called the Gaussian matrix mean based estimator, is also introduced by slightly modifying the free probability based estimator. This estimator is shown to give unbiased estimation of the moments of the channel matrix for any number of observations. Also, the estimator has this property when we extend to MIMO channels with phase off-set and frequency drift, for which no estimator has been provided so far in the literature. It is also shown that both the free probability based and the Gaussian matrix mean based estimator are asymptotically unbiased capacity estimators as the number of transmit antennas go to infinity, regardless of whether phase off-set and frequency drift are present. The limitations in the two estimators are also explained. Simulations are run to assess the performance of the estimators for a low number of antennas and samples to confirm the usefulness of the asymptotic results.