On the Capacity of Block Multiantenna Channels

TL;DR

This paper establishes a generalized capacity theorem for block multiantenna channels with symmetries, enabling efficient asymptotic capacity computation without requiring Gaussian or independent entries.

Contribution

It extends Telatar's theorem to broader channel models and introduces free probability methods for asymptotic capacity analysis.

Findings

Capacity theorem reduces optimization complexity

Asymptotic capacity independent of matrix dimension

Efficient numerical approximation of capacity and optimal inputs

Abstract

In this paper we consider point-to-point multiantenna channels with certain block distributional symmetries which do not require the entries of the channel matrix to be either Gaussian, or independent, or identically distributed. A main contribution is a capacity theorem for these channels, which might be regarded as a generalization of Telatar's theorem (1999), which reduces the numerical optimization domain in the capacity computation. With this information theoretic result and some free probability arguments, we prove an asymptotic capacity theorem that, in addition to reducing the optimization domain, does not depend on the dimension of the channel matrix. This theorem allows us to apply free probability techniques to numerically compute the asymptotic capacity of the channels under consideration. These theorems provide a very efficient method for numerically approximating both the capacity and a capacity achieving input covariance matrix of certain channels.