From Multi-Keyholes to Measure of Correlation and Power Imbalance in MIMO Channels: Outage Capacity Analysis

TL;DR

This paper analyzes multi-keyhole MIMO channels, deriving asymptotic outage capacity results, introducing a simple correlation measure, and proving Telatar's conjecture, with implications for relay channels.

Contribution

It provides asymptotic analysis of multi-keyhole MIMO channels, introduces a new scalar measure of correlation and power imbalance, and proves Telatar's conjecture for certain channels.

Findings

Outage capacities are asymptotically equal to Rayleigh channels in large systems.

Instantaneous capacity is asymptotically Gaussian with closed-form mean and variance.

A simple measure of correlation and power imbalance effectively quantifies their impact.

Abstract

An information-theoretic analysis of a multi-keyhole channel, which includes a number of statistically independent keyholes with possibly different correlation matrices, is given. When the number of keyholes or/and the number of Tx/Rx antennas is large, there is an equivalent Rayleigh-fading channel such that the outage capacities of both channels are asymptotically equal. In the case of a large number of antennas and for a broad class of fading distributions, the instantaneous capacity is shown to be asymptotically Gaussian in distribution, and compact, closed-form expressions for the mean and variance are given. Motivated by the asymptotic analysis, a simple, full-ordering scalar measure of spatial correlation and power imbalance in MIMO channels is introduced, which quantifies the negative impact of these two factors on the outage capacity in a simple and well-tractable way. It does not require the eigenvalue decomposition, and has the full-ordering property. The size-asymptotic results are used to prove Telatar's conjecture for semi-correlated multi-keyhole and Rayleigh channels. Since the keyhole channel model approximates well the relay channel in the amplify-and-forward mode in certain scenarios, these results also apply to the latter