Diversity-Multiplexing Tradeoff in Selective-Fading MIMO Channels

TL;DR

This paper determines the optimal diversity-multiplexing tradeoff for various selective-fading MIMO channels and provides a code design criterion ensuring DM-tradeoff optimality, using the Jensen channel analysis.

Contribution

It establishes the optimal DM-tradeoff for selective-fading MIMO channels and introduces a code design criterion based on the Jensen channel analysis.

Findings

Optimal DM-tradeoff characterized for time, frequency, and time-frequency selective-fading MIMO channels.

Classical rank criterion for space-time code design is sufficient for DM-tradeoff optimality.

Jensen channel analysis simplifies the complex mutual information problem.

Abstract

We establish the optimal diversity-multiplexing (DM) tradeoff of coherent time, frequency and time-frequency selective-fading MIMO channels and provide a code design criterion for DM-tradeoff optimality. Our results are based on the analysis of the "Jensen channel" associated to a given selective-fading MIMO channel. While the original problem seems analytically intractable due to the mutual information being a sum of correlated random variables, the Jensen channel is equivalent to the original channel in the sense of the DM-tradeoff and lends itself nicely to analytical treatment. Finally, as a consequence of our results, we find that the classical rank criterion for space-time code design (in selective-fading MIMO channels) ensures optimality in the sense of the DM-tradeoff.