Diversity-Multiplexing Tradeoff in the Low-SNR Regime

TL;DR

This paper extends the diversity-multiplexing tradeoff framework to low-SNR regimes, revealing that diversity gain becomes redundant and providing explicit outage probability formulas for various channels.

Contribution

It introduces a low-SNR adaptation of the DMT framework, showing the SNR-independence of outage probability and deriving explicit formulas for broad channel classes.

Findings

Outage probability is SNR-independent in the low-SNR regime.

Explicit closed-form outage probability formulas are derived.

The SNR-asymptotic DMT has limitations at small multiplexing gains.

Abstract

An extension of the popular diversity-multiplexing tradeoff framework to the low-SNR (or wideband) regime is proposed. The concept of diversity gain is shown to be redundant in this regime since the outage probability is SNR-independent and depends on the multiplexing gain and the channel power gain statistics only. The outage probability under the DMT framework is obtained in an explicit, closed form for a broad class of channels. The low and high-SNR regime boundaries are explicitly determined for the scalar Rayleigh-fading channel, indicating a significant limitation of the SNR-asymptotic DMT when the multiplexing gain is small.