Diversity-Multiplexing Tradeoff via Asymptotic Analysis of Large MIMO Systems

TL;DR

This paper analyzes the finite-SNR diversity-multiplexing tradeoff in large MIMO systems, showing how different definitions of multiplexing gain affect convergence to the asymptotic DMT and highlighting the impact of channel correlation.

Contribution

It derives finite-SNR DMT for various channels using recent outage capacity results and clarifies how multiplexing gain definitions influence convergence and accuracy.

Findings

Finite-SNR DMT converges at realistic SNR when using ergodic capacity-based multiplexing gain.

Slow convergence occurs with high-SNR asymptote-based multiplexing gain, especially for large systems.

Correlation and power imbalance reduce diversity gain, which is captured by size-asymptotic DMT but not by SNR-asymptotic DMT.

Abstract

Diversity-multiplexing tradeoff (DMT) presents a compact framework to compare various MIMO systems and channels in terms of the two main advantages they provide (i.e. high data rate and/or low error rate). This tradeoff was characterized asymptotically (SNR-> infinity) for i.i.d. Rayleigh fading channel by Zheng and Tse [1]. The asymptotic DMT overestimates the finite-SNR one [2]. In this paper, using the recent results on the asymptotic (in the number of antennas) outage capacity distribution, we derive and analyze the finite-SNR DMT for a broad class of channels (not necessarily Rayleigh fading). Based on this, we give the convergence conditions for the asymptotic DMT to be approached by the finite-SNR one. The multiplexing gain definition is shown to affect critically the convergence point: when the multiplexing gain is defined via the mean (ergodic) capacity, the convergence takes place at realistic SNR values. Furthermore, in this case the diversity gain can also be used to estimate the outage probability with reasonable accuracy. The multiplexing gain definition via the high-SNR asymptote of the mean capacity (as in [1]) results in very slow convergence for moderate to large systems (as 1/ln(SNR)^2) and, hence, the asymptotic DMT cannot be used at realistic SNR values. For this definition, the high-SNR threshold increases exponentially in the number of antennas and in the multiplexing gain. For correlated keyhole channel, the diversity gain is shown to decrease with correlation and power imbalance of the channel. While the SNR-asymptotic DMT of Zheng and Tse does not capture this effect, the size-asymptotic DMT does.