How to Achieve the Optimal DMT of Selective Fading MIMO Channels?

TL;DR

This paper extends the non-vanishing determinant criterion to selective fading MIMO channels, proposing a new code construction that achieves the optimal diversity-multiplexing tradeoff and resolves a longstanding debate.

Contribution

It introduces a systematic method to attain the optimal DMT for selective fading channels by extending the NVD criterion and proposing a novel code construction.

Findings

Achieves the optimal DMT for selective fading MIMO channels.

Proposes a new code construction based on split NVD parallel codes.

Settles a long-standing debate on the DMT of selective fading channels.

Abstract

In this paper, we consider a particular class of selective fading channel corresponding to a channel that is selective either in time or in frequency. For this class of channel, we propose a systematic way to achieve the optimal DMT derived in Coronel and B\"olcskei, IEEE ISIT, 2007 by extending the non-vanishing determinant (NVD) criterion to the selective channel case. A new code construction based on split NVD parallel codes is then proposed to satisfy the NVD parallel criterion. This result is of significant interest not only in its own right, but also because it settles a long-standing debate in the literature related to the optimal DMT of selective fading channels.