The Impact of Delay on the Diversity, Multiplexing, and ARQ Tradeoff

A substantial amount of research has focused on analyzing and achieving the diversity-multiplexing tradeoff in multiple antenna (MIMO) wireless communications. Recently, ARQ protocols have been added to these formulations and shown to perform as a type of diversity. Our goal in this paper is to find the optimal operating point in the diversity-multiplexing-ARQ tradeoff, with a particular focus on delay sensitive systems. Previous results in this area construct performance measures through the use of high SNR asymptotic approximations. While effective, these approximations tend to trivialize the delay performance of MIMO systems. We present a dynamic programming formulation for finding the optimal diversity gain, multiplexing gain, and ARQ window size, without relying on a high SNR approximation. Our results show that the a delay sensitive system requires one to adapt diversity and multiplexing to the time-requires workload in the system. We provide numerical examples that demonstrate the significant performance gains that can be achieved by choosing an adaptive policy over a static allocation of diversity and multiplexing.