The MIMO ARQ Channel: Diversity–Multiplexing–Delay Tradeoff

In this paper, the fundamental performance tradeoff of the delay-limited multiple-input multiple-output (MIMO) automatic retransmission request (ARQ) channel is explored. In particular, we extend the diversity-multiplexing tradeoff investigated by Zheng and Tse in standard delay-limited MIMO channels with coherent detection to the ARQ scenario. We establish the three-dimensional tradeoff between reliability (i.e., diversity), throughput (i.e., multiplexing gain), and delay (i.e., maximum number of retransmissions). This tradeoff quantifies the ARQ diversity gain obtained by leveraging the retransmission delay to enhance the reliability for a given multiplexing gain. Interestingly, ARQ diversity appears even in long-term static channels where all the retransmissions take place in the same channel state. Furthermore, by relaxing the input power constraint allowing variable power levels in different retransmissions, we show that power control can be used to dramatically increase the diversity advantage. Our analysis reveals some important insights on the benefits of ARQ in slow-fading MIMO channels. In particular, we show that 1) allowing for a sufficiently large retransmission delay results in an almost flat diversity-multiplexing tradeoff, and hence, renders operating at high multiplexing gain more advantageous; 2) MIMO ARQ channels quickly approach the ergodic limit when power control is employed. Finally, we complement our information-theoretic analysis with an incremental redundancy lattice space-time (IR-LAST) coding scheme which is shown, through a random coding argument, to achieve the optimal tradeoff(s). An integral component of the optimal IR-LAST coding scheme is a list decoder, based on the minimum mean-square error (MMSE) lattice decoding principle, for joint error detection and correction. Throughout the paper, our theoretical claims are validated by numerical results