The MIMO ARQ Channel

In this paper, the fundamental performance tradeoff of the delay-limited multiple-input multiple-output (MIMO) auto- matic retransmission request (ARQ) channel is explored. In par- ticular, 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-di- mensional tradeoff between reliability (i.e., diversity), throughput (i.e., multiplexing gain), and delay (i.e., maximum number of re- transmissions). This tradeoff quantifies the ARQ diversity gain ob- tained by leveraging the retransmission delay to enhance the reli- ability for a given multiplexing gain. Interestingly, ARQ diversity appears even in long-term static channels where all the retrans- missions take place in the same channel state. Furthermore, by re- laxing 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 anal- ysis 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 chan- nels quickly approach the ergodic limit when power control is em- ployed. Finally, we complement our information-theoretic anal- ysis with an incremental redundancy lattice space-time (IR-LAST) coding scheme which is shown, through a random coding argu- ment, 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.