We develop a framework to optimize the tradeoff between diversity,multiplexing, and delay in MIMO systems to minimize end-to-end distortion. Wefirst focus on the diversity-multiplexing tradeoff in MIMO systems, and developanalytical results to minimize distortion of a vector quantizer concatenatedwith a space-time MIMO channel code. In the high SNR regime we obtain aclosed-form expression for the end-to-end distortion as a function of theoptimal point on the diversity-multiplexing tradeoff curve. For large butfinite SNR we find this optimal point via convex optimization. We then considerMIMO systems using ARQ retransmission to provide additional diversity at theexpense of delay. For sources without a delay constraint, distortion isminimized by maximizing the ARQ window size. This results in an ARQ-enhancedmultiplexing-diversity tradeoff region, with distortion minimized over thisregion in the same manner as without ARQ. Under a source delay constraint theproblem formulation changes to account for delay distortion associated withrandom message arrival and random ARQ completion times. We use a dynamicprogramming formulation to capture the channel diversity-multiplexing tradeoffat finite SNR as well as the random arrival and retransmission dynamics; wesolve for the optimal multiplexing-diversity-delay tradeoff to minimizeend-to-end distortion associated with the source encoder, channel, and ARQretransmissions. Our results show that a delay-sensitive system should adaptits operating point on the diversity-multiplexing-delay tradeoff region to thesystem dynamics. We provide numerical results that demonstrate significantperformance gains of this adaptive policy over a static allocation ofdiversity/multiplexing in the channel code and a static ARQ window size.
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