Diversity Versus Multiplexing in Narrowband MIMO Channels: A Tradeoff Based on Euclidean Distance

Multiple-input multiple-output (MIMO) communication systems use antenna arrays at both the transmitter and the receiver to offer substantial benefits in terms of rate and reliability. Two standard approaches for communicating in MIMO systems are spatial multiplexing and transmit diversity. Multiplexing sends independent information streams across the transmit antennas to maximize rate while transmit diversity sends redundant information streams to maximize reliability. In this paper the tradeoff between spatial multiplexing and transmit diversity is analyzed for narrowband MIMO channels based on the minimum Euclidean distance of the codebook at the receiver. The proposed characterization methodology is based on instantaneous channel information and is independent of the channel statistics. The Demmel condition number of the matrix channel is shown to provide a sufficient condition for multiplexing to outperform diversity in terms of minimum Euclidean distance. Using the Demmel condition number characterization, the probability that multiplexing outperforms diversity is studied for complex Gaussian matrix channels as a function of the rate and number of antennas. As a byproduct of the Euclidean distance comparison, a fixed-rate spatially adaptive modulation scheme is proposed that selects either multiplexing or diversity based on a low rate feedback channel. Monte Carlo simulations demonstrate improvement over either multiplexing or diversity individually in terms of bit error rate. Keyword: MIMO systems, space-time coding, transmit diversity ∗A portion of these results have appeared in the Proceedings of the 2000 Allerton Conference on Communication, Control, and Computers and the Proceedings of the 2001 International Conference on Communications