Optimal Diversity Multiplexing Tradeoff of Constrained Asymmetric MIMO Systems

In a MIMO downlink channel it is often that the number of transmit antennas is strictly larger than the number of receive, and such channel is termed asymmetric MIMO channel. To employ simple decoding techniques in this channel, such as zero-forcing or sphere decoding, the number of active transmit antennas must be constrained to be no larger than the number of receive, and the resulting system is coined "constrained asymmetric MIMO system." For the case of two receive antennas and for any number of transmit antennas, an optimal transmission scheme is presented in this paper and is shown to achieve the same performance as the unconstrained ones in terms of the diversity-multiplexing tradeoff. The construction of optimal constrained codes is also provided.