Analysis on the diversity-multiplexing tradeoff for ordered MIMO SIC receivers

The diversity-multiplexing tradeoff for multiple-input multiple-output (MIMO) point-to-point channels and multiple access channels were first proposed and studied by Zheng and Tse recently. While the optimal tradeoff curves for MIMO channels have been explicitly explored, those corresponding to some suboptimal and practical MIMO schemes are still open. One such important problem is the diversity-multiplexing tradeoff for a V-BLAST type system employing ordered successive interference cancellation (SIC) receivers with zero forcing (ZF) or minimum mean square error (MMSE) processing at each stage. In this paper, we take a novel geometrical approach and rigorously verify that under general settings, the optimal ordering rule for a V-BLAST SIC receiver will not improve its performance regarding diversity-multiplexing tradeoff in point-to- point channels. The same geometrical tool is then applied to MIMO spatial-division multiple access channels, leading to some first results in this area. Particularly, we reveal that when the rates of data streams are fixed (i.e., zero spatial multiplexing gain), the diversity order is not improved by user ordering.