The Effect of Ordered Detection and Antenna Selection on Diversity Gain of Decision Feedback Detector

The decision feedback detector (DFD) can achieve the high spectral efficiency of a MIMO channel in that it converts the MIMO channel into multiple parallel layers, through which independently coded data substreams may be spatially multiplexed and be transmitted over the same time and frequency slot. Because of independent coding/decoding, the DFD may apply arbitrarily ordered detection. In this paper, we analyze the effect of detection ordering on the diversity gain per layer of the DFD in a MIMO Rayleigh-fading channel. For a MIMO channel with M _t transmit and M _r (M _r ges M _t) receive antennas, we derive an upper bound to the diversity gain per layer for any detection ordering, i.e., D _i les (M _r - i + 1)(M _t - i + 1) for 1 les i les Mt. We show that the DFD using the so-called greedy ordering rule can achieve the diversity gain upper bound. We further study the diversity-multiplexing (D-M) gain tradeoff of DFD in a pruned MIMO channel where L _t (L _t les M_t) transmit and Lr (Lt les Lr les M _r) receive antennas are selected out of the full system. It is shown that the D-M tradeoff of DFD in an optimally pruned channel is ddfd,opt (r) = (M _r - Lt + 1)(Mt - Lt + 1)(1 - r/L _t). Such a tradeoff-optimally pruned system can be obtained by a fast antenna selection algorithm. This result has interesting implications to the multi-access communications with user selection. The theoretical analysis is validated by the numerical examples.