Optimal Detection Ordering for Coded V-BLAST

Optimum ordering strategies for the coded Vertical Bell Labs Layered Space-Time (V-BLAST) architecture with capacity achieving temporal codes on each stream are analytically studied, including 4 different power/rate allocation strategies among data streams. Compact closed-form solutions are obtained for the case of zero-forcing (ZF) V-BLAST with two transmit antennas and necessary optimality conditions are found for the general case. The optimal rate allocation is shown to have a major impact (stronger streams are detected last) while the optimal power allocation does not alter the original Foschini ordering (stronger streams are detected first). Sufficient conditions for the optimality of the greedy ordering are established: it is optimal for the ZF V-BLAST under an optimal rate allocation with two transmit antennas at any SNR and with any number of antennas in the low and high SNR regimes. It satisfies the necessary optimality conditions for larger systems at any SNR and is nearly-optimal in many cases. An SNR gain of ordering is introduced and studied, including closed-form expressions as well as lower and upper bounds and the conditions for their achievability. For the minimum mean square error (MMSE) V-BLAST under an optimal rate allocation, any ordering is shown to deliver the same system capacity. All the results also apply to a multiple-access channel with the successive interference cancelation receiver.