Optimal rate allocation for group zero forcing

MIMO systems have been shown to provide significant performance gains over traditional single antennas systems that fall in two categories: diversity and multiplexing rate. A tradeoff between these gains was recently put in evidence and has been quantified with the optimal detection. We consider the evaluation of such tradeoff when group detection is applied and particularly when the group zero forcing (GZF) receiver structure is considered. To do so, we define and evaluate the outage probability per group and derive the tradeoff obtained by each of the groups. The overall system tradeoff is then given by the minimum group tradeoff performance. Optimal rate allocation is also proposed so as to maximize GZF tradeoff performance. Comparison for a given group partition with equal rate allocation shows that optimal rate allocation allows us to both maximize the diversity and the multiplexing rate of GZF. Furthermore, considering a fixed number of antennas, we find the minimum required number of groups for a given tradeoff level, as well as the optimal group partition that maximizes the system tradeoff. Numerical results demonstrate the optimality of this scheme. Significant diversity gains are put in evidence demonstrating that GZF can efficiently bridge the gap between BLAST and the optimal receiver while offering lower levels of complexity.