Optimal diversity-multiplexing tradeoff with group detection for MIMO systems

It is well known that multiple-input multiple-output (MIMO) systems provide two types of gains: diversity gains and spatial multiplexing gains. Recently, a tradeoff function of these two gains has been derived for a point-to-point MIMO system when optimal detection is used. In this paper, we extend the previous work to a more general MIMO system, where the transmitted data is coded in groups. Group detection is applied at the receiver to retrieve the data. It consists of a zero-forcing decorrelation that separates the groups, followed by a joint detection for each of the groups. Two receiver structures are considered in this paper; namely, group zero forcing (GZF) and group successive interference cancellation (GSIC). We assess the diversity-multiplexing tradeoff function of each of these receivers over a richly scattered Rayleigh fading channel. Three rate-allocation algorithms will be considered here; namely, equal rate, group-size proportional rate, and optimal-rate allocation. An explicit expression of the system tradeoff will be derived for both receivers with these three rate allocations. The obtained results will first be optimized over all possible group partitions for a given number of groups. Next, the number of groups will be varied to further optimize the system-tradeoff performance. An overall optimum tradeoff for a general MIMO system with group detection will then be obtained. Numerical results will indicate that optimum performance can be approached with very-low-complexity schemes for a wide range of data rates. It will be also demonstrated that group detection bridges the gap between the traditional decorrelator and the optimal receiver tradeoff performances.