Outage analysis for group detectors in MIMO fading channels

Multiple-input multiple-output (MIMO) techniques are now being commonplace in wireless communication systems as they provide diversity and spatial multiplexing gains compared to single-input single-output (SISO) systems. Due to the induced high complexity of maximum likelihood (ML) detection for MIMO systems, suboptimal detection is usually employed but at a performance loss. This loss has been fully characterized for linear receivers, namely, zero-forcing (ZF) and minimum mean square error (MMSE) detectors. Interestingly, it has been noticed that in case of coding across transmit antennas, the MMSE receiver showed significant improvement over ZF in terms of outage probability at low spectral efficiencies, whereas for high spectral efficiencies, both receivers showed similar behaviour. We fill the gap between the two extreme cases (i.e., ML and linear receivers) through relaxing the linearity constraint by considering group receivers (viz. group zero-forcing (GZF) and group minimum mean square error (GMMSE) detectors) with coding across transmit antennas. We first derive the diversity-multiplexing tradeoff (DMT) for those group detectors. Next, we characterize the peculiar rate-dependent outage behaviour of the GMMSE, where it is found that tolerating additional detection complexity provides performance advantage w.r.t the MMSE at specific ranges of spectral efficiency. We corroborate our theoretical analysis via numerical simulations.