Orthotope sphere decoding and parallelotope decoding-reduced complexity optimum detection algorithms for MIMO channels

The complexity of maximum likelihood detection (MLD) in multiple input multiple output (MIMO) systems with N transmit antennas typically grows exponentially with N. This makes MLD too complex to implement, particularly if higher order modulation schemes such as quadrature amplitude modulation are employed. Recently, generalised sphere decoding (GSD) was proposed, which provides the same performance as MLD, but complexity is only a polynomial function of N for small values of N. This is achieved by only considering lattice points that lie within a hypersphere centred at the received signal. Determining which lattice points lie within the sphere requires a complex distance calculation, so this paper investigates an different approach, called parallelotope decoding (PD) or alternatively the Kannan strategy. This method fits a parallelotope around the sphere, and simplifies the distance calculation. It turns out that PD performs poorly under certain channel conditions, so a novel hybrid scheme called orthotope sphere decoding is also proposed. This decoder is a hybrid of PD and GSD and is usually the most cost effective of the four optimal algorithms under discussion. Simulation results are presented to compare the performance and complexity of the optimal detectors described in the paper and the sub-optimal V-BLAST algorithm.