Low complexity ML detection based on search for the closest lattice point

The design of maximum likelihood detection algorithms for linear multidimensional constellations and lattice codes transmitted over Gaussian fading channels is considered. The linearity of the constellations over the field of complex numbers facilitates the design of maximum likelihood detectors using number theoretic tools for searching the closest lattice point. In particular, the Pohst enumeration method and the Schnorr-Euchner refinement of the Pohst strategy are used to develop two maximum likelihood detection algorithms. The first algorithm is shown to offer a significant reduction in complexity compared to the Viterbo-Boutros implementation of the Pohst strategy. The second algorithm is more suited to maximum likelihood detection than the Agrell et al. implementation of the Schnorr-Euchner strategy. Further, the two algorithms are compared to extract insights on the lowest complexity approach in different scenarios. The results obtained indicate that the distance between the nulling and cancellation solution and the maximum likelihood solution plays a major role in determining the lowest complexity algorithm.