On maximum-likelihood detection and the search for the closest lattice point

Maximum likelihood decoding algorithms for Gaussian MIMO linear channels are considered. Linearity over the field of real numbers facilitates the design of maximum likelihood decoders using number theoretic tools for searching the closest lattice point. These decoders are collectively referred to as sphere decoders in the literature. In this paper, a fresh look at this class of decoding algorithms is taken. In particular, two novel algorithms are developed. The first algorithm is inspired by the Pohst enumeration strategy and is shown to offer a significant reduction in complexity compared to the Viterbo-Boutros sphere decoder. The connection between the proposed algorithm and the stack sequential decoding algorithm is then established. This connection is utilized to construct the second algorithm which can also be viewed as an application of the Schnorr-Euchner strategy to maximum likelihood decoding. Aided with a detailed study of pre-processing algorithms, a variant of the second algorithm is developed and shown to offer significant reductions in the computational complexity compared to all previously proposed sphere decoders with a near maximum likelihood detection performance. This claim is supported by intuitive arguments and simulation results in many relevant scenarios.