Complexity assessment of sphere decoding methods for MIMO detection

Sphere Decoding (SD) algorithms have been shown to provide maximum likelihood (ML) detection over Gaussian multiple input-multiple output (MIMO) channels with lower complexity than the exhaustive search. These methods are based on a closest lattice point search over a limited search space (hypersphere). There exist several implementations of these algorithms pursuiting different search strategies and working either within a set of real numbers, thus called real sphere decoders (RSD), or performing the search directly within a set of complex numbers, commonly known as complex sphere decoders (CSD). In this paper, a performance comparison between the real and the complex version of the Schnorr-Euchner (SE) sphere decoder has been carried out in order to find out which algorithm is the most suitable depending on the application. Furthermore a recently appeared fixed-complexity version of the SE decoder (FSD) has been evaluated both in terms of complexity and performance and the results have been compared with the original version. In contrast to yet existing complexity analyses, not only the number of visited nodes has been investigated but also the total number of operations.