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A Fast Generalized Sphere Decoder for Optimum Decoding of Under-determined MIMO systems

A new Generalized Sphere Decoder (GSD) is proposed for optimum decoding of lattice points in a system with fewer equations than unknowns. The proposed algorithm is significantly faster than the one proposed in [1] and is a natural extension of the sphere decoding philosophy introduced in [2, 3]. The complexity reduction is achieved by partitioning the entire range of maximum likelihood hypotheses for the GSD into ordered subsets. Such a partition enables the rejection of several hypothesis at once. A parameter called the depth of the GSD is shown to offer additional complexity reduction as the gap between the number of equations and the number of unknowns grows. Numerical results are presented to show the application of the proposed GSD for various Multiple-Input Multiple-Output (MIMO) systems.