Maximum likelihood detection of a MIMO system using second order cone programming approach

Optimum receiver structure is maximum likelihood sequence estimation (MLSE). However, the computational complexity of the ML decoding requires us to solve an integer least square (ILS) problem, which is, in general, NP-hard. Recently, semidefinite programming (SDP) relaxation approach has been proposed to approximately solve NP-hard problems in polynomial time. Its worst case computational complexity is O(n^3.5), where n is the number of variables. Even the SDP approaches are computationally expensive for large systems. The other approach currently used for ML decoding is sphere decoding scheme [H. Vikalo et al., (2002)]. The average case complexity of this scheme is O(n³), when radius, r, is correctly chosen (which is NP-hard problem). Also at low SNRs the complexity of the sphere decoder explodes. We propose to apply second order cone programming (SOCP) approach to resolve large system problem, offers substantial computational savings over SDP relaxation scheme (by reducing the number of variables) and sphere decoding, while maintaining performance arbitrarily close to ML. The computational complexity of SOCP approach is O(n³) and is independent of SNR. Simulations shows promising results.