Geometric Decoding Of PAM and QAM Lattices

A geometric decoding technique for finite lattices was presented by Seethaler et al. for flat-fading multiple-input multiple-output channels in the case of linear modulations with constant amplitude (PSK). In this paper, geometric decoding is extended to square PAM and QAM constellations. Geometric decoding is suboptimal but has the advantage that the search is done in the vicinity of a X-dimensional affine set. Therefore, a very small subset of the whole lattice is considered in decoding. This makes the worst case complexity very low. For a MIMO channel with Lt transmit antennas and M-QAM constellation, the complexity is about O ((radicML_t)^K). Simulation results show that geometric decoding performs very close to maximum likelihood in many practical scenarios.