MMSE-GDFE lattice decoding for solving under-determined linear systems with integer unknowns

Minimum mean square error generalized decision-feedback equalizer (MMSE-GDFE) lattice decoding is shown to be an efficient decoding strategy for under-determined linear channels. The proposed algorithm consists of an MMSE-GDFE front-end followed by a lattice reduction algorithm with a greedy ordering technique and, finally, a lattice search stage. By introducing flexibility in the termination strategy of the lattice search stage, we allow for trading performance for a reduction in the complexity. The proposed algorithm is shown, through experimental results in MIMO quasistatic channels, to offer significant gains over the state of the art decoding algorithms in terms of performance enhancement and complexity reduction. On the one hand, when the search is pursued until the best lattice point is found, the performance of the proposed algorithm is shown to be within a small fraction of a dB from the maximum likelihood (ML) decoder while offering a large reduction in complexity compared to the most efficient implementation of ML decoding proposed by Dayal and Varanasi (e.g., an order of magnitude in certain representative scenarios). On the other hand, when the search is terminated after the first point is found, the algorithm only requires linear complexity while offering significant performance gains (in the order of several dBs) over the linear complexity algorithm proposed recently by Yao and Wornell.