MMSE-GDFE lattice decoding for under-determined linear channels

Recently, the authors established the fundamental role of minimum mean square error generalized decision-feedback equalizer (MMSE-GDFE) lattice decoding in achieving the optimal diversity-vs-multiplexing tradeo ? of delay limited multiple-input multiple-output (MIMO) channels. This optimality motivates the current work where we exploit this technique in constructing an e?cient decoding algorithm 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, ?nally, a lattice search stage. By introducing ?exibility 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 quasi-static channels, to o?er signi?cant gains over the state of the art decoding algorithms in terms of performance enhancement and complexity reduction. From one side, 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 o?ering a large reduction in complexity compared to the most e?cient implementation of ML decoding proposed by Dayal and Varanasi (e.g., an order of magnitude in certain representative scenarios). On the other side, when the search is terminated after the ?rst point is found, the algorithm only requires linear complexity while o?ering signi?cant performance gains (in the order of several dBs) over the linear complexity algorithm proposed recently by Yao and Wornell, and independently by Windpassinger and Fisher.