LR-aided MMSE lattice decoding is DMT optimal for all approximately universal codes

Currently for the n_T times n_R MIMO channel, any explicitly constructed space-time (ST) designs that achieve optimality with respect to the diversity multiplexing tradeoff (DMT) are known to do so only when decoded using maximum likelihood (ML) decoding, which may incur prohibitive decoding complexity. In this paper we prove that MMSE regularized lattice decoding, as well as the computationally efficient lattice reduction (LR) aided MMSE decoder, allows for efficient and DMT optimal decoding of any approximately universal latticebased code. The result identifies for the first time an explicitly constructed encoder and a computationally efficient decoder that achieve DMT optimality for all multiplexing gains and all channel dimensions. The results hold irrespective of the fading statistics.