General DMT optimality of LR-aided linear MIMO-MAC transceivers with worst-case complexity at most linear in sum-rate

In the setting of multiple-access MIMO channels, the work establishes the DMT optimality of lattice-reduction (LR)-aided regularized linear decoders. This is achieved irrespective of the lattice design applied by each user. The decoding algorithms employ efficient solutions to the Nearby Vector Problem with Preprocessing in the presence of a regularized non-Euclidean metric, and in the presence of time-outs. The decoders´ optimality induces a worst-case computational complexity that is at most linear in the users´ sum-rate. This constitutes a substantial improvement over the state of art of DMT optimal decoding, including ML decoders with complexity that is exponential in the sum-rate, or lattice decoders based on solutions to the NP-hard closest vector problem (CVP). The optimality of the efficient decoders is established for all channel statistics, for all channel dimensions, for any number of users, and irrespective of the different rates. The findings directly apply to different computationally intensive multi-user settings such as multi-user MIMO, multi-user cooperative communications, and multi-user MIMO-OFDM.