LLL Reduction Achieves the Receive Diversity in MIMO Decoding

Diversity order is an important measure for the performance of communication systems over multiple-input-multiple-output (MIMO) fading channels. In this correspondence, we prove that in MIMO multiple- access systems (or MIMO point-to-point systems with V-BLAST transmission), lattice-reduction-aided decoding achieves the maximum receive diversity (which is equal to the number of receive antennas). Also, we prove that the naive lattice decoding (which discards the out-of-region decoded points) achieves the maximum diversity.