  In this contribution, the evaluation of the diversity of the MIMO MMSE
receiver is addressed for finite rates in both flat fading channels and
frequency selective fading channels with cyclic prefix. It has been observed
recently that in contrast with the other MIMO receivers, the MMSE receiver has
a diversity depending on the aimed finite rate, and that for sufficiently low
rates the MMSE receiver reaches the full diversity - that is, the diversity of
the ML receiver. This behavior has so far only been partially explained. The
purpose of this paper is to provide complete proofs for flat fading MIMO
channels, and to improve the partial existing results in frequency selective
MIMO channels with cyclic prefix.
