Diversity of MMSE MIMO Receivers

In most multiple-input multiple-output (MIMO) systems, the family of waterfall error curves, calculated at different spectral efficiencies, are asymptotically parallel at high signal-to-noise ratio. In other words, most MIMO systems exhibit a single diversity value for all fixed rates. The MIMO minimum mean square error (MMSE) receiver does not follow this pattern and exhibits a varying diversity in its family of error curves. This paper analyzes this interesting behavior of the MMSE MIMO receiver and produces the MMSE MIMO diversity at all rates. The diversity of the quasi-static flat-fading MIMO channel consisting of any arbitrary number of transmit and receive antennas is fully characterized, showing that full spatial diversity is possible if and only if the rate is within a certain bound which is a function of the number of antennas. For other rates, the available diversity is fully characterized. At sufficiently low rates, the MMSE receiver has a diversity similar to the maximum likelihood receiver (maximal diversity), while at high rates, it performs similarly to the zero-forcing receiver (minimal diversity). Linear receivers are also studied in the context of the MIMO multiple-access channel. Then, the quasi-static frequency selective MIMO channel is analyzed under zero-padding and cyclic-prefix (CP) block transmissions and MMSE reception, and lower and upper bounds on diversity are derived. For the special case of SIMO under CP, it is shown that the aforementioned bounds are tight.