The Diversity-Multiplexing Tradeoff of Linear MIMO Receivers

While most literature on MIMO (multiple-input, multiple-output) multiantenna communications and space-time coding has considered optimal decoding, or bounded-distance approximations thereof, the current standardization trend in wireless local area network (WLAN) systems such as IEEE 802.11n, that will use MIMO as an integral component of their physical layer, focuses on simpler schemes, where a linear space-time equalizer is used to separate the signals from the M transmit antennas, thus creating a set of M "virtual" parallel channels. The output of these parallel channels is then fed to a standard SISO (single-input, single-output) decoder. Surprisingly, the diversity-multiplexing tradeoff (DMT) of this simple scheme has not been fully characterized before. We provide such characterization in this work, where we show that both linear zero-forcing (ZF) and linear minimum mean-square error (MMSE) receivers achieve the same DMT, which is equal to that of *one* of the parallel channels, even though coding and decoding is performed across the antennas. Hence, linear receivers incur a dramatic loss of diversity gain with respect to other non-linear schemes. Furthermore, we comment on the different behavior of the MMSE and ZF receivers at finite rate (zero multiplexing gain).