  Minimizing the symbol error in the uplink of multi-user multiple input
multiple output systems is important, because the symbol error affects the
achieved signal-to-interference-plus-noise ratio (SINR) and thereby the
spectral efficiency of the system. Despite the vast literature available on
minimum mean squared error (MMSE) receivers, previously proposed receivers for
block fading channels do not minimize the symbol error in time-varying Rayleigh
fading channels. Specifically, we show that the true MMSE receiver structure
does not only depend on the statistics of the CSI error, but also on the
autocorrelation coefficient of the time-variant channel. It turns out that
calculating the average SINR when using the proposed receiver is highly
non-trivial. In this paper, we employ a random matrix theoretical approach,
which allows us to derive a quasi-closed form for the average SINR, which
allows to obtain analytical exact results that give valuable insights into how
the SINR depends on the number of antennas, employed pilot and data power and
the covariance of the time-varying channel. We benchmark the performance of the
proposed receiver against recently proposed receivers and find that the
proposed MMSE receiver achieves higher SINR than the previously proposed ones,
and this benefit increases with increasing autoregressive coefficient.
