A Study of the Extreme Effects of Fading Correlation and the Impact of Imperfect MMSE Channel Estimation on the Performance of SIMO Zero-Forcing Receivers and on the Capacity-Maximizing Strategy in SIMO Links

In this paper, we shall consider best- and worst-case fading correlation scenarios, i.e., uncorrelated and fully correlated fading channels and will study the performance of a single-input-multiple-output (SIMO) link that uses a practical imperfect online training-based minimum mean square error (MMSE) channel estimator and a zero-forcing (ZF) receiver under these two conditions. Considering the extremes of correlation and focusing on frequency-nonselective Rayleigh block fading, we will find the probability distribution function (pdf) of the postprocessing signal-to-noise ratio (SNR) in each case and shall provide closed-form expressions for the symbol error probability (SEP) of these systems when using M-ary pulse amplitude modulation (M-ary PAM). Moreover, a lower bound will be provided for the information capacity of fully correlated SIMO links with training-based MMSE channel estimation, which will further be optimized to yield its maximum under different conditions. Monte Carlo simulations perfectly verify the analysis.