Optimal detection in MIMO Rayleigh fast fading channels with imperfect channel estimation

An optimal detector for signals with pilot symbol assisted modulation in MIMO Rayleigh fast fading channels with imperfect channel estimation is derived. This detector does not estimate the channel explicitly but jointly processes the received data and pilot symbols to recover the data. We investigate and compare its performance with that of mismatched detectors treating the maximum likelihood, regularized maximum likelihood or minimum mean squared error (MMSE) channel estimates as perfect channel information in spatially uncorrelated MIMO channels with BPSK and 16-QAM modulation by simulation. The channel is modeled by using basis functions; in particular, we use B-splines. Among these mismatched detectors, the one with MMSE channel estimates provides the best performance. In SISO channels, the performance of the optimal detector is close to that of the mismatched detector with MMSE channel estimates. However, in MIMO channels when the number of antennas increases, the optimal detector significantly outperforms the mismatched detector with MMSE channel estimates.