Effects of inaccurate training-based minimum mean square error channel estimation on the performance of multiple input-multiple output Vertical Bell Laboratories Space-Time zero-forcing receivers

The authors investigate the effects of an imperfect channel estimate, rendered through the employment of a practical, online training-based minimum mean square error estimator, on uncoded multiple input-multiple output Vertical Bell Laboratories Space-Time architecture with a zero-forcing receiver in the presence of uncorrelated frequency-non-selective Rayleigh block fading. The post-processing signal to interference plus noise ratio and its probability distribution function will be derived using no approximation. Exact closed-form expressions will be provided for the average symbol probability of error for M-ary PAM modulation. For quadrature phase shift keying (QPSK) modulation, the symbol error probability is derived in the form of an integral, which has an analytical solution only when the number of receive antennas equals or exceeds that of the transmit antennas by one and may otherwise be numerically calculated. The average outage probability will be exactly calculated. All this is accomplished by an approximation-free mathematical approach and by taking into account the fundamental limitations between the accuracy of the channel estimate and the channel capacity. Perfect agreement is seen to exist between our analysis and Monte Carlo simulations.