In this paper, the uplink performance of Multi-User Multiple Input Multiple Output (MU-MIMO) Zero Forcing (ZF) receiver is investigated over correlated Rayleigh fading channels with channel estimation error. A mathematical expression for the sub-streams' output Signal to Noise Ratio (SNR) with transmit and receive-correlation is derived in the presence of erroneous channel estimates. Besides, an approximate and accurate expression for the Bit Error Rate (BER) of ZF receiver for 16-Quadrature Amplitude Modulation (QAM) with transmit-correlation is deduced in terms of the hypergeometric function. Subsequently, the developed analytical BER is verified by Monte-Carlo trails accounting various system parameters. The simulation results indicate that ZF receiver's BER relies solely on the transmit-correlation for the same number of transmit and receive-antennas at higher average SNR values per transmitted symbol (Es/N0). Also, a logarithmic and exponential growth in the BER is observed with an increase in the Mean Square estimation Error (MSE) and correlation coefficient, respectively.

We have investigated the BER performance of TC 8PSK with 2 branch SC and MRC diversities on spatially correlated Rayleigh fading channel. The upper bounds using the transfer function bounding technique are derived several numerical results are shown. Although the correlation between branches causes signal-to-noise (SNR) loss (relative to uncorrelated fading case) for SC and MRC diversities, the diversity can lead to achieve the diversity gain compared to the system without diversity. It is found that the diversity gain of 4-state TC 8PSK is larger than 8-state TC 8PSK. It is also shown that the BER performance of TC 8PSK is decreased as the antenna separation is decreased.