Performance analysis of receive diversity under time-varying and spatially correlated channels using partial CSI

In this paper, a single input multiple output system is considered with L receive antennas and the underlying channels are assumed to be time varying with temporal correlation coefficient a and spatially correlated with correlation coefficient $$\rho $$ ρ . Further, the channel is assumed to be identically distributed using Rayleigh fading channels and characterized by first order autoregressive model. For the detection, we assume partial channel state information (CSI) available at the receiver. The partial CSI is in the form of a known preamble (one symbol) only before beginning of a frame of size N symbols. Further, the preamble is imperfectly known with a variance of error $$\sigma _e^2$$ σ e 2 . For the assumed system, closed form expressions of symbol error rate (SER) are derived for M-PSK and M-QAM constellations under the compound effect of spatially correlated channels, temporally correlated channels and partial CSI at the Receiver. The derived expressions are functions of average SNR per symbol, $$\rho $$ ρ , a, $$\sigma _e^2$$ σ e 2 , N, L and modulation order M. Further, these expressions are reduced for some special cases and compared with prevailing results in literature. The analytical expressions are also validated by comparing them with the corresponding simulation results. The derived expressions are very useful to select N, L and M to overcome the deterioration in SER due to adverse effects of $$\rho $$ ρ , a and $$\sigma _e^2$$ σ e 2 .