On non-coherent Rician fading channels with average and peak power limited input

Communication over a discrete time-varying Rician fading channel is considered, where neither the transmitter nor the receiver has the knowledge of the channel state information (CSI) except the fading statistics. We provide closed form expressions to the mutual information under both average and peak input power constraint when its distribution is complex Gaussian. The results are compared with the existing capacity results showing the importance of the perfect CSI at the receiver at moderate and high signal to noise ratio (SNR). Furthermore, we show that the peak input power constraint gives better mutual information compared to the average power constraint input in Rician fading. Also, we show the information loss with a Gaussian distributed input compared to channel capacity is negligible at low SNR. Hence, there is no penalty for not knowing the channel perfectly at the receiver in the low SNR regime.