Rayleigh flat fading channels' capacity

In this paper, we consider single-user transmission over a Rayleigh flat fading channel, in which the channel state information (CSI) is known by the receiver only. Subject to an average transmit power constraint, we study the capacity of an additive white Gaussian noise (AWGN) channel with Rayleigh fading. Under an independently identically distributed fading assumption, lower and upper bounds of the channel capacity are given and proved and they are compared to the capacity results numerically computed. Besides, an approximation result of such channel capacity is proposed, and by conducting numerical comparison it is shown that our suggested approximation result has a better performance in approximating Rayleigh fading channels capacity than the bounds given above. In addition, the channel capacity with outage probability is discussed and compared with different outage probabilities.