Bounds on Mutual Information of Rayleigh Fading Channels with Gaussian Input

The mutual information of a discrete time Rayleigh fading channel is considered, where neither the transmitter nor the receiver has the knowledge of the channel state information. We specifically derive a lower bound for the mutual information of this channel when the input distribution is Gaussian. The bound is expressed in terms of the capacity of the corresponding non fading channel and the capacity when the perfect channel state information is known at the receiver