The capacity of discrete-time memoryless Rayleigh-Fading channels

We consider transmission over a discrete-time Rayleigh fading channel, in w hich successive symbols face independent fading, and where neither the tran smitter nor the receiver has channel state information. Subject to an avera ge power constraint, we study the capacity-achieving distribution of this c hannel and prove it to be discrete with a finite number of mass points, one of them located at the origin. We numerically compute the capacity and the corresponding optimal distribution as a function of the signal-to-noise ra tio (SNR), The behavior of the channel at low SNR is studied and finally a comparison is drawn with the ideal additive white Gaussian noise channel.