On the Capacity-Achieving Distribution of the Noncoherent Rician Fading Channel

Transmission of information over a discrete-time memoryless Rician fading channel is considered. The noncoherent scenario, where neither the receiver nor the transmitter knows the fading coefficients, is assumed. If the input is subject to a peak-power constraint, it is shown that uniformly distributed phase is optimal and the capacity-achieving amplitude distribution is discrete with a finite number of mass points. It is also proven that if the input has only an average power constraint, the optimal input amplitude distribution has bounded support. Then, the Rician fading channel with uniform phase noise in the specular component is analyzed. It is shown that under an average power limitation, the optimal input amplitude distribution is discrete with a finite number of mass points.