The noncoherent Rician fading channel - Part I: Structure of the capacity-achieving input

Transmission of information over a discrete-time memoryless Rician fading channel is considered, where neither the receiver nor the transmitter knows the fading coefficients. First, the structure of the capacity-achieving input signals is investigated when the input is constrained to have limited peakedness by imposing either a fourth moment or a peak constraint. When the input is subject to second and fourth moment limitations, it is shown that the capacity-achieving input amplitude distribution is discrete with a finite number of mass points in the low-power regime. A similar discrete structure for the optimal amplitude is proven over the entire signal-to-noise ratio (SNR) range when there is only a peak-power constraint. The Rician fading with the phase-noise channel model, where there is phase uncertainty in the specular component, is analyzed. For this model, it is shown that, with only an average power constraint, the capacity-achieving input amplitude is discrete with a finite number of levels. For the classical average-power-limited Rician fading channel, it is proven that the optimal input amplitude distribution has bounded support.