  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 SNR range when there is only a
peak power constraint. The Rician fading with 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.
