  Transmission of information over a discrete-time memoryless Rician fading
channel is considered where neither the receiver nor the transmitter knows the
fading coefficients. The spectral-efficiency/bit-energy tradeoff in the
low-power regime is examined when the input has limited peakedness. It is shown
that if a fourth moment input constraint is imposed or the input
peak-to-average power ratio is limited, then in contrast to the behavior
observed in average power limited channels, the minimum bit energy is not
always achieved at zero spectral efficiency. The low-power performance is also
characterized when there is a fixed peak limit that does not vary with the
average power. A new signaling scheme that overlays phase-shift keying on
on-off keying is proposed and shown to be optimally efficient in the low-power
regime.
