Spectral Efficiency of the Noncoherent Rician Fading Channel in the Low-power Regime

Transmission of information over a discrete-time memoryless Rician fading channel is considered where neither the receiver nor the transmitter knows the fading coefficients and the input amplitude is subject to second and fourth moment constraints. The main focus is on the power-limited (i.e., wideband, low-power) regime. First the structure of the capacity-achieving input signals is investigated. It is shown that uniform phase is optimal if there is a line of sight component and that the capacity-achieving input amplitude distribution is discrete in the low-power regime. The spectralefficiency/bit-energy tradeoff in the power-limited regime is examined and it is shown that the minimum bit energy is not always achieved at zero spectral efficiency. In this case, it is argued that one should avoid operating in the region where the spectral efficiency is lower than the spectral efficiency of the minimum bit energy point.