Capacity Results for Block-Stationary Gaussian Fading Channels with a Peak Power Constraint

A peak-power-limited single-antenna block-stationary Gaussian fading channel is studied, where neither the transmitter nor the receiver knows the channel state information, but both know the channel statistics. This model subsumes most previously studied Gaussian fading models. The asymptotic channel capacity in the high signal-to-noise ratio (SNR) regime is first computed, and it is shown that the behavior of the channel capacity depends critically on the channel model. For the special case where the fading process is symbol-by-symbol stationary, it is shown that the codeword length must scale at least logarithmically with SNR in order to guarantee that the communication rate can grow logarithmically with SNR with decoding error probability bounded away from one. An expression for the capacity per unit energy is also derived. Furthermore, it is shown that the capacity per unit energy is achievable using temporal on-off signaling with optimally allocated on symbols, where the optimal on-symbol allocation scheme may depend on the peak power constraint.