Properties of the Capacity-Achieving Input of Non-Coherent Rayleigh Fading Channels

This work studies non-coherent Rayleigh fading channels subject to average- and peak-power constraints. Several properties of the optimal input distribution are derived based on the Karush-Kuhn- Tucker conditions. In particular, the capacity-achieving distribution is characterized in the small peak and average power regimes, upper and lower bounds on the optimal input probabilities are presented, insights about the locations of the support points are provided, and bounds on the channel capacity are established.