On the Capacity of the Wiener Phase-Noise Channel: Bounds and Capacity Achieving Distributions


During this paper, the capability of the additive white Gaussian noise (AWGN) channel, tormented by time-varying Wiener section noise is investigated. Tight upper and lower bounds on the capability of this channel are developed. The upper certain is obtained by using the duality approach, and by considering a selected distribution over the output of the channel. So as to lower-bound the capacity, first a family of capacity-achieving input distributions is found by solving a functional optimization of the channel mutual information. Then, lower bounds on the capacity are obtained by drawing samples from the proposed distributions through Monte Carlo simulations. The proposed capacity-achieving input distributions are circularly symmetric, non-Gaussian, and the input amplitudes are correlated over time. The evaluated capacity bounds are tight for a wide range of signal-to-noise-ratio (SNR) values, and thus they can be used to quantify the capacity. Specifically, the bounds follow the well-known AWGN capability curve at low SNR, while at high SNR, they coincide with the high-SNR capability result obtainable within the literature for the phase-noise channel.

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