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

机译：维纳相噪信道的容量：边界和容量实现分布

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摘要

In this paper, the capacity of the additive white Gaussian noise (AWGN) channel, affected by time-varying Wiener phase noise is investigated. Tight upper and lower bounds on the capacity of this channel are developed. The upper bound is obtained by using the duality approach, and by considering a specific distribution over the output of the channel. In order 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 capacity curve at low SNR, while at high SNR, they coincide with the high-SNR capacity result available in the literature for the phase-noise channel.
机译：本文研究了时变维纳相位噪声对加性高斯白噪声（AWGN）信道容量的影响。发展了该通道容量的上下限。通过使用对偶方法并考虑通道输出上的特定分布来获得上限。为了降低容量的上限，首先通过解决信道互信息的功能优化来找到可实现容量分配的输入族。然后，通过蒙特卡洛模拟从建议的分布中抽取样本，从而获得容量的下界。所提出的实现容量的输入分布是圆形对称的非高斯分布，并且输入幅度随时间而相关。对于大范围的信噪比（SNR）值，所评估的容量边界是紧密的，因此可以将它们用于量化容量。具体而言，在低SNR时，边界遵循众所周知的AWGN容量曲线，而在高SNR时，边界与文献中可用于相位噪声信道的高SNR容量结果一致。

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