In this paper, the capacity of the oversampled Wiener phase noise (OWPN) channel is investigated. The OWPN channel is a discrete-time point-to-point channel with a multi-sample receiver in which the channel output is affected by both additive and multiplicative noise. The additive noise is a white standard Gaussian process while the multiplicative noise is a Wiener phase noise process. This channel generalizes a number of channel models previously studied in the literature which investigate the effects of phase noise on the channel capacity, such as the Wiener phase noise channel and the non-coherent channel. We derive upper and inner bounds to the capacity of OWPN channel: (i) an upper bound is derived through the I-MMSE relationship by bounding the Fisher information when estimating a phase noise sample given the past channel outputs and phase noise realizations, then (ii) two inner bounds are shown: one relying on coherent combining of the oversampled channel outputs and one relying on non-coherent combining of the samples. After capacity, we study generalized degrees of freedom (GDoF) of the OWPN channel for the case in which the oversampling factor grows with the average transmit power $P$ as $P$? and the frequency noise variance as $P^{\alpha}$?. Using our new capacity bounds, we derive the GDoF region in three regimes: regime (i) in which the GDoF region equals that of the classic additive white Gaussian noise (for $\beta \leq 1$), one (ii) in which GDoF region reduces to that of the non-coherent channel (for $\beta \geq \min \{\alpha,1\}$) and, finally, one in which partially-coherent combining of the over-samples is asymptotically optimal (for $2 \alpha-1\leq \beta \leq 1$). Overall, our results are the first to identify the regimes in which different oversampling strategies are asymptotically optimal.

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关于过采样维纳相位噪声信道的容量

在本文中，研究了过采样维纳相位噪声 (OWPN) 通道的容量。OWPN 通道是一个离散时间点对点通道，具有多采样接收器，其中通道输出受加性和乘性噪声的影响。加性噪声是白标准高斯过程，而乘性噪声是维纳相位噪声过程。该信道概括了先前在文献中研究的许多信道模型，这些模型研究了相位噪声对信道容量的影响，例如维纳相位噪声信道和非相干信道。我们推导出 OWPN 信道容量的上限和内限：(i) 在给定过去的通道输出和相位噪声实现的情况下估计相位噪声样本时，通过限制 Fisher 信息，通过 I-MMSE 关系推导出上限，然后 (ii) 显示两个内界：一个依赖于相干组合过采样的通道输出和一个依赖于样本的非相干组合。在容量之后，我们研究了 OWPN 信道的广义自由度 (GDoF)，在这种情况下，过采样因子随着平均发射功率 $P$ 作为 $P$? 和频率噪声方差为 $P^{\alpha}$?。使用我们的新容量界限，我们推导出三种状态的 GDoF 区域：状态 (i)，其中 GDoF 区域等于经典加性高斯白噪声（对于 $\beta \leq 1$），一 (ii) 其中 GDoF 区域减少到非相干通道的区域（对于 $\beta \geq \min \{\alpha,1\}$），最后，在其中部分相干组合过-samples 是渐近最优的（对于 $2 \alpha-1\leq \beta \leq 1$）。总的来说，我们的结果是第一个确定不同过采样策略渐近最优的机制。