论文标题
关于超采样的维纳相噪声通道的能力
On the Capacity of the Oversampled Wiener Phase Noise Channel
论文作者
论文摘要
在本文中，研究了过采样的维纳相噪声（OWPN）通道的能力。 OWPN通道是一个离散的点对点通道，具有多样本接收器，其中通道输出受添加剂和乘法噪声的影响。加性噪声是白色标准高斯过程，而乘法噪声是维纳相相位噪声过程。该通道概括了先前在文献中研究的许多通道模型，这些通道模型研究了相位噪声对通道容量的影响，例如Wiener相位噪声通道和非连锁通道。我们在OWPN通道的能力上得出上层和内部的边界：（i）在给定过去的通道输出和相位噪声实现的情况下，通过估算相位噪声样本时，通过i-MMSE关系来得出上界，然后显示两个内部界限：一个内部界限：一个依赖于过度采样的频道输出和一个依赖的依赖于coernerts nocerny combernents组合的内部界限。容量之后，我们研究了OWPN频道的广义自由度（GDOF），其中超采样因子以平均发射功率$ p $为$ p $增长的情况？频率噪声方差为$ p^α$？使用我们的新容量范围，我们将GDOF区域得出三个制度：制度（i），其中GDOF区域等同于经典的添加剂白色高斯噪声（对于$β\ leq 1 $）中的GDOF区域，其中一个（ii）是GDOF区域的一个（II），其中gdof区域减少了一个非社交通道（对于$β\ geq \ geq \ geq \ geq \ min \ min \ n in cy）\ a和1 c。过度样本的部分结合是渐近的最佳选择（价格为$2α-1\ leqβ\ leq 1 $）。总体而言，我们的结果是第一个确定不同过度采样策略在渐近上最佳的制度的结果。
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 $P^α$?. 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 $β\leq 1$), one (ii) in which GDoF region reduces to that of the non-coherent channel (for $β\geq \min \{α,1\}$) and, finally, one in which partially-coherent combining of the over-samples is asymptotically optimal (for $2 α-1\leq β\leq 1$). Overall, our results are the first to identify the regimes in which different oversampling strategies are asymptotically optimal.
