  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.
