  A discrete-time Wiener phase noise channel with an integrate-and-dump
multi-sample receiver is studied. An upper bound to the capacity with an
average input power constraint is derived, and a high signal-to-noise ratio
(SNR) analysis is performed. If the oversampling factor grows as
$\text{SNR}^\alpha$ for $0\le \alpha \le 1$, then the capacity pre-log is at
most $(1+\alpha)/2$ at high SNR.
