Upper Bound on the Capacity of Discrete-Time Wiener Phase Noise Channels
  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. 
Luca Barletta, Gerhard Kramer
cs.IT math.IT