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 SNR^α for 0 ≤ α ≤ 1, then the capacity pre-log is at most (1 + α)/2 at high SNR.