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The discrete-time Wiener phase noise channel with an integrate-and-dumpmulti-sample receiver is studied.  A novel outer bound on the capacity with an average input power constraint isderived as a function of the oversampling factor.  This outer bound yields the degrees of freedom for the scenario in which theoversampling factor grows with the transmit power $P$ as $P^{\alpha}$.  The result shows, perhaps surprisingly, that the largest pre-log that can beattained with phase modulation at high signal-to-noise ratio is at most $1/4$.

Capacity Outer Bound and Degrees of Freedom of Wiener Phase Noise Channels with Oversampling