text: abstract—the discrete-time wiener phase noise channel with
  an integrate-and-dump multi-sample receiver is studied. a novel
  outer bound on the capacity with an average input power
  constraint is derived as a function of the oversampling factor.
  this outer bound yields the degrees of freedom for the scenario
  in which the oversampling factor grows with the transmit power
  p as p α . the result shows, perhaps surprisingly, that the largest
  pre-log that can be attained with phase modulation at high signalto-noise ratio is at most 1/4.