Phase Modulation for Discrete-time Wiener Phase Noise Channels with Oversampling at High SNR

A discrete-time Wiener phase noise channel model is introduced in which multiple samples are available at the output for every input symbol. A lower bound on the capacity is developed. At high signal-to-noise ratio (SNR), if the number of samples per symbol grows with the square root of the SNR, the capacity pre-log is at least 3/4. This is strictly greater than the capacity pre-log of the Wiener phase noise channel with only one sample per symbol, which is 1/2. It is shown that amplitude modulation achieves a pre-log of 1/2 while phase modulation achieves a pre-log of at least 1/4.