Capacity of Discrete-Time Wiener Phase Noise Channels to Within a Constant Gap

Abstract

The capacity of the discrete-time channel affected by both additive Gaussian noise and Wiener phase noise is studied. Novel inner and outer bounds are presented, which differ of at most 7.36 bit-per-channel-use for all channel parameters. The capacity of this model can be subdivided in three regimes: (i) for large values of the frequency noise variance, the channel behaves similarly to a channel with circularly uniform iid phase noise; (ii) when the frequency noise variance is small, the effect of the additive noise dominates over that of the phase noise, while (iii) for intermediate values of the frequency noise variance, the transmission rate over the phase modulation channel has to be reduced due to the presence of phase noise.