On the Degrees of Freedom of the Oversampled Wiener Phase Noise Channel

Abstract

The discrete-time Wiener phase noise channel with an integrate-and-dump multi-sample receiver, referred to as the Oversampled Wiener Phase Noise (OWPN) channel is studied. The capacity of this channel is characterized by three parameters: transmit power P, oversampling factor L, and the variance of the Wiener phase noise sigma(2). The capacity of this model is connected to the capacity of two related models: the Oversampled Non-Coherent (ONC) channel and the Additive White Gaussian Noise (AWGN) channel. More precisely, it is shown that (i) the capacity of the OWPN is close to the ONC channel when sigma(2) > L while (ii) the capacity of the OWPN is close to that of the AWGN channel when sigma(2) < P-1.