Tight Upper and Lower Bounds to the Information Rate of the Phase Noise Channel

TL;DR

This paper develops numerical upper and lower bounds for the information rate of a Gaussian noise channel affected by complex ARMA phase noise, using particle and Kalman filtering techniques, effectively approximating the channel capacity.

Contribution

It introduces a novel approach to estimate the information rate of multidimensional ARMA phase noise channels using advanced filtering methods, overcoming limitations of traditional trellis-based models.

Findings

Upper and lower bounds are very close, approximating the actual information rate.

The lower bound is nearly capacity-achieving with a Kalman filter-based demodulator.

The proposed methods effectively handle multidimensional ARMA phase noise models.

Abstract

Numerical upper and lower bounds to the information rate transferred through the additive white Gaussian noise channel affected by discrete-time multiplicative autoregressive moving-average (ARMA) phase noise are proposed in the paper. The state space of the ARMA model being multidimensional, the problem cannot be approached by the conventional trellis-based methods that assume a first-order model for phase noise and quantization of the phase space, because the number of state of the trellis would be enormous. The proposed lower and upper bounds are based on particle filtering and Kalman filtering. Simulation results show that the upper and lower bounds are so close to each other that we can claim of having numerically computed the actual information rate of the multiplicative ARMA phase noise channel, at least in the cases studied in the paper. Moreover, the lower bound, which is virtually capacity-achieving, is obtained by demodulation of the incoming signal based on a Kalman filter aided by past data. Thus we can claim of having found the virtually optimal demodulator for the multiplicative phase noise channel, at least for the cases considered in the paper.