Iterative graphical algorithms for phase noise channels.

Abstract

This thesis proposes algorithms based on graphical models to detect signals and charac- terise the performance of communication systems in the presence of Wiener phase noise. The algorithms exploit properties of phase noise and consequently use graphical models to develop low complexity approaches of signal detection. The contributions are presented in the form of papers. The first paper investigates the effect of message scheduling on the performance of graphical algorithms. A serial message scheduling is proposed for Orthogonal Frequency Division Multiplexing (OFDM) systems in the presence of carrier frequency offset and phase noise. The algorithm is shown to have better convergence compared to non-serial scheduling algorithms. The second paper introduces a concept referred to as circular random variables which is based on exploiting the properties of phase noise. An iterative algorithm is proposed to detect Low Density Parity Check (LDPC) codes in the presence of Wiener phase noise. The proposed algorithm is shown to have similar performance as existing algorithms with very low complexity. The third paper extends the concept of circular variables to detect coherent optical OFDM signals in the presence of residual carrier frequency offset and Wiener phase noise. The proposed iterative algorithm shows a significant improvement in complexity compared to existing algorithms. The fourth paper proposes two methods based on minimising the free energy function of graphical models. The first method combines the Belief Propagation (BP) and the Uniformly Re-weighted BP (URWBP) algorithms. The second method combines the Mean Field (MF) and the URWBP algorithms. The proposed methods are used to detect LDPC codes in Wiener phase noise channels. The proposed methods show good balance between complexity and performance compared to existing methods. The last paper proposes parameter based computation of the information bounds of the Wiener phase noise channel. The proposed methods compute the information lower and upper bounds using parameters of the Gaussian probability density function. The results show that these methods achieve similar performance as existing methods with low complexity.