Algorithms for Joint Phase Estimation and Decoding for MIMO Systems in the Presence of Phase Noise and Quasi-Static Fading Channels

In this work, we derive the maximum a posteriori (MAP) symbol detector for a multiple-input multiple-output system in the presence of Wiener phase noise due to noisy local oscillators. As in single-antenna systems, the computation of the optimum receiver is an analytically intractable problem and is unimplementable in practice. In this purview, we propose three suboptimal, low-complexity algorithms for approximately implementing the MAP symbol detector, which involve joint phase noise estimation and data detection. Our first algorithm is obtained by means of the sum-product algorithm, where we use the multivariate Tikhonov canonical distribution approach. In our next algorithm, we derive an approximate MAP symbol detector based on the smoother-detector framework, wherein the detector is properly designed by incorporating the phase noise statistics from the smoother. The third algorithm is derived based on the variational Bayesian framework. By simulations, we evaluate the performance of the proposed algorithms for both uncoded and coded data transmissions, and we observe that the proposed techniques significantly outperform the other important algorithms from prior works, which are considered in this work. Index Terms – Maximum a posteriori (MAP) detection, phase noise, sum-product algorithm (SPA), variational Bayesian (VB) framework, extended Kalman smoother (EKS), MIMO

Joint-Polarization Phase-Noise Estimation and Symbol Detection for Optical Coherent Receivers

The problem of optimal symbol detection in the presence of laser phase noise is studied, for uncoded polarization-multiplexed fiber-optic transmission. To this end, the maximum a posteriori (MAP) symbol detector is presented. Specifically, it is emphasized that obtaining phase-noise point estimates, and treating them as the true values of the phase noise, is in general suboptimal. Furthermore, a pilot-based algorithm that approximates the MAP symbol detector is developed, using approaches adopted from the wireless literature. The algorithm performs joint-polarization phase-noise estimation and symbol detection, for arbitrary modulation formats. Through Monte Carlo simulations, the algorithm is compared to existing solutions from the optical communications literature. It is demonstrated that joint-polarization processing can significantly improve upon the single-polarization case, with respect to linewidth tolerance. Finally, it is shown that with less than 3% pilot overhead, the algorithm can be used with lasers having up to 6 times larger linewidths than the most well-performing blind algorithms can tolerate

Iterative Detection and Phase-Noise Compensation for Coded Multichannel Optical Transmission

The problem of phase-noise compensation for correlated phase noise in coded multichannel optical transmission is investigated. To that end, a simple multichannel phase-noise model is considered and the maximum a posteriori detector for this model is approximated using two frameworks, namely factor graphs (FGs) combined with the sum–product algorithm (SPA), and a variational Bayesian (VB) inference method. The resulting pilot-aided algorithms perform iterative phase-noise compensation in cooperation with a decoder, using extended Kalman smoothing to estimate the a posteriori phase-noise distribution jointly for all channels. The system model and the proposed algorithms are verified using experimental data obtained from space-division multiplexed multicore-fiber transmission. Through Monte Carlo simulations, the algorithms are further evaluated in terms of phase-noise tolerance for coded transmission. It is observed that they significantly outperform the conventional approach to phase-noise compensation in the optical literature. Moreover, the FG/SPA framework performs similarly or better than the VB framework in terms of phase-noise tolerance of the resulting algorithms, for a slightly higher computational complexity

Iterative graphical algorithms for phase noise channels.

Doctoral Degree. University of KwaZulu-Natal, Durban.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