Chuanzong Zhang

Iterative Receiver Design for ISI Channels Using Combined Belief- and Expectation-Propagation

In this letter, a message-passing algorithm that combines belief propagation and expectation propagation is applied to design an iterative receiver for intersymbol interference channels. We detail the derivation of the messages passed along the nodes of a vector-form factor graph representing the underlying probabilistic model. We also present a simple but efficient method to cope with the “negative variance” problem of expectation propagation. Simulation results show that the proposed algorithm outperforms, in terms of bit-error-rate and convergence rate, a LMMSE turbo-equalizer based on Gaussian message passing with the same order of computational complexity.

A low complexity OFDM receiver with combined GAMP and MF message passing

With a unified belief propagation (BP) and mean field (MF) framework, we propose an iterative message passing receiver, which performs joint channel state and noise precision (the reciprocal of noise variance) estimation and decoding for OFDM systems. The recently developed generalized approximate message passing (GAMP) is incorporated to the BP–MF framework, where MF is used to handle observation factor nodes with unknown noise precision and GAMP is used for channel estimation in the time–frequency domain. Compared to state-of-the-art algorithms in the literature, the proposed algorithm either delivers similar performance with much lower complexity, or delivers much better performance with similar complexity. In addition, the proposed algorithm exhibits fastest convergence.

Variational message passing-based localisation algorithm with Taylor expansion for wireless sensor networks

For localisation algorithms of wireless sensor networks (WSNs), the communication overhead and the computational complexity are two main bottlenecks that should be considered beside the positioning accuracy. In this study, the authors focus on cooperative localisation in WSNs and propose a low-complexity distributed cooperative localisation algorithm by employing variational message passing (VMP) on factor graphs. In order to decrease the communication overhead, Gaussian parametric message representation is adopted. With regard to the non-Gaussian messages caused by the non-linear ranging model, they approximate them to Gaussian messages by exploiting second-order Taylor expansion to reduce the computational complexity. Simulation results show that the proposed algorithm performs quite similar to sum-product algorithm over a wireless network and Gaussian VMP algorithm based on minimising Kullback–Leibler divergence with lower computational complexity.

Message-Passing Receivers for Single Carrier Systems with Frequency-Domain Equalization

In this letter, we design iterative receiver algorithms for joint frequency-domain equalization and decoding in a single carrier system assuming perfect channel state information. Based on an approximate inference framework that combines belief propagation (BP) and the mean field (MF) approximation, we propose two receiver algorithms with, respectively, parallel and sequential message-passing schedules in the MF part. A recently proposed receiver based on generalized approximate message passing (GAMP) is used as a benchmarking reference. The simulation results show that the BP-MF receiver with sequential passing of messages achieves the best BER performance at the expense of higher computational complexity compared to that of the GAMP receiver. The parallel BP-MF receiver has complexity similar to that of GAMP, but its low convergence rate yields poor performance, especially under high signal-to-noise ratio conditions.

Message Passing localisation algorithm combining BP with VMP for mobile wireless sensor networks

For large-scale wireless sensor networks (WSNs) with thousands of sensors, cooperative self-localisation is a key task and has caused extensive concerns. In this study, the authors propose a message passing algorithm for cooperative self-localisation of mobile WSNs by using belief propagation (BP) and variational message passing (VMP) on factor graphs. The sensors locate themselves through two steps: a prediction operation accounting for the sensors’ mobility and a correction operation accounting for ranging measurements between neighbouring sensors. All the messages for computing and transmitting are restricted to be Gaussian to reduce communication overhead and computational complexity. According to the linear state-transition model and the non-linear ranging model, BP and VMP methods are employed to perform prediction and correction, respectively. Simulation results show that when the standard deviations of the prior distributions is small, the positioning accuracy of the proposed algorithm is comparable with that of sum-product algorithm over a wireless network (SPAWN) with much low communication overhead and computational complexity.

An Auxiliary Variable-Aided Hybrid Message Passing Approach to Joint Channel Estimation and Decoding for MIMO-OFDM

This letter deals with message passing receiver design for joint channel estimation and decoding in MIMO-OFDM with unknown noise variance. The conventional factor graph representation for the system involves observation factors, which are functions of a number of variables in the form of multiplication and summation. In this work, by introducing some auxiliary variables, we further break each of the observation factors into several factors, which enables the use of hybrid mean field (MF), belief propagation (BP), and expectation propagation (EP) message passing to tackle the observation factors. It turns out that our approach is much more efficient than the existing approaches, leading to remarkable performance improvement as shown by simulation results.

A BP–MF–EP Based Iterative Receiver for Joint Phase Noise Estimation, Equalization, and Decoding

In this letter, with combined belief propagation (BP), mean field (MF), and expectation propagation (EP), an iterative receiver is designed for joint phase noise estimation, equalization, and decoding in a coded communication system. The presence of the phase noise results in a nonlinear observation model. Conventionally, the nonlinear model is directly linearized by using the first-order Taylor approximation, e.g., in the state-of-the-art soft-input extended Kalman smoothing approach (Soft-in EKS). In this letter, MF is used to handle the factor due to the nonlinear model, and a second-order Taylor approximation is used to achieve Gaussian approximation to the MF messages, which is crucial to the low-complexity implementation of the receiver with BP and EP. It turns out that our approximation is more effective than the direct linearization in the Soft-in EKS, leading to a significant performance improvement with similar complexity as demonstrated by simulation results.

Joint Spare Channel Estimation and Decoding for OFDM Using Combined Message Passing

In this study, the authors investigate the use of combined belief propagation (BP), mean field (MF) and expectation propagation (EP) message passing to achieve joint channel estimation and decoding (JCED) for orthogonal frequency division multiplexing where the channel sparsity is exploited, and a low-complexity BP–MF–EP-based JCED receiver is designed. Moreover, comparisons in message updating of state-of-the-art message passing-based JCED receivers are provided to illustrate the merits of the proposed one. In addition, message passing schedules are optimised to achieve better system performance. Simulation results verify the superiority of the proposed combined message passing receiver in terms of both bit-error-rate performance and convergence speed.

Combined Message Passing Based SBL With Dirichlet Process Prior for Sparse Signal Recovery With Multiple Measurement Vectors

This paper concerns the problem of sparse signal recovery with multiple measurement vectors, where the sparse signal vectors share multiple supports (i.e., the signal vectors can be clustered and the vectors in a cluster share a common support) and the prior knowledge on the supports of the vectors is unknown. This problem can be solved using sparse Bayesian learning (SBL) with Dirichlet process (DP) as hyper-prior, which is named DP-SBL in this paper. This paper aims to design efficient inference algorithms. The variational inference for DP mixtures, in particular mean field (MF) inference, has been studied, and applying it to the problem in this paper leads to an MF-DP-SBL algorithm. In this paper, we propose a combined message passing (CMP) approach, where a factor graph representation is designed to enable a more efficient implementation with both the MF and approximate message passing (AMP), leading to a CMP-DP-SBL algorithm. It is shown that, compared with MF-DP-SBL and CMP-DP-SBL delivers the same or even better performance with significantly lower complexity. As an example, we apply it to massive MIMO channel estimation where, due to the large number of antennas deployed at the base station, the channel impulse responses measured at receive antennas can share multiple supports. It is shown that CMP-DP-SBL delivers considerably better performance than existing algorithms.

Combined Message Passing Algorithms for Iterative Receiver Design in Wireless Communication Systems

Statistical inference using message passing on factor graphs provides a useful and versatile tool for the design of iterative receivers in wireless communications, as shown by the large number of research articles proposing such solutions during the last decade. Among the different methods, belief propagation (BP), the mean field (MF) approximation, and expectation propagation (EP) have been prevalent. Each of these methods is especially suited for different types of problems, which has motivated the use of algorithms combining two or more of them. These combinations, whether heuristic or based on well-founded theoretical grounds, allow for overcoming tractability and complexity issues present in the individual methods. In this thesis, we research the application of message passing methods and – combination thereof – to the design of receivers for various wireless communication systems. BP is firstly considered as it typically leads to better performance, while MF or EP can be used when the computation of BP messages is highly complex or intractable. Among others, we study the design of message passing receivers for turbo-equalization of inter-symbol interference channels, frequency domain turbo-equalization, channel estimation and decoding in multicarrier systems, and phase noise estimation and decoding. By appropriately combining message computation rules belonging to different frameworks, we obtain designs that are superior to the state-of-art counterparts in decoding performance, computational complexity, or both. Moreover, in order to obtain feasible receiver algorithms for these concrete problems, we propose approximations of intractable messages produced by BP, that are shown to be practical, have low-complexity, and do not degrade the performance of the receivers significantly. Based on the good performance of our proposed receivers, we conclude that there is the room and the need for further research towards the theoretical formalization of statistical inference algorithms combining two or more message passing methods. This would further expand the set of tools available for finding the best possible compromise between receiver performance and computational complexity in future wireless receivers.