Holographic multiple-input and multiple-output (HMIMO) is a promising technology with the potential to achieve high energy and spectral efficiencies, enhance system capacity and diversity, etc. In this work, we address the challenge of HMIMO near field (NF) channel estimation, which is complicated by the intricate model introduced by the dyadic Green’s function. Despite its complexity, the channel model is governed by a limited set of parameters. This makes parametric channel estimation highly attractive, offering substantial performance enhancements and enabling the extraction of valuable sensing parameters, such as user locations, which are particularly beneficial in mobile networks. However, the relationship between these parameters and channel gains is nonlinear and compounded by integration, making the estimation a formidable task. To tackle this problem, we propose a novel neural network (NN) assisted hybrid method. With the assistance of NNs, we first develop a novel hybrid channel model with a significantly simplified expression compared to the original one, thereby enabling parametric channel estimation. Using the readily available training data derived from the original channel model, the NNs in the hybrid channel model can be effectively trained offline. Then, building upon this hybrid channel model, we formulate the parametric channel estimation problem with a probabilistic framework and design a factor graph representation for Bayesian estimation. Leveraging the factor graph representation and unitary approximate message passing (UAMP), we develop an effective message passing-based Bayesian channel estimation algorithm. Extensive simulations demonstrate the superior performance of the proposed method.

Grant-free random access is promising in achieving massive connectivity with sporadic transmissions in massive machine-type communications (mMTCs) for Internet of Things (IoT) applications, where the handshaking between the access point (AP) and users is skipped, leading to high multiple access efficiency. In grant-free random access, the AP needs to identify the active users and perform channel estimation and signal detection. Conventionally, pilot signals are required for the AP to achieve user activity detection and channel estimation before active user signal detection, which may still result in substantial overhead and latency. In this article, to further reduce the overhead and latency, we investigate the problem of grant-free random access without the use of pilot signals in a millimeter-wave (mmWave) multiple input and multiple output (MIMO) system, where the AP performs blind joint user activity detection, channel estimation, and signal detection (UACESD). We show that the blind joint UACESD can be formulated as a constrained composite matrix factorization problem, which can be solved by exploiting the structures of the channel matrix and signal matrix. Leveraging a unitary approximate message passing-based matrix factorization (UAMP-MF) algorithm, we design a message passing-based Bayesian algorithm to solve the blind joint UACESD problem. Extensive simulation results demonstrate the effectiveness of the blind grant-free random access scheme.

This article considers a challenging scenario of machine-type communications, where we assume Internet of Things (IoT) devices send short packets sporadically to an access point (AP) and the devices are not synchronized in the packet level. High-transmission efficiency and low latency are concerned. Motivated by the great potential of multiple-input-multiple-output nonorthogonal multiple access (MIMO-NOMA) in massive access, we design a grant-free MIMO-NOMA scheme, and in particular differential modulation is used so that expensive channel estimation at the receiver (AP) can be bypassed. The receiver at AP needs to carry out active device detection and multidevice data detection. The active user detection is formulated as the estimation of the common support of sparse signals, and a message-passing-based sparse Bayesian learning (SBL) algorithm is designed to solve the problem. Due to the use of differential modulation, we investigate the problem of noncoherent multidevice data detection, and develop a message-passing-based Bayesian data detector, where the constraint of differential modulation is exploited to drastically improve the detection performance, compared to the conventional noncoherent detection scheme. Simulation results demonstrate the effectiveness of the proposed active device detector and noncoherent multidevice data detector.

Quasi-cyclic low density parity check (QC-LDPC) is widely used in various modern communication standards due to its excellent performance and convenient hardware implementation, but its commonly used pipelined layered decoder faces update conflicts that lead to performance degradation. This letter proposes a shortcut-based decoder to mitigate this problem. When the conflicts occur, we avoid the read/write operations of the log-likelihood ratios (LLRs) and abandon the use of the barrel shifters, and feed those LLRs directly to the next layer. we also attempt to utilize the latest messages for inevitable conflicts. Moreover, the proposed architecture significantly reduces the possibility of conflicts by reordering the base graph matrix (BGM) with a shorter update interval of LLRs, which can achieve maximum utilization in the updated messages. Compared to the state-of-the-art approach in the case of DVB-S2, the proposed architecture can deliver up to 0.25 dB performance gain with faster convergence.

The design of message passing (MP) algorithms on factor graphs is an effective manner to implement channel estimation (CE) in wireless communication systems, which performance can be further improved by exploiting prior probability models that accurately match the channel characteristics. In this work, we study the CE problem in a downlink massive multiple-input multiple-output (MIMO) orthogonal frequency division multi-plexing (OFDM) system. As the prior probability, we propose the Markov chain two-state Gaussian mixture with large variance differences (TSGM-LVD) model to exploit the structured sparsity in the angle-frequency domain of the channel. Existing single and combined MP rules cannot deal with the message computation of the proposed probability model. To overcome this issue, we present a general method to derive the hybrid message passing (HMP) rule, which allows the calculation of messages described by mixed linear and non-linear functions. Accordingly, we design the HMP-TSGM-LVD algorithm under the structured turbo framework (STF). Simulation results demonstrate that the proposed algorithm converges faster and obtains better and more stable performance than its counterparts. In particular, the gain of the proposed approach is maximum (3 dB) in the high signal-to-noise ratio regime, while benchmark approaches experience oscillating behavior due to the improper prior model characterization.

Reconfigurable intelligent surface (RIS) is very promising for wireless networks to achieve high energy efficiency, extended coverage, improved capacity, massive connectivity, etc. To unleash the full potentials of RIS-aided communications, acquiring accurate channel state information is crucial, which however is very challenging. For RIS-aided multiple-input and multiple-output (MIMO) communications, the existing channel estimation methods have computational complexity growing rapidly with the number of RIS units$N$(e.g., in the order of$N^{2}$or$N^{3}$) and/or have special requirements on the matrices involved (e.g., the matrices need to be sparse for algorithm convergence to achieve satisfactory performance), which hinder their applications. In this work, instead of using the conventional signal model in the literature, we derive a new signal model obtained through proper vectorization and reduction operations. Then, leveraging the unitary approximate message passing (UAMP), we develop a more efficient channel estimator that has complexity linear with$N$and does not have special requirements on the relevant matrices, thanks to the robustness of UAMP. These facilitate the applications of the proposed algorithm to a general RIS-aided MIMO system with a larger$N$. Moreover, extensive numerical results show that the proposed estimator delivers much better performance and/or requires significantly less number of training symbols, thereby leading to notable reductions in both training overhead and latency.

The orthogonal-time-frequency-space (OTFS) modulation has emerged as a promising modulation scheme for high mobility wireless communications. To harvest the time and frequency diversity promised by OTFS, some promising detectors, especially message passing based ones, have been developed by taking advantage of the sparsity of the channel in the delay-Doppler domain. However, when the number of channel paths is relatively large or fractional Doppler shifts have to be considered, the complexity of existing detectors is a concern, and the existing message passing based detectors suffer from performance loss. In this work, we investigate the design of OTFS detectors based on the approximate message passing (AMP). In particular, leveraging the unitary AMP (UAMP), we design new detectors that enjoy the structure of the channel matrix and allow efficient implementation. In addition, the estimation of noise variance is incorporated into the UAMP-based detectors. Thanks to the robustness of UAMP relative to AMP, the UAMP-based detectors deliver superior performance, and outperform state-of-the-art detectors significantly. We also investigate iterative joint detection and decoding in a coded OTFS system, where the OTFS detectors are integrated into a powerful turbo receiver, leading to considerable performance gains.

In this article, we study a robust beamforming design for multiuser multiple-input–multiple-output secrecy networks with simultaneous wireless information and power transfer (SWIPT). In this system, an access point, multiple Internet-of-Things (IoT) devices under the nonlinear energy harvesting (EH) model with a help of one cooperative jammer (CJ). We employ artificial noise (AN) generation to facilitate efficient wireless energy transfer and secure transmission. To achieve EH fairness, we aim to maximize the minimum harvested energy among users subject to secrecy rate constraint and total transmit power constraint in the presence of channel estimation errors. By incorporating a norm-bounded channel uncertainty model, the original robust problem is transformed into a two-layer optimization problem, where the inner layer problem is reformulated as semidefinite programming (SDP) and the outer layer problem is solved by a one-dimensional (1-D) line search algorithm. In addition, in order to reduce computational complexity, we propose an algorithm based on sequential parametric convex approximation (SPCA). Finally, simulation results show that the proposed SPCA method achieves the same performance as the two-layer algorithm with much lower complexity.

The orthogonal time frequency space (OTFS) modulation has emerged as a promising modulation scheme for high mobility wireless communications. To enable efficient OTFS detection in the delay-Doppler (DD) domain, the DD domain channels need to be acquired accurately. To achieve the low latency requirement in future wireless communications, the time duration of the OTFS block should be small, therefore fractional Doppler shifts have to be considered to avoid significant modelling errors due to the assumption of integer Doppler shifts. However there lack investigations on the estimation of OTFS channels with fractional Doppler shifts in the literature. In this work, we develop a channel estimator for OTFS with particular attention to fractional Doppler shifts, and both bi-orthogonal waveform and rectangular waveform are considered. Instead of estimating the DD domain channel directly, we estimate the channel gains and (fractional) Doppler shifts that parameterize the DD domain channel. The estimation is formulated as a structured sparse signal recovery problem with a Bayesian treatment. Based on a factor graph representation of the problem, an efficient message passing algorithm is developed to recover the structured sparse signal (thereby the OTFS channel). The Cramer-Rao Lower Bound (CRLB) for the estimation is developed and the effectiveness of the algorithm is demonstrated through simulations.

This letter deals with variational inference for Dirichlet process mixtures (DPM) models. We propose a combined message-passing algorithm introducing belief propagation (BP) into the original mean field (MF) rules, which leads to a more precise approximate posterior in DPM. To compute the BP message, we change an exponential distribution to a non-exponential utilizing a flexible expression of Dirac delta function. Therefore, BP rules can be used to handle such functions, resulting to a local exact expectation instead of approximate expectation from the original MF method. Simulation results show that the proposed combined BP-MF algorithm results in a significant performance improvement compared to the state-of-the-art inference methods.

In this paper, we study a multi-user multiple-inputmultiple- output secrecy simultaneous wireless information and power transfer (SWIPT) channel which consists of one transmitter, one cooperative jammer (CJ), multiple energy receivers (potential eavesdroppers, ERs), and multiple co-located receivers (CRs). We exploit the dual of artificial noise (AN) generation for facilitating efficient wireless energy transfer and secure transmission. Our aim is to maximize the minimum harvested energy among ERs and CRs subject to secrecy rate constraints for each CR and total transmit power constraint. By incorporating norm-bounded channel uncertainty model, we propose a iterative algorithm based on sequential parametric convex approximation to find a near-optimal solution. Finally, simulation results are presented to validate the performance of the proposed algorithm outperforms that of the conventional AN-aided scheme and CJaided scheme.

Wireless energy transfer over radio frequency has been recognized as a promising alternative solution to powering the low power low complexity wireless equipments in future cellular networks. In this work, simultaneous wireless information and power transfer (SWIPT) operation for secure multi-user multipleinput multiple-output (MIMO) broadcast system is investigated with imperfect channel state information at the transmitter. The corresponding robust secure beamforming problem is studied, where the transmit power is to be minimized subject to the secrecy rate outage probability constraint for legitimate information users, and the harvested energy outage probability constraint for energy harvesting receivers. The original problem is shown to be non-convex due to the presence of the probabilistic constraints. These outage constraints are then transformed into deterministic forms by using the Bernstein-type inequalities. Based on successive convex approximation (SCA), a low-complexity approach, which reformulates the original problem as second order cone programming (SOCP), is proposed. Simulation results show that the proposed scheme outperforms the conventional method with lower complexity.

In this paper, an energy harvesting scheme for a multi-user multiple-input-multiple-output (MIMO) secrecy channel with artificial noise (AN) transmission is investigated. Joint optimization of the transmit beamforming matrix, the AN covariance matrix, and the power splitting ratio is conducted to minimize the transmit power under the target secrecy rate, the total transmit power, and the harvested energy constraints. The original problem is shown to be non-convex, which is tackled by a two-layer decomposition approach. The inner layer problem is solved through semi-definite relaxation, and the outer problem is shown to be a single-variable optimization that can be solved by one-dimensional (1-D) line search. To reduce computational complexity, a sequential parametric convex approximation (SPCA) method is proposed to find a near-optimal solution. Furthermore, tightness of the relaxation for the 1-D search method is validated by showing that the optimal solution of the relaxed problem is rank-one. Simulation results demonstrate that the proposed SPCA method achieves the same performance as the scheme based on 1-D search method but with much lower complexity.

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.

We investigate multiple‐input single‐output secured cognitive radio networks relying on simultaneous wireless information and power transfer (SWIPT), where a multiantenna secondary transmitter sends confidential information to multiple single‐antenna secondary users (SUs) in the presence of multiple single‐antenna primary users (PUs) and multiple energy‐harvesting receivers (ERs). In order to improve the security of secondary networks, we use the artificial noise (AN) to mask the transmit beamforming. Optimization design of AN‐aided transmit beamforming is studied, where the transmit power of the information signal is minimized subject to the secrecy rate constraint, the harvested energy constraint, and the total transmit power. Based on a successive convex approximation (SCA) method, we propose an iterative algorithm which reformulates the original problem as a convex problem under the perfect channel state information (CSI) case. Also, we give the convergence of the SCA‐based iterative algorithm. In addition, we extend the original problem to the imperfect CSI case with deterministic channel uncertainties. Then, we study the robust design problem for the case with norm‐bounded channel errors. Also, a robust SCA‐based iterative algorithm is proposed by adopting the ‐Procedure. Simulation results are presented to validate the performance of the proposed algorithms.

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.

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.

In this paper, an energy harvesting scheme for a multi-user multiple-input-multiple-output secrecy channel with artificial noise (AN) transmission is investigated. Joint optimization of the transmit beamforming matrix, the AN covariance matrix, and the power splitting ratio is conducted to minimize the transmit power under the target secrecy rate, the total transmit power, and the harvested energy constraints. The original problem is shown to be non-convex, which is tackled by a two-layer decomposition approach. The inner layer problem is solved through semi-definite relaxation, and the outer problem, on the other hand, is shown to be a single-variable optimization that can be solved by 1-D line search. To reduce computational complexity, a sequential parametric convex approximation method is proposed to find a near-optimal solution. This paper is then extended to the imperfect channel state information case with norm-bounded channel errors. Furthermore, tightness of the relaxation for the proposed schemes is validated by showing that the optimal solution of the relaxed problem is rank-one. Simulation results demonstrate that the proposed SPCA method achieves the same performance as the scheme based on 1-D but with much lower complexity.

In this paper, we study an energy harvesting scheme for a multiple-input-single-output secrecy channel under imperfect channel state information case with either deterministic and statistical channel uncertainties. The system consists of one multi-antenna transmitter, several multi-antenna energy receivers (ERs) and one single-antenna co-located receiver (CR) who adopts a power splitter to decode information and harvest power simultaneously. We consider the artificial noise (AN) embedded information-bearing signal to interfere potential eavesdroppers (i.e., ERs) and capture the harvested power. We perform joint optimization for the masked beamforming matrix, the AN covariance matrix and the power splitting ratio, such that the transmit power is minimized to satisfy the target secrecy rate of the CR, the total transmit power and the energy harvesting constraints for the CR and the ERs. By incorporating norm-bounded channel uncertainty model, we propose a robust joint design method to obtain the optimal solution. Also, a suboptimal algorithm for the outage constrained robust optimization problem is proposed by adopting the Bernstein-type inequality. Furthermore, the tightness of the relaxation for the proposed schemes are verified by showing that the optimal solution of the relaxed problem is rank-one. Finally, simulation results are presented to validate the performance of our proposed schemes.

In this paper, we study simultaneous wireless information and power transfer (SWIPT) for multiuser multipleinput- single-output (MISO) secrecy multicasting channels with imperfect channel state information. First, a robust secure beamfoming design is considered, where the transmit power is minimized subject to the secrecy rate outage probability constraint for legitimate users and the harvested energy outage probability constraint for energy harvesting receivers. The original problem is non-convex due to the presence of the probabilistic constraints. By utilizing Bernstein-type inequalities, we transform the outage constraints into the deterministic forms. In order to identify a local optimal rank-one solution, we propose an efficient approach based on a constrained concave convex procedure method to convert the original problem into a sequence of convex programming problems. Finally, simulation results are provided to validate the performance of our proposed design methods.

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.

In this study, the authors study simultaneous wireless information and power transfer for multiuser multiple‐input–single‐output secure multicasting channels with imperfect channel state information. First, a robust secure beamforming design is considered, where the transmit power is minimised subject to the secrecy rate outage probability constraint for legitimate users and the harvested energy outage probability constraint for energy harvesting receivers. The original problem is non‐convex due to the presence of the probabilistic constraints. By utilising Bernstein‐type inequalities, the authors transform the outage constraints into the deterministic forms. In order to identify a local optimal rank‐one solution, the authors propose an efficient approach based on a constrained concave convex procedure method to convert the original problem into a sequence of convex programming problems. Finally, simulation results are provided to validate the performance of the proposed design methods.

In this study, the authors study the robust transmit beamforming and receive power splitting design for simultaneous wireless information and power transfer in multiuser multiple‐input–single‐output interference channel with imperfect channel‐state information at the transmitter. Following the worst‐case model, they minimise the average total transmit power subject to a set of energy harvesting constraints and signal‐to‐interference‐and‐noise ratio constraints. On the basis of the Lagrangian multiplier method, they propose a robust design method based on tight bounds that is able to achieve an approximate optimum. To reduce the complexity, they transform this original problem into a relaxed semi‐definite programming problem based on loose bounds, which can be solved efficiently. It is shown from simulation results that their proposed methods outperform the non‐robust scheme.

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.

This letter deals with turbo equalization for coded data transmission over intersymbol interference (ISI) channels. We propose a message-passing algorithm that uses the expectation propagation rule to convert messages passed from the demodulator and decoder to the equalizer and computes messages returned by the equalizer by using a partial Gaussian approximation (PGA). We exploit the specific structure of the ISI channel model to compute the latter messages from the beliefs obtained using a Kalman smoother/equalizer. Doing so leads to a significant complexity reduction compared to the initial PGA implementation. Results from Monte Carlo simulations show that the proposed approach leads to a significant performance improvement compared to state-of-the-art turbo equalizers and allows for trading performance with complexity.

In this paper, we investigate simultaneous wireless information and power transfer systems for multiuser multiple-input single-output secure broadcasting channels. Considering imperfect channel state information, we introduce a robust secure beamforming design, where the transmit power is minimized subject to the secrecy rate outage probability constraint for legitimate users and the harvested energy outage probability constraint for energy harvesting receivers. The original problem is non-convex due to the presence of the probabilistic constraints. With the aid of Bernstein-type inequalities, we transform the outage constraints into the deterministic forms. Based on a successive convex approximation (SCA) method, we propose a low-complexity approach, which reformulates the original problem as a second-order cone programming problem. Also, we prove the convergence of the SCA-based iterative algorithm. Simulation shows that the proposed scheme outperforms the conventional method with lower complexity.

We address a new robust optimization problem in a multiuser multiple-input single-output broadcasting system with simultaneous wireless information and power transmission. Assuming that perfect channel- state information (CSI) for all channels is not available at the BS, the uncertainty of the CSI is modeled by an norm-bounded uncertainty set. To optimally design transmit beamforming weights and receive power splitting, an average total transmit power minimization problem is investigated subject to the individual harvested power constraint and the received signal-to-interference-plus-noise ratio constraint at each user. The original design problem is reformulated to a relaxed semidefinite program, and then two different approaches based on convex programming are proposed, which can be solved efficiently by the interior point algorithm. Interestingly, we show that the semidefinite relaxation (SDR) is tight. Numerical results are provided to validate the robustness of the proposed algorithms.

In this paper, we investigate a multiuser downlink distributed antenna system with simultaneous wireless information and power transmission under the assumption of imperfect channel state information at the distributed antenna (DA) port. To optimally design robust transmit beamforming vectors and receive power splitting factors, our design objective is to maximize the average worst-case signal-to-interference-plus-noise ratio while simultaneously achieving the individual energy harvesting (EH) constraint for each user and the per-DA port power constraint. We solve this non- convex problem by reformulating it into a two-stage problem. Simulation results are shown to validate the robustness and effectiveness of the proposed algorithms.

Abstract Because of the broadcast nature of the wireless communication medium, their security issues are receiving extensive concern. In this paper, we propose a spectrum‐sparse signal based on multi‐carrier modulation for secure wireless communication. The proposed signal is a summation of multiple sub‐band signals over several equally spaced carriers. The power spectrum density of the proposed signal can be reduced to a level even lower than the background noise, provided the number of sub‐bands is sufficiently large. Thus, the proposed signal possesses a favorable low probability detection property similar to that of spread spectrum signals. At the intended receiver, an under‐sampling method based on active aliasing is proposed. In this way, the intended receiver can coherently collect the transmitted signal power over all sub‐bands and extract the information reliably. We also derive a closed‐form expression for bit error rate performance of the proposed scheme in additive white Gaussian channel with binary phase shift keying modulation. Finally, numerical and simulation results to testify the effectiveness of the proposed scheme are generated for both binary phase shift keying and eight‐phase shift keying modulations in additive white Gaussian channel. Copyright © 2015 John Wiley & Sons, Ltd.

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.

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.