The space-air-ground integrated network (SAGIN) paradigm has emerged as a pivotal enabler for the evolution of next-generation wireless systems. This article proposes a novel framework for covert communication in SAGINs, wherein a high-altitude platform (HAP), equipped with multiple antennas, serves terrestrial communication users (CUs) under the surveillance of multiple non-colluding wardens, with satellite assistance for warden location updates via space-air links. To safeguard the communication from detection by the wardens, the HAP employs artificial noise (AN) and robust beamforming techniques, addressing the challenges posed by imperfect channel state information (CSI) of the wardens. Subsequently, we formulate a non-convex optimization problem aimed at maximizing the number of served users, subject to stringent covertness constraints, satellite-HAP link outage probabilities, and maximum available power budgets. By employing ℓ0-norm relaxation, we convert the original problem into a mixed-integer optimization framework and develop a computationally efficient alternating optimization approach that combines bisection search, successive convex approximation (SCA), and semidefinite relaxation (SDR) techniques to tackle satellite power allocation, user scheduling, and beamforming design. Numerical simulations demonstrate that the proposed scheme significantly improves the user coverage while maintaining covertness, revealing a trade-off between covert communication and CU coverage capability in resource-constrained aerial-terrestrial environments, even under imperfect CSI conditions.

Tensor decomposition (TD) models are promising solutions for knowledge graph completion due to their simple structures but powerful representation capacities. The TD models typically adopt Tucker decomposition with a structured core tensor. Some models with a sparse core tensor, such as DistMult and ComplEx, are too simple and thus limit the interaction between embedding components, while other models with a dense core tensor are too complex and may lead to significant overfitting. To address these issues, we propose a new TD model called SPAC (Sparse Partitioning and Adaptive Core tensor pruning) model for knowledge graph completion. Specifically, SPAC captures coarse and fine-grained semantic information using a hybrid core tensor, where auxiliary cores are used to model sparse interactions and main cores for dense interactions. Moreover, SPAC introduces a gating mechanism to control the output of intermediate variables, enhancing the interaction between different partition groups. Furthermore, SPAC employs an adaptive pruning approach to dynamically adjust the shape of the core tensor. Due to the elaborate model design, the proposed TD model enhances expressive capacity and reduces the number of parameters in the core tensor. Experiments are conducted on datasets FB15k-237, WN18RR, and YAGO3-10. The results demonstrate that SPAC outperforms state-of-the-art tensor decomposition models, including MEIM and Tucker models. A series of ablation studies show that the gating mechanism and adaptive pruning strategy in SPAC are crucial for the performance improvement.

This paper proposes a novel integrated sensing and communication (ISAC) receiver design framework for OTFS (orthogonal time frequency space)-based MIMO (multi-input-multi-output) systems from a unified perspective of variational inference. We first construct a factor graph representation for the OTFS-based MIMO system according to the factorization of the a posteriori probability (APP). This representation establishes a direct probabilistic link between sensing and communication, allowing both functionalities to benefit from their integration. On this basis, we develop a low computational complexity message passing algorithm by minimizing the variational free energy associated with the global APP. In particular, belief propagation, mean field, and expectation maximization algorithms for data detection, channel coefficient estimation, and kinematic parameter sensing are derived, respectively. To reduce the communication overhead for the implementation of ISAC algorithm, we propose a federated learning scheme for distributed kinematic parameter sensing. Specifically, by solving the sensing problem in different fashions, three federated learning modes are devised. Simulation results validate the superior performance of the proposed scheme.

Large-aperturecoprime arrays(CAs) are expected to achieve higher sensing resolution than conventional dense arrays (DAs), yet with lower hardware and energy cost. However, existing CA far-field localization methods cannot be directly applied to near-field scenarios due to channel model mismatch. To address this issue, in this paper, we propose an efficient near-field localization method for CAs. Specifically, we first construct an effective covariance matrix, which allows to decouple the target angle-and-range estimation. Then, a customized two-phase multiple signal classification (MUSIC) method for CAs is proposed, which first detects all possible angles of targets by using an angular-domain MUSIC method, followed by a second phase to resolve the true angles of targets and their ranges by devising a range-domain MUSIC method. We show that the proposed method can achieve near-optimal multi-target localization performance as conventional two-dimensional (2D)-MUSIC method with much lower computational complexity. Additionally, we characterize the Cramér-Rao bounds for symmetric CAs and provide interesting insights. Finally, numerical results demonstrate that our proposed method is able to localize more targets than the existing subarray-based method as well as achieve lower root mean square error than DAs.

In this paper, we develop a graph neural network (GNN)-assisted bilinear inference approach to enhance the receiver performance of the MIMO system through message passing-based joint channel estimation and data detection (JCD). Specifically, based on the bilinear generalized approximate message passing (BiG-AMP) framework and conditional correlation of signal, we propose a GNN-assisted BiG-AMP (GNN-BiGAMP) approach, which integrates a GNN module into the data-detection-loop to compensate the inaccurate marginal likelihood approximation. By leveraging the coupling between the channel and received symbols, a bilinear GNN-assisted BiG-AMP (BiGNN-BiGAMP) JCD receiver is further proposed. This method incorporates two GNNs with similar graph representation into the bilinear posterior estimation loops, which not only compensates for approximation errors but also alleviates performance loss due to premature variance convergence, thereby enhancing the receiver performance significantly. To fully exploit the supervised information from channel estimation and data detection, we propose a multitask learning based training scheme, which coordinates GNNs with different tasks in two loops. Simulation results show that our proposed GNN-assisted JCD receivers significantly outperform other JCD counterparts in terms of both channel estimation and data detection.

Existing communication signal-based sensing systems mainly rely on the orthogonal frequency division multiplexing (OFDM) technique due to its remarkable communication performance. However, extracting Doppler shifts from the received signal is not straightforward for OFDM and usually requires additional operations. The recently emerging orthogonal time frequency space (OTFS) modulation, which employs the Delay-Doppler (DD) domain for data transmission, can reveal the physical wireless propagation environments and provide the DD information directly. This paper investigates the moving multi-target sensing problem based on OTFS signaling. In particular, we attempt to tackle sensing and data association tasks concurrently by using the time delay (TD) and Doppler information from OTFS channel estimation. To this end, we formulate a mixed-integer optimization problem and approximate it as a convex problem. Simulation results has demonstrated the effectiveness of the proposed method.

To leverage distributed data communication and learning in sensor networks effectively, edge learning (EL) methods have garnered significant attention. In the realm of distributed sensor networks, achieving consensus estimation of interested variables stands as a pivotal challenge. To address this challenge using EL methods, several approaches have been proposed combining message passing (MP) algorithms. In this article, we first describe the distributed consensus algorithm based on MP and summarize the sampling-based and parameter-based representation of the beliefs exchanged in the distributed MP algorithm. To improve the accuracy of estimation while retaining the low-complexity advantage of the parametric representation method, we propose a distributed consensus framework based on the Gaussian mixture model (GMM) MP. We approximate and keep the form beliefs as GMM in the iterations. Two different simulation scenarios are performed to shed light on the proposed distributed consensus estimation framework, i.e., static target localization and dynamic target tracking. Finally, simulation results show the performance advantages of the algorithm proposed.

Fingerprint-based indoor localization holds great potential for the Internet of Things. Despite numerous studies focusing on its algorithmic and practical aspects, a notable gap exists in theoretical performance analysis in this domain. This paper aims to bridge this gap by deriving several lower bounds and approximations of mean square error (MSE) for fingerprint-based localization. These analyses offer different complexity and accuracy trade-offs. We derive the equivalent Fisher information matrix and its decomposed form based on a wireless propagation model, thus obtaining the Cramér-Rao bound (CRB). By approximating the Fisher information provided by constraint knowledge, we develop a constraint-aware CRB. To more accurately characterize nonlinear transformation and constraint information, we introduce the Ziv-Zakai bound (ZZB) and modify it for adapt deterministic parameters. The Gauss–Legendre quadrature method and the trust-region reflective algorithm are employed to make the calculation of ZZB tractable. We introduce a tighter extrapolated ZZB by fitting the quadrature function outside the well-defined domain based on the Q-function. For the constrained maximum likelihood estimator, an approximate MSE expression, which can characterize map constraints, is also developed. The simulation and experimental results validate the effectiveness of the proposed bounds and approximate MSE.

In this paper, we investigate the realization of covert communication in a general radar-communication cooperation system, which includes integrated sensing and communications as a special example. We explore the possibility of utilizing the sensing ability of radar to track and jam the aerial adversary target attempting to detect the transmission. Based on the echoes from the target, the extended Kalman filtering technique is employed to predict its trajectory as well as the corresponding channels. Depending on the maneuvering altitude of adversary target, two channel state information (CSI) models are considered, with the aim of maximizing the covert transmission rate by jointly designing the radar waveform and communication transmit beamforming vector based on the constructed channels. For perfect CSI under the free-space propagation model, by decoupling the joint design, we propose an efficient algorithm to guarantee that the target cannot detect the transmission. For imperfect CSI due to the multi-path components, a robust joint transmission scheme is proposed based on the property of the Kullback-Leibler divergence. The convergence behaviour, tracking MSE, false alarm and missed detection probabilities, and covert transmission rate are evaluated. Simulation results show that the proposed algorithms achieve accurate tracking. For both channel models, the proposed sensing-assisted covert transmission design is able to guarantee the covertness, and significantly outperforms the conventional schemes.

Indoor localization is of pivotal significance for a wide variety of services in the context of the Internet of Things (IoT). Both ranging-based and fingerprint-based localization techniques are promising for employment in harsh indoor environments. Hence, we propose a unified framework based on factor graphs for ubiquitous high-accuracy indoor localization. Our unified framework efficiently integrates ranging and fingerprinting for striking an appealing accuracy versus deployment cost tradeoff, where the crowdsourcing required for the construction of fingerprinting databases can also be addressed with little human intervention. By intrinsically amalgamating the global grid sampling and the regularized importance-resampling techniques, a nonparametric belief propagation algorithm is proposed for achieving the accurate position estimation at the cost of a moderate computational complexity. For improving the robustness to environmental variations, a likelihood-ratio-based approach is employed to detect ranging outliers. Moreover, a low-complexity serial scheduling scheme defined over factor graphs is designed for real-time localization. We design a hybrid ultrawide bandwidth and Wi-Fi localization system relying on off-the-shelf commercial devices and evaluate the proposed unified framework in a typical office building. Our experimental results show that the proposed algorithm outperforms the existing state-of-the-art methods and it is capable of achieving submeter localization accuracy.

The spectrally efficient multicarrier faster-than-Nyquist (MFTN) signaling provides an efficient and robust solution for enhancing transmission rate and resisting channel impairments. In this paper, an evolutionary non-orthogonal physical waveform is proposed for simultaneously achieving high spectral and energy efficiency via combining MFTN signaling with index modulation (IM). Exploiting the implicit transmission of IM, the inactivated subcarriers alleviate the inherent two-dimensional interferences imposed by time-frequency packing in MFTN. Then, we develop a pair of iterative equalization algorithms based on vector approximate message passing (VAMP). For the first time-domain equalization (TDE), an extended constellation set is constructed for uniformly characterizing the activated and inactivated subcarriers. To further reducing the computational complexity, we establish a subcarrier-based segment-wise frequency-domain received signal model and accordingly develop low-complexity VAMP-based frequency-domain equalization (FDE) combined with interference elimination. Corroborated by simulations, the novel MFTN-IM waveform achieves superior bit error rate (BER) performance over benchmark waveforms in the high signal noise ratio (SNR) regions. Interestingly, while the proposed VAMP-TDE outperforms the proposed VAMP-FDE in BER performance, the latter is more competitive in balancing demodulation performance and computational complexity.

The integration of terrestrial and satellite communications (Satcom) is advocated for satisfying the challenging requirements of seamless, high-performance services. However, both the bandwidth and the power available are limited over satellite channels. In this paper, we propose index modulation (IM) and code-aided Satcom by conveying information by a pair of distinguishable constellation modes and their permutations. In order to combat both the linear and nonlinear distortion imposed by satellite channels, we conceive a factor graph (FG)-based iterative detection algorithm for Satcom relying on dual-mode (DM) IM (Sat-DMIM). The correlation amongst Sat-DMIM symbols imposed by both the channel-induced dispersion and the mode-selection mapping is explicitly represented by the FG constructed. Then the amalgamated belief propagation (BP) and mean field (MF) message passing algorithm is derived over this FG for detecting both the IM bits and the classic constellation mapping bits, while eliminating both the linear and nonlinear distortions. The complexity of the iterative detection algorithm is reduced by linearizing some high-order terms appearing in nonlinear distortion components using thea posterioriestimates of the Sat-DMIM symbols obtained from the previous iteration. Our simulation results demonstrate the power of the proposed amalgamated BP-MF-based and partial linearization approximation-based iterative detection algorithms.

Network localization is capable of providing accurate and ubiquitous position information for numerous wireless applications. This paper studies the accuracy of cooperative network localization in large-scale wireless networks. Based on a decomposition of the equivalent Fisher information matrix (EFIM), we develop a random-walk-inspired approach for the analysis of EFIM, and propose a position information routing interpretation of cooperative network localization. Using this approach, we show that in large lattice and stochastic geometric networks, when anchors are uniformly distributed, the average localization error of agents grows logarithmically with the reciprocal of anchor density in an asymptotic regime. The results are further illustrated using numerical examples.

Belief propagation (BP) is a popular message passing algorithm for distributed cooperative localization. However, due to the nonlinearity of measurement functions, BP implementation has no closed-form expression and requires message approximations. While nonparametric BP can be used, it suffers from a high computational complexity, thus being impractical in energy-constrained networks. In this paper, a parametric Bayesian method with Gaussian BP implementation is proposed for distributed cooperative localization. With linearization of the Euclidean norm in ranging measurements, the joint posterior distribution of agents’ locations is successively approximated with a sequence of high-dimensional Gaussian distributions. At each iteration of the successive Gaussian approximation, vector-valued Gaussian BP is further adopted to compute the marginal distributions of agents’ locations in a distributed way. It is proved by the principle of majorization-minimization that the proposed successive Gaussian approximation is guaranteed to converge, and the sequence of the estimated agents’ locations converges to a stationary point of the objective function of the maximum a posteriori estimation. Furthermore, although cooperative localization involves loopy network topologies, in which convergence property of Gaussian BP is generally unknown, it is proved in this paper that vector-valued Gaussian BP converges, making the proposed parametric BP-based method being the first one achieving convergence guarantee. Compared to the nonparametric BP counterpart, the proposed method has a much lower computational complexity and communication overhead. Simulation results demonstrate that the proposed method achieves a superior performance in localization accuracy compared to existing cooperative localization methods.

A low-complexity parametric bilinear generalized approximate message passing (PBiGAMP)-based receiver is conceived for multi-carrier faster-than-Nyquist (MFTN) signaling over frequency-selective fading channels. To mitigate the inherent ill-conditioning problem of MFTN signaling, we construct a segment-based frequency-domain received signal model in the form of a block circulant linear transition matrix, which can be efficiently calculated by applying a two dimensional fast Fourier transform. Based on the eigenvalue decomposition of the block circulant matrices, we can diagonalize the covariance matrix of the complex-valued colored noise process imposed by the associated two dimensional non-orthogonal matched filtering. Building on this model, a PBiGAMP-based parametric joint channel estimation and equalization (JCEE) algorithm is proposed for MFTN systems. In this algorithm, we introduce a pair of additive terms for characterizing the interferences arising from adjacent segments and employ the exact discretea prioriprobabilities of the transmitted symbols for improving the bit error rate (BER) performance. To further enhance the system’s robustness in the presence of ill-conditioned matrices, we develop a refined PBiGAMP-based JCEE algorithm by introducing a series of scaled identity matrices. Moreover, the proposed PBiGAMP-based JCEE algorithms may be readily decomposed into GAMP-based equalization algorithms, when the channel state information is perfectly known. The overall complexity of the proposed algorithms only increases logarithmically with the total number of transmitted symbols. Our simulation results demonstrate the benefits of the proposed PBiGAMP-based iterative message passing receiver conceived for MFTN signaling.

This paper proposes a low-complexity joint phase noise (PHN) estimation and decoding algorithm for orthogonal frequency division multiplexing relying on index modulation (OFDM-IM) systems. A factor graph (FG) is constructed based on the truncated discrete cosine transform (DCT) expansion model for the variation of PHN. In order to explicitly take into account the structured and sparse a priori information of the frequency-domain symbols provided by the soft-in soft-out (SISO) decoder, the generalized approximate message passing (GAMP) algorithm is employed. Furthermore, to solve the unknown and nonlinear transform matrix problem introduced by the PHN, the mean-field (MF) method is invoked at the observation nodes on the FG. Monte Carlo simulations show the superiority of the proposed algorithm over the existing variational inference (VI) and extended Kalman filter (EKF) methods in terms of their bit error rate (BER) performance and complexity. In addition, we demonstrate that the OFDM-IM scheme outperforms its conventional OFDM counterpart in the presence of PHN.

Gaussian belief propagation (BP) finds extensive applications in signal processing but it is not guaranteed to converge in loopy graphs. In order to determine whether Gaussian BP would converge, one could directly use the classical convergence conditions of Gaussian BP, such as diagonal dominance, walk-summability, and convex decomposition. These classical conditions assume that the convergence conditions for Gaussian BP precisions and means are the same, which has been proved to be unnecessary. Generally, the condition for guaranteeing the convergence of Gaussian BP precisions is looser than that of Gaussian BP means. Moreover, the convergence of Gaussian BP means could be improved by damping when Gaussian BP precisions converge. Therefore, the convergence of Gaussian BP precisions is a prerequisite for guaranteeing the convergence of Gaussian BP means. This paper derives a simple convergence condition for Gaussian BP precisions, which can be verified in a distributed way. Through numerical examples, it is found that there exists scenarios where the new condition is satisfied but the classical conditions are not.

Both faster than Nyquist (FTN) signaling and non-orthogonal multiple access (NOMA) are promising next generation wireless communications techniques as a benefit of their capability of improving the system's spectral efficiency. This paper considers an uplink system that combines the advantages of FTN and NOMA. Consequently, an improved spectral efficiency is achieved by deliberately introducing both inter-symbol interference (ISI) and inter-user interference (IUI). More specifically, we propose a grant-free transmission scheme to reduce the signaling overhead and transmission latency of the considered NOMA system. To distinguish the active and inactive users, we develop a novel message passing receiver that jointly estimates the channel state, detects the user activity, and performs decoding. We conclude by quantifying the significant spectral efficiency gain achieved by our amalgamated FTN-NOMA scheme compared to the orthogonal transmission system, which is up to 87.5%.

This article proposes a novel orthogonal frequency-division multiplexing (OFDM) autoencoder featuring convolutional neural networks (CNNs)-based channel estimation for marine communications with complex and fast-changing environments. We demonstrate that the proposed OFDM autoencoder system can be generalized to work under various channel environments, different throughputs, while outperforming the traditional OFDM counterparts, especially when working at high throughputs. In addition, since OFDM systems require accurate channel estimations to function properly, this treatise also proposes a new channel estimation algorithm for OFDM systems that combine the power of deep learning (DL) with the philosophy of super-resolution reconstruction, which uses dense convolutional neural networks (Dense-Nets) to reconstruct low-resolution pilot information images into high-resolution full-channel impulse responses (CIRs). The Dense-Net structure has the characteristics of dense connections and feature multiplexing. The simulation results show that under slow fading, the proposed channel estimator (CE) can estimate the CIRs perfectly. Under fast fading, the proposed CE outperforms the existing learning-based algorithms with fewer neural network parameters. Therefore, the proposed novel autoencoder scheme and the powerful CE are potentially attractive approaches for the Internet of Vessels (IoV).

Gaussian belief propagation (BP) is widely used for distributed inference. Its computational complexity, and communication overhead depend on the total number of messages updated, and transmitted among variable nodes, respectively. For large, and dense networks, both computational complexity, and communication overhead could be extremely high. To this end, a variant of Gaussian BP called Gaussian SPAWN (sum-product algorithm over a wireless network) could be applied, where outgoing messages are approximated by beliefs. Similar to Gaussian BP, the convergence of Gaussian SPAWN is not guaranteed for loopy graphs. Therefore, we analyze the convergence of belief means, and variances in Gaussian SPAWN. Numerical results are presented to corroborate the newly established theories and a comparison of Gaussian BP, and Gaussian SPAWN is illustrated.

Spectrally efficient frequency division multiplexing (SEFDM) relying on index modulation (IM) has emerged as a promising multicarrier technique. In this paper, we develop a joint channel estimation and equalization method based on factor graphs for SEFDM-IM signaling over frequency-selective fading channels. By approximating the interference in the frequency domain, we reformulate the problem to obey a linear state-space model and construct a multi-layer factor graph. To support a reconfigurable architecture, non-orthogonal demodulation is adopted and the colored noise encountered is approximated by a complex auto-regressive (CAR) model. For deriving a low-complexity parametric Gaussian message passing (GMP)-based method, we exploit an expectation propagation (EP)-based technique for approximating the discrete a posteriori distributions of the transmitted symbols in a Gaussian form. To further simplify the result, variational message passing (VMP) is applied to an equivalent soft node to obtain a Gaussian form. Moreover, we also derive the Cramér-Rao lower bound (CRLB) in closed-form. The overall complexity only grows linearly with the number of subcarriers and logarithmically with the length of the channel's memory. Compared to its Nyquist signaling based counterpart, SEFDM-IM signaling relying on the proposed algorithm exhibits up to 25% higher bandwidth efficiency without any bit error rate (BER) performance degradation.

In order to glean benefits from orthogonal frequency division multiplexing combined with index modulation (OFDM-IM) in the presence of strong Phase-Noise (PHN), in this paper, low-complexity joint PHN estimation and decoding methods are developed in the framework of message passing on a factor graph. Both the Wiener process and the truncated discrete cosine transform (DCT) expansion model are considered for approximating the PHN variation. Then based on these a factor graph is constructed for explicitly representing the joint estimation and detection problem. Taking full account of the sparse and structured a priori information arriving from the soft-in soft-out (SISO) decoder of a turbo receiver, a modified generalized approximate message passing (GAMP) algorithm is invoked for decoupling the frequency-domain symbols. In the decoupling step, mean field (MF) approximation is employed for solving the unknown nonlinear transform matrix problem imposed by PHN. Furthermore, merged belief propagation and MF (BP-MF) methods amalgamated both with sequential and parallel message passing schedules are introduced and compared to the proposed GAMP based algorithms in terms of their bit error ratio (BER) vs. complexity. Our simulation results demonstrate the efficiency of the proposed algorithms in the presence of both perfect and imperfect channel state information.

Given the requirements of increased data rate and massive connectivity in the Internet-of-things (IoT) applications of the fifth-generation communication systems (5G), non-orthogonal multiple access (NOMA) was shown to be capable of supporting more users than OMA. As a further potential enhancement, the faster-than-Nyquist (FTN) signaling is also capable of increasing the symbol rate. Since NOMA and FTN signaling impose non-orthogonalities from different perspectives, it is possible to achieve further increased spectral efficiency by exploiting both. Hence we investigate the FTN-NOMA uplink in the context of random access. Although random access schemes reduce the signaling overheads as well as latency, they require the base station to identify active users before performing data detection. As both inter-symbol and inter-user interferences exist, performing optimal detection requires a prohibitively high complexity. Moreover, in typical mobile communication environments, the channel envelope of users fluctuates violently, which imposes challenges on the receiver design. To tackle this problem, we propose a joint user activity tracking and data detection algorithm based on the factor graph framework, which relies on a sophisticated amalgam of expectation maximization (EM) and hybrid message passing algorithms. The complexity of the algorithm advocated only increases linearly with the number of active users. Our simulation results show that the proposed algorithm is effective in tracking user activity and detecting data symbols in dynamic random access systems.

The sparse code multiple access (SCMA) is a promising candidate for bandwidth-efficient next generation wireless communications, since it can support more users than the number of resource elements. On the same note, faster-than-Nyquist (FTN) signaling can also be used to improve the spectral efficiency. Hence in this paper, we consider a combined uplink FTN-SCMA system in which the data symbols corresponding to a user are further packed using FTN signaling. As a result, a higher spectral efficiency is achieved at the cost of introducing intentional inter-symbol interference (ISI). To perform joint channel estimation and detection, we design a low complexity iterative receiver based on the factor graph framework. In addition, to reduce the signaling overhead and transmission latency of our SCMA system, we intrinsically amalgamate it with grant-free scheme. Consequently, the active and inactive users should be distinguished. To address this problem, we extend the aforementioned receiver and develop a new algorithm for jointly estimating the channel state information, detecting the user activity and for performs data detection. In order to further reduce the complexity, an energy minimization based approximation is employed for restricting the user state to Gaussian. Finally, a hybrid message passing algorithm is conceived. Our Simulation results show that the FTN-SCMA system relying on the proposed receiver design has a higher throughput than conventional SCMA scheme at a negligible performance loss.

Faster-than-Nyquist (FTN) signaling with index modulation (IM) is an attractive non-orthogonal transmission scheme characterized by high spectral efficiency and energy efficiency. In this paper, we develop a hybrid belief propagation (BP) and expectation propagation (EP) based iterative receiver for FTN-IM systems. To approach the optimal maximum a posteriori (MAP) receiver, we derive the factorization of marginal posterior probability and construct the corresponding factor graph by ignoring trivial interferences. To address the inherent colored noise imposed by FTN signaling, we employ autoregressive (AR) model to approximate the correlated noise samples. To further design low-complexity parametric message passing receiver, we resort to expectation propagation (EP) to derive Gaussian approximation of discrete transmitted symbols containing specific inactivated zeros. As a result, the overall complexity grows linearly with the number of transmitted symbols. Simulation results show that the coded FTN-IM system relying on the proposed iterative receiver can improve the spectral efficiency up to 43% without performance loss. For identical spectral efficiency with the Nyquist counterpart, FTN-IM signaling achieves 0.80 dB performance gain with proper packing factor and coding rate.

Passive localization based on time of arrival (TOA) measurements is investigated, where the transmitted signal is reflected by a passive target and then received at several distributed receivers. After collecting all measurements at receivers, we can determine the target location. The aim of this paper is to provide a unified factor graph-based framework for passive localization in wireless sensor networks based on TOA measurements. Relying on the linearization of range measurements, we construct a Forney-style factor graph model and conceive the corresponding Gaussian message passing algorithm to obtain the target location. It is shown that the factor graph can be readily modified for handling challenging scenarios such as uncertain receiver positions and link failures. Moreover, a distributed localization method based on consensus-aided operation is proposed for a large-scale resource constrained network operating without a fusion center. Furthermore, we derive the Cramér-Rao bound (CRB) to evaluate the performance of the proposed algorithm. Our simulation results verify the efficiency of the proposed unified approach and of its distributed implementation.

This paper considers a passive localization scenario relying on a single transmitter, several receivers, and multiple moving targets to be located. The so-called “passive” targets equipped with RFID reflectors are capable of reflecting the signals from the transmitter to the receivers. Existing approaches assume that the transmitter and receivers are synchronous or quasi-synchronous, which is not always realistic in practical scenarios. Hence, an asynchronous wireless network is considered, where different clock offsets are assumed at different receivers. We propose a centralized expectation-maximization-based passive localization method for asynchronous receivers (EMpLaR) by treating the clock offsets as hidden variables. Thereby, the proposed algorithm makes use of Taylor expansions to arrive at a closed-form maximization. Furthermore, to improve the robustness to link failures and to reduce the energy consumption, we propose a distributed localization approach based on average consensus formulation to locate the target at each receiver. By applying a quadratic polynomial approximation of the function on which consensus has to be reached, both the computational complexity and the communications overhead are significantly reduced. The Cramér-Rao bound of the target location is derived as a benchmark of our proposed algorithms. Our simulation results show that the proposed centralized and distributed EMpLaR algorithms match the Cramér-Rao bound and significantly improve the localization performance compared with the conventional methods.

Wireless networks are growing in the value of application in many areas, in which accurate clock synchronization is required when tasks are performed in a collaborative fashion among nodes. Especially, cooperative synchronization techniques lead to significant performance improvement compared with traditional methods. However, the correlation among agents renders the performance analysis of cooperative network synchronization difficult. In this paper, we introduce the concept of information coupling intensity to the analysis of interaction between agents. Our approach enables us to derive closed-form asymptotic expressions under specific network topologies, and relate them to various network parameters.

This paper considers the issue of passive localization based on time of arrival (TOA) measurement in the presence of receiver detection failures. In passive localization, the signal sent from the transmitter is reflected or relayed by "passive" target and then received at several distributed receivers. The target's position can be determined by collecting range mea- surements from all receivers. With a linearized model for range measurements, we build a factor graph model and implement Gaussian message passing algorithm to obtain target location and detect link failures. The Cramer-rao bound (CRB) is also derived to evaluate the performance of proposed algorithm. Simulation results verify the effectiveness of proposed factor graph approach.

Faster-than-Nyquist (FTN) signaling has attracted a lot of attentions for the fifth-generation (5G) cellular communication systems. However, low-complexity receiver design for FTN signaling becomes challenging. In this paper, we develop frequency-domain joint channel estimation and decoding methods for FTN signaling transmitting systems over frequency-selective fading channels. To deal with the colored noise inherent in FTN signaling, we propose to approximate the corresponding autocorrelation matrix by a circulant matrix, the special eigenvalue decomposition of which facilitates an efficient fast Fourier transform operation and decoupling the noise in frequency domain. Through a specific partition of the received symbols, many independent estimates are obtained and combined to further improve the accuracy of the channel estimation and data detection. Moreover, instead of assuming the data symbols to be Gaussian random variables, a generalized approximated message passing-based equalization is developed and embedded in the turbo iterations between the channel estimation and the soft-in soft-out decoder. Simulation results show that the proposed algorithm outperforms the cyclic prefix-based and overlap-based frequency-domain equalization methods. With the proposed algorithms, FTN signaling reaches up to 67% higher transmission rate compared to the Nyquist counterpart without substantially consuming more transmitter energy per bit, and the overall complexities grow logarithmically with the length of the observations.

The rapid development of mobile communications requires even higher spectral efficiency. Non-orthogonal multiple access (NOMA) has emerged as a promising technology to further increase the access efficiency of wireless networks. Among several NOMA schemes, it has been shown that sparse code multiple access (SCMA) is able to achieve better performance. In this paper, we consider a downlink MIMO-SCMA system over frequency selective fading channels. For optimal detection, the complexity increases exponentially with the product of the number of users, the number of antennas and the channel length. To tackle this challenge, we propose near optimal low-complexity iterative receivers based on factor graph. By introducing auxiliary variables, a stretched factor graph is constructed and a hybrid belief propagation (BP) and expectation propagation (EP) receiver, named stretch-BP-EP, is proposed. Considering the convergence problem of BP algorithm on loopy factor graph, we convexify the Bethe free energy and propose a convergence-guaranteed BP-EP receiver, named conv-BP-EP. We further consider cooperative network and propose two distributed cooperative detection schemes to exploit the diversity gain, namely, belief consensus-based algorithm and the Bregman alternative direction method of multipliers (ADMM)-based method. Simulation results verify the superior performance of the proposed conv-BP-EP receiver compared with other methods. The two proposed distributed cooperative detection schemes can improve the bit error rate performance by exploiting the diversity gain. Moreover, Bregman ADMM method outperforms the belief consensus-based algorithm in noisy inter-user links.

Modern wireless communication raise the demand for higher spectral efficiency, faster-than-Nyquist (FTN) signaling is able to increase transmission rate without expanding signaling bandwidth. In this paper, we develop a graph-based iterative FTN detector in the presence of phase noise (PHN). Wiener process is employed to model the time evolution of nonstationary channel phase. The colored noise imposed by sampling of FTN signaling is approximated by autoregressive model. Based on the factor graph constructed, messages are derived on the two subgraphs, i.e., PHN estimation subgraph, and the FTN symbol detection subgraph. We propose a combined sum-product and variational message passing (SP-VMP) method to update the messages between subgraphs, which enables low- complexity parametric message passing and provides closed-form expressions for parameters updating. Simulation results show the superior performance of the proposed algorithm compared with the existing methods and verify the advantage of FTN signaling compared with the Nyquist counterpart.

As the mobile communications develop rapidly, ever higher spectral efficiency is required. The sparse code multiple access (SCMA) has been recognized as a promising technology to further increase the access efficiency of wireless networks. In this paper, we consider the receiver design problem for SCMA system over frequency selective channels. The conventional minimum mean squared error (MMSE) detection method suffers from huge complexity due to the the multi-user and inter-symbol interferences. To this end, we propose a near optimal low complexity message passing receiver. By approximating the discrete log-likelihood ratio as Gaussian random variable, all messages on factor graph can be obtained as Gaussian distributions. Furthermore, we propose to introduce auxiliary variables to the factor graph and develop a novel hybrid belief propagation (BP) and expectation propagation (EP) receiver. Simulation results show that the proposed hybrid BP-EP method performs close to the MMSE-based receiver with reduced complexity. Also, compared to the orthogonal multiple access scheme, the considered SCMA system with the proposed receiver is able to support 50% more users.

Location-aware wireless networks can provide precise location information in harsh environments, however, which is only possible when all nodes are well-functioning. In this paper, we propose algorithms and analyze the performance limits for both non-cooperative and cooperative localization networks in the presence of ranging outliers. Especially, we show that the localization performance can be boosted by using the cooperative outlier detection scheme. An algorithm based on expectation-maximization is proposed for non-cooperative localization networks, while a variational message passing-based algorithm is proposed for the cooperative counterparts. Performance limits are investigated using Cramér-Rao lower bound. Further inspection on the performance limits confirms the performance gain from the cooperative detection scheme. Stochastic geometric analysis is also carried out to account for the stochastic nature of wireless networks, as well as to provide simpler expressions and additional insights. Simulation results corroborate the analytical results, and show that both of the proposed algorithms are capable of attaining the corresponding performance limits at a significantly reduced computational cost compared with existing algorithms.

In this paper, we develop a joint channel estimation and decoding method for faster-than-Nyquist signaling (FTNS) transmitting over (quasi-static) time-varying frequency-selective fading channels based on the variational Bayesian (VB) framework. In contrast to existing methods, ours is capable of performing explicit frequency-domain channel estimation and decoding in a turbo mode without requiring any cyclic prefix (CP), as well preserving the computational complexity at a logarithmic level. In view of the colored noise inherent in FTNS, we propose to approximate the corresponding autocorrelation matrix by a circulant matrix, the special eigenvalue decomposition of which facilitates an efficient fast Fourier transform operation and decoupling the noise in frequency domain. In addition, through a specific partition of the received symbols, many independent estimates are obtained and combined to further improve the accuracy of the channel estimation and data detection. Simulation results show that the proposed algorithm outperforms the conventional CP-based and overlap-based frequency-domain equalization methods with known channel impulse response (CIR). Moreover, ours come within 1dB of the counterpart Nyquist system with 25% higher spectral efficiency achieved when the CIR is unknown.

Modern mobile communication applications raise the requirement of high quality support for high mobility users. In this paper, we present a Bayesian graphical model based frequency domain equalization method for faster-than-Nyquist (FTN) signaling in doubly selective channels. The conventional frequency domain minimum mean squared error (FD-MMSE) equalizer suffers high complexity due to the interferences induced by adjacent frequency symbols. To tackle this problem, a low complexity iterative message passing method namely, belief propagation is employed on the Bayesian graphical model to detect the FTN symbols. Compared to the low complexity variational inference method, the proposed algorithm considers the conditional dependencies between symbols and therefore can improve the performance. Simulation results show that the proposed equalization method has similar performance of the MMSE equalizer and outperforms the variational inference method.

Obtaining the location of a “passive” target in wireless sensor networks has attracted numerous interest in recent years. This paper considers the passive localization based on time-of-arrival measurements in an asynchronous sensor network where the receivers are with both clock skew and offset. Based on the factor graph model, the beliefs (approximated marginal) of target location and clock parameters can be obtained by executing iterative message passing algorithms. To reduce the huge complexity of particle based method, we propose two approximate approaches to determine parametric Gaussian message passing. Simulation results show that the proposed low complexity algorithm performs close to the particle-based method and attain the Cramer-Rao bound.

A maximum likelihood-based code-aided joint carrier phase estimation and ambiguity resolution algorithm is proposed for coded amplitude and phase shift keying (APSK) signals. The proposed estimator iteratively uses the a posteriori probability of coded bits obtained from the channel decoder to improve the performance of phase estimation and ambiguity resolution. Two initialization schemes are employed for systems with and without pilot symbols, which reduce the number of initial phase values required to bootstrap the iterative estimation algorithm. Compared with the existing estimators, simulation results demonstrate the performance improvement of the proposed algorithm in both mean-squared estimation error and bit error rate with lower computational complexity.

Oscillator phase noise (PHN) can result in significant performance loss in coherent communication systems if not compensated appropriately. Most existing studies focus on either PHN estimation over additive white Gaussian noise channels or channel impulse response (CIR) estimation in the absence of PHN. In this study, joint CIR estimation and decoding over time‐selective flat‐fading channels impacted by PHN is studied. Both the time evolutions of CIR and PHN are approximated by autoregressive models. Building on this, factor graph of the joint a posteriori probability function is constructed and the sum–product algorithm is applied to derive messages on factor graph. Due to the non‐linearity of PHN, no closed‐form expressions of the messages can be obtained. To this end, the authors use canonical distribution approach, which approximates the messages by Gaussian and Tikhonov probability density functions on the sub‐graphs of CIR and PHN, respectively. Accordingly, the messages can be calculated by updating the parameters of the canonical distributions. A mixed serial‐parallel message passing schedule is presented to implement the algorithm, which enables the compromise between the bit error rate performance and the processing throughput. Simulation results show that the proposed joint estimation and decoding algorithm significantly outperforms the existing methods in fading channels impacted by PHN.

This work deals with frequency-domain equalization for faster-than-Nyquist (FTN) signaling in doubly selective channels (DSCs). To handle the interference of frequency-domain symbols, the minimum mean square error (MMSE) equalizer involves high complexity in DSCs. To overcome the problem, we propose low-complexity receivers based on two variational methods, i.e., mean field (MF) and Bethe approximations. Compared with the MF method, the Bethe approximation takes into account the conditional dependencies of pairwise symbols. By only considering a small set of the frequency-domain symbols that have strong interference to each other, the complexity of the proposed algorithms increases linearly with the block length. Simulation results demonstrate that the proposed algorithms for FTN signaling are able to perform close to the MMSE equalizer in DSCs while with significantly reduced computational complexity.

In this paper, we study the time of arrival (TOA)-based distributed passive localization in asynchronous wireless network. Performing synchronization between receivers before target localization is possible but costs extra energy and bandwidth. To this end, We propose an expectation maximization (EM) algorithm to locate the passive target in the presence of receivers' clock offsets. To improve the robustness of the proposed algorithm, we employ the average consensus scheme to obtain the location of target at each receiver in a distributed way. A quadratic polynomial approximation is proposed to reduce the communication overhead and computational complexity. To evaluate the performance of the proposed algorithm, the Cramer-Rao bound (CRB) of the target's position estimation is derived. Simulation results show that the proposed distributed EM algorithm performs close to the centralized counterpart. It outperforms the conventional two step estimation method and the one based on time difference of arrival. Moreover, the proposed algorithm can attain the derived CRB, which demonstrates the effectiveness of the algorithm.

In wireless sensor networks, acquiring accurate timing information is a crucial requirement for time-based sensor localization. Utilizing a joint localization and synchronization method in sensor networks can improve positioning speed and accuracy. In this paper, we present a unified factor graph framework based on time of arrival (TOA) measurements to solve the problem of joint localization and time synchronization. A novel distributed cooperative joint estimation method based on belief propagation (BP) is proposed. We linearize the nonlinear terms in messages on factor graph in order to obtain a closed Gaussian form solution of message update. Accordingly, only the means and variances have to be updated and transmitted, which significantly reduce the communication overhead and computational complexity. To further reduce the communication overhead, we propose a message passing schedule. Simulation results show that the proposed BP method reach close performance to particle-based approaches with lower complexity.

Baseband predistortion is a popular and efficient method to linearize high power amplifier (HPA) in wireless communication systems. Polynomial (POLY) and look-up-table (LUT) are two methods to design baseband predistorter (PD). However, on the one hand, POLY-based method is complex to implement. On the other hand, LUT-based predistorter suffers convergence time and quantization error problem. In this paper, we propose a hybrid POLY and LUT predistorter for memory nonlinear system in wideband scenarios, it is also suitable for memoryless channel. Simulations show that the proposed hybrid structure outperforms the traditional one with lower complexity.

The evaluation of Cramer-Rao Bounds (CRBs) for phase estimation of coded linearly modulated signals are difficult due to the intractable expectations of the likelihood function with respect to coded symbols. In this paper, we propose two methods towards this end. The first one is a semi-analytical method for coded QPSK signals. Based on Gaussian approximation of extrinsic information, the expression of CRB is derived in terms of signal-to-noise ratio (SNR) and the mean of extrinsic information in closed form. For high-order modulations, e.g., 16QAM signal, we propose a numerical method based on multidimensional Gauss-Hermite Quadrature (GHQ). It is shown that, without suffering from the linearization error, the results of numerical method by GHQ outperform the semi-analytical results, and the former are consistent with that of the Monte Carlo simulations for systems with different codes and numbers of decoding iterations.

Localization in wireless sensor networks has become an attractive research field in recent years. Most studies focus on the mitigation of measurement noise by assuming the positions of anchors are perfectly known, which may become impractical due to some inevitable errors in the observations of anchors' positions. This paper addresses the problem by taking into account the a priori position information of inaccurate anchors. Considering that the maximum likelihood (ML) algorithm suffers from the intractable integrals involved, we resort to expectation maximization (EM) algorithm to solve this problem iteratively. The a posteriori probability of the anchor position is approximated by circularly symmetric Gaussian distribution, with parameters optimized by minimizing Kullback-Leibler divergence of the two distributions. Building on this approximation, we are able to derive the expectation step in closed form. Particle swarm optimization is then followed to perform the maximization step. Numerical results demonstrate that the proposed EM estimator is less sensitive to the anchors' uncertainties and it significantly outperforms the traditional ML estimator which ignores the prior information of anchors.

In this treatise, a novel modulation scheme aimed for achieving high-rates MIMO systems is proposed, which is termed as 3-Dimensional Shift Keying (3- DSK). In the proposed 3-DSK scheme, the information bits can be mapped onto three distinguished information carriers, namely, spatial domain, matrix domain and signal dimension. Since the novel 3-DSK principle is capable of encoding information bits into three information carriers, high throughout can be achieved. Moreover, this 3-DSK framework subsumes diverse existing MIMO arrangements, such as Spatial Modulation (SM), Generalized Space-Time Shift Keying (GSTSK) scheme and Vertical Bell Lab's Layered Space-Time structure due to its high design flexibility. Additionally, a potential full transmit diversity can be achieved by jointly exploiting the spatial and temporal dimensions. At the receiver, a Maximum Likelihood decoder is adopted in order to jointly recover the information bits. Finally, we demonstrate through numerous simulation results that the 3-DSK architecture is capable of achieving a lower BER performance over SM and GSTSK as well as LDC schemes, while achieving high rates.

Localisation in wireless sensor networks (WSNs) has received much attention, where most studies focus on mitigating the effects of measurement noise under the assumption of accurate anchors’ positions. However, anchors’ positions could be inaccurate for the inevitable errors in practical observations. This paper studies the sensor localisation with both inaccurate anchors’ positions and noisy range measurements in WSNs. To solve the intractable integrals in likelihood function, the authors propose to use expectation‐maximisation (EM) algorithm to obtain the maximum likelihood (ML) estimation iteratively. The ‘a posteriori’ distribution of the anchor's position uncertainty is approximated to a circularly symmetric Gaussian distribution by minimising the Kullback‐Leibler divergence between them. Building on this, the authors derive the expectation step in a closed‐form expression. In the maximisation step, based on the Taylor expansion of the confluent hypergeometric function of the first kind presented in the expectation step, analytical solutions are obtained. Simulation results show that the proposed EM estimator significantly outperforms the approximated ML estimator. The performance gain by using the EM estimator becomes larger as the increase of anchors’ position uncertainties. Moreover, the performance of the EM estimator is close to that of the Monte Carlo‐based estimator with much less computational complexities.

A code-aided (CA) iterative signal-to-noise ratio (SNR) estimator based on Expectation Maximization (EM) algorithm is proposed for M-ary amplitude phase shift keying (APSK) signals. The estimation algorithm utilizes a posteriori probabilities of coded bits obtained from channel decoder to improve estimation precision at low SNRs. Furthermore, Cramer-Rao bound (CRB) of the proposed CA iterative SNR estimator for M-APSK is derived and simulated numerically. Compared with the non-data-aided (NDA) EM-based estimator and moments-based estimators for M-APSK signals, computer simulation results show that the proposed estimator exploiting a posteriori information has more excellent performance, especially at low SNRs. It is also demon-strated that the performances of the proposed CA SNR estimator for 16- and 32-APSK signals are very close to the derived CRB.

This paper presents a message passing approach to joint channel estimation, data detection and decoding over time-selective Rayleigh fading channel with residual carrier frequency offset (CFO). The proposed algorithm utilizes the sum product algorithm (SPA) implemented on a factor graph (FG) representing the joint a posteriori probability distribution of the unknown CFO, information bits and channel coefficients vector given the channel output. A combination of particle filtering and Gaussian parameterization is employed to approximate the exact probability density function in message passing for CFO and channel estimation. Computer simulations demonstrate the effectiveness of the proposed algorithm in combating the CFO over unknown Rayleigh fading channels.

Code-aided (CA) iterative carrier phase synchronizer can improve the phase estimation performance significantly. However, due to the coupling involved between phase recovery and decoding, most studies depend on extensive simulations rather than on theoretical analysis to evaluate the performance of CA phase recovery. In this paper, we propose analytical methods to fill this void. The first step is to model the cross-talks caused by phase offset as an additional Gaussian noise at low signal-to-noise ratios (SNRs). Then, a semi-analytical method is proposed to express the distribution of extrinsic information from channel decoder as a function of phase offset. Building on this model, both the open-loop and closed-loop performance of CA iterative hard/soft decision-directed phase synchronizers are derived in closed-form. The analytical results explicitly reveal how extrinsic information contributes to the performance improvement of carrier phase estimation. Monte Carlo simulation results corroborate that the proposed methods are able to accurately characterize the performance of CA iterative carrier phase recovery for systems with different channel codes.

Predistortion technology is an adaptive, low cost and potential linearization method. Proper loop-delay estimation and compensation are important preconditions for ensuring the predistorter working well. But traditional loop-delay estimation algorithms are vulnerable to the amplifier's memory and nonlinear distortion. In this paper, based on the relationship between the system loop-delay and the amplitude of predistorter error output, we propose a new loop-delay estimation algorithm which improves the algorithm estimation accuracy in memory nonlinear distortion. Simulation results show that the NMSE converging curve is very close to the ideal one and a good power spectral density (PSD) performance is achieved. The new algorithm realizes the synchronous work of the predistorter and the loop-delay estimation that maintains the reliability and continuity of signal transmission.

Digital baseband predistortion technology can effectively reduce the system nonlinear distortion. However, the predistortion algorithms based on indirect structure are sensitive to measurement noise and the traditional loop-delay estimation algorithms are vulnerable to the amplifier's nonlinear distortion especially in the amplifier saturation region. In this paper, we first present an adaptive nonlinear predistorter based on direct learning structure and then propose a new loop-delay estimation algorithm which applies to PA nonlinear distortion conditions by analyzing the relationship between the system loop-delay misalignment and the amplitude of HPA model identification error output. Simulation results show that the power spectral density (PSD) after the predistortion is very close to that of the ideal signal and a good NMSE performance is achieved.

In this paper, we propose a novel signal-to-noise ratio (SNR) estimation method for linear modulations on additive white Gaussian noise (AWGN) channel. It estimates noise power directly without estimating the received total power. The estimation mean and mean square error (MSE) are analyzed theoretically and verified by simulations. Results show that the proposed SNR estimator performs better at low SNR than the conventional estimators while it suffers a little degradation at high SNR. Moreover, the proposed estimator can be implemented with less real multiplications than the conventional ones.

In this paper, we propose an improved iterative receiver scheme for low density parity check (LDPC) codes transmitted over unknown channels affected by a strong phase noise. For achieving joint channel parameter estimation, data detection and decoding, the proposed algorithm utilizes the sum product algorithm (SPA) implemented on the factor graph (FG) that represents the joint a posteriori probability of information symbols and channel parameters given the channel output. Through the iterative use of the soft information on coded symbols from channel decoder, the proposed algorithm employs forward-backward recursions for message passing on the graph. Numerical results for binary LDPC codes show that, the proposed algorithm can be able to cope with a strong phase noise under unknown channel information and achieve nearly the same performance as the optimal coherent receiver under DVB-S2 compliant ESA phase noise model, and only a slightly decrease under strong Wiener model.

Code-aided (CA) iterative carrier phase synchroniser can greatly improve the accuracy of phase estimation in turbo receivers. However, because of the iteration involved between phase recovery and decoding, most existing studies depend on extensive simulations rather than on theoretical analysis to evaluate the performance improvement of phase recovery by exploiting the coding constraints. In this study, the authors propose analytical methods to fill this void. The first step is to approximate the cross-talks caused by phase offset as Gaussian noise at low signal-to-noise ratios. Then, a semi-analytical method is proposed to express the distribution of extrinsic information from channel decoder as a function of phase offset. Building on this model, both the open-loop and closed-loop performances of CA iterative phase synchronisers are derived in closed-form. The analytical results explicitly reveal how extrinsic information contributes to the performance of carrier phase estimation. Monte Carlo simulation results corroborate that the proposed methods are able to accurately characterise the performance of CA iterative carrier phase recovery for systems with different channel codes.

This study studies the feedforward (FF) non-data-aided (NDA) carrier phase estimation of the amplitude and phase shift keying (APSK) signals. The true Cramer–Rao bounds (CRBs) for NDA phase estimation of APSK signals are derived and evaluated numerically using Gauss–Hermite quadrature. The jitter variance of the FF Viterbi–Viterbi (V&V) algorithm is analysed assuming the absence of data pattern noise. It is proved that, when the design parameter μ=2, the jitter variance is able to converge asymptotically to the modified CRB (MCRB) at high signal-to-noise ratios (SNRs). For practical application, the parameter μ is also optimised for 16/32/64-APSK signals at different SNRs. The analytical results of the jitter variance are verified by Monte-Carlo evaluations. It is shown that, for 32/64-APSK signals, the plain V&V algorithm cannot approach the CRBs due to the data pattern noise. A modified V&V algorithm based on the constellation partition and a linear combination of the sub-estimators is proposed to eliminate the divergence. Simulation results show that the jitter variance of the proposed estimator is very close to the CRB at the SNRs of interest and converges to the MCRB at high SNRs.

We analyze the performance of a code-aided (CA) decision-directed (DD) timing synchronizer, which can exploit the dependence structure across coded symbols to improve the timing recovery accuracy. Due to the inherent coupling between timing recovery and decoding, most existing studies rely on extensive simulation rather than on analytical methods to evaluate performance of timing recovery for coded systems. We propose analytical methods in this paper towards this end. A first key step is to approximate timing-offset-induced inter-symbol interference (ISI) as an additive Gaussian noise, since in the low signal-to-noise ratio (SNR) regime the background noise is large enough to mask the ISI. Then, we derive semi-analytical expressions for the mean and variance of extrinsic information as functions of timing offset, building on which we characterize both open-loop and closed-loop performance of decision-directed timing synchronizers. Monte Carlo simulation results corroborate that the proposed method accurately characterizes the performance of CA DD timing recovery, for systems with a wide range of channel bandwidth and different channel codes.

In this paper, we consider the effect of different rules of symbol decision on the performance of decision-directed synchronizers for LDPC-coded systems. Different from the conventional hard symbol decision based on the Maximum-A- Posteriori (MAP) criterion, soft symbol decision can be considered as the Minimum-Mean-Square-Error (MMSE) estimation of the transmitted symbol. By whether or not the coding constraints are taken into account, soft symbol decision is derived in non-code-aided (NCA) mode and code-aided (CA) mode, respectively. The performance of the soft decision-directed (SDD) synchronizer is compared with that of the hard decision-directed (HDD) counterpart in both NCA and CA mode. Simulation results show that, without much implementation complexity increase, the jitter performance of the synchronizer in CA mode significantly outperforms that in NCA mode. It is also observed that, in the scenario of this paper, SDD synchronizer works only slightly better than HDD synchronizer.

In this paper, based on analyzing some existing phase lock detectors for quadratic phase-shift keying (QPSK),we propose a novel method of estimating the signal-to-noise ratio (SNR) operating with the lock metric value of classical Mth-power (M=4) phase lock detector. The proposed lock detector-based SNR estimator can perform better than the conventional SNR estimator in terms of mean estimated value (MEV) at medium to high SNR when phase recovery loop is in-lock status. And its normalized mean squared error (NMSE) can reach Cramer-Rao bounds (CRBs) at that SNR. Moreover, the computational complexity of new estimator operating in phase recovery loop is analyzed with less additional multiplications than that of conventional one. This estimation method can also be applied to other similar phase lock detectors.

An improved data-aided (DA) frequency error detector (FED) and a frequency lock detector are proposed under large frequency offset for Digital Video Broadcasting Satellite Second Generation (DVB-S2) system. Computer simulations results show that the proposed error detector can increase the frequency acquisition range and decrease the acquisition time without complexity increase. Its closed-loop normalized frequency root mean square error (RMSE) improves at least 1.5 dB compared with that of conventional error detector. The proposed lock detector shows good lock indication. Its modified version can save more symbols to indicate the locking status.

For the symbol timing recovery techniques which are susceptible to carrier phase offset, clockless phase recovery is necessary in advance. In this paper, we propose a clockless nondata-aided (NDA) feedback phase error detector (PED) for M-ary phase-shift keying (MPSK) signal. Its derivation is given based on maximum likelihood (ML) criterion. The clockless NDA (Mthpower)PED can also be generalized with a design parameter 0≤m≤M to improve performance at low SNR. The openloop S-curves and closed-loop phase error variances of these PEDs are given with extensive simulations. Results show that the S-curve of clockless Mth-power PED is robust to signal-tonoise ratio (SNR). Its phase error variance is investigated with excellent performance under different shaping roll-off factors and parameter m. We also analyze the clockless decision-directed (DD) PED which may not be a good choice for over-sampled signals due to its unstable equilibrium point of S-curve.

Data-aided (DA) signal-to-noise ratio (SNR) estimation is required especially at low SNR. The conventional maximum likelihood (ML) DA SNR estimator requires perfect carrier phase estimation and frequency recovery. In this paper, we propose a novel carrier frequency robust DA SNR estimator with its improved variant using autocorrelation of received MPSK symbols. Computer simulations are used to examine their performance in terms of mean estimation value (MEV) and normalized mean square error (NMSE). For the example system in simulations, the MEV of proposed estimator is accurate enough with normalized frequency error on the order of symbol rate. However, its NMSE can not reach DA normalized Cramer-Rao bound (NCRB) even with large observatory length, whereas its NMSE may perform a little worse at high SNR for short pilot symbols. On the other hand, fortunately the its improved variant can reach NCRB with enough pilot symbols. What's more, the proposed DA SNR estimators can operate under large frequency errors or before the frequency recovery unit with baud rate. The implementation complexity is also analyzed.

In this study, the authors propose an exact maximum likelihood (ML) signal-to-noise ratio (SNR) estimator for coded linearly modulated signals. The estimator is expressed in terms of the marginal a posteriori probabilities (APPs) of the coded symbols, which can be obtained efficiently by the Bahl–Cocke–Jelinek–Raviv (BCJR) algorithm for codes defined on trellises. Simulation results show that the proposed ML code-aided (CA) SNR estimator significantly outperforms the non-data-aided (NDA) estimators in the low SNR regime. The Cramer–Rao bound (CRB) for CA SNR estimator is also derived and evaluated numerically. It is shown that the proposed ML-CA estimator performs very close to the derived bound. Comparisons of the CRBs for CA and NDA scenarios with different linearly modulated signals further illustrate the intrinsic performance improvement by exploiting the channel coding constraints.

In the above-referenced paper, equations (18) and (19) in page 691 are incorrectly printed. They are corrected herein.

A modified M&M frequency estimation algorithm for DVB-S2 system is proposed in this paper. This estimator provides a larger estimation range compared to the well known Fitz and L&R methods and achieves CRB in the whole SNR operation range of DVB-S2, with a little increase in computational complexity. The enlarged estimation range will reduce the acquisition time of the coarse frequency synchronizer in a two-step carrier frequency recovery scheme. Minimum accumulation lengths to achieve a certain RMS frequency estimation error for the L&R and modified M&M estimator at different SNR are presented. A variable accumulation length scheme based on SNR estimation or coding/modulation scheme employed in system is proposed to minimize the acquisition time in the fine frequency recovery.