Factor Graph Framework Research Articles

A factor graph-based iterative detection of faster-than-Nyquist signaling in the presence of phase noise and carrier frequency offset

With the increasing demand for higher spectral efficiency in wireless communications, faster-than-Nyquist (FTN) signaling has been rediscovered to increase transmission rate without expanding signaling bandwidth. Most existing studies focus on low-complexity FTN receiver design by assuming perfect synchronization. In practice, however, phase noise (PHN) and carrier frequency offset (CFO) may degrade the performance of FTN detector significantly. In this paper, we develop iterative FTN detector in the presence of PHN and CFO in a factor graph framework. 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 and CFO estimation subgraph and the FTN symbol detection subgraph. We propose two methods to update the messages between subgraphs, namely, Gaussian approximation via Kullback–Leibler divergence (KLD) minimization and the combined sum-product and variational message passing (SP-VMP), both of which enable low-complexity parametric message passing. The proposed SP-VMP algorithm can provide closed-form expressions for parameters updating. Moreover, conjugate gradient (CG) method is adopted to solve the maximum a posteriori probability (MAP) estimation of CFO with fast convergence speed. 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.

Joint interference estimation and cancellation for coherent frequency hopping multiple-access systems

In this paper, we propose an iterative detection algorithm that reconstructs and cancels the multiple-access interference jointly without the knowledge of hopping patterns of the interfering users for SFH/BPSK systems in an ad hoc scenario. Since users are asynchronous in this scenario, signal in one hop of the desired users is affected by partial signals in unaligned hops, called the interference fragments, of the interfering users. We address the interference model by defining a virtual user, which has the same hopping pattern as that of the desired user and contains the feature of the interfering fragments. Then, we derive the joint interference reconstruction and multiple-user detection (MUD) algorithm using the factor graph framework. Simulation results show that the performance of the proposed algorithm can be improved by up to 2 dB than that of the traditional single user detection (SUD) in AWGN at the packet error rate of 10−2 for a total of 8 users over 20 hopping frequencies, and an outstanding performance may also be achieved in the channel with Doppler.

MapSentinel: Can the Knowledge of Space Use Improve Indoor Tracking Further?

Estimating an occupant’s location is arguably the most fundamental sensing task in smart buildings. The applications for fine-grained, responsive building operations require the location sensing systems to provide location estimates in real time, also known as indoor tracking. Existing indoor tracking systems require occupants to carry specialized devices or install programs on their smartphone to collect inertial sensing data. In this paper, we propose MapSentinel, which performs non-intrusive location sensing based on WiFi access points and ultrasonic sensors. MapSentinel combines the noisy sensor readings with the floormap information to estimate locations. One key observation supporting our work is that occupants exhibit distinctive motion characteristics at different locations on the floormap, e.g., constrained motion along the corridor or in the cubicle zones, and free movement in the open space. While extensive research has been performed on using a floormap as a tool to obtain correct walking trajectories without wall-crossings, there have been few attempts to incorporate the knowledge of space use available from the floormap into the location estimation. This paper argues that the knowledge of space use as an additional information source presents new opportunities for indoor tracking. The fusion of heterogeneous information is theoretically formulated within the Factor Graph framework, and the Context-Augmented Particle Filtering algorithm is developed to efficiently solve real-time walking trajectories. Our evaluation in a large office space shows that the MapSentinel can achieve accuracy improvement of compared with the purely WiFi-based tracking system.

Block-Processing Soft-Input Soft-Output Demodulator for Coded PSK Using DCT-Based Phase Noise Estimation

This paper considers the detection of coded phaseshift keying signals subjected to additive white Gaussian noise and oscillator phase noise. We propose a detector that partitions the received frame into smaller blocks and models the unknown phasor variations over each block as a truncated discrete cosine transform (DCT) expansion. Detection and decoding are iteratively performed between a soft-input soft-output (SISO) demodulator, a SISO demapper, and a SISO decoder based on the sum-product algorithm and the factor graph framework, whereas the expectation-maximization algorithm is used in the demodulator for the DCT coefficients estimation. The resulting demodulator is shown to have an excellent performance/complexity tradeoff and to be well-suited for parallel processing on multiple cores.

Joint Channel Estimation and Channel Decoding in Physical-Layer Network Coding Systems: An EM-BP Factor Graph Framework

This paper addresses the problem of joint channel estimation and channel decoding in physical-layer network coding (PNC) systems. In PNC, multiple users transmit to a relay simultaneously. PNC channel decoding is different from conventional multi-user channel decoding: specifically, the PNC relay aims to decode a network-coded message rather than the individual messages of the users. Although prior work has shown that PNC can significantly improve the throughput of a relay network, the improvement is predicated on the availability of accurate channel estimates. Channel estimation in PNC, however, can be particularly challenging because of 1) the overlapped signals of multiple users; 2) the correlations among data symbols induced by channel coding; and 3) time-varying channels. We combine the expectation-maximization (EM) algorithm and belief propagation (BP) algorithm on a unified factor-graph framework to tackle these challenges. In this framework, channel estimation is performed by an EM subgraph, and channel decoding is performed by a BP subgraph that models a virtual encoder matched to the target of PNC channel decoding. Iterative message passing between these two subgraphs allow the optimal solutions for both to be approached progressively. We present extensive simulation results demonstrating the superiority of our PNC receivers over other PNC receivers.

A Modified Nonparametric Message Passing Algorithm for Soft Iterative Channel Estimation

Based on the factor graph framework, we derived a Modified Nonparametric Message Passing Algorithm (MNMPA) for soft iterative channel estimation in a Low Density Parity-Check (LDPC) coded Bit-Interleaved Coded Modulation (BICM) system. The algorithm combines ideas from Particle Filtering (PF) with popular factor graph techniques. A Markov Chain Monte Carlo (MCMC) move step is added after typical sequential Important Sampling (SIS) -resampling to prevent particle impoverishment and to improve channel estimation precision. To reduce complexity, a new max-sum rule for updating particle based messages is reformulated and two proper update schedules are designed. Simulation results illustrate the effectiveness of MNMPA and its comparison with other sum-product algorithms in a Gaussian or non-Gaussian noise environment. We also studied the effect of the particle number, pilot symbol spacing and different schedules on BER performance.

IDMA for the Multiuser MIMO-OFDM Uplink: A Factor Graph Framework for Joint Data Detection and Channel Estimation

Interleave-division multiple access (IDMA) has recently been proposed as a promising alternative to code-division multiple access (CDMA). In this paper, we consider the use of IDMA within a multiple-input multiple-output orthogonal frequency-division multiplexing (MIMO-OFDM) multiuser system employing higher-order modulation and transmitting over frequency-selective MIMO channels. Based on a factor graph/message passing framework and the sum-product algorithm, we devise an iterative receiver that jointly performs pilot-aided channel estimation, multiuser detection, and channel decoding. The use of Gaussian message approximations results in a receiver complexity that scales only linearly with the number of users. A further complexity reduction is obtained by a novel selective message updating scheme. We also present a simulation-based comparison of the maximum rate achievable with our MIMO-OFDM-IDMA receiver with the information-theoretic capacity of the multiple-access channel. Finally, we provide simulation results illustrating the bit error rate (BER) performance of our receiver. It is observed that the proposed turbo-like integration of channel estimation in the iterative multiuser detection and channel decoding scheme yields a dramatic BER reduction, and that the proposed selective message updating scheme results in a significant reduction of complexity.

On Achieving an Asymptotically Error-Free Fixed-Point of Iterative Decoding for Perfect A Priori Information

In this paper we provide necessary and sufficient conditions for constituent codes in (multiple) concatenated and graph-based coding schemes to achieve an asymptotically error-free iterative decoding fixed-point if the maximum possible a priori information is available. At least one constituent code in an iterative decoding scheme must satisfy these conditions in order to ensure an asymptotically vanishing bit error probability at the convergence point of the decoder. Our results are proved for arbitrary binary-input symmetric memoryless channels (BISMCs) and thus can be universally applied to many transmission scenarios. Specifically, using a factor graph framework, it is shown that non-inner codes in a serial concatenation or check nodes in generalized LDPC codes achieve perfect extrinsic information if and only if the minimum Hamming distance between codewords is two or greater. For inner codes in a serial concatenation, constituent codes in a parallel concatenation, or variable nodes in doubly-generalized LDPC codes the corresponding encoder condition for acquiring perfect extrinsic information is an infinite codeword weight for a weight-one input sequence. For this case we provide a general proof which holds for all linear encoders and BISMCs. We also show that these results can improve the performance of concatenated coding schemes.

Iterative Multiuser Detection of Spectrally Efficient FDMA CPM

This paper presents two new iterative multiuser detection algorithms for spectrally efficient frequency division multiple access continuous phase modulation in additive white Gaussian noise. The detectors are derived from the sum-product algorithm and the factor graph framework, performing approximate maximum a posteriori (MAP) bit detection. A factor graph of the actual multiuser detection problem is considered, rather than only factor graphs of the individual single user detection problems combined with ad-hoc inter-user interference cancellation. The practical implementation of the detectors is based on the assumption that a suitable set of sum-product messages can be approximated by a Gaussian distribution. This methodology allows to considerably reduce the computational complexity and memory size requirements as compared to a straightforward application of the sum-product rules. The proposed algorithms further succeed in achieving a good error performance.

A Low-Complexity Iterative Phase Noise Tracker for Bit-Interleaved Coded CPM Signals in AWGN

This paper considers iterative detection of bit-interleaved coded continuous phase modulation in the presence of both phase noise (PN) and additive white Gaussian noise (AWGN). The proposed receiver iterates between a detection module and an estimation module. The detection module operates according to the sum-product algorithm and the factor graph framework in order to perform coherent maximum a posteriori bit detection in AWGN, using a PN estimate provided by the estimation module. The latter module, which results from the expectation-maximization algorithm for maximum likelihood estimation of the unknown PN samples, is implemented as a smoothing phase-locked loop that uses soft decisions provided by the detector. The separation between the detection and the estimation modules allows the use of an off-the-shelf (coherent) bit detector. The technique is further characterized by a very low computational complexity, a small error performance degradation and a small number of overhead symbols.

Non-Line-of-Sight Mobile Positioning Using Factor Graphs

Utilizing time-of-arrival measurements, we propose a recursive algorithm for estimating the location of a mobile station in a non-line-of-sight environment. By formulating the problem in a factor graph framework, messages are iteratively passed to obtain the mobile station position. Numerical results show that the proposed algorithm is more computationally attractive or reliable than existing methods and is able to achieve performance very close to the optimum benchmarks.

A novel indoor RSS-based position location algorithm using factor graphs

A low-complexity and accurate receive-signal strength (RSS)-based algorithm is proposed to estimate a target location. To achieve the aim of low complexity, a local linearization technique based on the local linearity in the surface of power decay profile (PDP), established by training logarithmic RSS measurements and collected from each individual access point (AP), was devised. To achieve a near-optimum solution, the stochastic properties of measurement errors and the reliability of the measurement data are introduced into the factor graph framework. Numerical experiments show that the proposed algorithm not only achieves a near maximum likelihood (ML) solution based on training RSS measurements, but also enjoys low complexity.

Figure-ground segmentation using factor graphs

Foreground–background segmentation has recently been applied [S.X. Yu, J. Shi, Object-specific figure-ground segregation, Computer Vision and Pattern Recognition (CVPR), 2003; S. Kumar, M. Hebert, Man-made structure detection in natural images using a causal multiscale random field, Computer Vision and Pattern Recognition (CVPR), 2003] to the detection and segmentation of specific objects or structures of interest from the background as an efficient alternative to techniques such as deformable templates [A.L. Yuille, Deformable templates for face recognition. Journal of Cognitive Neuroscience 3 (1) (1991)]. We introduce a graphical model (i.e. Markov random field)-based formulation of structure-specific figure-ground segmentation based on simple geometric features extracted from an image, such as local configurations of linear features, that are characteristic of the desired figure structure. Our formulation is novel in that it is based on factor graphs, which are graphical models that encode interactions among arbitrary numbers of random variables. The ability of factor graphs to express interactions higher than pairwise order (the highest order encountered in most graphical models used in computer vision) is useful for modeling a variety of pattern recognition problems. In particular, we show how this property makes factor graphs a natural framework for performing grouping and segmentation, and demonstrate that the factor graph framework emerges naturally from a simple maximum entropy model of figure-ground segmentation. We cast our approach in a learning framework, in which the contributions of multiple grouping cues are learned from training data, and apply our framework to the problem of finding printed text in natural scenes. Experimental results are described, including a performance analysis that demonstrates the feasibility of the approach.

Data Fusion of TOA and AOA Measurements for Target Location Estimation in Heterogeneous Wireless Sensor Networks Using Factor Graphs

This paper considers the problem of target location estimation in heterogeneous wireless sensor networks and proposes a novel algorithm using a factor graph to fuse the heterogeneous measured data. In the proposed algorithm, we map the problem of target location estimation to a factor graph framework and then use the sum-product algorithm to fuse the heterogeneous measured data so that heterogeneous sensors can collaborate to improve the accuracy of target location estimation. Simulation results indicate that the proposed algorithm provides high location estimation accuracy.

A Novel Strategy Using Factor Graphs and the Sum-Product Algorithm for Satellite Broadcast Scheduling Problems

This paper presents a low complexity algorithmic framework for finding a broadcasting schedule in a low-altitude satellite system, i. e., the satellite broadcast scheduling (SBS) problem, based on the recent modeling and computational methodology of factor graphs. Inspired by the huge success of the low density parity check (LDPC) codes in the field of error control coding, in this paper, we transform the SBS problem into an LDPC-like problem through a factor graph instead of using the conventional neural network approaches to solve the SBS problem. Based on a factor graph framework, the soft-information, describing the probability that each satellite will broadcast information to a terminal at a specific time slot, is exchanged among the local processing in the proposed framework via the sum-product algorithm to iteratively optimize the satellite broadcasting schedule. Numerical results show that the proposed approach not only can obtain optimal solution but also enjoys the low complexity suitable for integral-circuit implementation.

Simplified Soft-Output Detection of CPM Signals Over Coherent and Phase Noise Channels

We consider continuous phase modulations (CPMs) in iteratively decoded serially concatenated schemes. Although the overall receiver complexity mainly depends on that of the CPM detector, almost all papers in the literature consider the optimal maximum a posteriori (MAP) symbol detection algorithm and only a few attempts have been made to design low-complexity suboptimal schemes. This problem is faced in this paper by first considering the case of an ideal coherent detection, then extending it to the more interesting case of a transmission over a typical satellite channel affected by phase noise. In both cases, we adopt a simplified representation of an M-ary CPM signal based on the principal pulses of its Laurent decomposition. Since it is not possible to derive the exact detection rule by means of a probabilistic reasoning, the framework of factor graphs (FGs) and the sum-product algorithm (SPA) is used. In the case of channels affected by phase noise, continuous random variables representing the phase samples are explicitly introduced in the FG. By pursuing the principal approach to manage continuous random variables in a FG, i.e., the canonical distribution approach, two algorithms are derived which do not require the presence of known (pilot) symbols, thanks to the intrinsic differential encoder embedded in the CPM modulator.

Joint Source–Channel Turbo Techniques for Discrete-Valued Sources: From Theory to Practice

<para xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> The principles which have been prevailing so far for designing communication systems rely on Shannon's source and channel coding separation theorem. This theorem states that source and channel optimum performance bounds can be approached as close as desired by designing independently the source and channel coding strategies. However, this theorem holds only under asymptotic conditions, where both codes are allowed infinite length and complexity. If the design of the system is constrained in terms of delay and complexity, if the sources are not stationary, or if the channels are nonergodic, separate design and optimization of the source and channel coders can be largely suboptimal. For practical systems, joint source–channel (de)coding may reduce the end-to-end distortion. It is one of the aspects covered by the term cross-layer design, meaning a rethinking of the layer separation principle. This article focuses on recent developments of joint source–channel turbo coding and decoding techniques, which are described in the framework of normal factor graphs. The scope is restricted to lossless compression and discrete-valued sources. The presented techniques can be applied to the quantized values of a lossy source codec but the quantizer itself and its impact are not considered. </para>

Factor-Graph Algorithms for Equalization

In this paper, we use the factor-graph framework to describe the statistical relationships that arise in the equalization of data transmitted over an intersymbol interference channel, and use it to develop several new algorithms for linear and decision feedback approaches. Specifically, we examine both unconstrained and constrained linear equalization and decision feedback equalization of a sequence of nonidentically distributed symbols that are transmitted over a linear, possibly time-varying, finite-length channel and then corrupted by additive white noise. Factor graphs are used to derive algorithms for each of these equalization tasks, including fast implementations. One important application of these algorithms is linear turbo equalization, which requires a linear equalizer that can process observations of nonidentically distributed transmitted symbols. We show how the output of these factor-graph-based algorithms can be used in an efficient implementation of a linear turbo equalizer

Network-side mobile position location using factor graphs

A low-complexity high-accuracy algorithm is proposed to estimate the location of a target MS based on network-side time-of-arrival (TOA) measurements. Under a factor graph framework, the proposed algorithm first constructs a graphical model for the mobile position location problem by dividing the problem into many mutually-interactive local constraints. Each local constraint is enforced by a separate local processing unit. Efficient exchange of soft-information among local processing units in the mobile switching center (MSC) then iteratively purifies the estimate of the MS location. Numerical results show that the proposed algorithm not only enjoys low complexity, suitable for integrated-circuit implementation, but it is also able to achieve performance very close to the optimum achievable solution accuracy, the maximum likelihood (ML) solution accuracy

Mobile position location using factor graphs

Making use of the time-of-arrival measurements and their stochastic properties, we propose a low-complexity high-accuracy algorithm to estimate the location of a target mobile station (MS). Under a factor graph framework, in the proposed algorithm, soft-information is efficiently exchanged among local processing units to iteratively purify the estimate of the MS location. Numerical results show that the proposed algorithm not only enjoys advantages of low complexity, suitable for integrated-circuit implementation, but it is also able to achieve performance very close to the optimum achievable bound, the maximum-likelihood bound.