Bernoulli Gaussian Research Articles

A low-complexity DOA estimation algorithm using UAMP with Bernoulli-Gaussian prior

In this paper, we design a low-complexity direction-of-arrival (DOA) estimation algorithm based on the unitary approximate message passing (UAMP) and Bernoulli-Gaussian (BG) prior. We first show that the estimation of DOA can be transferred into a sparse signal recovery problem, where we turn to UAMP with damping technique to solve this problem. Furthermore, we assume the BG prior on the sparse vector to be estimated, resulting in the fast estimation of the positions of non-zero elements. Moreover, expectation maximum (EM) is leveraged to automatically learn the BG parameters. Compared to the state-of-the-art UAMP-based algorithm with sparse Bayesian learning (SBL), the proposed approach can achieve the same DOA mean square error (MSE) performance with a much faster convergence speed.

Sparse Decomposition of Heart Rate Using a Bernoulli-Gaussian Model: Application to Sleep Apnoea Detection

In this paper, we propose a sparse decomposition of the heart rate during sleep with an application to apnoea-RERA detection. We observed that the tachycardia following an apnoea event has a quasi-deterministic shape with a random amplitude. Accordingly, we model the apnoea-perturbed heart rate as a Bernoulli-Gaussian (BG) process convolved with a deterministic reference signal that allows the identification of tachycardia and bradycardia events. The problem of determining the BG series indicating the presence or absence of an event and estimating its amplitude is a deconvolution problem for which sparsity is imposed. This allows an almost syntactic representation of the heart rate on which simple detection algorithms are applied.

GMM-Based Symbol Error Rate Analysis for Multicarrier Systems With Impulsive Noise Suppression

Theoretical analysis of orthogonal frequency division multiplexing (OFDM) systems, equipped at the receiver by a non-linear impulsive noise suppressor, is very challenging. Indeed, although an exact closed-form expression for the output signal-to-noise ratio (SNR) of such OFDM systems is available for widely used impulsive noise models, theoretical analysis of the associated symbol error rate (SER) is still open. The analytical SER available in the literature, exploit a Gaussian approximation of the non-linear distortion noise, which however holds true only under specific conditions. Conversely, this work develops an accurate analytical closed-form expression of the distortion noise distribution at the nonlinearity output, as well as its approximation by a Gaussian mixture model (GMM). By using GMMs we unify the SER analysis for communication systems equipped by non-linear impulsive noise suppressors, typically also used in vehicular communications. Closed form expressions for the SER are derived both for non-fading and frequency-selective Rayleigh/Rician fading channels affected by impulsive noise, which is also modeled by a GMM, including Bernoulli-Gaussian (BG), Middleton Class-A, and alpha-stable noises. Theoretical SER performance are compared with simulations, showing very good agreement for all the impulsive noise scenarios and the non-linear suppressors.

Planar Array Diagnosis Based on Bayesian Learning With a Bernoulli–Gaussian Prior Model

A new approach is proposed for the planar array failure diagnosis from a set of far-field measurements. Under the framework of Bayesian learning, a Bernoulli–Gaussian (BG) model is constructed to exploit the binary prior information of the unknown failure elements. Subsequently, the variational expectation maximization (EM) strategy is used to perform the Bayesian inference. Moreover, the damped generalized approximate message passing (GAMP) is further adopted to circumvent the matrix inversion in the variational EM procedure, thus making the overall process computationally very efficient. A set of representative numerical experiments are provided to validate the accuracy, efficiency, and flexibility of the proposed method.

Performance of NOMA-Based Dual-Hop Hybrid Powerline-Wireless Communication Systems

The mixture of wireless and power line communications (PLC) is vital for implementing new applications in smart grid and vehicular communications. In this work, we investigate the performance of non-orthogonal multiple access (NOMA) based dual-hop hybrid communication systems with decode-and-forward relay. The wireless channel is characterized by Nakagami- <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">m</i> fading under an additive white Gaussian noise (AWGN), while the PLC channels are characterized by Log-normal distribution with Bernoulli Gaussian noise including both background and impulsive noise components. New closed-form expressions for the outage probability, the asymptotic outage probability and ergodic capacity are derived and verified via extensive representative simulations. For more insights on the outage performance, we analyze the diversity order. Additionally, we proposed a power allocation optimization technique to achieve an outage-optimal performance. The results show that the system outage probability improves as the impulsive noise index and the arrival probability of the impulsive component of the PLC additive noise decrease, while their effect is negligible on the ergodic capacity. Finally, the performance of the proposed system is compared against a benchmark OMA-based system.

A fully Bayesian approach based on Bernoulli–Gaussian prior for the identification of sparse vibratory sources from displacement measurements

This paper introduces a fully Bayesian approach to the Force Analysis Technique (FAT), which aims at identifying sparse vibratory sources from displacement measurements. Being based on the local equation of motion of a structure, the FAT allows for the estimation of vibratory sources without the need of specifying boundary conditions. Nevertheless, since it involves the calculation of higher-order spatial derivatives of the measured displacements, it is highly sensitive to noise perturbations and thus requires careful regularization. Besides, although sparse excitations are commonplace in structural vibrations, standard regularization strategies tend to over-smooth them in the reconstruction process. This paper shows how to reconcile the two goals of regularization and sparsity enforcement in the FAT by setting up a hierarchical Bayesian model rooted on a Bernoulli–Gaussian prior. Inference of all the parameters in the model is achieved with a Gibbs sampler whose convergence is efficiently accelerated with a partial collapsing strategy.

Bayesian Sparse Blind Deconvolution Using MCMC Methods Based on Normal-Inverse-Gamma Prior

Bayesian estimation methods for sparse blind deconvolution problems conventionally employ Bernoulli-Gaussian (BG) prior for modeling sparse sequences and utilize Markov Chain Monte Carlo (MCMC) methods for the estimation of unknowns. However, the discrete nature of the BG model creates computational bottlenecks, preventing efficient exploration of the probability space even with the recently proposed enhanced sampler schemes. To address this issue, we propose an alternative MCMC method by modeling the sparse sequences using the Normal-Inverse-Gamma (NIG) prior. We derive effective Gibbs samplers for this prior and illustrate that the computational burden associated with the BG model can be eliminated by transferring the problem into a completely continuous-valued framework. In addition to sparsity, we also incorporate time and frequency domain constraints on the convolving sequences. We demonstrate the effectiveness of the proposed methods via extensive simulations and characterize computational gains relative to the existing methods that utilize BG modeling.

Adaptive Geman-McClure Estimator for Robust Distributed Channel Estimation

Communication systems are affected by channel distortions. Impulsive noise is one of the significant factors for channel impairments. The standard additive white Gaussian noise (AWGN) channel model and conventional estimation algorithms like least mean square (LMS) and its variants tend to be ineffective under such conditions. This paper presents a robust adaptive channel estimation algorithm using the Geman-McClure estimator in a diffusion-based distributed network. The analytical study on mean stability and mean square analysis is carried out under two separate noise statistics: Symmetric α-stable ( SαS) and Bernoulli-Gaussian (BG) distribution. The computer simulations confirm the proposed algorithm's competitive robustness compared to the Maximum Correntropy Criterion and Minimum Kernel Risk Sensitive Loss algorithms at a high impulsive noise environment without exponential cost function. Further, the efficiency is also verified by simulating the bit error rate by designing a minimum mean square error (MMSE) equalizer with the estimated coefficients.

Parameter estimation of impulsive noise for channel coded communication systems

In this paper, an impulsive noise estimation algorithm for generating bit log-likelihood ratios (LLRs) for channel coded systems in impulsive noise environments is proposed. This approach is to design the LLR detector in the maximum-likelihood (ML) sense, which requires the parameters of the impulsive noise. The expectation-maximisation (EM) algorithm is utilised to estimate the parameters of the Bernoulli–Gaussian (B–G) impulsive noise model. The estimated parameters is then used to generate the bit LLRs for the soft-input channel decoder. Simulation results show that over a wide range of impulsive noise power, the proposed algorithm approaches the optimal performance (with ideal estimation) even under Middleton class-A (M-CA) impulsive noise models.

Modelling impulsive noise in indoor powerline communication systems

Powerline communication (PLC) is an emerging technology that has an important role in smart grid systems. Due to making use of existing transmission lines for communication purposes, PLC systems are subject to various noise effects. Among those, the most challenging one is the impulsive noise compared to the background and narrowband noise. In this paper, we present a comparative study on modelling the impulsive noise amplitude in indoor PLC systems by utilising several impulsive distributions. In particular, as candidate distributions, we use the symmetric alpha -Stable (Salpha S), generalised Gaussian, Bernoulli Gaussian and Student’s t distribution families as well as the Middleton Class A distribution, which dominates the literature as the impulsive noise model for PLC systems. Real indoor PLC system noise measurements are investigated for the simulation studies, which show that the Salpha S distribution achieves the best modelling success when compared to the other families in terms of the statistical error criteria, especially for the tail characteristics of the measured data sets.

A Bernoulli–Gaussian Binary Inversion Method for High-Frequency Electromagnetic Imaging of Metallic Reflectors

High-frequency electromagnetic inverse scattering of conductors has many practical applications. Its goal is to reconstruct the shape of conductors from their scattered fields at some distances. When viewed from the pixelated imaging viewpoint, any pixel in the imaging domain is either a conductor or background (air); thus such an inverse scattering problem has binary solutions for all pixels. Under the high-frequency physical optics (PO) approximation, the scattered field is formulated as a linear problem in terms of a local binary shape function. A binary inversion method is proposed for the detection and shape reconstruction of a flat PEC reflector from high-frequency scattered field measurements. To exploit the underlying binary structure, a Bernoulli–Gaussian (BG) prior model is employed to perform a binary enforcement mechanism. This binary enforcement mechanism can push each pixel of the inversion domain to have a value equal to either zero or one. Then, the damped generalized approximate message passing (GAMP) is integrated with the proposed prior model to address the binary linear inverse problem from the Bayesian inference perspective. Numerical examples are presented to demonstrate the effectiveness and robustness of the proposed BG Binary Inversion method. The performance improvement of the proposed method is attributed to the exploitation of the binary prior information of the solution and GAMP technique.

Impulsive Noise Mitigation With Interleaving Based on MUSIC in Power Line Communication

In power line communication, impulsive noise (IN) greatly degrades the performance of signal transmission. Generally, an IN model adopts Middleton Class A or Bernoulli Gaussian model with the assumption that IN is sparse and memoryless. However, IN collected in fields appears in bursts. In this paper, interleaving in time domain is applied to create a special structure in frequency domain for IN burst. Based on the special structure, IN support is determined by using multiple signal classification (MUSIC) and its amplitude is estimated by least squares method in frequency domain, exploiting the noise information on null subcarriers in orthogonal frequency division multiplexing system. In addition, sparse Bayesian Learning algorithm with IN support based on MUSIC is also investigated. Simulations are conducted to evaluate the proposed IN estimation performance, with varying ratio of IN power to background noise power, and number of null subcarriers.

Impulsive Noise Models Used in Power Line Communications

In a communication system, noise has always been considered as a serious cause of error. Although most common noises can be modeled by well-known Gaussian distributions, some communication systems experience other types of noise. Power Line Communication (PLC) is one of these systems which run on a difficult medium since it uses the preexisting power line network for transmission. PLC experiences several different types of human-made and natural noise which are mostly impulsive and cannot be modeled simply by Gaussian. Different statistical models are used for characterizing the impulsive noise of PLC systems in the literature. The purpose of this study is to go over the impulsive noise models previously presented in order to have a contribution to this hot topic. We point out the similarities and differences of the models, namely Middleton Class A, Bernoulli Gaussian and Alpha Stable statistical models. It is presented that all have heavy tails which make them appropriate for impulsive noise. Although Middleton Class A is more generic, Bernoulli Gaussian model is wide enough and can be preferable because of its compact simple form especially when analytical results are needed.

An Approximate Message Passing Framework for Side Information

Approximate message passing (AMP) methods have gained recent traction in sparse signal recovery. Additional information about the signal, or \emph{side information} (SI), is commonly available and can aid in efficient signal recovery. This work presents an AMP-based framework that exploits SI and can be readily implemented in various settings for which the SI results in separable distributions. To illustrate the simplicity and applicability of our approach, this framework is applied to a Bernoulli-Gaussian (BG) model and a time-varying birth-death-drift (BDD) signal model, motivated by applications in channel estimation. We develop a suite of algorithms, called AMP-SI, and derive denoisers for the BDD and BG models. Numerical evidence demonstrating the advantages of our approach are presented alongside empirical evidence of the accuracy of a proposed state evolution.

Merging the Bernoulli–Gaussian and symmetric [formula omitted]-stable models for impulsive noises in narrowband power line channels

To model impulsive noise in power line channels, both the Bernoulli–Gaussian model and the symmetric α-stable model are usually applied. Towards a merge of existing noise measurement databases and a simplification of communication system design, the compatibility between the two models is of interest. In this paper, we show that they can be approximately converted to each other under certain constrains, although never generally unified. Based on this, we propose a fast model conversion.

Detection of Sparse Signals in Sensor Networks via Locally Most Powerful Tests

We consider the problem of detection of sparse stochastic signals with a distributed sensor network. Multiple sensors in the network are assumed to observe sparse signals, which share the joint sparsity pattern. The Bernoulli–Gaussian (BG) distribution with sparsity-enforcing capability is imposed on the sparse signals. The sparsity degree in the BG model is positive and close to zero in the presence of the sparse signals and is zero in the absence of the signals. Motivated by this, the problem of detection of the sparse signals with a distributed sensor network is formulated as the problem of close and one-sided hypothesis testing on the sparsity degree. For this problem, we propose a detector based on the locally most powerful test (LMPT) to decide on the presence or absence of sparse signals with sensor networks. The proposed LMPT detector does not require signal recovery, which alleviates the complexity of the detection system in sensor networks. Simulation results illustrate the performance of the proposed LMPT detector and corroborate our theoretical analysis. Simulation results also show that, compared to the detector based on matching pursuit, the proposed LMPT detector significantly reduces the computational burden without noticeable performance loss.

PSFM—A Probabilistic Source Filter Model for Noise Robust Glottal Closure Instant Detection

Accurate estimation of glottal closure instant (GCI) enables several pitch synchronous speech analysis, such as prosody modifications, glottal inverse filtering, and study of pathological speech. We propose a probabilistic source-filter model (PSFM) for voiced speech, where the source is modeled using the Bernoulli Gaussian distribution, which models the GCI locations and the all-pole filter coefficients are modeled using Gaussian distribution. The probability of GCIs at each speech sample is estimated using the Gibbs sampling. We propose a cost to estimate the exact GCI locations using the N-best dynamic programming. A key feature of the proposed PSFM is that it allows us to include the second-order statistics of the noise for estimating the GCI locations, thereby resulting in a noise robust GCI detection technique, although it has high computational complexity. Evaluation on archivable priority list actual-word database (APLAWD) database shows the proposed algorithm performs at par with the state-of-the-art GCI detection method on clean speech. However, when evaluated in noisy conditions using five types of noises at six different signal-to-noise ratio (SNR) levels, we observe that the proposed method performs better than the best of the existing GCI detection scheme, particularly at low SNR condition indicating the noise robustness of the proposed method.

Estimation of the Parameters of a Bernoulli–Gaussian Communications Channel

A model is presented for a digital subscriber line in the form of a Bernoulli–Gaussian communications channel that is indirectly described in the form of a likelihood function. An expression is presented for the accuracy of the standard estimate of the pulse characteristics based on traditional averaging. A lower bound is formalized for the dispersion of the estimate of the pulse characteristics of a communications channel, demonstrating the possibility of improving the accuracy of the effective estimate.

A Message Passing Approach to Acquire mm-Wave Channel State Information Based on Out-of-Band Data

Millimeter-wave (mm-wave) communication is a practicable scheme for big data communication, such as next-generation cellular communication. However, because mm-wave frequencies have an extremely large path loss, in order to mitigate the mm-wave path loss, a large number of antennas are packed for beamforming. Conventional multiple-input multiple-output (MIMO) beamforming uses digital processing, which leads to needing extremely giant energy. Hybrid analog/digital beamforming could serve as an awesome technique to reduce the cost. It is essential for achieving high beamfroming gain that accurate mm-wave channel information should be attained at the transmitter. This paper concentrates on the channel state information (CSI) acquirement problem in mm-wave communication systems with massive MIMO arrays. Because of the CSI acquirement, a method of significant overhead, we consider an accurate channel estimation scheme with low overhead. Not only do we in this paper propose using support information extracted at Sub-6GHz to aid the mm-wave CSI acquirement but also introduce a strategy used in the mm-wave channel estimation. We, in particular, formulate mm-wave CSI acquirement as a compressive sensing problem and obtain the CSI by using Bernoulli–Gaussian generalized approximate message passing (BG-GAMP) algorithm. We also extend the BG-GAMP algorithm with support distribution information from sub-6-GHz channel. Furthermore, based on the $K$ nearest neighbor idea, we redesign the BG-GAMP algorithm depending on sub-6-GHz support distribution information. Details of BG-GAMP with the nearest neighbor learning algorithm that is built on support distribution information from sub-6-GHz channel would also be revealed. Simulation results show the out-of-band information aided mm-wave channel estimation is capable of reducing the pilot overhead greatly and channel estimation accuracy improved as well.

Reconstruction of Dispersion Curves in the Frequency-Wavenumber Domain Using Compressed Sensing on a Random Array

In underwater acoustics, shallow-water environments act as modal dispersive waveguides when considering low-frequency sources, and propagation can be described by modal theory. In this context, propagated signals are composed of few modal components, each of them propagating according to its own wavenumber. Frequency-wavenumber $(f-k)$ representations are classical methods allowing modal separation. However, they require large horizontal line sensor arrays aligned with the source. In this paper, to reduce the number of sensors, a sparse model is proposed and combined with prior knowledge on the wavenumber physics. The method resorts to a state-of-the-art Bayesian algorithm exploiting a Bernoulli–Gaussian model. The latter, well suited to the sparse representations, makes possible a natural integration of prior information through a wise choice of the Bernoulli parameters. The performance of the method is quantified on simulated data and finally assessed through a successful application on real data.