Dmitriy Shutin

Sparse Variational Bayesian SAGE Algorithm With Application to the Estimation of Multipath Wireless Channels

In this paper, we develop a sparse variational Bayesian (VB) extension of the space-alternating generalized expectation-maximization (SAGE) algorithm for the high resolution estimation of the parameters of relevant multipath components in the response of frequency and spatially selective wireless channels. The application context of the algorithm considered in this contribution is parameter estimation from channel sounding measurements for radio channel modeling purpose. The new sparse VB-SAGE algorithm extends the classical SAGE algorithm in two respects: i) by monotonically minimizing the variational free energy, distributions of the multipath component parameters can be obtained instead of parameter point estimates and ii) the estimation of the number of relevant multipath components and the estimation of the component parameters are implemented jointly. The sparsity is achieved by defining parametric sparsity priors for the weights of the multipath components. We revisit the Gaussian sparsity priors within the sparse VB-SAGE framework and extend the results by considering Laplace priors. The structure of the VB-SAGE algorithm allows for an analytical stability analysis of the update expression for the sparsity parameters. This analysis leads to fast, computationally simple, yet powerful, adaptive selection criteria applied to the single multipath component considered at each iteration. The selection criteria are adjusted on a per-component-SNR basis to better account for model mismatches, e.g., diffuse scattering, calibration and discretization errors, allowing for a robust extraction of the relevant multipath components. The performance of the sparse VB-SAGE algorithm and its advantages over conventional channel estimation methods are demonstrated in synthetic single-input-multiple-output (SIMO) time-invariant channels. The algorithm is also applied to real measurement data in a multiple-input-multiple-output (MIMO) time-invariant context.

Fast Variational Sparse Bayesian Learning With Automatic Relevance Determination for Superimposed Signals

In this work, a new fast variational sparse Bayesian learning (SBL) approach with automatic relevance determination (ARD) is proposed. The sparse Bayesian modeling, exemplified by the relevance vector machine (RVM), allows a sparse regression or classification function to be constructed as a linear combination of a few basis functions. It is demonstrated that, by computing the stationary points of the variational update expressions with noninformative (ARD) hyperpriors, a fast version of variational SBL can be constructed. Analysis of the computed stationary points indicates that SBL with Gaussian sparsity priors and noninformative hyperpriors corresponds to removing components with signal-to-noise ratio below a 0 dB threshold; this threshold can also be adjusted to significantly improve the convergence rate and sparsity of SBL. It is demonstrated that the pruning conditions derived for fast variational SBL coincide with those obtained for fast marginal likelihood maximization; moreover, the parameters that maximize the variational lower bound also maximize the marginal likelihood function. The effectiveness of fast variational SBL is demonstrated with synthetic as well as with real data.

Sparse estimation using Bayesian hierarchical prior modeling for real and complex linear models

In sparse Bayesian learning (SBL), Gaussian scale mixtures (GSMs) have been used to model sparsity-inducing priors that realize a class of concave penalty functions for the regression task in real-valued signal models. Motivated by the relative scarcity of formal tools for SBL in complex-valued models, this paper proposes a GSM model - the Bessel K model - that induces concave penalty functions for the estimation of complex sparse signals. The properties of the Bessel K model are analyzed when it is applied to Type I and Type II estimation. This analysis reveals that, by tuning the parameters of the mixing pdf different penalty functions are invoked depending on the estimation type used, the value of the noise variance, and whether real or complex signals are estimated. Using the Bessel K model, we derive sparse estimators based on a modification of the expectation-maximization algorithm formulated for Type II estimation. The estimators include as special instances the algorithms proposed by Tipping and Faul 1] and Babacan et al. 2]. Numerical results show the superiority of the proposed estimators over these state-of-the-art algorithms in terms of convergence speed, sparseness, reconstruction error, and robustness in low and medium signal-to-noise ratio regimes. HighlightsA GSM is proposed to model sparsity-inducing priors for real and complex signal models.By using the GSM in combination with a novel modification of the EM algorithm, sparse estimators are devised.The sparsity-inducing property of the GSM depends on whether the signal model is real or complex.The proposed sparse estimators encompass other existing estimators.The proposed estimators outperform these sparse estimators in low and moderate SNR regimes.

Application of Bayesian hierarchical prior modeling to sparse channel estimation

Existing methods for sparse channel estimation typically provide an estimate computed as the solution maximizing an objective function defined as the sum of the log-likelihood function and a penalization term proportional to the ℓ1-norm of the parameter of interest. However, other penalization terms have proven to have strong sparsity-inducing properties. In this work, we design pilot-assisted channel estimators for OFDM wireless receivers within the framework of sparse Bayesian learning by defining hierarchical Bayesian prior models that lead to sparsity-inducing penalization terms. The estimators result as an application of the variational message-passing algorithm on the factor graph representing the signal model extended with the hierarchical prior models. Numerical results demonstrate the superior performance of our channel estimators as compared to traditional and state-of-the-art sparse methods.

LDACS: future aeronautical communications for air-traffic management

A major modernization process in air traffic management for civil aviation is currently taking place under the framework of SESAR and NextGen in Europe and the United States, respectively. Air traffic management modernization is required to meet the needs sustainable air traffic growth in Europe, the United States, and worldwide are posing. A key enabler for this modernization process is the introduction of improved communications, navigation, and surveillance technologies. In this article, new developments in aeronautical communications for air traffic management are presented, with special focus on the air/ground communications technology L-band Digital Aeronautical Communications System (LDACS). The most promising LDACS technology candidate, LDACS1, is described in detail, and possible extensions toward navigation and surveillance are discussed. With these extensions, LDACS1 is well placed to become the first integrated communications, navigation, and surveillance technology for civil aviation. Utilizing a common ground infrastructure, such an integrated approach simplifies deployment and reduces costs for both deployment and maintenance.

Delay-Dependent Doppler Probability Density Functions for Vehicle-to-Vehicle Scatter Channels

Novel joint delay Doppler probability density functions for vehicle-to-vehicle communications channels are introduced. Prior measurements of vehicle-to-vehicle channels have unveiled their nonstationarity; thus, the wide-sense stationary and also the uncorrelated scattering assumption for such channels is often violated, which makes their modeling challenging. In this work it is proposed to exploit geometry-based stochastic modeling to cope with the nonstationarity of vehicle-to-vehicle channels. To this end, delay-dependent Doppler pdfs are derived for arbitrary times. It is assumed that scatterers are randomly distributed on an ellipse with two moving vehicles being in its foci. The proposed approach allows reducing the dimensionality of the resulting problem. This in turn leads to a significantly simplified derivation of the delay-dependent Doppler pdfs for general vehicle-to-vehicle propagation environments; moreover, the resulting computations can be performed almost fully analytically. By combining the calculated Doppler pdf with a delay pdf, the joint pdf of delay and Doppler is obtained. The joint pdf then can be put into relation with the generalized local scattering function. The presented modeling approach is simple yet very scalable and accurate, which allows its application in different vehicular scenarios. The obtained modeling results correspond very well with measurement data reported in prior works.

Mitigation of Impulsive Frequency-Selective Interference in OFDM Based Systems

In this paper, an algorithm for mitigating impulsive interference in OFDM based systems is presented. It improves the conventional blanking nonlinearity approach for interference mitigation, which typically distorts the entire received signal, by combining the blanked and the original signal. The algorithm uses a Neyman-Pearson like testing procedure to detect interference at individual sub-carriers. Provided interference is detected, the blanked and the original received signals are then optimally combined such as to maximize the signal-to-interference-and-noise ratio. The algorithm does not require any prior knowledge about the impulsive interference and only marginally increases computational complexity as compared to the conventional blanking nonlinearity approach. Numerical results demonstrate the superior performance of the proposed scheme.

Cluster analysis of wireless channel impulse responses with hidden Markov models

This paper introduces a novel wireless channel clustering technique, based on the Saleh-Valenzuela channel model. The channel impulse response is regarded as a realization of the probabilistic channel model, based on which the prior density functions of cluster arrival times are derived. Cluster analysis is done by means of extending the Saleh-Valenzuela model to a non-stationary case and re-interpreting it in terms of mixture models. The parameters of the mixture are then learned with hidden Markov models. Once trained, the HMM could be used to optimally cluster the channel taps with the Viterbi algorithm. The proposed method has been applied to simulated as well as measured channel impulse responses and showed reasonably good performance.

Fast adaptive variational sparse Bayesian learning with automatic relevance determination

In this work a new adaptive fast variational sparse Bayesian learning (V-SBL) algorithm is proposed that is a variational counterpart of the fast marginal likelihood maximization approach to SBL. It allows one to adaptively construct a sparse regression or classification function as a linear combination of a few basis functions by minimizing the variational free energy. In the case of non-informative hyperpriors, also referred to as automatic relevance determination, the minimization of the free energy can be efficiently realized by computing the fixed points of the update expressions for the variational distribution of the sparsity parameters. The criteria that establish convergence to these fixed points, termed pruning conditions, allow an efficient addition or removal of basis functions; they also have a simple and intuitive interpretation in terms of a components signal-to-noise ratio. It has been demonstrated that this interpretation allows a simple empirical adjustment of the pruning conditions, which in turn improves sparsity of SBL and drastically accelerates the convergence rate of the algorithm. The experimental evidence collected with synthetic data demonstrates the effectiveness of the proposed learning scheme.

Incremental Reformulated Automatic Relevance Determination

In this work, the relationship between the incremental version of sparse Bayesian learning (SBL) with automatic relevance determination (ARD)-a fast marginal likelihood maximization (FMLM) algorithm-and a recently proposed reformulated ARD scheme is established. The FMLM algorithm is an incremental approach to SBL with ARD, where the corresponding objective function-the marginal likelihood-is optimized with respect to the parameters of a single component provided that the other parameters are fixed; the corresponding maximizer is computed in closed form, which enables a very efficient SBL realization. Wipf and Nagarajan have recently proposed a reformulated ARD (R-ARD) approach, which optimizes the marginal likelihood using auxiliary upper bounding functions. The resulting algorithm is then shown to correspond to a series of reweighted l1-constrained convex optimization problems. This correspondence establishes and analyzes the relationship between the FMLM and R-ARD schemes. Specifically, it is demonstrated that the FMLM algorithm realizes an incremental approach to the optimization of the R-ARD objective function. This relationship allows deriving the R-ARD pruning conditions similar to those used in the FMLM scheme to analytically detect components that are to be removed from the model, thus regulating the estimated signal sparsity and accelerating the algorithm convergence.