No abstract

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 a sparse estimator based on a modification of the expectation-maximization algorithm formulated for Type II estimation. The estimator includes as a special instance the algorithms proposed by Tipping and Faul [1] and by Babacan et al. [2]. Numerical results show the superiority of the proposed estimator over these state-of-the-art estimators in terms of convergence speed, sparseness, reconstruction error, and robustness in low and medium signal-to-noise ratio regimes.

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.Index Terms-Geometric-stochastic channel modeling, nonstationary modeling, scatter channel, vehicle-to-vehicle channel, wideband channel model.

No abstract

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.