Mihai Alin Badiu

Merging Belief Propagation and the Mean Field Approximation: A Free Energy Approach

We present a joint message passing approach that combines belief propagation and the mean field approximation. Our analysis is based on the region-based free energy approximation method proposed by Yedidia et al. We show that the message passing fixed-point equations obtained with this combination correspond to stationary points of a constrained region-based free energy approximation. Moreover, we present a convergent implementation of these message passing fixed-point equations provided that the underlying factor graph fulfills certain technical conditions. In addition, we show how to include hard constraints in the part of the factor graph corresponding to belief propagation. Finally, we demonstrate an application of our method to iterative channel estimation and decoding in an orthogonal frequency division multiplexing system.

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.

Message-passing algorithms for channel estimation and decoding using approximate inference

We design iterative receiver schemes for a generic communication system by treating channel estimation and information decoding as an inference problem in graphical models. We introduce a recently proposed inference framework that combines belief propagation (BP) and the mean field (MF) approximation and includes these algorithms as special cases. We also show that the expectation propagation and expectation maximization (EM) algorithms can be embedded in the BP-MF framework with slight modifications. By applying the considered inference algorithms to our probabilistic model, we derive four different message-passing receiver schemes. Our numerical evaluation in a wireless scenario demonstrates that the receiver based on the BP-MF framework and its variant based on BP-EM yield the best compromise between performance, computational complexity and numerical stability among all candidate algorithms.

Message-Passing Receiver Architecture with Reduced-Complexity Channel Estimation

We propose an iterative receiver architecture which allows for adjusting the complexity of estimating the channel frequency response in OFDM systems. This is achieved by approximating the exact Gaussian channel model assumed in the system with a Markov model whose state-space dimension is a design parameter. We apply an inference framework combining belief propagation and the mean field approximation to a probabilistic model of the system which includes the approximate channel model. By doing so, we obtain a receiver algorithm with adjustable complexity which jointly performs channel and noise precision estimation, equalization and decoding. Simulation results show that low-complexity versions of the algorithm - obtained by selecting low state-space dimensions - can closely attain the performance of a receiver devised based on the exact channel model.

A sparse Bayesian learning algorithm with dictionary parameter estimation

This paper concerns sparse decomposition of a noisy signal into atoms which are specified by unknown continuous-valued parameters. An example could be estimation of the model order, frequencies and amplitudes of a superposition of complex sinusoids. The common approach is to reduce the continuous parameter space to a fixed grid of points, thus restricting the solution space. In this work, we avoid discretization by working directly with the signal model containing parameterized atoms. Inspired by the “fast inference scheme” by Tipping and Faul we develop a novel sparse Bayesian learning (SBL) algorithm, which estimates the atom parameters along with the model order and weighting coefficients. Numerical experiments for spectral estimation with closely-spaced frequency components, show that the proposed SBL algorithm outperforms state-of-the-art subspace and compressed sensing methods.

Link performance prediction methods for cooperative relaying in wireless networks

Next generation wireless networks are likely to include cooperative relaying in their design. The performance of certain cooperation schemes in realistic scenarios should be evaluated by system level simulations (SLS). Moreover, the link adaptation (LA) and radio resource management become more complex, since cooperation schemes involve transmissions on more than one link and joint processing at the receiver. Both LA and SLS require quality metrics of the composite cooperative links, which capture the performance of the transmission scheme. This paper proposes performance prediction methods which rely on mutual information based metrics for two cooperation schemes which use one relay. Simulations show that, yet simple, these methods are accurate in predicting the coded block error rate (BLER).

Variational Bayesian Inference of Line Spectra

We address the fundamental problem of line spectral estimation in a Bayesian framework. We target model order and parameter estimation via variational inference in a probabilistic model in which the frequencies are continuous-valued, i.e., not restricted to a grid; and the coefficients are governed by a Bernoulli-Gaussian prior model turning model order selection into binary sequence detection. Unlike earlier works which retain only point estimates of the frequencies, we undertake a complete Bayesian treatment by estimating the posterior probability density functions (pdfs) of the frequencies and computing expectations over them. Thus, we additionally capture and operate with the uncertainty of the frequency estimates. Aiming to maximize the model evidence, variational optimization provides analytic approximations of the posterior pdfs and also gives estimates of the additional parameters. We propose an accurate representation of the frequency pdfs by mixtures of von Mises pdfs, which yields closed-form expectations. We define the algorithm VALSE in which the estimates of the pdfs and parameters are iteratively updated. VALSE is a gridless, convergent method, does not require parameter tuning, can easily include prior knowledge about the frequencies and provides approximate posterior pdfs based on which the uncertainty in line spectral estimation can be quantified. Simulation results show that accounting for the uncertainty of frequency estimates, rather than computing just point estimates, significantly improves the performance. The performance of VALSE is superior to that of state-of-the-art methods and closely approaches the Cramér-Rao bound computed for the true model order.

Link adaptation algorithm for distributed coded transmissions in relay-aided OFDMA systems

We propose a link adaptation algorithm for cooperative transmissions in an OFDMA-based wireless system. The algorithm aims at maximizing the spectral efficiency of a relay-aided communication link, while satisfying the block error rate constraints at both the relay and the destination nodes. The optimal solution would be to perform an exhaustive search over a high-dimensional space determined by all possible combinations of modulations, code rates and information block lengths on the individual links; clearly, such an approach has an intractable complexity. Our solution is to use a link performance prediction method and a trellis diagram representation such that the resulting algorithm outputs a link configuration that conveys as many as possible information bits and also fulfills the block error rate constraints. The proposed link adaptation algorithm has linear complexity with the number of available resource blocks, but still provides a very good performance, as shown by simulation results.

Link adaptation algorithm for distributed coded transmissions in cooperative OFDMA systems

This paper proposes a link adaptation algorithm for cooperative transmissions in the down-link connection of an OFDMA-based wireless system. The algorithm aims at maximizing the spectral efficiency of a relay-aided communication link, while satisfying the block error rate constraints at both the relay and the destination nodes. The optimal solution would be to perform an exhaustive search over a high-dimensional space determined by all possible combinations of modulations, code rates and information block lengths on the individual channels of the cooperative link; clearly, such an approach has an intractable complexity. Our solution is to use a link performance prediction method and a trellis diagram representation such that the resulting algorithm outputs the link configuration that conveys as many information bits as possible and also fulfilling the block error rate constraints. The proposed link adaptation algorithm has linear complexity with the number of available resource blocks, while still provides a very good performance, as shown by simulation results.

Interference alignment using variational mean field annealing

We study the problem of interference alignment in the multiple-input multiple-output interference channel. Aiming at minimizing the interference leakage power relative to the receiver noise level, we use the deterministic annealing approach to solve the optimization problem. In the corresponding probabilistic formulation, the precoders and the orthonormal bases of the desired signal subspaces are variables distributed on the complex Stiefel manifold. To enable analytically tractable computations, we resort to the variational mean field approximation and thus obtain a novel iterative algorithm for interference alignment. We also show that the iterative leakage minimization algorithm by Gomadam et al. and the alternating minimization algorithm by Peters and Heath, Jr. are instances of our method. Finally, we assess the performance of the proposed algorithm through computer simulations.