In this paper, we propose a procedure to accelerate the resolution of the well-known "Elastic-Net" problem. Our procedure is based on the (partial) identification of the solution support and the reformulation of the original problem into a problem of reduced dimension. The identification of the support leverages the novel concept of "safe relaxing" where one aims to identify non-zero coefficients of the solution. It can be viewed as a dual approach to "safe screening" introduced in the last decade and allowing to reduce the problem dimension using the identification of zero coefficients of the solution. We show numerically that combining both methodologies in a "Screen & Relax" strategy enables to significantly improve the trade-off between complexity and accuracy achievable by standard resolution techniques.

We present a novel screening methodology to safely discard irrelevant nodes within a generic branch-and-bound (BnB) algorithm solving the ℓ0-penalized least-squares problem. Our contribution is a set of two simple tests to detect sets of feasible vectors that cannot yield optimal solutions. This allows to prune nodes of the BnB search tree, thus reducing the overall optimization time. One cornerstone of our contribution is a nesting property between tests at different nodes that allows to implement them with a low computational cost. Our work leverages the concept of safe screening, well known for sparsity-inducing convex problems, and some recent advances in this field for ℓ0-penalized regression problems.

Antisparse coding aims at spreading the information uniformly over representation coefficients and can be expressed as the solution of an ℓ∞-norm regularized problem. In this paper, we propose a new methodology, coined "safe squeezing", accelerating the computation of antisparse representations. The idea consists in identifying saturated entries of the solution via simple tests and compacting their contribution to achieve some form of dimensionality reduction. Numerical experiments show that the proposed approach leads to significant computational gain.

Reduced modeling in high-dimensional reproducing kernel Hilbert spaces offers the opportunity to approximate efficiently non-linear dynamics. In this work, we devise an algorithm based on low rank constraint optimization and kernel-based computation that generalizes a recent approach called "kernel-based dynamic mode decomposition". This new algorithm is characterized by a gain in approximation accuracy, as evidenced by numerical simulations, and in computational complexity.

This paper deals with efficient atom selection procedure in a continuous dictionary, as required for instance in a Frank-Wolfe approach within a BLASSO problem for the one-dimensional deconvolution problem. We show that efficient maximization of a correlation between any given vector and an atom sweeping a continuous dictionary can be performed through a particular piece-wise linear approximation of dictionaries: the polar approximation. We finally identify the polar approximation as being optimal in a mean square error sense for dictionaries with raised-cosine Toeplitz kernels.

In this work, we present new theoretical results on sparse recovery guarantees for a greedy algorithm, orthogonal matching pursuit (OMP), in the context of continuous parametric dictionaries, i.e., made up of an infinite uncountable number of atoms. We build up a family of dictionaries for which k-step recovery is possible with OMP for 1-dimensional parameters. In higher dimension, algebraic conditions become necessary and will lead us to revisit some well-known k-step discrete analyses. Finally, a toy-example illustrates the level of tightness of our sufficient conditions.

In the last years, Neural Networks have enriched the state-of-the-art in probabilistic modeling. This is principally due to the advances in deep learning which allow a better understanding of complex systems. However, the stochastic representation of spatio-temporal fields is still an open challenge that may benefit from the recent advances in probabilistic modelization. In this work, we explore neural network to derive a stochastic representation of spatio-temporal dynamical systems based on ensemble forecasting. Trough the implementation of our stochastic model in a classical Kalman filtering scheme, we demonstrate the relevance of the proposed architecture in the reconstruction of geophysical fields with respect to the state-of-the-art approaches.

In this work, we propose an alternative to the Ensemble Kalman filter through the implementation of a neural networks filtering scheme based on a parametric stochastic model. From our numerical experiment, we prove the relevance of the proposed architecture in the reconstruction of geophysical fields with respect to the state-of-the-art schemes.

Recent studies have investigated the identification of governing equations of geophysical systems from data. Here, we investigate such identification issues for ocean surface dy-namcis from ocean remote sensing data. From a methodological point of view, we address the learning of data-driven dynamical models when only provided with a noisy training dataset. We propose a novel architecture that relies on data assimilation schemes to learn the underlying dynamical model through the minimization of a reconstruction cost. We demonstrate the relevance of the proposed architecture with respect to the state-of-the-art approaches in the identification and forecasting of synthetic and real case-studies.

This paper focusses on “safe” screening techniques for the LASSO problem. Motivated by the need for low-complexity algorithms, we propose a new approach, dubbed “joint screening test”, allowing to screen a set of atoms by carrying out one single test. The approach is particularized to two different sets of atoms, respectively expressed as sphere and dome regions. After presenting the mathematical derivations of the tests, we elaborate on their relative effectiveness and discuss the practical use of such procedures.

The forecasting and reconstruction of ocean and atmosphere dynamics from satellite observation time series are key challenges. While model-driven representations remain the classic approaches, data-driven representations become more and more appealing to benefit from available large-scale observation and simulation datasets. In this work we investigate the relevance of recently introduced bilinear residual neural network representations, which mimic numerical integration schemes such as Runge-Kutta, for the forecasting and assimilation of geophysical fields from satellite-derived remote sensing data. As a case-study, we consider satellite-derived Sea Surface Temperature time series off South Africa, which involves intense and complex upper ocean dynamics. Our numerical experiments demonstrate that the proposed patch-level neural-network-based representations outperform other data-driven models, including analog schemes, both in terms of forecasting and missing data interpolation.

Current Elastic SfT (Shape from Template) methods are based on ℓ2-norm minimization. None can accurately recover the spatial location of the acting forces since ℓ2-norm based minimization tends to find the best tradeoff among noisy data to fit an elastic model. In this work, we study shapes that are deformed with spatially sparse set of forces. We propose two formulations for a new class of SfT problems dubbed here SLE-SfT (Sparse Linear Elastic-SfT). The First ideal formulation uses an ℓ0-norm to minimize the cardinal of non-zero components of the deforming forces. The second relaxed formulation uses an ℓ1-norm to minimize the sum of absolute values of force components. These new formulations do not use Solid Boundary Constraints (SBC) which are usually needed to rigidly position the shape in the frame of the deformed image. We introduce the Projective Elastic Space Property (PESP) that jointly encodes the reprojection constraint and the elastic model. We prove that filling this property is necessary and sufficient for the relaxed formulation to: (i) retrieve the ground-truth 3D deformed shape, (ii) recover the right spatial domain of non-zero deforming forces. (iii) It also proves that we can rigidly place the deformed shape in the image frame without using SBC. Finally, we prove that when filling PESP, resolving the relaxed formulation provides the same ground-truth solution as the ideal formulation. Results with simulated and real data show substantial improvements in recovering the deformed shapes as well as the spatial location of the deforming forces.

In this paper we focus on the problem of estimating the directions of arrival (DOA) of a set of incident plane waves. Unlike many previous works, which assume that the received observations are only affected by additive noise, we consider the setup where some phase noise also corrupts the data (as for example observed in atmospheric sound propagation or underwater acoustics). We propose a new methodology to solve this problem in a Bayesian framework by resorting to a variational mean-field approximation. Our simulation results illustrate the benefits of carefully accounting for the phase noise in the DOA estimation process.

Dynamic Mode Decomposition (DMD) has emerged as a powerful tool for analyzing the dynamics of non-linear systems from experimental datasets. Recently, several attempts have extended DMD to the context of low-rank approximations. This extension is of particular interest for reduced-order modeling in various applicative domains, e.g., for climate prediction, to study molecular dynamics or microelectromechanical devices. This low-rank extension takes the form of a non-convex optimization problem. To the best of our knowledge, only sub-optimal algorithms have been proposed in the literature to compute the solution of this problem. In this paper, we prove that there exists a closed-form optimal solution to this problem and design an effective algorithm to compute it based on Singular Value Decomposition (SVD). A toy-example illustrates the gain in performance of the proposed algorithm compared to state-of-the-art techniques.

The objective of this paper is to investigate how noisy and incomplete observations can be integrated in the process of building a reduced-order model. This problematic arises in many scientific domains where there exists a need for accurate low-order descriptions of highly-complex phenomena, which can not be directly and/or deterministically observed. Within this context, the paper proposes a probabilistic framework for the construction of "POD-Galerkin" reduced-order models. Assuming a hidden Markov chain, the inference integrates the uncertainty of the hidden states relying on their posterior distribution. Simulations show the benefits obtained by exploiting the proposed framework.

This paper focusses on safe screening techniques for the LASSO problem. We derive a new sphere test, coined RFNE, exploiting the firmly non-expansiveness of projection operators. Our test generalizes some methods of the literature but, unlike the latter, exploits approximated primal-dual solutions of the LASSO problem while remaining safe and effective. Our simulation results show that the proposed RFNE test outperforms the best methodology of the state of the art, namely the GAP test derived by Fercoq et al.

In this work, we propose a novel procedure for video superresolution, that is, the recovery of a sequence of high-resolution images from its low-resolution counterpart. Our approach is based on a “sequential” model (i.e., each high-resolution frame is supposed to be a displaced version of the preceding one) and considers the use of sparsity-enforcing priors. Both the recovery of the high-resolution images and the motion fields relating them is tackled. This leads to a large-dimensional, nonconvex and nonsmooth problem. We propose an algorithmic framework to address the latter. Our approach relies on fast gradient evaluation methods and modern optimization techniques for nondifferentiable/nonconvex problems. Unlike some other previous works, we show that there exists a provably convergent method with a complexity linear in the problem dimensions. We assess the proposed optimization method on several video benchmarks and emphasize its good performance with respect to the state of the art.

We propose extended coherence-based conditions for exact sparse support recovery using orthogonal matching pursuit and orthogonal least squares. Unlike standard uniform guarantees, we embed some information about the decay of the sparse vector coefficients in our conditions. As a result, the standard condition μ <; 1/(2k - 1) (where μ denotes the mutual coherence and k the sparsity level) can be weakened as soon as the nonzero coefficients obey some decay, both in the noiseless and the bounded-noise scenarios. Furthermore, the resulting condition is approaching μ <; 1/k for strongly decaying sparse signals. Finally, in the noiseless setting, we prove that the proposed conditions, in particular the bound μ <; 1/k, are the tightest achievable guarantees based on mutual coherence.

Following recent contributions in non-linear sparse representations, this work focuses on a particular non-linear model, defined as the nested composition of functions. Recalling that most linear sparse representation algorithms can be straightforwardly extended to non-linear models, we emphasize that their performance highly relies on an efficient computation of the gradient of the objective function. In the particular case of interest, we propose to resort to a well-known technique from the theory of optimal control to evaluate the gradient. This computation is then implemented into the “ℓ1-reweighted” procedure proposed by Candès et al., leading to a non-linear extension of it.

This paper presents a new decoder for probabilistic binary traitor tracing codes under the marking assumption. It is based on a binary hypothesis testing rule which integrates a collusion channel relaxation so as to obtain numerical and simple accusation functions. This decoder is blind as no estimation of the collusion channel prior to the accusation is required. Experimentations show that using the proposed decoder gives better performance than the well-known symmetric version of the Tardos decoder for common attack channels.

Based on physical laws describing the multiscale structure of turbulent flows, this paper proposes a regularizer for fluid motion estimation from an image sequence. Regularization is achieved by imposing some scale invariance property between histograms of motion increments computed at different scales. By reformulating this problem from a Bayesian perspective, an algorithm is proposed to jointly estimate motion, regularization hyperparameters, and to select the most likely physical prior among a set of models. Hyperparameter and model inference are conducted by posterior maximization, obtained by marginalizing out non--Gaussian motion variables. The Bayesian estimator is assessed on several image sequences depicting synthetic and real turbulent fluid flows. Results obtained with the proposed approach exceed the state-of-the-art results in fluid flow estimation.

We address the exact recovery of a$k$-sparse vector in the noiseless setting when some partial information on the support is available. This partial information takes the form of either a subset of the true support or an approximate subset including wrong atoms as well. We derive a new sufficient and worst-case necessary (in some sense) condition for the success of some procedures based on$\ell _{p}$-relaxation, orthogonal matching pursuit (OMP), and orthogonal least squares (OLS). Our result is based on the coherence$\mu $of the dictionary and relaxes the well-known condition$\mu < 1/(2k-1)$ensuring the recovery of any$k$-sparse vector in the noninformed setup. It reads$\mu < 1/(2k-g+b-1)$when the informed support is composed of$g$good atoms and$b$wrong atoms. We emphasize that our condition is complementary to some restricted-isometry-based conditions by showing that none of them implies the other. Because this mutual coherence condition is common to all procedures, we carry out a finer analysis based on the null space property (NSP) and the exact recovery condition (ERC). Connections are established regarding the characterization of$\ell _{p}$-relaxation procedures and OMP in the informed setup. First, we emphasize that the truncated NSP enjoys an ordering property when$p$is decreased. Second, the partial ERC for OMP (ERC-OMP) implies in turn the truncated NSP for the informed$\ell _{1}$problem, and the truncated NSP for$p< 1$.

Tropp's analysis of orthogonal matching pursuit (OMP) using the exact recovery condition (ERC) is extended to a first exact recovery analysis of orthogonal least squares (OLS). We show that when the ERC is met, OLS is guaranteed to exactly recover the unknown support in at most$k$iterations where$k$denotes the support cardinality. Moreover, we provide a closer look at the analysis of both OMP and OLS when the ERC is not fulfilled. The existence of dictionaries for which some subsets are never recovered by OMP is proved. This phenomenon also appears with basis pursuit where support recovery depends on the sign patterns, but it does not occur for OLS. Finally, numerical experiments show that none of the considered algorithms is uniformly better than the other but for correlated dictionaries, guaranteed exact recovery may be obtained after fewer iterations for OLS than for OMP.

Taking advantage of the structures inherent in many sparse decompositions constitutes a promising research axis. In this paper, we address this problem from a Bayesian point of view. We exploit a Boltzmann machine, allowing to take a large variety of structures into account, and focus on the resolution of a joint maximum a posteriori problem. The proposed algorithm, called Structured Bayesian Orthogonal Matching Pursuit (SBOMP), is a structured extension of the Bayesian Orthogonal Matching Pursuit algorithm (BOMP) introduced in our previous work [1]. In numerical tests involving a recovery problem, SBOMP is shown to have good performance over a wide range of sparsity levels while keeping a reasonable computational complexity.

Selecting optimal models and hyperparameters is crucial for accurate optical-flow estimation. This paper provides a solution to the problem in a generic Bayesian framework. The method is based on a conditional model linking the image intensity function, the unknown velocity field, hyperparameters, and the prior and likelihood motion models. Inference is performed on each of the three levels of this so-defined hierarchical model by maximization of marginalized a posteriori probability distribution functions. In particular, the first level is used to achieve motion estimation in a classical a posteriori scheme. By marginalizing out the motion variable, the second level enables to infer regularization coefficients and hyperparameters of non-Gaussian M-estimators commonly used in robust statistics. The last level of the hierarchy is used for selection of the likelihood and prior motion models conditioned to the image data. The method is evaluated on image sequences of fluid flows and from the "Middlebury" database. Experiments prove that applying the proposed inference strategy yields better results than manually tuning smoothing parameters or discontinuity preserving cost functions of the state-of-the-art methods.

In this paper, we consider the problem of dictionary learning for sparse representations. Several algorithms dealing with this problem can be found in the literature. One of them, introduced by Sezer et al. in optimizes a dictionary made up of the union of orthonormal bases. In this paper, we propose a probabilistic interpretation of Sezer's algorithm and suggest a novel optimization procedure based on the EM algorithm. Comparisons of the performance in terms of missed detection rate show a clear superiority of the proposed approach.

This paper proposes a new compression algorithm based on the directional DCT (DDCT) bases introduced in [1]. We first explain how to extend the DDCT concept to rectangular bases and exploit them to build a set of bases using a bintree segmentation. We then use dynamic programming to select a basis from this set according to a rate-distortion criterion. Comparisons in terms of rate-distortion performance are finally made with the current compression standards JPEG and JPEG2000.

In this paper we address the problem of sparse representation (SR) within a Bayesian framework. We assume that the observations are generated from a Bernoulli-Gaussian process and consider the corresponding Bayesian inference problem. Tractable solutions are then proposed based on the “mean-field” approximation and the variational Bayes EM algorithm. The resulting SR algorithms are shown to have a tractable complexity and very good performance over a wide range of sparsity levels. In particular, they significantly improve the critical sparsity upon state-of-the-art SR algorithms.

This work addresses the bit-wise optimal data detection problem when unknown nuisance parameters influence the observation at the receiver. For an arbitrary communications system, the optimal maximum a-posteriori detection problem is first defined as a marginalization of a joint distribution which statistically models the interaction of available sets of variables/parameters. Then, using a factor graph representation with an accompanying sum-product message passing algorithm, it is shown that the marginalization can be performed iteratively. To alleviate complexity due to the marginalization over continuous natured nuisance parameters, variational Bayesian approximation is introduced and it is shown that, if the nuisance parameters are constant for a period of time, the receiver has linear complexity.

In this paper, we consider the problem of spatial prediction based on sparse representations. Several algorithms dealing with this problem can be found in the literature. We propose a novel method involving a mixture of sparse representations. We first place this approach into a probabilistic framework and then derive a practical procedure to solve it. Comparisons of the rate-distortion performance show the superiority of the proposed algorithm with regard to other state-of-the-art algorithms.

Reliability of the communication systems depends hugely on the receiver performance where the synchronization and detection tasks need to be performed. Classically these two tasks are attended separately resulting in simple yet non-optimal receivers. During the last decade, a family of iterative receivers has been introduced to approximate the optimal solution to joint estimation and detection problem by means of the turbo principle. With the help of graph theory and the belief propagation framework these receiver structures are unified and soft information driven schemes emerged, leading to more reliable detection. The essence of these schemes lays in factorization of a global function whose marginal corresponds to the objective function and obtained via simple message passing algorithms. On the other hand, as far as our knowledge, all of the proposed structures pursue a specific factorization while devising their respective schemes. In this work utilizing a different factorization, we introduce a novel iterative receiver for joint equalization/detection problem. With the aid of Variational Bayesian approximation we show that the complexity can be reduced without sacrificing the error performance drastically.

We consider the distributed compression of two (binary memoryless) correlated sources and propose a unique codec that can reach any point in the Slepian-Wolf region. In a previous method based on channel codes, the decoder multiply the compressed data by an inverse submatrix of the code. This multiplication presents two drawbacks. First, if turbo codes are used, the submatrix has no periodic structure s.t. the whole inverse has to be stored and no fast implementation exists for the multiplication. Second, this multiplication may lead to error propagation. In this paper, we propose a method that is both robust and fast.

We consider non-asymmetric distributed source coding (DSC) that achieves any point in the Slepian-Wolf (SW) region. We study the error propagation phenomena and propose a decoding algorithm which limits this phenomena. For the case of turbo-codes, design rules are derived in order for the decoder to recover the sources.

This paper presents a near-optimum, low-complexity, fixed-interval smoothing algorithm that approaches the performance of an optimal smoother for the price of two low-complexity sequential estimators (two PLLs). The proposed Smoothing PLL (S-PLL) algorithm is easy to implement and fits the Cramer-Rao bounds over a wide range of signal-to-noise ratios. Moreover we show that, compared to the conventional forward loop, the proposed scheme allows to have a large gain of several dBs and is able to track frequency offsets.

We consider a powerful iterative inference algorithm which has recently appeared in the literature. In this paper, we refer to this algorithm as iterative "pseudo likelihood" maximization (IPLFM) algorithm. We give a connection between this algorithm and the problem of Bethe free energy minimization and prove several important results concerning its fixed points and its convergence properties.

This contribution deals with code-aided hypothesis testing for wireless digital receivers. We provide a theoretical justification for a hypothesis testing algorithm that was previously introduced in (Wymeersch et al., 2006) based on ad-hoc arguments. Contrary to conventional hypothesis testing methods, the algorithm from Wymeersch et al. exploits the code structure within the received signal and does not require any pilot symbols. By doing so, it allows to improve the bandwidth-efficiency of the transmission. The present contribution shows that, under mild conditions, the performance of the algorithm from Wymeersch et al. coincides with the performance of the optimal Maximum A Posteriori (MAP) hypothesis test. Computer simulations support this result.

This paper aims at characterising the (mean) speed of convergence of the EM algorithm. We derive, under some simplifying assumptions, a relation between the EM algorithm mean convergence rate (MCR) and Cramer-Rao bounds (CRBs) associated to the so-called incomplete and complete data sets defined within the EM algorithm framework. We illustrate our derivations in the ease of carrier-phase estimation based on the EM algorithm, As far as our simulation setups are concerned, we show that the (mean) EM-algorithm behavior may be well predicted by means of the proposed CRB-based impression.

This paper deals with code-aided (CA) maximum-likelihood (ML) phase and timing ambiguity resolution. We propose a methodology based on the sum-product algorithm (SPA) to exactly solve this problem with a tractable complexity. In particular, we emphasize that the proposed ML ambiguity-resolution algorithm has a complexity which is at most equal to the complexity of recently-proposed powerful ML-like ambiguity-resolution methods. Finally, we compare through simulation results the ability of CA and conventional data-aided methods to resolve phase ambiguities.

This paper addresses soft estimation of time-varying frequency selective channels using Kalman smoothing. The proposed estimator uses soft extrinsic information provided by a channel decoder. It is intended to improve the performance of an already existing Kalman filtering-based estimator by exploiting all - rather than part of - the data at the receiver disposal. It is the linear estimator exhibiting for the case of interest the minimum mean-squared estimation error. Its complexity is shown to be quite low. An approximated analytical calculation of the mean- squared estimation error (MSEE), both for Kalman filtering and Kalman smoothing, is also proposed. Simulation results illustrate the performance gain of smoothing over filtering and validate our calculation of the MSEE.

The introduction of turbo and low-density parity-check (LDPC) codes with iterative decoding that almost attain Shannon capacity challenges the synchronization subsystems of a data modem. Fast and accurate signal synchronization has to be performed at a much lower value of signal-to-noise ratio (SNR) than in previous less efficiently coded systems. The solution to this issue is developing specific synchronization techniques that take advantage of the presence of the channel code and of the iterative nature of decoding: the so-calledturbo-synchronizationalgorithms. The aim of this paper within this special issue devoted to the turbo principle is twofold: on the one hand, it shows how the many turbo-synchronization algorithms that have already appeared in the literature can be cast into a simple and rigorous theoretical framework. On the other hand, it shows the application of such techniques in a few simple cases, and evaluates improvement that can be obtained from them, especially in the low-SNR regime.

In this paper, we address the issue of symbol timing recovery for a coded burst transmission system. As direct maximum-likelihood (ML) estimation is intractable, we resort to the expectation-maximization (EM) algorithm in order to derive a receiver that iterates between data detection and synchronization. Conventional data-aided (DA) and decision-directed (DD) synchronizers can be interpreted as special cases of the proposed algorithm. The EM-based technique takes into account code properties and is especially well suited to scenarios where conventional schemes fail to provide the detector with a reliable timing estimate. The performance of the proposed algorithm is compared with conventional techniques through computer simulations, both in terms of mean-square estimation error (MSEE) and bit error rate (BER).

Iterative channel estimation can improve the channel- state information (CSI) with respect to noniterative estimation. New iterative channel estimators based on the expectation-maximization (EM) algorithm are proposed in this paper. A first estimator, called the unbiased EM (UEM), is designed to unbias the EM estimates. A second estimator is then put forward, which is based on the expectation-conditional-maximization (ECM) algorithm, and its complexity is lower than that of the EM. An unbiased ECM (UECM) estimator is also proposed. Although the unbiasedness of the UEM and UECM estimators is not rigorously proved, the use of these names is explained in the paper. The new estimators are compared with well-known ones, such as the EM, the decision-directed (DD), and the data-aided (DA) estimators. Simulations are reported for a turbo receiver operating over frequency-selective multiple-input multiple-output channels. It is shown that the UEM channel estimator outperforms the EM, and that the ECM-based estimators are very close to the EM-based ones.

This paper deals with iterative maximum-likelihood synchronization of a scalar parameter. An efficient implementation of the Newton-Raphson (NR) maximum-search method is proposed. Considering the latter implementation, the NR approach is shown to be an attractive alternative to synchronization methods based on the expectation-maximization (EM) algorithm. Simulation results for the case of phase-offset synchronization show that NR method usually increases the speed of convergence of the synchronization algorithm

This paper analytically calculates the expectation and the variance of a soft-information-based best linear unbiased estimator of amplitude and carrier phase offset. Long data frames are considered. The calculation includes the impact on the performance of the presence of training symbols as well as non-Gaussianity of the log-likelihood ratios (LLRs) fed to the estimator input. It is also analyzed how the properties of the estimator are affected when the ratio between the mean and variance of the LLRs is not equal to 1/2

This paper addresses the issue of code-aided hypothesis testing in communication systems, i.e., the estimation of discrete-valued nuisance parameters. A hypothesis testing procedure optimal in the sense of the minimization of the frame-error rate (FER) is derived. Its complexity is shown to be comparable to other recently-proposed code-aided hypothesis procedures. Moreover, when a conditional maximum a posteriori decision rule is used to make the decisions about the transmitted sequence, it is shown that the proposed hypothesis testing procedure combined with sequence detection reduces, in a good approximation, to a joint maximum-likelihood problem. Finally, as an illustrative example, we show the case of phase ambiguity resolution for a convolutionally-coded transmission.

This paper proposes a semi-analytical method for predicting the performance degradation of a turbo-equalization scheme due to signal-to-noise ratio (SNR) estimation errors. In other words, sensitivity of turbo-equalization to an imperfect knowledge of the SNR (or, equivalently, channel noise variance) is analyzed. The considered turbo-equalizer uses the Wang and Poor's soft-in/soft-out (SISO) Minimum Mean Square Error (MMSE) / Interference Cancellation (IC) equalizer and a SISO convolutional decoder. The proposed method is applied to BPSK data modulation and single-user context but may be extended to the multi-user case. This paper shows that the equalizer behavior may be very reliably predicted totally by calculations (no simulations are needed) in the presence of imperfectly known SNR at the receiver. As far as the prediction of the decoder behavior is concerned, it requires simulations for only one independent input parameter. Long frames and perfect channel knowledge at the receiver are assumed in the paper.

The current paper addresses the issue of estimating the user propagation delays, received carrier phase offsets and received amplitudes in an asynchronous DS-CDMA environment with frequency non-selective propagation channels. The proposed synchronizer is based on the expectation-maximization (EM) algorithm and takes benefit from the soft information delivered by the receiver which is of the turbo type. The performance of the proposed synchronizer is illustrated by simulation results. In particular, the mean and the mean squared error of the estimator, as well as the bit error rate reached by the synchronized system, are reported.

The paper addresses the issue of estimating the sampling instant in turbo receivers. The proposed synchronizer is based on the expectation-maximization (EM) algorithm and takes benefit from the soft information delivered by the turbo system. Performance of the proposed synchronizer is illustrated by simulation results. In particular, the mean and the variance of the estimator as well as the bit error rate reached by the synchronized system are reported.

This paper is devoted to turbo synchronization, that is to say the use of soft information to estimate parameters like carrier phase, frequency offset or timing within a turbo receiver. It is shown how maximum-likelihood estimation of those synchronization parameters can be implemented by means of the iterative expectation-maximization (EM) algorithm [A.P. Dempster, et al., 1977]. Then we show that the EM algorithm iterations can be combined with those of a turbo receiver. This leads to a general theoretical framework for turbo synchronization. The soft decision-directed ad-hoc algorithm proposed in V. Lottici and M. Luise, [2002] for carrier phase recovery turns out to be a particular instance of this implementation. The proposed mathematical framework is illustrated by simulations reported for the particular case of carrier phase estimation combined with iterative demodulation and decoding [S. ten Brink, et al., 1998].