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In this paper we propose a novel turbo equalizer based on the expectation propagation (EP) algorithm. Optimal equalization is computationally unfeasible when high-order modulations and/or large memory channels are used. In these scenarios, low-cost and suboptimal equalizers, such as those based on the linear minimum mean square error (LMMSE), are commonly used. The LMMSE-based equalizer can be efficiently implemented with a Kalman smoother (KS), i.e., a forward and backward Kalman filtering whose predictions are merged in a posterior smoothing step. Recently, it was shown that applying EP at the forward and backward stages of a KS equalizer could significantly improve its performance. In this paper, we investigate applying EP at the smoothing level instead. Also, we propose some further modifications to better exploit the information coming from the channel decoder in turbo equalization schemes. Overall, we remarkably reduce the computational complexity while highly improving the performance in terms of bit error rate.

We propose a novel adaptive kernel based regression method for complex-valued signals: the generalized complex-valued kernel least-mean-square (gCKLMS). We borrow from the new results on widely linear reproducing kernel Hilbert space (WL-RKHS) for nonlinear regression and complex-valued signals, recently proposed by the authors. This paper shows that in the adaptive version of the kernel regression for complex-valued signals we need to include another kernel term, the so-called pseudo-kernel. This new solution is endowed with better representation capabilities in complex-valued fields, since it can efficiently decouple the learning of the real and the imaginary part. Also, we review previous realizations of the complex KLMS algorithm and its augmented version to prove that they can be rewritten as particular cases of the gCKLMS. Furthermore, important conclusions on the kernels design are drawn that help to greatly improve the convergence of the algorithms. In the experiments, we revisit the nonlinear channel equalization problem to highlight the better convergence of the gCKLMS compared to previous solutions. Also, the flexibility of the proposed generalized approach is tested in a second experiment with non-independent real and imaginary parts. The results illustrate the significant performance improvements of the gCKLMS approach when the complex-valued signals have different properties for the real and imaginary parts., Submitted to IEEE Transactions on Signal Processing

We investigate a turbo soft detector based on the expectation propagation (EP) algorithm for large-scale multiple-input multiple-output (MIMO) systems. Optimal detection in MIMO systems becomes computationally unfeasible for high-order modulations and/or large number of antennas. In this situation, the linear minimum mean square error (LMMSE) exhibits a low-complexity with a good performance, however far from optimal. To improve the performance, the EP algorithm can be used. In this paper, we review previous EP-based detectors and enhance their estimation in terms of complexity and performance. Specifically, we improve the convergence of the self-iterated EP stage by replacing the uniform prior by a non-uniform one, which better characterizes the information returned by the decoder once the turbo procedure starts. We also review the EP parameters to avoid instabilities when using high-order modulations and to reduce the computational complexity. Simulation results illustrate the robustness and enhanced performance of this novel detector in comparison with previous approaches found in the literature. Results also show that the proposed detector is robust in the presence of imperfect channel state information (CSI).

In this chapter, we introduce Gaussian processes for machine learning and their application to designing digital communication receivers. Gaussian processes for machine learning are Bayesian nonlinear tools for solving regression and classification problems. Gaussian processes for regression (GPR) were introduced in the mid-nineties to solve nonparametric estimation problems from a Bayesian perspective. They place a Gaussian process (GP) prior over the possible regressors and use the available data to obtain a posterior regressor, which it is able to explain the observations without overfitting. The covariance matrix of the GP prior describes the different solutions that can be achieved, e.g. linear, polynomial, or universal regressors. The solution of GPR is analytical given its covariance function and, besides providing point estimates, it also assigns confidence intervals for the predictions. Furthermore, the covariance function can be optimized by maximum likelihood to better represent the data, which adds additional flexibility to our regression approximation. GPR can be generalized to solve classification problems, namely Gaussian processes for classification (GPC). GPC extends the idea of GPR for a classification likelihood model. For this likelihood, the GPC posterior is no longer analytically tractable and we need to approximate it. Expectation Propagation (EP), which matches the mean and covariance of the GP posterior to a Gaussian distribution, is the most widely used approximation. Unlike most state-of-the-art classifiers, GPC does not return point-wise decisions, but it provides an accurate posterior probability for each classification decision. This is a major advantage to be exploited by subsequent applications for reducing the base error produced by our nonlinear classifiers. Nonlinear regression and classification techniques have been widely used for designing digital communication receivers for nonlinear channels or whenever there is little information about the channel model or for nonlinear model. These nonlinear tools must use short training sequences to learn the channel and to adapt to a wide range of scenarios, from linear minimum phase to nonlinear and non-minimum phase and from single to multi-user 11

Article number 9438636 In this paper we address the problem of offline handwritten text recognition (HTR) in historical documents when few labeled samples are available and some of them contain errors in the train set. Our three main contributions are: first, we analyze how to perform transfer learning (TL) from a massive database to a smaller historical database, analyzing which layers of the model need fine-tuning. Second, we analyze methods to efficiently combine TL and data augmentation (DA). Finally, we propose an algorithm to mitigate the effects of incorrect labeling in the training set. The methods are analyzed over the ICFHR 2018 competition database, Washington and Parzival. Combining all these techniques, we demonstrate a remarkable reduction of CER (up to 6 percentage points in some cases) in the test set with little complexity overhead.

This paper focuses on the offline handwriting text recognition problem (HTR) with small training data sets. Some techniques such as transfer learning or data augmentation have recently been applied to this problem, improving the performance of the recognition. In these scenarios, we found that errors in the labelling of the training samples, present in some databases, have a great impact in the character error rates (CER). Accordingly, we propose a novel cross validation technique to remove incorrect labelled lines. In this approach, after a first training stage, transcript lines with CER above a threshold are discarded, where the threshold is a function of the available data. Less available data favours larger CER, even for healthy lines, suggesting higher thresholds for fewer lines. This new technique and the validation of the threshold are analyzed over the ICFHR 2018 competition on automated HTR and other well known databases such as Washington and Parzival. For the Ricordi database in the ICFHR 2018, with transcription errors, we report a reduction of CER by 2%.

We propose a new iterative detection and decoding algorithm for multiple-input multiple-output (MIMO) based on expectation propagation (EP) with application to massive MIMO scenarios. Two main results are presented. We first introduce EP to iteratively improve the Gaussian approximations of both the estimation of the posterior by the MIMO detector and the soft output of the channel decoder. With this novel approach, denoted by double-EP (DEP), the convergence is very much improved with a computational complexity just two times the one of the linear minimum mean square error (LMMSE), as illustrated by the included experiments. Besides, as in the LMMSE MIMO detector, when the number of antennas increases, the computational cost of the matrix inversion operation required by the DEP becomes unaffordable. In this work we also develop approaches of DEP where the mean and the covariance matrix of the posterior are approximated by using the Gauss-Seidel and Neumann series methods, respectively. This low-complexity DEP detector has quadratic complexity in the number of antennas, i.e., the same as the low-complexity LMMSE techniques. Experimental results show that the new low-complexity DEP achieves the performance of the DEP as the ratio between the number of transmitting and receiving antennas decreases

In this paper, we propose a novel Bayesian solution for nonlinear regression in complex fields. Previous solutions for kernels methods usually assume a complexification approach, where the real-valued kernel is replaced by a complex-valued one. This approach is limited. Based on the results in complex-valued linear theory and Gaussian random processes, we show that a pseudo-kernel must be included. This is the starting point to develop the new complex-valued formulation for Gaussian process for regression (CGPR). We face the design of the covariance and pseudo-covariance based on a convolution approach and for several scenarios. Just in the particular case where the outputs are proper, the pseudo-kernel cancels. Also, the hyperparameters of the covariance can be learned maximizing the marginal likelihood using Wirtinger’s calculus and patterned complex-valued matrix derivatives. In the experiments included, we show how CGPR successfully solves systems where the real and imaginary parts are correlated. Besides, we successfully solve the nonlinear channel equalization problem by developing a recursive solution with basis removal. We report remarkable improvements compared to previous solutions: a 2–4-dB reduction of the mean squared error with just a quarter of the training samples used by previous approaches.

A routine task for art historians is painting diagnostics, such as dating or attribution. Signal processing of the X-ray image of a canvas painting provides useful information about its fabric. However, previous methods may fail when very old and deteriorated artworks or canvases of small size are studied. We present a new framework to analyze and further characterize the paintings from their radiographs. First, we start from a general analysis of lattices and provide new unifying results about the theoretical spectra of weaves. Then, we use these results to infer the main structure of the fabric, like the type of weave and the thread densities. We propose a practical estimation of these theoretical results from paintings with the averaged power spectral density (PSD), which provides a more robust tool. Furthermore, we found that the PSD provides a characterization of the whole cloth. We search and discuss some distinctive features we may find in this characterization. We apply these results to several masterpieces of the 17th and 18th centuries from the Museo Nacional del Prado to show that this approach yields accurate results in thread counting and is very useful for paintings comparison, even in situations where previous methods fail.

In this paper, we propose a widely linear reproducing kernel Hilbert space (WL-RKHS) for nonlinear regression with complex-valued signals. Our approach is a nonlinear extension of WL signal processing that has been proven to be more versatile than linear systems for dealing with complex-value signals. To be able to use the WL concept in kernel methods, we need to introduce a pseudo-kernel to complement the standard kernel in RKHS, which is not defined in previous RKHS approaches in the existing literature. In this paper, we present WL-RKHS, its properties, and the kernel and pseudo-kernel designs. We illustrate the need of the pseudo-kernel with simply verifiable examples that allow understanding the intuitions behind this kernel. We conclude this paper, showing that in the all-relevant nonlinear equalization problem the pseudo-kernel plays a significant role and previous approaches that do not rely on this kernel clearly underperform.

In this paper, we face the soft equalization of channels with inter-symbol interference for large constellation sizes, $ \mathtt {M}$ . In this scenario, the optimal BCJR solution and most of their approximations are intractable, as the number of states they track grows fast with $ \mathtt {M}$ . We present a probabilistic equalizer to approximate the posterior distributions of the transmitted symbols using the expectation propagation (EP) algorithm. The solution is presented as a recursive sliding window approach to ensure that the computational complexity is linear with the length of the frame. The estimations can be further improved with a forward–backward approach. This novel soft equalizer, denoted as smoothing EP (SEP), is also tested as a turbo equalizer, with a low-density parity-check (LDPC) channel decoder. The extensive results reported reveal remarkably good behavior of the SEP. In low dimensional cases, the bit error rate (BER) curves after decoding are closer than 1 dB from those of the BJCR, robust to the channel response. For large $ \mathtt {M}$ , the SEP exhibits gains in the range of 3–5 dB compared to the linear minimum mean square error algorithm.

This letter deals with the application of the expectation propagation (EP) algorithm to turbo equalization. The EP has been successfully applied to obtain either a better approximation at the output of the equalizer or at the output of the channel decoder to better initialize the Gaussian prior used by the equalizer. In this letter we combine both trends to propose a novel double EP-based equalizer that is able to decrease the number of iterations needed, reducing the computational complexity to twice that of the linear MMSE. This novel equalizer is developed in three different implementations: a block design that exploits the whole vector of observations, a Wiener filter-type approach that just uses the observations within a predefined window and a Kalman smoothing filter-type approach that emulates the BCJR behavior. Finally, we include some experimental results to compare the three different implementations and to detail their improvements with respect to other EP-based proposals in the literature.

This letter presents a novel time-of-arrival (TOA) blind estimation technique for ultra wideband energy detection receivers with reduced complexity. The proposed method is blind in the sense that it does not exploit any information about channel or noise power. This new approach is based on a set of approximations of the exact likelihood function (ELF) of the observed energy. Even though these approximations achieve an important reduction of complexity, the shape of the new approximated function is accurate enough compared to the ELF. Application of a threshold to the differential of the approximated log-likelihood function completes the procedure. Simulations show that the performance of the proposed method in terms of the cumulative distribution function of the estimation error approaches that of a method based on the ELF and a genie-aided algorithm with perfect knowledge of the optimal threshold.

In this paper we deal with the offline handwriting text recognition (HTR) problem with reduced training datasets. Recent HTR solutions based on artificial neural networks exhibit remarkable solutions in referenced databases. These deep learning neural networks are composed of both convolutional (CNN) and long short-term memory recurrent units (LSTM). In addition, connectionist temporal classification (CTC) is the key to avoid segmentation at character level, greatly facilitating the labeling task. One of the main drawbacks of the CNNLSTM-CTC (CLC) solutions is that they need a considerable part of the text to be transcribed for every type of calligraphy, typically in the order of a few thousands of lines. Furthermore, in some scenarios the text to transcribe is not that long, e.g. in the Washington database. The CLC typically overfits for this reduced number of training samples. Our proposal is based on the transfer learning (TL) from the parameters learned with a bigger database. We first investigate, for a reduced and fixed number of training samples, 350 lines, how the learning from a large database, the IAM, can be transferred to the learning of the CLC of a reduced database, Washington. We focus on which layers of the network could be not re-trained. We conclude that the best solution is to re-train the whole CLC parameters initialized to the values obtained after the training of the CLC from the larger database. We also investigate results when the training size is further reduced. The differences in the CER are more remarkable when training with just 350 lines, a CER of 3.3% is achieved with TL while we have a CER of 18.2% when training from scratch. As a byproduct, the learning times are quite reduced. Similar good results are obtained from the Parzival database when trained with this reduced number of lines and this new approach., Comment: ICFHR 2018 Conference

In this paper, we address the estimation of a time-varying spatial field of received signal strength (RSS) by relying on measurements from randomly placed and not very accurate sensors. We employ a radio propagation model where the path loss exponent and the transmitted power are unknown with Gaussian priors whose hyper-parameters are estimated by applying the empirical Bayes method. We consider the locations of the sensors to be imperfectly known, which entails that they represent another source of error in the model. The propagation model includes shadowing which is considered to be a zero-mean Gaussian process where the correlation of attenuation between two spatial points is quantified by an exponential function of the distance between the points. The location of the transmitter is also unknown and estimated from the data with a weighted centroid approach. We propose to estimate time-varying RSS fields by a recursive Bayesian method and crowdsourcing. The method is based on Gaussian processes (GP), and it produces the joint distribution of the spatial field. Further, it summarizes all the acquired information by keeping the size of the needed memory bounded. We also present the Bayesian Cram\'er-Rao bound (BCRB) of the estimated parameters. Finally, we illustrate the performance of our method with experimental results on synthetic data sets., Comment: This manuscript has been submitted to IEEE Transactions on Signal Processing on May 11, 2018; revised on August 9, 2018 and November 15, 2018; accepted on December 10, 2018

In this work we present some results on the development and test of software for thread counting in X-rays images of plain-weave canvas. We have reviewed the state of the art in this area to select good and simple approaches to be implemented. Hence, we propose the fast Fourier transform (FFT) as the core of our software. We show how with little modifications of the software the frequency of line patterns in simple twills and zig-zag twills can be also analyzed. The algorithm looks for most probable and mean values within a predefined range of frequency values. The method provides as output a couple of images with the local frequency in every point of the selected area. It also includes the estimated degree deviation from the vertical and horizontal for vertical and horizontal lines (threads in simple-weave) for every point, as images. The histograms of the frequencies found in the X-ray are also displayed. The software was designed following the requirements of the Museo Nacional del Prado Conservation and Research department. It was tested with X-rays authored by 17th century painters Miguel de Pret, Claudio de Lorena, Van Dyck and Rubens. In the analysis of a single image, the results of the software have proved useful in the automatic frequency estimation, detection of cusping and analysis of cut edges or areas. In the two images comparison, the method has been already used to draw conclusions on the canvas coming from the same roll, based on the thread counting. Furthermore, we propose the analysis of the histogram as a useful feature to help in the comparison.

The dependence-testing (DT) bound is one of the strongest achievability bounds for the binary erasure channel (BEC) in the finite block length regime. In this paper, we show that maximum likelihood decoded regular low-density parity-check (LDPC) codes with at least 5 ones per column almost achieve the DT bound. Specifically, using quasi-regular LDPC codes with block length of 256 bits, we achieve a rate that is less than 1% away from the rate predicted by the DT bound for a word error rate below10 −3 . The results also indicate that the maximum-likelihood solution is computationally feasible for decoding block codes over the BEC with several hundred bits. Index Terms—LDPC codes, finite blocklength regime, ML de- coding, binary erasure channel, random coding.

This manuscript has been submitted to Transactions on Communications on September 7, 2017; revised on January 10, 2018 and March 27, 2018; and accepted on April 25, 2018 We propose a novel filter-type equalizer to improve the solution of the linear minimum-mean squared-error (LMMSE) turbo equalizer, with computational complexity constrained to be quadratic in the filter length. When high-order modulations and/or large memory channels are used the optimal BCJR equalizer is unavailable, due to its computational complexity. In this scenario, the filter-type LMMSE turbo equalization exhibits a good performance compared to other approximations. In this paper, we show that this solution can be significantly improved by using expectation propagation (EP) in the estimation of the a posteriori probabilities. First, it yields a more accurate estimation of the extrinsic distribution to be sent to the channel decoder. Second, compared to other solutions based on EP the computational complexity of the proposed solution is constrained to be quadratic in the length of the finite impulse response (FIR). In addition, we review previous EP-based turbo equalization implementations. Instead of considering default uniform priors we exploit the outputs of the decoder. Some simulation results are included to show that this new EP-based filter remarkably outperforms the turbo approach of previous versions of the EP algorithm and also improves the LMMSE solution, with and without turbo equalization.

In this paper, we put forward the tree-structured expectation propagation (TEP) algorithm for decoding block and convolutional low-density parity-check codes over any binary channel. We have already shown that TEP improves belief propagation (BP) over the binary erasure channel (BEC) by imposing marginal constraints over a set of pairs of variables that form a tree or a forest. The TEP decoder is a message-passing algorithm that sequentially builds a tree/forest of erased variables to capture additional information disregarded by the standard BP decoder, which leads to a noticeable reduction of the error rate for finite-length codes. In this paper, we show how the TEP can be extended to any channel, specifically to binary memoryless symmetric (BMS) channels. We particularly focus on how the TEP algorithm can be adapted for any channel model and, more importantly, how to choose the tree/forest to keep the gains observed for block and convolutional LDPC codes over the BEC.

We propose a decoding algorithm for LDPC codes that achieves the maximum likelihood (ML) solution over the binary erasure channel (BEC). In this channel, the tree-structured expectation propagation (TEP) decoder improves the peeling decoder (PD) by processing check nodes of degree one and two. However, it does not achieve the ML solution, as the tree structure of the TEP allows only for approximate inference. In this paper, we provide the procedure to construct the structure needed for exact inference. This algorithm, denoted as generalized tree-structured expectation propagation (GTEP), modifies the code graph by recursively eliminating any check node and merging this information in the remaining graph. The GTEP decoder upon completion either provides the unique ML solution or a tree graph in which the number of parent nodes indicates the multiplicity of the ML solution. We also explain the algorithm as a Gaussian elimination method, relating the GTEP to other ML solutions. Compared to previous approaches, it presents an equivalent complexity, it exhibits a simpler graphical message-passing procedure and, most interesting, the algorithm can be generalized to other channels.

Low-density parity-check convolutional (LDPCC) codes asymptotically achieve channel capacity under belief propagation (BP) decoding. In this paper, we decode LDPCC codes using the Tree-Expectation Propagation (TEP) decoder, recently proposed as an alternative decoding method to the BP algorithm for the binary erasure channel (BEC). We show that, for LDPCC codes, the TEP decoder improves the BP solution with a comparable complexity or, alternatively, it allows using shorter codes to achieve similar error rates. We also propose a window-sliding scheme for the TEP decoder to reduce the decoding latency.

This work provides a novel technological solution to jamming in wireless systems, particularly to remotely detect interfered communications in a cellular network. The new system is focused on the detection of a failure in a link between a base station and a fixed wireless terminal located in a residential or business area. It has an important impact in security systems based on wireless terminals to transmit an alarm to a central station. In these systems, non-authorised people can prevent the transmission of the alarm by using a short-range jammer. The main advantage of this proposal is that it is non-intrusive; that is, no modification is needed in the base station, and no protocol modification is performed in the terminal. The detection is implemented in an external unit developed on a software-defined radio platform. The novel system proposed is valid for any cellular system and operator. In this work, we focus on its implementation in the GSM/GPRS system to illustrate its benefits and outline the method for Universal Mobile Telecommunications System. We describe the results of some experiments where the system successfully detects the presence of a short-range jammer in a real scenario. Copyright © 2012 John Wiley & Sons, Ltd.

The authors present a blind channel estimation of cyclic prefix (CP) orthogonal frequency-division multiplexing (OFDM) systems with nonredundant precoding based on second-order statistics. The study analyzes first the mean square error for the estimation of the covariance matrix of the received symbols. We prove that, for high and medium signal-to-noise ratios (SNRs), the estimation error in the diagonal entries of the covariance matrix exhibits a lower error than that in the off-diagonal elements. This behavior holds for SNR values in digital communication. Contrary to general belief, we prove that the diagonal of this matrix can be used for channel estimation. Hence, we develop a novel algorithm that utilizes this result. We also develop a low-complexity version that provides acceptable results with reduced computational requirements. Finally, we analyze the covariance matrix and propose another new algorithm with noise suppression capabilities. Some experimental results for Rayleigh channels are included to support these conclusions. In addition, they illustrate better performance of the new methods, compared with previous proposals and with the Cramer-Rao bound (CRB).

The authors propose a novel method to evaluate the interference conditions in a cellular network. The method takes advantage of the signal strength and quality measurements available at a Base Station. Measurements from both up-link and down-link are jointly processed to remotely detect the presence of a medium-range frequency jammer and other situations involving abnormal interference levels, as a malfunctioning of the power control algorithm, a bad radio optimization and planning or an outer interference, among others. The proposed method can be adapted to any cellular system. In this paper we focus on its application to GSM/GPRS system. We include some experiments where real cell data recordings were analyzed.

In this letter we focus on the application of independent component analysis (ICA) to a class of overdetermined blind source separation (BSS) problems. The mixing matrix in the BSS model is the product of an unknown square diagonal matrix and a projection matrix. The last matrix performs a known projection to the same or larger dimensional space. We demonstrate the conditions for the model to be strictly separable and identifiable under the statistical independence condition, paying attention to permutations and relative scalings. These results find application, e.g., in the channel estimation of ZP-OFDM and precoded-OFDM systems.

In this paper we present Gaussian processes for Regression (GPR) as a novel detector for CDMA digital communications. Particularly, we propose GPR for constructing analytical nonlinear multiuser detectors in CDMA communication systems. GPR can easily compute the parameters that describe its nonlinearities by maximum likelihood. Thereby, no cross-validation is needed, as it is typically used in nonlinear estimation procedures. The GPR solution is analytical, given its parameters, and it does not need to solve an optimization problem for building the nonlinear estimator. These properties provide fast and accurate learning, two major issues in digital communications. The GPR with a linear decision function can be understood as a regularized MMSE detector, in which the regularization parameter is optimally set. We also show the GPR receiver to be a straightforward nonlinear extension of the linear minimum mean square error (MMSE) criterion, widely used in the design of these receivers. We argue the benefits of this new approach in short codes CDMA systems where little information on the users' codes, users' amplitudes or the channel is available. The paper includes some experiments to show that GPR outperforms linear (MMSE) and nonlinear (SVM) state-ofthe- art solutions.

We propose Gaussian processes for regression (GPR) as a novel nonlinear equalizer for digital communications receivers. GPR's main advantage, compared to previous nonlinear estimation approaches, lies on their capability to optimize the kernel hyperparameters by maximum likelihood, which improves its performance significantly for short training sequences. Besides, GPR can be understood as a nonlinear minimum mean square error estimator, a standard criterion for training equalizers that trades off the inversion of the channel and the amplification of the noise. In the experiment section, we show that the GPR-based equalizer clearly outperforms support vector machine and kernel adaline approaches, exhibiting outstanding results for short training sequences.

A Business Intelligence (BI) system employs tools from several areas of knowledge to deliver information that supports the decision making process. Throughout the present work, we aim to enhance the predictive stage of the BI system maintained by the Brazilian Federal Patrimony Department. The proposal is to use Gaussian Process for Regression (GPR) to model the intrinsic characteristics of the tax collection financial time series that is kept by this BI system, improving its error metrics. GPR natively returns a full statistical description of the estimated variable, which can be treated as a measure of confidence and also be used as a trigger to classify trusted and untrusted data. In our approach, a bidimensional dataset reshape model is used in order to take into account the multidimensional structure of the input data. The resulting algorithm, with GPR at its core, outperforms classical predictive schemes in this scenario such as financial indicators and artificial neural networks.

We propose a new method for the blind robust watermarking of digital images based on independent component analysis (ICA). We apply ICA to compute some statistically independent transform coefficients where we embed the watermark. The main advantages of this approach are twofold. On the one hand, each user can define its own ICA-based transformation. These transformations behave as ''private-keys'' of the method. On the other hand, we will show that some of these transform coefficients have white noise-like spectral properties. We develop an orthogonal watermark to blindly detect it with a simple matched filter. We also address some relevant issues as the perceptual masking of the watermark and the estimation of the detection probability. Finally, some experiments have been included to illustrate the robustness of the method to common attacks and to compare its performance to other transform domain watermarking algorithms.

In this paper we investigate the conditions that complex kernels must satisfy for proper complex-valued signals. We study the structure that complex kernels for proper complex-valued signals must have. Also, we demonstrate that complex kernels that have been previously proposed and used in adaptive filtering of complex-valued signals assume that those signals are proper, i.e, they are not correlated with their complex conjugate. We provide an example of how a complex-valued kernel suitable for a particular model is designed, with a procedure that could help in other designs. The experiments included show the good behavior of the proposed kernel in the task of nonlinear channel equalization.

Actual communications systems use high-order modulations and channels with memory. However, as the memory of the channels and the order of the constellations grow, optimal equalization such as BCJR algorithm is computationally intractable, as their complexity increases exponentially with the number of taps and size of modulation. In this paper, we propose a novel low-complexity hard and soft output equalizer based on the Expectation Propagation (EP) algorithm that provides high-accuracy posterior probability estimations at the input of the channel decoder with similar computational complexity than the linear MMSE. We experimentally show that this quasi-optimal solution outperforms classical solutions reducing the bit error probability with low complexity when LDPC channel decoding is used, avoiding the curse of dimensionality with channel memory and constellation size.

Blind source separation (BSS) aims at the reconstruction of unknown mutually independent signals, so-called sources, from their mixtures observed at the output of a sensor array. The BSS of instantaneous linear mixtures, which finds application in numerous fields, can be solved through the statistical tool of independent component analysis (ICA). This paper concentrates on the analytic solutions for the fundamental two-signal ICA scenario. A novel estimation class, so-called general weighted fourth-order estimator (GWFOE), is put forward, which is based on the fourth- order statistics of the whitened sensor output. By means of a weight parameter, the GWFOE is able to unify a variety of apparently disparate estimation expressions previously scattered throughout the literature, including the well-known JADE method in the two- signal case. A theoretical asymptotic performance analysis is carried out, resulting in the GWFOE large-sample mean square error and the source-dependent weight value of the most efficient estimator in the class. To extend the pairwise estimators to the general scenario of more than two sources, an improved Jacobi-like optimization technique is proposed. The approach consists of calculating the necessary sensor-output fourth-order statistics at the initialization stage of the algorithm, which can lead to significant computational savings when large sample blocks are processed. Based on this idea, adaptive algorithms are also devised, showing very satisfactory convergence characteristics. Experiments illustrate the good performance of these optimal pairwise ICA strategies, in both off- and on-line processing modes.

The authors propose a new solution to the blind separation of sources (BSS) based on statistical independence. In the two-dimensional (2-D) case, we prove that, under the whiteness constraint, the fourth-order moment-based approximation of the marginal entropy (ME) cost function yields a sinusoidal objective function. Therefore, we can minimize it by simply estimating its phase. We prove that this estimator is consistent for any source distribution. In addition, such results are useful for interpreting other algorithms such as the cumulant-based independent component analysis (CuBICA) and the weighted approximate maximum likelihood (WAML) [or weighted estimator (WE)]. Based on the WAML, we provide a general unifying form for several previous approximations to the ME contrast. The bias and the variance of this estimator have been included. Finally, simulations illustrate the good consistency, convergence, and accuracy of the proposed method.

In this paper, we explore the significance of second- and higher-order statistics learning in communication systems. The final goal in spread-spectrum communication systems is to receive a signal of interest completely free from interference caused by other concurrent signals. To achieve this end, we exploit the structure of the interference by designing second-order statistics detectors, such as the minimum square error, in conjunction with higher-order statistics (HOS) techniques, such as the blind source separation (BSS). This hybrid higher-order statistics (HyHOS) approach enables us to alleviate BSS algorithms of one of their main problems, that is, their sensitiveness to high levels of noise. In addition, we benefit from remarkable properties of BSS in learning such as fast learning (superefficiency) and independence of the initial settings of the problem (equivariance). We successfully applied the results of this approach to the design of multiuser detectors in code-division multiple access channels. Teoría de la Señal y Comunicaciones

Business Intelligence (BI) systems are designed to provide information to support the decision making process in companies and governmental institutions. In this scenario, future events depend on the decisions and on the previous events. Therefore, the mathematical analysis of past data can be an important tool for the decision making process and to detect anomalies. Depending on the amount and the type of data to be analyzed, techniques from statistics, Machine Learning (ML), data mining and signal processing can be used to automate all or part of the system. In this paper, we propose to incorporate Gaussian Process for Regression (GPR) in BI systems in order to predict the data. As presented in this work, fraud detection is one important application of BI systems. We show that such application is possible with the use of GPR in the predictive stage, considering that GPR natively returns a full statistical description of the estimated variable, which can be used as a trigger measure to classify trusted and untrusted data. We validate our proposal with real world BI data provided by the Brazilian Federal Patrimony Department (SPU), regarding the monthly collection of federal taxes. In order to take into account the multidimensional structure of this specific data, we propose a pre-processing stage for reshaping the original time series into a bidimensional structure. The resulting algorithm, with GPR at its core, outperforms classical predictive schemes such as Artificial Neural Network (ANN).

The authors propose a family of algorithms to solve the blind source separation (BSS) problem, focusing on digital communications. We first include a revision of the equivariant adaptive separation via independence (EASI). These results provide a better characterization of the stability condition. Starting from this analysis we propose a new method, the Median EASI, whose stability condition presents useful properties. Next, we prove this method to be more noise-robust for some sources such as digitally modulated signals. Some experiments are included to show how the Median EASI allows phase recovering, an important issue in communications. Finally, we propose the median EASI as a blind asynchronous CDMA multiuser detector.

In this paper, we propose Tree-structured Expectation Propagation (TEP) algorithm to decode finite-length Low-Density Parity-Check (LDPC) codes. The TEP decoder is able to continue decoding once the standard Belief Propagation (BP) decoder fails, presenting the same computational complexity as the BP decoder. The BP algorithm is dominated by the presence of stopping sets (SSs) in the code graph. We show that the TEP decoder, without previous knowledge of the graph, naturally avoids some fairly common SSs. This results in a significant improvement in the system performance.

In this paper we develop the complex-valued version of the Gaussian processes for regression (GPR) for proper complex signals. This tool has proved to be useful in the nonlinear detection in digital communications in real valued models. GPRs can be cast as nonlinear MMSE where hyperparameters can be tuned optimizing a marginal likelihood (ML). This feature allows for a flexible kernel that can easily adapt either to a linear or nonlinear solution. We introduce the complex-valued form of the GPR, and develop it for the proper complex case. We also deal with the optimization of the ML. Some experiments included illustrate the good performance of the proposal.

The subject of this paper is the compensation for nonlinearities in digital communication systems by means of predistortion. In this work, we apply the generalized cerebellar model articulation controller (GCMAC) to simplify and accelerate the predistorter convergence. The range of analyzed predistorters includes: 1) a symbol-rate data predistorter that, for a given time span, achieves a similar level of compensation provided by present techniques, but with faster convergence; 2) a fractionally spaced data predistorter that controls, at the same time, the signal constellation and the transmitted spectrum; 3) a decision-feedback scheme that compensates for remote nonlinearities; and 4) a digital signal data predistorter. The performance of the proposed data and signal predistorters is evaluated using typical linear and nonlinear modulated transmitted signals such as QAM and GMSK.

This paper deals with nonlinear compensation in code-division multiple-access communications systems. We analyze the performance of the generalized cerebellar model articulation controller neural network in two problems: predistortion in nonlinear transmitters and adaptive interference cancellation in multiuser and multipath scenarios. Our examples demonstrate the performance of the compensators in typical mobile channels.

In this paper, we propose the tree-structured expectation propagation (TEP) algorithm for low-density parity-check (LDPC) decoding over the binary additive white Gaussian noise (BI-AWGN) channel. By approximating the posterior distribution by a tree-structure factorization, the TEP has been proven to improve belief propagation (BP) decoding over the binary erasure channel (BEC). We show for the AWGN channel how the TEP decoder is also able to capture additional information disregarded by the BP solution, which leads to a noticeable reduction of the error rate for finite-length codes. We show that for the range of codes of interest, the TEP gain is obtained with a slight increase in complexity over that of the BP algorithm. An efficient way of constructing the tree-like structure is also described.

Spatially-coupled (SC) LDPC codes are constructed from a set of L regular sparse codes of length M. In the asymptotic limit of these parameters, SC codes present an excellent decoding threshold under belief propagation (BP) decoding, close to the maximum a posteriori (MAP) threshold of the underlying regular code. In the finite-length regime, we need both dimensions, L and M, to be sufficiently large, yielding a very large code length and decoding latency. In this paper, and for the erasure channel, we show that the finite-length performance of SC codes is improved if we consider the tree-structured expectation propagation (TEP) algorithm in the decoding stage. When applied to the decoding of SC LDPC codes, it allows using shorter codes to achieve similar error rates. We also propose a window-sliding scheme for the TEP decoder to reduce the decoding latency.

In this paper, we propose the tree-structured expectation propagation (TEP) algorithm for low-density parity-check (LDPC) decoding over the additive white Gaussian noise (AWGN) channel. By imposing a tree-like approximation over the graphical model of the code, this algorithm introduces pairwise marginal constraints over pairs of variables, which provide joint information of the variables related. Thanks to this, the proposed TEP decoder improves the performance of the standard belief propagation (BP) solution. An efficient way of constructing the tree-like structure is also described. The simulation results illustrate the TEP decoder gain in the finite-length regime, compared to the standard BP solution. For code lengths shorter than n = 512, the gain in the waterfall region achieves up to 0.25 dB. We also notice a remarkable reduction of the error floor.

In this work, we analyze the finite-length performance of low-density parity check (LDPC) ensembles decoded over the binary erasure channel (BEC) using the tree-expectation propagation (TEP) algorithm. In a previous paper, we showed that the TEP improves the BP performance for decoding regular and irregular short LDPC codes, but the perspective was mainly empirical. In this work, given the degree-distribution of an LDPC ensemble, we explain and predict the range of code lengths for which the TEP improves the BP solution. In addition, for LDPC ensembles that present a single critical point, we propose a scaling law to accurately predict the performance in the waterfall region. These results are of critical importance to design practical LDPC codes for the TEP decoder.

We describe the channel equalization problem, and its prior estimate of the channel state information (CSI), as a joint Bayesian estimation problem to improve each symbol posterior estimates at the input of the channel decoder. Our approach takes into consideration not only the uncertainty due to the noise in the channel, but also the uncertainty in the CSI estimate. However, this solution cannot be computed in linear time, because it depends on all the transmitted symbols. Hence, we also put forward an approximation for each symbol's posterior, using the expectation propagation algorithm, which is optimal from the Kullback-Leibler divergence viewpoint and yields an equalization with a complexity identical to the BCJR algorithm. We also use a graphical model representation of the full posterior, in which the proposed approximation can be readily understood. The proposed posterior estimates are more accurate than those computed using the ML estimate for the CSI. In order to illustrate this point, we measure the error rate at the output of a low-density parity-check decoder, which needs the exact posterior for each symbol to detect the incoming word and it is sensitive to a mismatch in those posterior estimates. For example, for QPSK modulation and a channel with three taps, we can expect gains over 0.5 dB with same computational complexity as the ML receiver.

We present the tree-structure expectation propagation (Tree-EP) algorithm to decode low-density parity-check (LDPC) codes over discrete memoryless channels (DMCs). EP generalizes belief propagation (BP) in two ways. First, it can be used with any exponential family distribution over the cliques in the graph. Second, it can impose additional constraints on the marginal distributions. We use this second property to impose pair-wise marginal constraints over pairs of variables connected to a check node of the LDPC code's Tanner graph. Thanks to these additional constraints, the Tree-EP marginal estimates for each variable in the graph are more accurate than those provided by BP. We also reformulate the Tree-EP algorithm for the binary erasure channel (BEC) as a peeling-type algorithm (TEP) and we show that the algorithm has the same computational complexity as BP and it decodes a higher fraction of errors. We describe the TEP decoding process by a set of differential equations that represents the expected residual graph evolution as a function of the code parameters. The solution of these equations is used to predict the TEP decoder performance in both the asymptotic regime and the finite-length regime over the BEC. While the asymptotic threshold of the TEP decoder is the same as the BP decoder for regular and optimized codes, we propose a scaling law (SL) for finite-length LDPC codes, which accurately approximates the TEP improved performance and facilitates its optimization.

In this paper, we propose a decoding algorithm for LDPC codes that achieves the MAP solution over the BEC. This algorithm, denoted as generalized tree-structured expectation propagation (GTEP), extends the idea of our previous work, the TEP decoder. The GTEP modifies the graph by eliminating a check node of any degree and merging this information with the remaining graph. The GTEP decoder upon completion either provides the unique MAP solution or a tree graph in which the number of parent nodes indicates the multiplicity of the MAP solution. This algorithm can be easily described for the BEC, and it can be cast as a generalized peeling decoder. The GTEP naturally optimizes the complexity of the decoder, by looking for checks nodes of minimum degree to be eliminated first.

In this work we address the design of degree distributions (DD) of low-density parity-check (LDPC) codes for the tree-expectation propagation (TEP) decoder. The optimization problem to find distributions to maximize the TEP decoding threshold for a fixed-rate code can not be analytically solved. We derive a simplified optimization problem that can be easily solved since it is based in the analytic expressions of the peeling decoder. Two kinds of solutions are obtained from this problem: we either design LDPC ensembles for which the BP threshold equals the MAP threshold or we get LDPC ensembles for which the TEP threshold outperforms the BP threshold, even achieving the MAP capacity in some cases. Hence, we proved that there exist ensembles for which the MAP solution can be obtained with linear complexity even though the BP threshold does not achieve the MAP threshold.

In this paper we focus on the probabilistic channel equalization in digital communications. We face the single input single output (SISO) model to show how the statistical information about the multipath channel can be exploited to further improve our estimation of the a posteriori probabilities (APP) during the equalization process. We consider not only the uncertainty due to the noise in the channel, but also in the estimate of the channel estate information (CSI). Thus, we resort to a Bayesian approach for the computation of the APP. This novel algorithm has the same complexity as the BCJR, exhibiting lower bit error rate at the output of the channel decoder than the standard BCJR that considers maximum likelihood (ML) to estimate the CSI