Abstract In this paper, we introduce a novel algorithm designed to improve thread density estimation in canvas analysis. Our approach incorporates three major contributions. First, we eliminate the need for post-segmentation processing by integrating regression techniques, enabling the deep learning (DL) model to directly compute thread density. This does not only reduce computational time but also shifts the training focus from locating crossing points to minimizing thread counting errors, thereby enhancing accuracy. We develop and rigorously evaluate various models, selecting the one with optimal performance through a hyperparameter search. Second, we refine the data generation process by dynamically adjusting filter lengths based on initial thread density estimates and incorporating equalization. We also enhance data augmentation. Third, we implement semi-supervised training to expand the dataset and fine-tune model weights. This involves incorporating new inputs into the training set when both the DL model and Fourier transform yield similar density estimates for new paintings. Our proposed algorithm demonstrates superior performance in thread density error reduction and operational efficiency compared to previous DL segmentation solutions for masterpieces from Ribera, Velázquez, or Poussin. Additionally, it has been effectively applied to identify fabric matches between canvases attributed to different authors, showcasing its practical applicability in art analysis.

The Gaussian process (GP) is a well-established Bayesian nonparametric tool for inference in nonlinear estimation problems. When GPs are used for regression, the goal is to estimate a target signal${y}$from an input vector$\mathbf {x}$without assuming that they are linearly related, but with a probabilistic model$p({y}|\mathbf {x})$that is Gaussian distributed. Therefore, GPs can be understood as a natural nonlinear extension to MMSE estimation. For real-valued GPs, this has been analyzed in the existing literature, and it is concluded that they are the natural nonlinear Bayesian extension to the linear minimum mean-squared error (LMMSE) estimation. In this letter, we show that, consequently, complex-valued GP regression (GPR) models are the natural nonlinear Bayesian extension of the widely linear minimum mean squared-error (WLMMSE) estimation. As in the real-valued case, complex-valued GPs are able to better model many regression problems by making use of the information that the complementary kernel or pseudo-kernel provides.

In the forensic studies of painting masterpieces, the analysis of the support is of major importance. For plain weave fabrics, the densities of vertical and horizontal threads are used as main features, while angle deviations from the vertical and horizontal axis are also of help. These features can be studied locally through the canvas. In this work, deep learning is proposed as a tool to perform these local densities and angle studies. We trained the model with samples from 36 paintings by Velázquez, Rubens or Ribera, among others. The data preparation and augmentation are dealt with at a first stage of the pipeline. We then focus on the supervised segmentation of crossing points between threads. The U-Net with inception and Dice loss are presented as good choices for this task. Densities and angles are then estimated based on the segmented crossing points. We report test results of the analysis of a few canvases and a comparison with methods in the frequency domain, widely used in this problem. We concluded that this new approach successes in some cases where the frequency analysis tools fail, while improves the results in others. Besides, our proposal does not need the labeling of part of the to be processed image. As case studies, we apply this novel algorithm to the analysis of two pairs of canvases by Velázquez and Murillo, to conclude that the fabrics used came from the same roll.

We propose a new iterative detection and decoding (IDD) 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) based IDD, 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, 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.

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%.

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. This novel equalizer is presented 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 illustrate their improvements with respect to other EP-based proposals in the literature.

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.

In this paper we deal with the offline handwriting text recognition (HTR) problem with reduced training data sets. 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 CNN-LSTM-CTC (CRNN) 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 CRNN 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 CRNN of a reduced database, Washington. We focus on which layers of the network could not be re-trained. We conclude that the best solution is to re-train the whole CRNN parameters initialized to the values obtained after the training of the CRNN from the larger database. We also investigate results when the training size is further reduced. For the sake of comparison, we study the character error rate (CER) with no dictionary or any language modeling technique. 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.

Deep Gaussian Processes (DGPs) are hierarchical generalizations of Gaussian Processes that combine well calibrated uncertainty estimates with the high flexibility of multilayer models. One of the biggest challenges with these models is that exact inference is intractable. The current state-of-the-art inference method, Variational Inference (VI), employs a Gaussian approximation to the posterior distribution. This can be a potentially poor unimodal approximation of the generally multimodal posterior. In this work, we provide evidence for the non-Gaussian nature of the posterior and we apply the Stochastic Gradient Hamiltonian Monte Carlo method to generate samples. To efficiently optimize the hyperparameters, we introduce the Moving Window MCEM algorithm. This results in significantly better predictions at a lower computational cost than its VI counterpart. Thus our method establishes a new state-of-the-art for inference in DGPs.

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. In addition, we review the 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 the previous versions of the EP algorithm and also improves the LMMSE solution, with and without turbo equalization.

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.

In probabilistic equalization of channels with intersymbol interference, the BCJR algorithm and its approximations become intractable for high-order modulations, even for moderate channel dispersions. In this paper, we introduce a novel soft equalizer to approximate the symbol a posteriori probabilities (APP), where the expectation propagation (EP) algorithm is used to provide an accurate estimation. This new soft equalizer is presented as a block solution, denoted as block-EP (BEP), where the structure of the matrices involved is exploited to reduce the complexity order to O(LN2), i.e., linear in the length of the channel, L, and quadratic in the frame length, N. The solution is presented in complex-valued formulation within a turbo equalization scheme. This algorithm can be cast as a linear minimum-mean-squared-error (LMMSE) turbo equalization with double feedback architecture, where constellations being discrete is a restriction exploited by the EP that provides a first refinement of the APP. In the experiments included, the BEP exhibits a robust performance, regardless of the channel response, with gains in the range 1.5-5 dB compared with the LMMSE equalization.

In this paper, we face the soft equalization of channels with inter-symbol interference for large constellation sizes, 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 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 M, the SEP exhibits gains in the range of 3-5 dB compared to the linear minimum mean square error algorithm.

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 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.

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.

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 present the tree-structure expectation propagation (Tree-EP) algorithm to decode low-density parity-check (LDPC) codes over discrete memoryless channels (DMCs). Expectation propagation 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 pairwise 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 regimes 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 for finite-length LDPC codes, which accurately approximates the TEP improved performance and facilitates its optimization.

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.

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 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 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.

We show an application of a tree structure for approximate inference in graphical models using the expectation propagation algorithm. These approximations are typically used over graphs with short-range cycles. We demonstrate that these approximations also help in sparse graphs with long-range loops, as the ones used in coding theory to approach channel capacity. For asymptotically large sparse graph, the expectation propagation algorithm together with the tree structure yields a completely disconnected approximation to the graphical model but, for for finite-length practical sparse graphs, the tree structure approximation to the code graph provides accurate estimates for the marginal of each variable.

Expectation Propagation is a generalization to 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 distribution constraints in some check nodes of the LDPC Tanner graph. These additional constraints allow decoding the received codeword when the BP decoder gets stuck. In this paper, we first present the new decoding algorithm, whose complexity is identical to the BP decoder, and we then prove that it is able to decode codewords with a larger fraction of erasures, as the block size tends to infinity. The proposed algorithm can be also understood as a simplification of the Maxwell decoder, but without its computational complexity. We also illustrate that the new algorithm outperforms the BP decoder for finite block-size codes.

Low-density parity-check (LPDC) decoders assume the channel estate information (CSI) is known and they have the true a posteriori probability (APP) for each transmitted bit. But in most cases of interest, the CSI needs to be estimated with the help of a short training sequence and the LDPC decoder has to decode the received word using faulty APP estimates. In this paper, we study the uncertainty in the CSI estimate and how it affects the bit error rate (BER) output by the LDPC decoder. To improve these APP estimates, we propose a Bayesian equalizer that takes into consideration not only the uncertainty due to the noise in the channel, but also the uncertainty in the CSI estimate, reducing the BER after the LDPC decoder.

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 the above letter (ibid., vol. 17, no. 3, pp. 285-288, Mar. 10), equation (12) on. p. 287 was shown incorrectly. The correct version is presented here.

The authors propose a new tool to analyze the performance of a cellular base station. The analysis is based on the joint processing of the received power and quality measurements, both in the uplink (UL) and the downlink (DL). These measurements are originally designed for power control and handover purposes. The main objective of the paper is to fully describe and, therefore, to detect situations involving abnormal interference levels in UL and DL. These situations can be a consequence of a malfunctioning of the power control algorithm, a bad radio optimization and planning or the presence of an outer interference, among others. The novel tool proposed is valid for any cellular system, in this paper we focus on its application to GSM/GPRS system to illustrate its benefits. We include some experiments where real cell data recordings were analyzed.

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 present Gaussian processes (GPs) for digital communications. GPs can be used to construct analytical nonlinear regression functions, which can be suitable for digital communications in which linear solutions under perform. GPs can be cast as nonlinear MMSE and its hyperparameters can be easily learnt by maximum likelihood. We present some experimental results regarding multi-user detection in CDMA systems and show the GPs outperform linear and nonlinear state-of-the-art solutions

In this paper we propose a new receiver for digital communications. We focus on the application of Gaussian Processes (GPs) to the multiuser detection (MUD) in code division multiple access (CDMA) systems to solve the near-far problem. Hence, we aim to reduce the interference from other users sharing the same frequency band. While usual approaches minimize the mean square error (MMSE) to linearly retrieve the user of interest, we exploit the same criteria but in the design of a nonlinear MUD. Since the optimal solution is known to be nonlinear, the performance of this novel method clearly improves that of the MMSE detectors. Furthermore, the GP based MUD achieves excellent interference suppression even for short training sequences. We also include some experiments to illustrate that other nonlinear detectors such as those based on Support Vector Machines (SVMs) exhibit a worse performance.

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.

In this paper, novel structures for dynamic removal of multiuser interference are proposed. The natural gradient (NG) is used either to compute whitening matrices in linear blind minimum MSE or to develop new structures. As a result, we propose a family of centralized and non-centralized multiuser detectors (MUDs). The NG provides the MUDs with the equivariant and superfficiency properties, making them near-far resistant by construction and their convergence optimal. Moreover, the complexity of these structures is significantly reduced. These novel solutions are successfully applied to the multiuser synchronous CDMA channel.

The authors propose a new solution to the watermarking of digital images. This approach uses independent component analysis (ICA) to project the image into a basis with its components as statistically independent as possible. The watermark is then introduced in this representation of the space. Thus, the change of basis is the key of the steganography problem. The algorithm applied to the fragile watermarking problem locates any change in the image since it also applies to the watermark. The problem of robust watermarking is also addressed from this new point of view. Some results are included to illustrate the method.

The authors propose a new solution to the independent component analysis (ICA) problem. In the two-dimensional case, we prove that under the whiteness constraint some fourth-order contrasts may be approximated by a sinusoid. Thus, the minimization of the contrast reduces to computing its phase. The novel approach, called SICA (sinusoidal ICA), uses the 'Jacobi optimization' to cope with higher dimensions. The method presented has a good performance along with a low computational cost. Some experiments with blind separation of audio and synthetic sources are included to compare the algorithm to other well-known approaches.

We present an adaptive interference canceler in multiuser and multipath scenarios. The detector has two key elements: an adaptive algorithm for separating the signal subspace from the noise subspace and a decision feedback equalizer (DFE) based on the generalized cerebellar model articulation controller (GCMAC) neural network. The combination of the separator and the GCMAC-based DFE provides a close approximation to a Bayesian receiver. Simulations results show that the performance of the proposed receiver is comparable to that of the minimum mean-square error (MMSE) receiver, which is known to approach the single-user bound. An important advantage of the proposed receiver is the inherent capability to recompute its coefficients under decision-directed operation. In particular, the receiver does not require retraining when the adjustable weights deviate from their optimum setting.

The authors present a set of adaptive algorithms for the blind separation of independent sources (BSS). Source separation consists of recovering a set of independent signals from some linear instant mixtures of them, the coefficients of the mixing matrix being unknown. The relative (or natural) gradient has been widely used in these problems. We propose to replace it by the median gradient. We extend the concept to the complex case to cope with digitally modulated signals. It results in a new family of methods with better performance and phase recovering properties. Examples include separation of instant mixtures of different communication signals to illustrate the solutions proposed. As a new result we apply the proposed algorithms to asynchronous CDMA.

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.

Predistortion in GSM has been introduced to deal with saturation in amplifcation at base transceiver stations (BTS). This paper will focus on the elements and architectures in signal predistortion for one carrier and multicarrier modulations. The GCMAC neural network has been introduced as predistorter to provide the design with adaptive, digital and practical features. The results show how the predistortion architectures proposed allows working in saturation regimen. This point is important since it gives flexibility in reassignment of cells by increasing the coverage when necessary. It also improves amplification characteristics avoiding co-channel interference, aging, intermodulation distortion, etc.

Predistortion in personal mobile telephony systems has been proposed to deal with saturation in amplification at the transmission stage. This paper discusses the elements and architectures in signal and data predistortion for GSM and UMTS. The GCMAC neural network has been introduced as a predistorter to provide the design with adaptive, digital and practical features. Modulation aspects of the technologies involved define the models to substitute the amplifiers in the proposed schemes. The results included show how the predistortion architectures developed allow working linearly in saturation regimen. This point is important since it provides base transceiver stations (BTS), repeaters or even terminals with a higher gain. A performance evaluation including convergence and spectrum characteristics is carried out.