## 2014 |

Taborda, Camilo G; Perez-Cruz, Fernando; Guo, Dongning New Information-Estimation Results for Poisson, Binomial and Negative Binomial Models Inproceedings 2014 IEEE International Symposium on Information Theory, pp. 2207–2211, IEEE, Honolulu, 2014, ISBN: 978-1-4799-5186-4. Abstract | Links | BibTeX | Tags: Bregman divergence, Estimation, estimation measures, Gaussian models, Gaussian processes, information measures, information theory, information-estimation results, negative binomial models, Poisson models, Stochastic processes @inproceedings{Taborda2014, title = {New Information-Estimation Results for Poisson, Binomial and Negative Binomial Models}, author = {Camilo G Taborda and Fernando Perez-Cruz and Dongning Guo}, url = {http://ieeexplore.ieee.org/articleDetails.jsp?arnumber=6875225}, doi = {10.1109/ISIT.2014.6875225}, isbn = {978-1-4799-5186-4}, year = {2014}, date = {2014-06-01}, booktitle = {2014 IEEE International Symposium on Information Theory}, pages = {2207--2211}, publisher = {IEEE}, address = {Honolulu}, abstract = {In recent years, a number of mathematical relationships have been established between information measures and estimation measures for various models, including Gaussian, Poisson and binomial models. In this paper, it is shown that the second derivative of the input-output mutual information with respect to the input scaling can be expressed as the expectation of a certain Bregman divergence pertaining to the conditional expectations of the input and the input power. This result is similar to that found for the Gaussian model where the Bregman divergence therein is the square distance. In addition, the Poisson, binomial and negative binomial models are shown to be similar in the small scaling regime in the sense that the derivative of the mutual information and the derivative of the relative entropy converge to the same value.}, keywords = {Bregman divergence, Estimation, estimation measures, Gaussian models, Gaussian processes, information measures, information theory, information-estimation results, negative binomial models, Poisson models, Stochastic processes}, pubstate = {published}, tppubtype = {inproceedings} } In recent years, a number of mathematical relationships have been established between information measures and estimation measures for various models, including Gaussian, Poisson and binomial models. In this paper, it is shown that the second derivative of the input-output mutual information with respect to the input scaling can be expressed as the expectation of a certain Bregman divergence pertaining to the conditional expectations of the input and the input power. This result is similar to that found for the Gaussian model where the Bregman divergence therein is the square distance. In addition, the Poisson, binomial and negative binomial models are shown to be similar in the small scaling regime in the sense that the derivative of the mutual information and the derivative of the relative entropy converge to the same value. |

Djuric, Petar M; Bravo-Santos, Ángel M Cooperative Mesh Networks with EGC Detectors Inproceedings 2014 IEEE 8th Sensor Array and Multichannel Signal Processing Workshop (SAM), pp. 225–228, IEEE, A Coruña, 2014, ISBN: 978-1-4799-1481-4. Abstract | Links | BibTeX | Tags: binary modulations, cooperative communications, cooperative mesh networks, decode and forward communication, decode and forward relays, Detectors, EGC detectors, Gaussian processes, Joints, Manganese, Mesh networks, multihop multibranch networks, Nakagami channels, Nakagami distribution, Nakagami distributions, relay networks (telecommunication), Signal to noise ratio, zero mean Gaussian @inproceedings{Djuric2014, title = {Cooperative Mesh Networks with EGC Detectors}, author = {Petar M Djuric and Ángel M Bravo-Santos}, url = {http://ieeexplore.ieee.org/articleDetails.jsp?arnumber=6882381}, isbn = {978-1-4799-1481-4}, year = {2014}, date = {2014-01-01}, booktitle = {2014 IEEE 8th Sensor Array and Multichannel Signal Processing Workshop (SAM)}, pages = {225--228}, publisher = {IEEE}, address = {A Coruña}, abstract = {We address mesh networks with decode and forward relays that use binary modulations. For detection, the nodes employ equal gain combining, which is appealing because it is very easy to implement. We study the performance of these networks and compare it to that of multihop multi-branch networks. We also examine the performance of the networks when both the number of groups and total number of nodes are fixed but the topology of the network varies. We demonstrate the performance of these networks where the channels are modeled with Nakagami distributions and the noise is zero mean Gaussian}, keywords = {binary modulations, cooperative communications, cooperative mesh networks, decode and forward communication, decode and forward relays, Detectors, EGC detectors, Gaussian processes, Joints, Manganese, Mesh networks, multihop multibranch networks, Nakagami channels, Nakagami distribution, Nakagami distributions, relay networks (telecommunication), Signal to noise ratio, zero mean Gaussian}, pubstate = {published}, tppubtype = {inproceedings} } We address mesh networks with decode and forward relays that use binary modulations. For detection, the nodes employ equal gain combining, which is appealing because it is very easy to implement. We study the performance of these networks and compare it to that of multihop multi-branch networks. We also examine the performance of the networks when both the number of groups and total number of nodes are fixed but the topology of the network varies. We demonstrate the performance of these networks where the channels are modeled with Nakagami distributions and the noise is zero mean Gaussian |

## 2013 |

Perez-Cruz, Fernando; Vaerenbergh, Steven Van; Murillo-Fuentes, Juan Jose; Lazaro-Gredilla, Miguel; Santamaria, Ignacio Gaussian Processes for Nonlinear Signal Processing: An Overview of Recent Advances Journal Article IEEE Signal Processing Magazine, 30 (4), pp. 40–50, 2013, ISSN: 1053-5888. Abstract | Links | BibTeX | Tags: adaptive algorithm, Adaptive algorithms, classification scenario, Gaussian processes, Learning systems, Machine learning, Noise measurement, nonGaussian noise model, Nonlinear estimation, nonlinear estimation problem, nonlinear signal processing, optimal Wiener filtering, recursive algorithm, Signal processing, Wiener filters, wireless digital communication @article{Perez-Cruz2013, title = {Gaussian Processes for Nonlinear Signal Processing: An Overview of Recent Advances}, author = {Fernando Perez-Cruz and Steven Van Vaerenbergh and Juan Jose Murillo-Fuentes and Miguel Lazaro-Gredilla and Ignacio Santamaria}, url = {http://ieeexplore.ieee.org/lpdocs/epic03/wrapper.htm?arnumber=6530761}, issn = {1053-5888}, year = {2013}, date = {2013-01-01}, journal = {IEEE Signal Processing Magazine}, volume = {30}, number = {4}, pages = {40--50}, abstract = {Gaussian processes (GPs) are versatile tools that have been successfully employed to solve nonlinear estimation problems in machine learning but are rarely used in signal processing. In this tutorial, we present GPs for regression as a natural nonlinear extension to optimal Wiener filtering. After establishing their basic formulation, we discuss several important aspects and extensions, including recursive and adaptive algorithms for dealing with nonstationarity, low-complexity solutions, non-Gaussian noise models, and classification scenarios. Furthermore, we provide a selection of relevant applications to wireless digital communications.}, keywords = {adaptive algorithm, Adaptive algorithms, classification scenario, Gaussian processes, Learning systems, Machine learning, Noise measurement, nonGaussian noise model, Nonlinear estimation, nonlinear estimation problem, nonlinear signal processing, optimal Wiener filtering, recursive algorithm, Signal processing, Wiener filters, wireless digital communication}, pubstate = {published}, tppubtype = {article} } Gaussian processes (GPs) are versatile tools that have been successfully employed to solve nonlinear estimation problems in machine learning but are rarely used in signal processing. In this tutorial, we present GPs for regression as a natural nonlinear extension to optimal Wiener filtering. After establishing their basic formulation, we discuss several important aspects and extensions, including recursive and adaptive algorithms for dealing with nonstationarity, low-complexity solutions, non-Gaussian noise models, and classification scenarios. Furthermore, we provide a selection of relevant applications to wireless digital communications. |

Salamanca, Luis; Olmos, Pablo M; Murillo-Fuentes, Juan Jose; Perez-Cruz, Fernando Tree Expectation Propagation for ML Decoding of LDPC Codes over the BEC Journal Article IEEE Transactions on Communications, 61 (2), pp. 465–473, 2013, ISSN: 0090-6778. Abstract | Links | BibTeX | Tags: approximate inference, Approximation algorithms, Approximation methods, BEC, binary codes, binary erasure channel, code graph, Complexity theory, equivalent complexity, Gaussian elimination method, Gaussian processes, generalized tree-structured expectation propagatio, graphical message-passing procedure, graphical models, LDPC codes, Maximum likelihood decoding, maximum likelihood solution, ML decoding, parity check codes, peeling decoder, tree expectation propagation, tree graph, Tree graphs, tree-structured expectation propagation, tree-structured expectation propagation decoder, trees (mathematics) @article{Salamanca2013b, title = {Tree Expectation Propagation for ML Decoding of LDPC Codes over the BEC}, author = {Luis Salamanca and Pablo M Olmos and Juan Jose Murillo-Fuentes and Fernando Perez-Cruz}, url = {http://ieeexplore.ieee.org/lpdocs/epic03/wrapper.htm?arnumber=6384612}, issn = {0090-6778}, year = {2013}, date = {2013-01-01}, journal = {IEEE Transactions on Communications}, volume = {61}, number = {2}, pages = {465--473}, abstract = {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.}, keywords = {approximate inference, Approximation algorithms, Approximation methods, BEC, binary codes, binary erasure channel, code graph, Complexity theory, equivalent complexity, Gaussian elimination method, Gaussian processes, generalized tree-structured expectation propagatio, graphical message-passing procedure, graphical models, LDPC codes, Maximum likelihood decoding, maximum likelihood solution, ML decoding, parity check codes, peeling decoder, tree expectation propagation, tree graph, Tree graphs, tree-structured expectation propagation, tree-structured expectation propagation decoder, trees (mathematics)}, pubstate = {published}, tppubtype = {article} } 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. |

Alvarez, Mauricio; Luengo, David; Lawrence, Neil D Linear Latent Force Models Using Gaussian Processes Journal Article IEEE Trans. Pattern Anal. Mach. Intell., 35 (11), pp. 2693–2705, 2013. Abstract | Links | BibTeX | Tags: Analytical models, Computational modeling, Data models, Differential equations, Force, Gaussian processes, Mathematical mode @article{Alvarez2013, title = {Linear Latent Force Models Using Gaussian Processes}, author = {Mauricio Alvarez and David Luengo and Neil D Lawrence}, url = {http://dblp.uni-trier.de/db/journals/pami/pami35.html#AlvarezLL13 http://ieeexplore.ieee.org/xpl/articleDetails.jsp?arnumber=6514873}, year = {2013}, date = {2013-01-01}, journal = {IEEE Trans. Pattern Anal. Mach. Intell.}, volume = {35}, number = {11}, pages = {2693--2705}, abstract = {Purely data-driven approaches for machine learning present difficulties when data are scarce relative to the complexity of the model or when the model is forced to extrapolate. On the other hand, purely mechanistic approaches need to identify and specify all the interactions in the problem at hand (which may not be feasible) and still leave the issue of how to parameterize the system. In this paper, we present a hybrid approach using Gaussian processes and differential equations to combine data-driven modeling with a physical model of the system. We show how different, physically inspired, kernel functions can be developed through sensible, simple, mechanistic assumptions about the underlying system. The versatility of our approach is illustrated with three case studies from motion capture, computational biology, and geostatistics.}, keywords = {Analytical models, Computational modeling, Data models, Differential equations, Force, Gaussian processes, Mathematical mode}, pubstate = {published}, tppubtype = {article} } Purely data-driven approaches for machine learning present difficulties when data are scarce relative to the complexity of the model or when the model is forced to extrapolate. On the other hand, purely mechanistic approaches need to identify and specify all the interactions in the problem at hand (which may not be feasible) and still leave the issue of how to parameterize the system. In this paper, we present a hybrid approach using Gaussian processes and differential equations to combine data-driven modeling with a physical model of the system. We show how different, physically inspired, kernel functions can be developed through sensible, simple, mechanistic assumptions about the underlying system. The versatility of our approach is illustrated with three case studies from motion capture, computational biology, and geostatistics. |

## 2010 |

Djuric, Petar M; Closas, Pau; Bugallo, Monica F; Miguez, Joaquin Evaluation of a Method's Robustness Inproceedings 2010 IEEE International Conference on Acoustics, Speech and Signal Processing, pp. 3598–3601, IEEE, Dallas, 2010, ISSN: 1520-6149. Abstract | Links | BibTeX | Tags: Electronic mail, Extraterrestrial measurements, Filtering, Gaussian processes, method's robustness, Random variables, robustness, sequential methods, Signal processing, statistical distributions, Telecommunications, uniform distribution, Wireless communication @inproceedings{Djuric2010, title = {Evaluation of a Method's Robustness}, author = {Petar M Djuric and Pau Closas and Monica F Bugallo and Joaquin Miguez}, url = {http://ieeexplore.ieee.org/lpdocs/epic03/wrapper.htm?arnumber=5495921}, issn = {1520-6149}, year = {2010}, date = {2010-01-01}, booktitle = {2010 IEEE International Conference on Acoustics, Speech and Signal Processing}, pages = {3598--3601}, publisher = {IEEE}, address = {Dallas}, abstract = {In signal processing, it is typical to develop or use a method based on a given model. In practice, however, we almost never know the actual model and we hope that the assumed model is in the neighborhood of the true one. If deviations exist, the method may be more or less sensitive to them. Therefore, it is important to know more about this sensitivity, or in other words, how robust the method is to model deviations. To that end, it is useful to have a metric that can quantify the robustness of the method. In this paper we propose a procedure for developing a variety of metrics for measuring robustness. They are based on a discrete random variable that is generated from observed data and data generated according to past data and the adopted model. This random variable is uniform if the model is correct. When the model deviates from the true one, the distribution of the random variable deviates from the uniform distribution. One can then employ measures for differences between distributions in order to quantify robustness. In this paper we describe the proposed methodology and demonstrate it with simulated data.}, keywords = {Electronic mail, Extraterrestrial measurements, Filtering, Gaussian processes, method's robustness, Random variables, robustness, sequential methods, Signal processing, statistical distributions, Telecommunications, uniform distribution, Wireless communication}, pubstate = {published}, tppubtype = {inproceedings} } In signal processing, it is typical to develop or use a method based on a given model. In practice, however, we almost never know the actual model and we hope that the assumed model is in the neighborhood of the true one. If deviations exist, the method may be more or less sensitive to them. Therefore, it is important to know more about this sensitivity, or in other words, how robust the method is to model deviations. To that end, it is useful to have a metric that can quantify the robustness of the method. In this paper we propose a procedure for developing a variety of metrics for measuring robustness. They are based on a discrete random variable that is generated from observed data and data generated according to past data and the adopted model. This random variable is uniform if the model is correct. When the model deviates from the true one, the distribution of the random variable deviates from the uniform distribution. One can then employ measures for differences between distributions in order to quantify robustness. In this paper we describe the proposed methodology and demonstrate it with simulated data. |

Koch, Tobias; Lapidoth, Amos Gaussian Fading Is the Worst Fading Journal Article IEEE Transactions on Information Theory, 56 (3), pp. 1158–1165, 2010, ISSN: 0018-9448. Abstract | Links | BibTeX | Tags: Additive noise, channel capacity, channels with memory, Distribution functions, ergodic fading processes, Fading, fading channels, flat fading, flat-fading channel capacity, Gaussian channels, Gaussian fading, Gaussian processes, H infinity control, high signal-to-noise ratio (SNR), Information technology, information theory, multiple-input single-output fading channels, multiplexing gain, noncoherent, noncoherent channel capacity, peak-power limited channel capacity, Signal to noise ratio, signal-to-noise ratio, single-antenna channel capacity, spectral distribution function, time-selective, Transmitters @article{Koch2010a, title = {Gaussian Fading Is the Worst Fading}, author = {Tobias Koch and Amos Lapidoth}, url = {http://ieeexplore.ieee.org/lpdocs/epic03/wrapper.htm?arnumber=5429105}, issn = {0018-9448}, year = {2010}, date = {2010-01-01}, journal = {IEEE Transactions on Information Theory}, volume = {56}, number = {3}, pages = {1158--1165}, abstract = {The capacity of peak-power limited, single-antenna, noncoherent, flat-fading channels with memory is considered. The emphasis is on the capacity pre-log, i.e., on the limiting ratio of channel capacity to the logarithm of the signal-to-noise ratio (SNR), as the SNR tends to infinity. It is shown that, among all stationary and ergodic fading processes of a given spectral distribution function and whose law has no mass point at zero, the Gaussian process gives rise to the smallest pre-log. The assumption that the law of the fading process has no mass point at zero is essential in the sense that there exist stationary and ergodic fading processes whose law has a mass point at zero and that give rise to a smaller pre-log than the Gaussian process of equal spectral distribution function. An extension of these results to multiple-input single-output (MISO) fading channels with memory is also presented.}, keywords = {Additive noise, channel capacity, channels with memory, Distribution functions, ergodic fading processes, Fading, fading channels, flat fading, flat-fading channel capacity, Gaussian channels, Gaussian fading, Gaussian processes, H infinity control, high signal-to-noise ratio (SNR), Information technology, information theory, multiple-input single-output fading channels, multiplexing gain, noncoherent, noncoherent channel capacity, peak-power limited channel capacity, Signal to noise ratio, signal-to-noise ratio, single-antenna channel capacity, spectral distribution function, time-selective, Transmitters}, pubstate = {published}, tppubtype = {article} } The capacity of peak-power limited, single-antenna, noncoherent, flat-fading channels with memory is considered. The emphasis is on the capacity pre-log, i.e., on the limiting ratio of channel capacity to the logarithm of the signal-to-noise ratio (SNR), as the SNR tends to infinity. It is shown that, among all stationary and ergodic fading processes of a given spectral distribution function and whose law has no mass point at zero, the Gaussian process gives rise to the smallest pre-log. The assumption that the law of the fading process has no mass point at zero is essential in the sense that there exist stationary and ergodic fading processes whose law has a mass point at zero and that give rise to a smaller pre-log than the Gaussian process of equal spectral distribution function. An extension of these results to multiple-input single-output (MISO) fading channels with memory is also presented. |

Perez-Cruz, Fernando; Rodrigues, Miguel R D; Verdu, Sergio MIMO Gaussian Channels With Arbitrary Inputs: Optimal Precoding and Power Allocation Journal Article IEEE Transactions on Information Theory, 56 (3), pp. 1070–1084, 2010, ISSN: 0018-9448. Abstract | Links | BibTeX | Tags: Collaborative work, Equations, fixed-point equation, Gaussian channels, Gaussian noise channels, Gaussian processes, Government, Interference, linear precoding, matrix algebra, mean square error methods, mercury-waterfilling algorithm, MIMO, MIMO communication, MIMO Gaussian channel, minimum mean-square error, minimum mean-square error (MMSE), multiple-input-multiple-output channel, multiple-input–multiple-output (MIMO) systems, Mutual information, nondiagonal precoding matrix, optimal linear precoder, optimal power allocation policy, optimal precoding, optimum power allocation, Phase shift keying, precoding, Quadrature amplitude modulation, Telecommunications, waterfilling @article{Perez-Cruz2010a, title = {MIMO Gaussian Channels With Arbitrary Inputs: Optimal Precoding and Power Allocation}, author = {Fernando Perez-Cruz and Miguel R D Rodrigues and Sergio Verdu}, url = {http://ieeexplore.ieee.org/lpdocs/epic03/wrapper.htm?arnumber=5429131}, issn = {0018-9448}, year = {2010}, date = {2010-01-01}, journal = {IEEE Transactions on Information Theory}, volume = {56}, number = {3}, pages = {1070--1084}, abstract = {In this paper, we investigate the linear precoding and power allocation policies that maximize the mutual information for general multiple-input-multiple-output (MIMO) Gaussian channels with arbitrary input distributions, by capitalizing on the relationship between mutual information and minimum mean-square error (MMSE). The optimal linear precoder satisfies a fixed-point equation as a function of the channel and the input constellation. For non-Gaussian inputs, a nondiagonal precoding matrix in general increases the information transmission rate, even for parallel noninteracting channels. Whenever precoding is precluded, the optimal power allocation policy also satisfies a fixed-point equation; we put forth a generalization of the mercury/waterfilling algorithm, previously proposed for parallel noninterfering channels, in which the mercury level accounts not only for the non-Gaussian input distributions, but also for the interference among inputs.}, keywords = {Collaborative work, Equations, fixed-point equation, Gaussian channels, Gaussian noise channels, Gaussian processes, Government, Interference, linear precoding, matrix algebra, mean square error methods, mercury-waterfilling algorithm, MIMO, MIMO communication, MIMO Gaussian channel, minimum mean-square error, minimum mean-square error (MMSE), multiple-input-multiple-output channel, multiple-input–multiple-output (MIMO) systems, Mutual information, nondiagonal precoding matrix, optimal linear precoder, optimal power allocation policy, optimal precoding, optimum power allocation, Phase shift keying, precoding, Quadrature amplitude modulation, Telecommunications, waterfilling}, pubstate = {published}, tppubtype = {article} } In this paper, we investigate the linear precoding and power allocation policies that maximize the mutual information for general multiple-input-multiple-output (MIMO) Gaussian channels with arbitrary input distributions, by capitalizing on the relationship between mutual information and minimum mean-square error (MMSE). The optimal linear precoder satisfies a fixed-point equation as a function of the channel and the input constellation. For non-Gaussian inputs, a nondiagonal precoding matrix in general increases the information transmission rate, even for parallel noninteracting channels. Whenever precoding is precluded, the optimal power allocation policy also satisfies a fixed-point equation; we put forth a generalization of the mercury/waterfilling algorithm, previously proposed for parallel noninterfering channels, in which the mercury level accounts not only for the non-Gaussian input distributions, but also for the interference among inputs. |

Olmos, Pablo M; Murillo-Fuentes, Juan Jose; Perez-Cruz, Fernando Joint Nonlinear Channel Equalization and Soft LDPC Decoding with Gaussian Processes Journal Article IEEE Transactions on Signal Processing, 58 (3), pp. 1183–1192, 2010, ISSN: 1053-587X. Abstract | Links | BibTeX | Tags: Bayesian nonlinear classification tool, Bit error rate, Channel Coding, channel equalizers, Channel estimation, Coding, equalisers, equalization, error statistics, Gaussian processes, GPC, joint nonlinear channel equalization, low-density parity-check (LDPC), low-density parity-check channel decoder, Machine learning, nonlinear channel, nonlinear codes, parity check codes, posterior probability estimates, soft LDPC decoding, soft-decoding, support vector machine (SVM) @article{Olmos2010a, title = {Joint Nonlinear Channel Equalization and Soft LDPC Decoding with Gaussian Processes}, author = {Pablo M Olmos and Juan Jose Murillo-Fuentes and Fernando Perez-Cruz}, url = {http://ieeexplore.ieee.org/lpdocs/epic03/wrapper.htm?arnumber=5290078}, issn = {1053-587X}, year = {2010}, date = {2010-01-01}, journal = {IEEE Transactions on Signal Processing}, volume = {58}, number = {3}, pages = {1183--1192}, abstract = {In this paper, we introduce a new approach for nonlinear equalization based on Gaussian processes for classification (GPC). We propose to measure the performance of this equalizer after a low-density parity-check channel decoder has detected the received sequence. Typically, most channel equalizers concentrate on reducing the bit error rate, instead of providing accurate posterior probability estimates. We show that the accuracy of these estimates is essential for optimal performance of the channel decoder and that the error rate output by the equalizer might be irrelevant to understand the performance of the overall communication receiver. In this sense, GPC is a Bayesian nonlinear classification tool that provides accurate posterior probability estimates with short training sequences. In the experimental section, we compare the proposed GPC-based equalizer with state-of-the-art solutions to illustrate its improved performance.}, keywords = {Bayesian nonlinear classification tool, Bit error rate, Channel Coding, channel equalizers, Channel estimation, Coding, equalisers, equalization, error statistics, Gaussian processes, GPC, joint nonlinear channel equalization, low-density parity-check (LDPC), low-density parity-check channel decoder, Machine learning, nonlinear channel, nonlinear codes, parity check codes, posterior probability estimates, soft LDPC decoding, soft-decoding, support vector machine (SVM)}, pubstate = {published}, tppubtype = {article} } In this paper, we introduce a new approach for nonlinear equalization based on Gaussian processes for classification (GPC). We propose to measure the performance of this equalizer after a low-density parity-check channel decoder has detected the received sequence. Typically, most channel equalizers concentrate on reducing the bit error rate, instead of providing accurate posterior probability estimates. We show that the accuracy of these estimates is essential for optimal performance of the channel decoder and that the error rate output by the equalizer might be irrelevant to understand the performance of the overall communication receiver. In this sense, GPC is a Bayesian nonlinear classification tool that provides accurate posterior probability estimates with short training sequences. In the experimental section, we compare the proposed GPC-based equalizer with state-of-the-art solutions to illustrate its improved performance. |

## 2009 |

Murillo-Fuentes, Juan Jose; Perez-Cruz, Fernando Gaussian Process Regressors for Multiuser Detection in DS-CDMA Systems Journal Article IEEE Transactions on Communications, 57 (8), pp. 2339–2347, 2009, ISSN: 0090-6778. Abstract | Links | BibTeX | Tags: analytical nonlinear multiuser detectors, code division multiple access, communication systems, Detectors, digital communication, digital communications, DS-CDMA systems, Gaussian process for regressi, Gaussian process regressors, Gaussian processes, GPR, Ground penetrating radar, least mean squares methods, maximum likelihood, maximum likelihood detection, maximum likelihood estimation, mean square error methods, minimum mean square error, MMSE, Multiaccess communication, Multiuser detection, nonlinear estimator, nonlinear state-ofthe- art solutions, radio receivers, Receivers, regression analysis, Support vector machines @article{Murillo-Fuentes2009, title = {Gaussian Process Regressors for Multiuser Detection in DS-CDMA Systems}, author = {Juan Jose Murillo-Fuentes and Fernando Perez-Cruz}, url = {http://ieeexplore.ieee.org/lpdocs/epic03/wrapper.htm?arnumber=5201027}, issn = {0090-6778}, year = {2009}, date = {2009-01-01}, journal = {IEEE Transactions on Communications}, volume = {57}, number = {8}, pages = {2339--2347}, abstract = {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.}, keywords = {analytical nonlinear multiuser detectors, code division multiple access, communication systems, Detectors, digital communication, digital communications, DS-CDMA systems, Gaussian process for regressi, Gaussian process regressors, Gaussian processes, GPR, Ground penetrating radar, least mean squares methods, maximum likelihood, maximum likelihood detection, maximum likelihood estimation, mean square error methods, minimum mean square error, MMSE, Multiaccess communication, Multiuser detection, nonlinear estimator, nonlinear state-ofthe- art solutions, radio receivers, Receivers, regression analysis, Support vector machines}, pubstate = {published}, tppubtype = {article} } 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. |

## 2008 |

Perez-Cruz, Fernando; Murillo-Fuentes, Juan Jose; Caro, S Nonlinear Channel Equalization With Gaussian Processes for Regression Journal Article IEEE Transactions on Signal Processing, 56 (10), pp. 5283–5286, 2008, ISSN: 1053-587X. Abstract | Links | BibTeX | Tags: Channel estimation, digital communications receivers, equalisers, equalization, Gaussian processes, kernel adaline, least mean squares methods, maximum likelihood estimation, nonlinear channel equalization, nonlinear equalization, nonlinear minimum mean square error estimator, regression, regression analysis, short training sequences, Support vector machines @article{Perez-Cruz2008c, title = {Nonlinear Channel Equalization With Gaussian Processes for Regression}, author = {Fernando Perez-Cruz and Juan Jose Murillo-Fuentes and S Caro}, url = {http://ieeexplore.ieee.org/lpdocs/epic03/wrapper.htm?arnumber=4563433}, issn = {1053-587X}, year = {2008}, date = {2008-01-01}, journal = {IEEE Transactions on Signal Processing}, volume = {56}, number = {10}, pages = {5283--5286}, abstract = {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.}, keywords = {Channel estimation, digital communications receivers, equalisers, equalization, Gaussian processes, kernel adaline, least mean squares methods, maximum likelihood estimation, nonlinear channel equalization, nonlinear equalization, nonlinear minimum mean square error estimator, regression, regression analysis, short training sequences, Support vector machines}, pubstate = {published}, tppubtype = {article} } 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. |