## 2015 |

## Journal Articles |

Ramírez, David; Schreier, Peter; Via, Javier; Santamaria, Ignacio; Scharf, Louis Detection of Multivariate Cyclostationarity (Journal Article) IEEE Transactions on Signal Processing, 63 (20), pp. 5395–5408, 2015, ISSN: 1053-587X. (Abstract | Links | BibTeX | Tags: ad hoc function, asymptotic GLRT, asymptotic LMPIT, block circulant, block-Toeplitz structure, Correlation, covariance matrices, Covariance matrix, covariance structure, cycle period, cyclic spectrum, Cyclostationarity, Detectors, Frequency-domain analysis, generalized likelihood ratio test, generalized likelihood ratio test (GLRT), hypothesis testing problem, locally most powerful invariant test, locally most powerful invariant test (LMPIT), Loe{&}{#}x0300, maximum likelihood estimation, multivariate cyclostationarity detection, power spectral density, random processes, s theorem, scalar valued CS time series, signal detection, spectral analysis, statistical testing, Testing, Time series, Time series analysis, Toeplitz matrices, Toeplitz matrix, ve spectrum, vector valued random process cyclostationary, vector valued WSS time series, wide sense stationary, Wijsman theorem, Wijsman{&}{#}x2019) @article{Ramirez2015, title = {Detection of Multivariate Cyclostationarity}, author = {Ramírez, David and Schreier, Peter J. and Via, Javier and Santamaria, Ignacio and Scharf, Louis L.}, url = {http://ieeexplore.ieee.org/articleDetails.jsp?arnumber=7134806}, doi = {10.1109/TSP.2015.2450201}, issn = {1053-587X}, year = {2015}, date = {2015-10-01}, journal = {IEEE Transactions on Signal Processing}, volume = {63}, number = {20}, pages = {5395--5408}, publisher = {IEEE}, abstract = {This paper derives an asymptotic generalized likelihood ratio test (GLRT) and an asymptotic locally most powerful invariant test (LMPIT) for two hypothesis testing problems: 1) Is a vector-valued random process cyclostationary (CS) or is it wide-sense stationary (WSS)? 2) Is a vector-valued random process CS or is it nonstationary? Our approach uses the relationship between a scalar-valued CS time series and a vector-valued WSS time series for which the knowledge of the cycle period is required. This relationship allows us to formulate the problem as a test for the covariance structure of the observations. The covariance matrix of the observations has a block-Toeplitz structure for CS and WSS processes. By considering the asymptotic case where the covariance matrix becomes block-circulant we are able to derive its maximum likelihood (ML) estimate and thus an asymptotic GLRT. Moreover, using Wijsman's theorem, we also obtain an asymptotic LMPIT. These detectors may be expressed in terms of the Loève spectrum, the cyclic spectrum, and the power spectral density, establishing how to fuse the information in these spectra for an asymptotic GLRT and LMPIT. This goes beyond the state-of-the-art, where it is common practice to build detectors of cyclostationarity from ad-hoc functions of these spectra.}, keywords = {ad hoc function, asymptotic GLRT, asymptotic LMPIT, block circulant, block-Toeplitz structure, Correlation, covariance matrices, Covariance matrix, covariance structure, cycle period, cyclic spectrum, Cyclostationarity, Detectors, Frequency-domain analysis, generalized likelihood ratio test, generalized likelihood ratio test (GLRT), hypothesis testing problem, locally most powerful invariant test, locally most powerful invariant test (LMPIT), Loe{&}{#}x0300, maximum likelihood estimation, multivariate cyclostationarity detection, power spectral density, random processes, s theorem, scalar valued CS time series, signal detection, spectral analysis, statistical testing, Testing, Time series, Time series analysis, Toeplitz matrices, Toeplitz matrix, ve spectrum, vector valued random process cyclostationary, vector valued WSS time series, wide sense stationary, Wijsman theorem, Wijsman{&}{#}x2019}, pubstate = {published}, tppubtype = {article} } This paper derives an asymptotic generalized likelihood ratio test (GLRT) and an asymptotic locally most powerful invariant test (LMPIT) for two hypothesis testing problems: 1) Is a vector-valued random process cyclostationary (CS) or is it wide-sense stationary (WSS)? 2) Is a vector-valued random process CS or is it nonstationary? Our approach uses the relationship between a scalar-valued CS time series and a vector-valued WSS time series for which the knowledge of the cycle period is required. This relationship allows us to formulate the problem as a test for the covariance structure of the observations. The covariance matrix of the observations has a block-Toeplitz structure for CS and WSS processes. By considering the asymptotic case where the covariance matrix becomes block-circulant we are able to derive its maximum likelihood (ML) estimate and thus an asymptotic GLRT. Moreover, using Wijsman's theorem, we also obtain an asymptotic LMPIT. These detectors may be expressed in terms of the Loève spectrum, the cyclic spectrum, and the power spectral density, establishing how to fuse the information in these spectra for an asymptotic GLRT and LMPIT. This goes beyond the state-of-the-art, where it is common practice to build detectors of cyclostationarity from ad-hoc functions of these spectra. |

## Inproceedings |

Nazabal, Alfredo; Artés-Rodríguez, Antonio Discriminative spectral learning of hidden markov models for human activity recognition (Inproceeding) 2015 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), pp. 1966–1970, IEEE, Brisbane, 2015, ISBN: 978-1-4673-6997-8. (Abstract | Links | BibTeX | Tags: Accuracy, Bayesian estimation, classify sequential data, Data models, Databases, Discriminative learning, discriminative spectral learning, Hidden Markov models, HMM parameters, Human activity recognition, learning (artificial intelligence), maximum likelihood, maximum likelihood estimation, ML, moment matching learning technique, Observable operator models, sensors, Spectral algorithm, spectral learning, Speech recognition, Training) @inproceedings{Nazabal2015, title = {Discriminative spectral learning of hidden markov models for human activity recognition}, author = {Nazabal, Alfredo and Artés-Rodríguez, Antonio}, url = {http://ieeexplore.ieee.org/lpdocs/epic03/wrapper.htm?arnumber=7178314}, doi = {10.1109/ICASSP.2015.7178314}, isbn = {978-1-4673-6997-8}, year = {2015}, date = {2015-04-01}, booktitle = {2015 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)}, pages = {1966--1970}, publisher = {IEEE}, address = {Brisbane}, abstract = {Hidden Markov Models (HMMs) are one of the most important techniques to model and classify sequential data. Maximum Likelihood (ML) and (parametric and non-parametric) Bayesian estimation of the HMM parameters suffers from local maxima and in massive datasets they can be specially time consuming. In this paper, we extend the spectral learning of HMMs, a moment matching learning technique free from local maxima, to discriminative HMMs. The resulting method provides the posterior probabilities of the classes without explicitly determining the HMM parameters, and is able to deal with missing labels. We apply the method to Human Activity Recognition (HAR) using two different types of sensors: portable inertial sensors, and fixed, wireless binary sensor networks. Our algorithm outperforms the standard discriminative HMM learning in both complexity and accuracy.}, keywords = {Accuracy, Bayesian estimation, classify sequential data, Data models, Databases, Discriminative learning, discriminative spectral learning, Hidden Markov models, HMM parameters, Human activity recognition, learning (artificial intelligence), maximum likelihood, maximum likelihood estimation, ML, moment matching learning technique, Observable operator models, sensors, Spectral algorithm, spectral learning, Speech recognition, Training}, pubstate = {published}, tppubtype = {inproceedings} } Hidden Markov Models (HMMs) are one of the most important techniques to model and classify sequential data. Maximum Likelihood (ML) and (parametric and non-parametric) Bayesian estimation of the HMM parameters suffers from local maxima and in massive datasets they can be specially time consuming. In this paper, we extend the spectral learning of HMMs, a moment matching learning technique free from local maxima, to discriminative HMMs. The resulting method provides the posterior probabilities of the classes without explicitly determining the HMM parameters, and is able to deal with missing labels. We apply the method to Human Activity Recognition (HAR) using two different types of sensors: portable inertial sensors, and fixed, wireless binary sensor networks. Our algorithm outperforms the standard discriminative HMM learning in both complexity and accuracy. |

## 2012 |

## Inproceedings |

Olmos, Pablo; Perez-Cruz, Fernando; Salamanca, Luis; Murillo-Fuentes, Juan Jose Finite-Length Performance of Spatially-Coupled LDPC Codes under TEP Decoding (Inproceeding) 2012 IEEE Information Theory Workshop, pp. 1–6, IEEE, Lausanne, 2012, ISBN: 978-1-4673-0223-4. (Links | BibTeX | Tags: asymptotic limit, belief propagation decoding, Complexity theory, convolutional codes, convolutional LDPC codes, Decoding, decoding latency, decoding threshold, erasure channel, Error analysis, error rates, finite-length analysis, finite-length performance, maximum a posteriori threshold, maximum likelihood estimation, parity check codes, regular sparse codes, spatially-coupled LDPC codes, TEP decoding, tree-structured expectation propagation, underlying regular code, very large code length, window-sliding scheme) @inproceedings{Olmos2012, title = {Finite-Length Performance of Spatially-Coupled LDPC Codes under TEP Decoding}, author = {Olmos, Pablo M. and Perez-Cruz, Fernando and Salamanca, Luis and Murillo-Fuentes, Juan Jose}, url = {http://ieeexplore.ieee.org/articleDetails.jsp?arnumber=6404722}, isbn = {978-1-4673-0223-4}, year = {2012}, date = {2012-01-01}, booktitle = {2012 IEEE Information Theory Workshop}, pages = {1--6}, publisher = {IEEE}, address = {Lausanne}, keywords = {asymptotic limit, belief propagation decoding, Complexity theory, convolutional codes, convolutional LDPC codes, Decoding, decoding latency, decoding threshold, erasure channel, Error analysis, error rates, finite-length analysis, finite-length performance, maximum a posteriori threshold, maximum likelihood estimation, parity check codes, regular sparse codes, spatially-coupled LDPC codes, TEP decoding, tree-structured expectation propagation, underlying regular code, very large code length, window-sliding scheme}, pubstate = {published}, tppubtype = {inproceedings} } |

## 2010 |

## Inproceedings |

Salamanca, Luis; Jose Murillo-Fuentes, Juan; Perez-Cruz, Fernando Bayesian BCJR for Channel Equalization and Decoding (Inproceeding) 2010 IEEE International Workshop on Machine Learning for Signal Processing, pp. 53–58, IEEE, Kittila, 2010, ISSN: 1551-2541. (Abstract | Links | BibTeX | Tags: a posteriori probability, Bayes methods, Bayesian BCJR, Bayesian methods, Bit error rate, channel decoding, channel estate information, Channel estimation, Decoding, digital communication, digital communications, equalisers, Equalizers, error statistics, Markov processes, Maximum likelihood decoding, maximum likelihood estimation, multipath channel, probabilistic channel equalization, Probability, single input single output model, SISO model, statistical information, Training) @inproceedings{Salamanca2010, title = {Bayesian BCJR for Channel Equalization and Decoding}, author = {Salamanca, Luis and Jose Murillo-Fuentes, Juan and Perez-Cruz, Fernando}, url = {http://ieeexplore.ieee.org/lpdocs/epic03/wrapper.htm?arnumber=5589201}, issn = {1551-2541}, year = {2010}, date = {2010-01-01}, booktitle = {2010 IEEE International Workshop on Machine Learning for Signal Processing}, pages = {53--58}, publisher = {IEEE}, address = {Kittila}, abstract = {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.}, keywords = {a posteriori probability, Bayes methods, Bayesian BCJR, Bayesian methods, Bit error rate, channel decoding, channel estate information, Channel estimation, Decoding, digital communication, digital communications, equalisers, Equalizers, error statistics, Markov processes, Maximum likelihood decoding, maximum likelihood estimation, multipath channel, probabilistic channel equalization, Probability, single input single output model, SISO model, statistical information, Training}, pubstate = {published}, tppubtype = {inproceedings} } 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. |

Salamanca, Luis; Murillo-Fuentes, Juan Jose; Perez-Cruz, Fernando Channel Decoding with a Bayesian Equalizer (Inproceeding) 2010 IEEE International Symposium on Information Theory, pp. 1998–2002, IEEE, Austin, TX, 2010, ISBN: 978-1-4244-7892-7. (Abstract | Links | BibTeX | Tags: a posteriori probability, Bayesian equalizer, Bayesian methods, BER, Bit error rate, Channel Coding, channel decoding, channel estate information, Communication channels, Decoding, equalisers, Equalizers, error statistics, low-density parity-check decoders, LPDC decoders, Maximum likelihood decoding, maximum likelihood detection, maximum likelihood estimation, Noise reduction, parity check codes, Probability, Uncertainty) @inproceedings{Salamanca2010a, title = {Channel Decoding with a Bayesian Equalizer}, author = {Salamanca, Luis and Murillo-Fuentes, Juan Jose and Perez-Cruz, Fernando}, url = {http://ieeexplore.ieee.org/lpdocs/epic03/wrapper.htm?arnumber=5513348}, isbn = {978-1-4244-7892-7}, year = {2010}, date = {2010-01-01}, booktitle = {2010 IEEE International Symposium on Information Theory}, pages = {1998--2002}, publisher = {IEEE}, address = {Austin, TX}, abstract = {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.}, keywords = {a posteriori probability, Bayesian equalizer, Bayesian methods, BER, Bit error rate, Channel Coding, channel decoding, channel estate information, Communication channels, Decoding, equalisers, Equalizers, error statistics, low-density parity-check decoders, LPDC decoders, Maximum likelihood decoding, maximum likelihood detection, maximum likelihood estimation, Noise reduction, parity check codes, Probability, Uncertainty}, pubstate = {published}, tppubtype = {inproceedings} } 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. |

## 2009 |

## Journal Articles |

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 = {Murillo-Fuentes, Juan Jose and Perez-Cruz, Fernando}, 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. |

## Inproceedings |

Miguez, Joaquin; Maiz, Cristina; Djuric, Petar; Crisan, Dan Sequential Monte Carlo Optimization Using Artificial State-Space Models (Inproceeding) 2009 IEEE 13th Digital Signal Processing Workshop and 5th IEEE Signal Processing Education Workshop, pp. 268–273, IEEE, Marco Island, FL, 2009. (Abstract | Links | BibTeX | Tags: Acceleration, Cost function, Design optimization, discrete-time dynamical system, Educational institutions, Mathematics, maximum a posteriori estimate, maximum likelihood estimation, minimisation, Monte Carlo methods, Optimization methods, Probability distribution, sequential Monte Carlo optimization, Sequential optimization, Signal design, State-space methods, state-space model, Stochastic optimization) @inproceedings{Miguez2009, title = {Sequential Monte Carlo Optimization Using Artificial State-Space Models}, author = {Miguez, Joaquin and Maiz, Cristina S. and Djuric, Petar M. and Crisan, Dan}, url = {http://ieeexplore.ieee.org/lpdocs/epic03/wrapper.htm?arnumber=4785933}, year = {2009}, date = {2009-01-01}, booktitle = {2009 IEEE 13th Digital Signal Processing Workshop and 5th IEEE Signal Processing Education Workshop}, pages = {268--273}, publisher = {IEEE}, address = {Marco Island, FL}, abstract = {We introduce a method for sequential minimization of a certain class of (possibly non-convex) cost functions with respect to a high dimensional signal of interest. The proposed approach involves the transformation of the optimization problem into one of estimation in a discrete-time dynamical system. In particular, we describe a methodology for constructing an artificial state-space model which has the signal of interest as its unobserved dynamic state. The model is "adapted" to the cost function in the sense that the maximum a posteriori (MAP) estimate of the system state is also a global minimizer of the cost function. The advantage of the estimation framework is that we can draw from a pool of sequential Monte Carlo methods, for particle approximation of probability measures in dynamic systems, that enable the numerical computation of MAP estimates. We provide examples of how to apply the proposed methodology, including some illustrative simulation results.}, keywords = {Acceleration, Cost function, Design optimization, discrete-time dynamical system, Educational institutions, Mathematics, maximum a posteriori estimate, maximum likelihood estimation, minimisation, Monte Carlo methods, Optimization methods, Probability distribution, sequential Monte Carlo optimization, Sequential optimization, Signal design, State-space methods, state-space model, Stochastic optimization}, pubstate = {published}, tppubtype = {inproceedings} } We introduce a method for sequential minimization of a certain class of (possibly non-convex) cost functions with respect to a high dimensional signal of interest. The proposed approach involves the transformation of the optimization problem into one of estimation in a discrete-time dynamical system. In particular, we describe a methodology for constructing an artificial state-space model which has the signal of interest as its unobserved dynamic state. The model is "adapted" to the cost function in the sense that the maximum a posteriori (MAP) estimate of the system state is also a global minimizer of the cost function. The advantage of the estimation framework is that we can draw from a pool of sequential Monte Carlo methods, for particle approximation of probability measures in dynamic systems, that enable the numerical computation of MAP estimates. We provide examples of how to apply the proposed methodology, including some illustrative simulation results. |

## 2008 |

## Journal Articles |

Perez-Cruz, Fernando; Murillo-Fuentes, Juan Jose; Caro, 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 = {Perez-Cruz, Fernando and Murillo-Fuentes, Juan Jose and Caro, S.}, 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. |

## Inproceedings |

Vazquez, Manuel; Miguez, Joaquin A Per-Survivor Processing Algorithm for Maximum Likelihood Equalization of MIMO Channels with Unknown Order (Inproceeding) 2008 International ITG Workshop on Smart Antennas, pp. 387–391, IEEE, Vienna, 2008, ISBN: 978-1-4244-1756-8. (Abstract | Links | BibTeX | Tags: Channel estimation, channel impulse response, computational complexity, Computer science education, Computer Simulation, Degradation, Frequency, frequency-selective multiple-input multiple-output, maximum likelihood detection, maximum likelihood equalization, maximum likelihood estimation, maximum likelihood sequence detection, maximum likelihood sequence estimation, MIMO, MIMO channels, MIMO communication, per-survivor processing algorithm, time-selective channels, Transmitting antennas) @inproceedings{Vazquez2008, title = {A Per-Survivor Processing Algorithm for Maximum Likelihood Equalization of MIMO Channels with Unknown Order}, author = {Vazquez, Manuel A. and Miguez, Joaquin}, url = {http://ieeexplore.ieee.org/articleDetails.jsp?arnumber=4475587}, isbn = {978-1-4244-1756-8}, year = {2008}, date = {2008-01-01}, booktitle = {2008 International ITG Workshop on Smart Antennas}, pages = {387--391}, publisher = {IEEE}, address = {Vienna}, abstract = {In the equalization of frequency-selective multiple-input multiple-output (MIMO) channels it is usually assumed that the length of the channel impulse response (CIR), also referred to as the channel order, is known. However, this is not true in most practical situations and, in order to avoid the serious performance degradation that occurs when the CIR length is underestimated, a channel with "more than enough" taps is usually considered. This possibly means overestimating the channel order, and is not desirable since the computational complexity of maximum likelihood sequence detection (MLSD) in frequency-selective channels grows exponentially with the channel order. In addition to that, the higher the channel order considered, the more the number of channel coefficients that need to be estimated from the same set of observations. In this paper, we introduce an algorithm for MLSD that incorporates the full estimation of the MIMO CIR parameters, including its order. The proposed technique is based on the per survivor processing (PSP) methodology, it admits both blind and semiblind implementations, depending on the availability of pilot data, and is designed to work with time-selective channels. Besides the analytical derivation of the algorithm, we provide computer simulation results that illustrate the effectiveness of the resulting receiver}, keywords = {Channel estimation, channel impulse response, computational complexity, Computer science education, Computer Simulation, Degradation, Frequency, frequency-selective multiple-input multiple-output, maximum likelihood detection, maximum likelihood equalization, maximum likelihood estimation, maximum likelihood sequence detection, maximum likelihood sequence estimation, MIMO, MIMO channels, MIMO communication, per-survivor processing algorithm, time-selective channels, Transmitting antennas}, pubstate = {published}, tppubtype = {inproceedings} } In the equalization of frequency-selective multiple-input multiple-output (MIMO) channels it is usually assumed that the length of the channel impulse response (CIR), also referred to as the channel order, is known. However, this is not true in most practical situations and, in order to avoid the serious performance degradation that occurs when the CIR length is underestimated, a channel with "more than enough" taps is usually considered. This possibly means overestimating the channel order, and is not desirable since the computational complexity of maximum likelihood sequence detection (MLSD) in frequency-selective channels grows exponentially with the channel order. In addition to that, the higher the channel order considered, the more the number of channel coefficients that need to be estimated from the same set of observations. In this paper, we introduce an algorithm for MLSD that incorporates the full estimation of the MIMO CIR parameters, including its order. The proposed technique is based on the per survivor processing (PSP) methodology, it admits both blind and semiblind implementations, depending on the availability of pilot data, and is designed to work with time-selective channels. Besides the analytical derivation of the algorithm, we provide computer simulation results that illustrate the effectiveness of the resulting receiver |

Vazquez, Manuel; Miguez, Joaquin A Per-Survivor Processing Algorithm for Maximum Likelihood Equalization of MIMO Channels with Unknown Order (Inproceeding) 2008 International ITG Workshop on Smart Antennas, pp. 387–391, IEEE, Vienna, 2008, ISBN: 978-1-4244-1756-8. (Abstract | Links | BibTeX | Tags: Channel estimation, channel impulse response, computational complexity, Computer science education, Computer Simulation, Degradation, Frequency, frequency-selective multiple-input multiple-output, maximum likelihood detection, maximum likelihood equalization, maximum likelihood estimation, maximum likelihood sequence detection, maximum likelihood sequence estimation, MIMO, MIMO channels, MIMO communication, per-survivor processing algorithm, time-selective channels, Transmitting antennas) @inproceedings{Vazquez2008a, title = {A Per-Survivor Processing Algorithm for Maximum Likelihood Equalization of MIMO Channels with Unknown Order}, author = {Vazquez, Manuel A. and Miguez, Joaquin}, url = {http://ieeexplore.ieee.org/lpdocs/epic03/wrapper.htm?arnumber=4475587}, isbn = {978-1-4244-1756-8}, year = {2008}, date = {2008-01-01}, booktitle = {2008 International ITG Workshop on Smart Antennas}, pages = {387--391}, publisher = {IEEE}, address = {Vienna}, abstract = {In the equalization of frequency-selective multiple-input multiple-output (MIMO) channels it is usually assumed that the length of the channel impulse response (CIR), also referred to as the channel order, is known. However, this is not true in most practical situations and, in order to avoid the serious performance degradation that occurs when the CIR length is underestimated, a channel with "more than enough" taps is usually considered. This possibly means overestimating the channel order, and is not desirable since the computational complexity of maximum likelihood sequence detection (MLSD) in frequency-selective channels grows exponentially with the channel order. In addition to that, the higher the channel order considered, the more the number of channel coefficients that need to be estimated from the same set of observations. In this paper, we introduce an algorithm for MLSD that incorporates the full estimation of the MIMO CIR parameters, including its order. The proposed technique is based on the per survivor processing (PSP) methodology, it admits both blind and semiblind implementations, depending on the availability of pilot data, and is designed to work with time-selective channels. Besides the analytical derivation of the algorithm, we provide computer simulation results that illustrate the effectiveness of the resulting receiver.}, keywords = {Channel estimation, channel impulse response, computational complexity, Computer science education, Computer Simulation, Degradation, Frequency, frequency-selective multiple-input multiple-output, maximum likelihood detection, maximum likelihood equalization, maximum likelihood estimation, maximum likelihood sequence detection, maximum likelihood sequence estimation, MIMO, MIMO channels, MIMO communication, per-survivor processing algorithm, time-selective channels, Transmitting antennas}, pubstate = {published}, tppubtype = {inproceedings} } In the equalization of frequency-selective multiple-input multiple-output (MIMO) channels it is usually assumed that the length of the channel impulse response (CIR), also referred to as the channel order, is known. However, this is not true in most practical situations and, in order to avoid the serious performance degradation that occurs when the CIR length is underestimated, a channel with "more than enough" taps is usually considered. This possibly means overestimating the channel order, and is not desirable since the computational complexity of maximum likelihood sequence detection (MLSD) in frequency-selective channels grows exponentially with the channel order. In addition to that, the higher the channel order considered, the more the number of channel coefficients that need to be estimated from the same set of observations. In this paper, we introduce an algorithm for MLSD that incorporates the full estimation of the MIMO CIR parameters, including its order. The proposed technique is based on the per survivor processing (PSP) methodology, it admits both blind and semiblind implementations, depending on the availability of pilot data, and is designed to work with time-selective channels. Besides the analytical derivation of the algorithm, we provide computer simulation results that illustrate the effectiveness of the resulting receiver. |