@article{Ram\'{i}rez2020,

title = {Multi-channel factor analysis with common and unique factors},

author = {David Ram\'{i}rez and Ignacio Santamar\'{i}a and L L Scharf and Steven Van Vaerenbergh},

doi = {10.1109/TSP.2019.2955829},

issn = {1053-587X},

year  = {2020},

date = {2020-01-01},

journal = {IEEE Trans. Signal Process.},

volume = {68},

pages = {113-126},

keywords = {Block minorization-maximization algorithms, expectation-maximization algorithms, maximum likelihood estimation, multi-channel factor analysis, multiple-input multiple-output channels, passive radar},

pubstate = {published},

tppubtype = {article}

}

@article{Ramirez2015,

title = {Detection of Multivariate Cyclostationarity},

author = {David Ram\'{i}rez and Peter J Schreier and Javier Via and Ignacio Santamaria and L L Scharf},

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}

}

@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}

}

@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}

}