## 2015 |

Ramírez, David; Schreier, Peter J; Via, Javier; Santamaria, Ignacio; Scharf, L L 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{&amp;amp;}{#}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{&amp;amp;}{#}x2019 @article{Ramirez2015, title = {Detection of Multivariate Cyclostationarity}, author = {David Ramírez 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{&amp;amp;}{#}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{&amp;amp;}{#}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. |

## 2011 |

Balasingam, Balakumar; Bolic, Miodrag; Djuric, Petar M; Miguez, Joaquin Efficient Distributed Resampling for Particle Filters Inproceedings 2011 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), pp. 3772–3775, IEEE, Prague, 2011, ISSN: 1520-6149. Abstract | Links | BibTeX | Tags: Approximation algorithms, Copper, Covariance matrix, distributed resampling, Markov processes, Probability density function, Sequential Monte-Carlo methods, Signal processing, Signal processing algorithms @inproceedings{Balasingam2011, title = {Efficient Distributed Resampling for Particle Filters}, author = {Balakumar Balasingam and Miodrag Bolic and Petar M Djuric and Joaquin Miguez}, url = {http://ieeexplore.ieee.org/lpdocs/epic03/wrapper.htm?arnumber=5947172}, issn = {1520-6149}, year = {2011}, date = {2011-01-01}, booktitle = {2011 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)}, pages = {3772--3775}, publisher = {IEEE}, address = {Prague}, abstract = {In particle filtering, resampling is the only step that cannot be fully parallelized. Recently, we have proposed algorithms for distributed resampling implemented on architectures with concurrent processing elements (PEs). The objective of distributed resampling is to reduce the communication among the PEs while not compromising the performance of the particle filter. An additional objective for implementation is to reduce the communication among the PEs. In this paper, we report an improved version of the distributed resampling algorithm that optimally selects the particles for communication between the PEs of the distributed scheme. Computer simulations are provided that demonstrate the improved performance of the proposed algorithm.}, keywords = {Approximation algorithms, Copper, Covariance matrix, distributed resampling, Markov processes, Probability density function, Sequential Monte-Carlo methods, Signal processing, Signal processing algorithms}, pubstate = {published}, tppubtype = {inproceedings} } In particle filtering, resampling is the only step that cannot be fully parallelized. Recently, we have proposed algorithms for distributed resampling implemented on architectures with concurrent processing elements (PEs). The objective of distributed resampling is to reduce the communication among the PEs while not compromising the performance of the particle filter. An additional objective for implementation is to reduce the communication among the PEs. In this paper, we report an improved version of the distributed resampling algorithm that optimally selects the particles for communication between the PEs of the distributed scheme. Computer simulations are provided that demonstrate the improved performance of the proposed algorithm. |

## 2010 |

Vinuelas-Peris, Pablo; Artés-Rodríguez, Antonio Bayesian Joint Recovery of Correlated Signals in Distributed Compressed Sensing Inproceedings 2010 2nd International Workshop on Cognitive Information Processing, pp. 382–387, IEEE, Elba, 2010, ISBN: 978-1-4244-6459-3. Abstract | Links | BibTeX | Tags: Bayes methods, Bayesian joint recovery, Bayesian methods, correlated signal, Correlation, correlation methods, Covariance matrix, Dictionaries, distributed compressed sensing, matrix decomposition, Noise measurement, sensors, sparse component correlation coefficient @inproceedings{Vinuelas-Peris2010, title = {Bayesian Joint Recovery of Correlated Signals in Distributed Compressed Sensing}, author = {Pablo Vinuelas-Peris and Antonio Artés-Rodríguez}, url = {http://ieeexplore.ieee.org/lpdocs/epic03/wrapper.htm?arnumber=5604103}, isbn = {978-1-4244-6459-3}, year = {2010}, date = {2010-01-01}, booktitle = {2010 2nd International Workshop on Cognitive Information Processing}, pages = {382--387}, publisher = {IEEE}, address = {Elba}, abstract = {In this paper we address the problem of Distributed Compressed Sensing (DCS) of correlated signals. We model the correlation using the sparse components correlation coefficient of signals, a general and simple measure. We develop an sparse Bayesian learning method for this setting, that can be applied to both random and optimized projection matrices. As a result, we obtain a reduction of the number of measurements needed for a given recovery error that is dependent on the correlation coefficient, as shown by computer simulations in different scenarios.}, keywords = {Bayes methods, Bayesian joint recovery, Bayesian methods, correlated signal, Correlation, correlation methods, Covariance matrix, Dictionaries, distributed compressed sensing, matrix decomposition, Noise measurement, sensors, sparse component correlation coefficient}, pubstate = {published}, tppubtype = {inproceedings} } In this paper we address the problem of Distributed Compressed Sensing (DCS) of correlated signals. We model the correlation using the sparse components correlation coefficient of signals, a general and simple measure. We develop an sparse Bayesian learning method for this setting, that can be applied to both random and optimized projection matrices. As a result, we obtain a reduction of the number of measurements needed for a given recovery error that is dependent on the correlation coefficient, as shown by computer simulations in different scenarios. |

## 2008 |

Rodrigues, Miguel R D; Perez-Cruz, Fernando; Verdu, Sergio Multiple-Input Multiple-Output Gaussian Channels: Optimal Covariance for Non-Gaussian Inputs Inproceedings 2008 IEEE Information Theory Workshop, pp. 445–449, IEEE, Porto, 2008, ISBN: 978-1-4244-2269-2. Abstract | Links | BibTeX | Tags: Binary phase shift keying, covariance matrices, Covariance matrix, deterministic MIMO Gaussian channel, fixed-point equation, Gaussian channels, Gaussian noise, Information rates, intersymbol interference, least mean squares methods, Magnetic recording, mercury-waterfilling power allocation policy, MIMO, MIMO communication, minimum mean-squared error, MMSE, MMSE matrix, multiple-input multiple-output system, Multiple-Input Multiple-Output Systems, Mutual information, Optimal Input Covariance, Optimization, Telecommunications @inproceedings{Rodrigues2008, title = {Multiple-Input Multiple-Output Gaussian Channels: Optimal Covariance for Non-Gaussian Inputs}, author = {Miguel R D Rodrigues and Fernando Perez-Cruz and Sergio Verdu}, url = {http://ieeexplore.ieee.org/lpdocs/epic03/wrapper.htm?arnumber=4578704}, isbn = {978-1-4244-2269-2}, year = {2008}, date = {2008-01-01}, booktitle = {2008 IEEE Information Theory Workshop}, pages = {445--449}, publisher = {IEEE}, address = {Porto}, abstract = {We investigate the input covariance that maximizes the mutual information of deterministic multiple-input multipleo-utput (MIMO) Gaussian channels with arbitrary (not necessarily Gaussian) input distributions, by capitalizing on the relationship between the gradient of the mutual information and the minimum mean-squared error (MMSE) matrix. We show that the optimal input covariance satisfies a simple fixed-point equation involving key system quantities, including the MMSE matrix. We also specialize the form of the optimal input covariance to the asymptotic regimes of low and high snr. We demonstrate that in the low-snr regime the optimal covariance fully correlates the inputs to better combat noise. In contrast, in the high-snr regime the optimal covariance is diagonal with diagonal elements obeying the generalized mercury/waterfilling power allocation policy. Numerical results illustrate that covariance optimization may lead to significant gains with respect to conventional strategies based on channel diagonalization followed by mercury/waterfilling or waterfilling power allocation, particularly in the regimes of medium and high snr.}, keywords = {Binary phase shift keying, covariance matrices, Covariance matrix, deterministic MIMO Gaussian channel, fixed-point equation, Gaussian channels, Gaussian noise, Information rates, intersymbol interference, least mean squares methods, Magnetic recording, mercury-waterfilling power allocation policy, MIMO, MIMO communication, minimum mean-squared error, MMSE, MMSE matrix, multiple-input multiple-output system, Multiple-Input Multiple-Output Systems, Mutual information, Optimal Input Covariance, Optimization, Telecommunications}, pubstate = {published}, tppubtype = {inproceedings} } We investigate the input covariance that maximizes the mutual information of deterministic multiple-input multipleo-utput (MIMO) Gaussian channels with arbitrary (not necessarily Gaussian) input distributions, by capitalizing on the relationship between the gradient of the mutual information and the minimum mean-squared error (MMSE) matrix. We show that the optimal input covariance satisfies a simple fixed-point equation involving key system quantities, including the MMSE matrix. We also specialize the form of the optimal input covariance to the asymptotic regimes of low and high snr. We demonstrate that in the low-snr regime the optimal covariance fully correlates the inputs to better combat noise. In contrast, in the high-snr regime the optimal covariance is diagonal with diagonal elements obeying the generalized mercury/waterfilling power allocation policy. Numerical results illustrate that covariance optimization may lead to significant gains with respect to conventional strategies based on channel diagonalization followed by mercury/waterfilling or waterfilling power allocation, particularly in the regimes of medium and high snr. |