Locally Most Powerful Invariant Tests for Correlation and Sphericity of Gaussian Vectors

In this paper we study the existence of locally most powerful invariant tests (LMPIT) for the problem of testing the covariance structure of a set of Gaussian random vectors. The LMPIT is the optimal test for the case of close hypotheses, among those satisfying the invariances of the problem, and in practical scenarios can provide better performance than the typically used generalized likelihood ratio test (GLRT). The derivation of the LMPIT usually requires one to find the maximal invariant statistic for the detection problem and then derive its distribution under both hypotheses, which in general is a rather involved procedure. As an alternative, Wijsman's theorem provides the ratio of the maximal invariant densities without even finding an explicit expression for the maximal invariant. We first consider the problem of testing whether a set of $N$-dimensional Gaussian random vectors are uncorrelated or not, and show that the LMPIT is given by the Frobenius norm of the sample coherence matrix. Second, we study the case in which the vectors under the null hypothesis are uncorrelated and identically distributed, that is, the sphericity test for Gaussian vectors, for which we show that the LMPIT is given by the Frobenius norm of a normalized version of the sample covariance matrix. Finally, some numerical examples illustrate the performance of the proposed tests, which provide better results than their GLRT counterparts

Testing blind separability of complex Gaussian mixtures

The separation of a complex mixture based solely on second-order statistics can be achieved using the Strong Uncorrelating Transform (SUT) if and only if all sources have distinct circularity coefficients. However, in most problems we do not know the circularity coefficients, and they must be estimated from observed data. In this work, we propose a detector, based on the generalized likelihood ratio test (GLRT), to test the separability of a complex Gaussian mixture using the SUT. For the separable case (distinct circularity coefficients), the maximum likelihood (ML) estimates are straightforward. On the other hand, for the non-separable case (at least one circularity coefficient has multiplicity greater than one), the ML estimates are much more difficult to obtain. To set the threshold, we exploit Wilks' theorem, which gives the asymptotic distribution of the GLRT under the null hypothesis. Finally, numerical simulations show the good performance of the proposed detector and the accuracy of Wilks' approximation

A regularized maximum likelihood estimator for the period of a cyclostationary process

We derive an estimator of the cycle period of a univariate cyclostationary process based on an information-theoretic criterion. Transforming the univariate cyclostationary process into a vector-valued wide-sense stationary process allows us to obtain the structure of the covariance matrix, which is block-Toeplitz, and its block size depends on the unknown cycle period. Therefore, we sweep the block size and obtain the ML estimate of the covariance matrix, required for the information-theoretic criterion. Since there are no closed-form ML estimates of block-Toeplitz matrices, we asymptotically approximate them as block-circulant. Finally, some numerical examples show the good performance of the proposed estimator.The work of P. Schreier was supported by the Alfried Krupp von Bohlen und Halbach Foundation, under its program “Return of German scientists from abroad”. The work of I. Santamaría and J. Vía was supported by the Spanish Government, Ministerio de Ciencia e Innovación (MICINN), under project RACHEL (TEC2013-47141-C4-3-R). The work of L. Scharf was supported by the Airforce Office of Scientific Research under contract FA9550-10-1-0241

An asymptotic GLRT for the detection of cyclostationary signals

We derive the generalized likelihood ratio test (GLRT) for detecting cyclostationarity in scalar- valued time series. The main idea behind our approach is Gladyshev’s relationship, which states that when the scalar-valued cyclostationary signal is blocked at the known cycle period it produces a vectorvalued wide-sense stationary (WSS) process. This result amounts to saying that the covariance matrix of the vector obtained by stacking all observations of the time series is block-Toeplitz if the signal is cyclostationary, and Toeplitz if the signal is wide-sense stationary. The derivation of the GLRT requires the maximum likelihood estimates of Toeplitz and block-Toeplitz matrices. This can be managed asymptotically (for large number of samples) exploiting Szegö’s theorem and its generalization for vector-valued processes. Simulation results show the good performance of the proposed GLRT.The work of L. Scharf was supported by the Airforce Office of Scientific Research under contract FA9550-10-1-0241. The work of I. Santamaría and J. Vía was supported by the Spanish Government, Ministerio de Ciencia e Innovación (MICINN), under project COSIMA (TEC2010-19545-C04-03) and project COMONSENS (CSD2008-00010, CONSOLIDER-INGENIO 2010 Program). The work of P. Schreier was supported by the Alfried Krupp von Bohlen und Halbach Foundation, under its program “Return of German scientists from abroad

An asymptotic LMPI test for cyclostationarity detection with application to cognitive radio

We propose a new detector of primary users in cognitive radio networks. The main novelty of the proposed detector in comparison to most known detectors is that it is based on sound statistical principles for detecting cyclostationary signals. In particular, the proposed detector is (asymptotically) the locally most powerful invariant test, i.e. the best invariant detector for low signal-to-noise ratios. The derivation is based on two main ideas: the relationship between a scalar-valued cyclostationary signal and a vector-valued wide-sense stationary signal, and Wijsman's theorem. Moreover, using the spectral representation for the cyclostationary time series, the detector has an insightful interpretation, and implementation, as the broadband coherence between frequencies that are separated by multiples of the cycle frequency. Finally, simulations confirm that the proposed detector performs better than previous approaches.The work of P. Schreier was supported by the Alfried Krupp von Bohlen und Halbach Foundation, under its program “Return of German scientists from abroad”. The work of I. Santamaría and J. Vía was supported by the Spanish Government, Ministerio de Ciencia e Innovación (MICINN), under project RACHEL (TEC2013-47141-C4-3-R). The work of L. Scharf was supported by the Airforce Office of Scientific Research under contract FA9550-10-1-0241

Detection of multivariate cyclostationarity

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 Loe`ve 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.The work of P. Schreier was supported by the Alfried Krupp von Bohlen und Halbach Foundation, under its program “Return of German scientists from abroad”. The work of I. Santamaría and J. Vía was supported by the Spanish Government, Ministerio de Ciencia e Innovación (MICINN), under project RACHEL (TEC2013-47141-C4-3-R). The work of L. Scharf was supported by the Airforce Office of Scientific Research under contract FA9550-10-1-0241

Propuesta de la Sociedad Española de Farmacia Comunitaria sobre prácticas tuteladas

La asignatura Prácticas Tuteladas (PT) es obligatoria en el grado de Farmacia, siendo la de mayor carga lectiva, entre 24 y 30 ECTS. Su objetivo es completar la formación del alumno e iniciarlo en las actividades asistenciales desarrolladas en la farmacia comunitaria (FC) y/o en la farmacia de hospital. Una gran mayoría de estudiantes las realizan en la FC donde, por primera vez, entran en contacto real con la profesión. Sin embargo cada universidad establece de manera autónoma la forma en que se imparten la asignatura, existiendo una gran diversidad en el desarrollo de las PT entre las distintas facultades de Farmacia.La Sociedad Española de Farmacia Comunitaria (SEFAC) elabora este documento para contribuir a homogeneizar la docencia de esta asignatura y unificar criterios entre todas las partes implicadas: responsables académicos, profesores asociados y farmacéuticos tutores encargados de la formación de los estudiantes. En definitiva, para contribuir a mejorar su calidad docente.Se propone la creación de un Departamento específico de PT, actualmente inexistente, se abordan los criterios para acreditar farmacias y farmacéuticos tutores (FT), se revisan las funciones del profesor asociado (PA) y de los coordinadores académicos, los requisitos que deben cumplir los alumnos para cursar esta asignatura, las competencias y habilidades mínimas que necesitan adquirir y los contenidos del programa docente. También se abordan la evaluación del alumno por el FT así como la evaluación de los profesores, de la metodología docente y de las FC donde se realizan las estancias por los estudiantes

Estimador competitivo de bajo coste computacional para deconvolución dispersa

This paper presents an efficient algorithm for computing the maximum a posteriori (MAP) estimate of a Bernouilli- Gaussian sequence distorted by a linear filter and corrupted by noise. The computational effort for the MAP estimator increases exponentially with the number of samples and is generally unfeasible. The approach used by Kormylo and Mendel in their pioneering work on the Single Most-Likely Replacement algorithm (SMLR) has been the sub-optimal reference to evaluate the efficiency of this new estimation method in computational effort and detection probability. This algorithm reduces drastically the SMLR computational load and allows real-time processing, because only few samples of the observation data are required by employing a windowing strategy. An extensive Monte Carlo analysis, using synthetic data, has been performed to compare the behaviour of the proposed estimators

Experimental evaluation in wireless communications

This editorial sums up relevant topics on the assessment of wireless communication systems covered by the especial issue entitled "Experimental Evaluation in Wireless Communications". The topics include practical aspects on the implementation of distributed asynchronous non-linear kernel methods over wireless sensor networks; localization methods based on the exploitation of radio-frequency identification (RFID) wireless sensors and cellular networks or on sparsity approximations; channel sounding and assessment of broadband orthogonal frequency-division multiplexing (OFDM)-based wireless systems in high-speed vehicular communications; coexistence analysis of femtocell-based and outdoor-to-indoor systems; techniques for peak-to-average power ratio (PAPR) reduction; new solutions for baseband and radio frequency (RF) hardware impairments in full-duplex wireless systems; and, finally, suitability of interference alignment for broadband indoor wireless communications

Measuring track vertical stiffness through dynamic monitoring

[EN] This paper proposes a methodology for the evaluation of the track condition by means of the measurement of the track stiffness. This magnitude is calculated from vertical acceleration data measured at the axle box of trains during their normal operation. From the corresponding vertical acceleration spectra, the dominant vibration frequencies for each track stretch are identified and the combined stiffness is then determined. Then the stiffness without the contribution of the rail is calculated. The results obtained for a High Speed ballasted track in several track stretches are within the range 120-130 kN/mm, a result consistent with direct stiffness measurements taken during previous studies. Therefore, the proposed methodology may be used to obtain a first insight to the track condition by means of a continuous measurement of the track combined stiffness. This offers an alternative to traditional stationary stiffness measuring devices and might be a useful complement to dedicated continuous monitoring vehicles.Cano, MJ.; Martínez Fernández, P.; Insa Franco, R. (2016). Measuring track vertical stiffness through dynamic monitoring. Proceedings of the Institution of Civil Engineers - Transport. 169(1). doi:10.1680/jtran.14.00081S169