Improved subspace estimation for multivariate observations of high dimension: the deterministic signals case

We consider the problem of subspace estimation in situations where the number of available snapshots and the observation dimension are comparable in magnitude. In this context, traditional subspace methods tend to fail because the eigenvectors of the sample correlation matrix are heavily biased with respect to the true ones. It has recently been suggested that this situation (where the sample size is small compared to the observation dimension) can be very accurately modeled by considering the asymptotic regime where the observation dimension $M$ and the number of snapshots $N$ converge to $+\infty$ at the same rate. Using large random matrix theory results, it can be shown that traditional subspace estimates are not consistent in this asymptotic regime. Furthermore, new consistent subspace estimate can be proposed, which outperform the standard subspace methods for realistic values of $M$ and $N$. The work carried out so far in this area has always been based on the assumption that the observations are random, independent and identically distributed in the time domain. The goal of this paper is to propose new consistent subspace estimators for the case where the source signals are modelled as unknown deterministic signals. In practice, this allows to use the proposed approach regardless of the statistical properties of the source signals. In order to construct the proposed estimators, new technical results concerning the almost sure location of the eigenvalues of sample covariance matrices of Information plus Noise complex Gaussian models are established. These results are believed to be of independent interest.Comment: New version with minor corrections. The present paper is an extended version of a paper (same title) to appear in IEEE Trans. on Information Theor

Performance analysis of an improved MUSIC DoA estimator

This paper adresses the statistical performance of subspace DoA estimation using a sensor array, in the asymptotic regime where the number of samples and sensors both converge to infinity at the same rate. Improved subspace DoA estimators were derived (termed as G-MUSIC) in previous works, and were shown to be consistent and asymptotically Gaussian distributed in the case where the number of sources and their DoA remain fixed. In this case, which models widely spaced DoA scenarios, it is proved in the present paper that the traditional MUSIC method also provides DoA consistent estimates having the same asymptotic variances as the G-MUSIC estimates. The case of DoA that are spaced of the order of a beamwidth, which models closely spaced sources, is also considered. It is shown that G-MUSIC estimates are still able to consistently separate the sources, while it is no longer the case for the MUSIC ones. The asymptotic variances of G-MUSIC estimates are also evaluated.Comment: Revised versio

Performance analysis and optimal selection of large mean-variance portfolios under estimation risk

We study the consistency of sample mean-variance portfolios of arbitrarily high dimension that are based on Bayesian or shrinkage estimation of the input parameters as well as weighted sampling. In an asymptotic setting where the number of assets remains comparable in magnitude to the sample size, we provide a characterization of the estimation risk by providing deterministic equivalents of the portfolio out-of-sample performance in terms of the underlying investment scenario. The previous estimates represent a means of quantifying the amount of risk underestimation and return overestimation of improved portfolio constructions beyond standard ones. Well-known for the latter, if not corrected, these deviations lead to inaccurate and overly optimistic Sharpe-based investment decisions. Our results are based on recent contributions in the field of random matrix theory. Along with the asymptotic analysis, the analytical framework allows us to find bias corrections improving on the achieved out-of-sample performance of typical portfolio constructions. Some numerical simulations validate our theoretical findings

Disseny d'un quadre de bicicleta amb suspensió de fabricació artesana

L’objectiu del projecte és el disseny, calcul i prototipatge d’un quadre de bicicleta de muntanya amb suspensió posterior i de fabricació artesanal.Aquest projecte té per objecte el disseny d’un quadre d’una bicicleta de muntanya amb suspensió per a ser fabricada a mida del ciclista mitjançant un procés artesanal de fabricació. Per aconseguir aquest disseny, prèviament es realitza una primera fase on s’analitza la posició correcta que ha de tenir el ciclista muntat sobre la bicicleta, segons un seguit de recomanacions extretes de la bibliografia del món ciclista i tenint en compte també els components que, juntament amb el quadre que es dissenya, conformen el conjunt de la bicicleta. Tot seguit s’analitza el principal problema que pateixen les bicicletes de muntanya amb suspensió posterior, que és la contaminació del pedaleig del ciclista que afecta al comportament de la suspensió. Es defineix un model amb el qual es parametritza la geometria gràcies a un programa informàtic i a la utilització d’una fulla de càlcul per analitzar-ne els resultats. Segons els criteris proposats, s’arriba a un model que és el que es dissenyarà. Definit el sistema de suspensió i l’ergonomia del ciclista es comença a dissenyar el quadre tenint en compte els components que influeixen en el disseny d’aquest. Un cop definida la geometria, es procedeix al dimensionament de les parts que conformen el quadre, validant els resultats segons els anàlisis realitzats a trencament i fatiga. Seguidament s’explica el procés constructiu d’un quadre, aconseguint així finalitzar el projecte amb el disseny realitzat i preparat per a poder ser fabricat de forma artesanal. Finalment es realitza un petit estudi sobre la viabilitat d’iniciar una activitat com a petit taller artesanal de fabricació de quadres de bicicleta a mida, on s’analitza a través de calcular quin seria el preu de venta de la bicicleta

Proyecto de un circuito de motocross para la rehabilitación de una cantera en Albinyana (Tarragona)

Este proyecto está dirigido a la reutilización de una antigua explotación minera que no ha cumplido la normativa catalana sobre canteras, (como es, la ley 12/1981 de 24 de diciembre, por la que se establecen normas adicionales de protección de los espacios de especial interés natural afectados por actividades extractivas, o el decreto 343/1983 de 15 de julio, sobre les normas de protección del medio ambiente de aplicación a dichas actividades). A tal fin, se ha realizado un estudio de la topografía del terreno, mediante un levantamiento, a partir del cual se obtendrá un plano a escala 1/500 representativo de la zona, gracias al cual poder idear un nuevo uso de la superficie en cuestión. Una vez plasmado el plano, se tendrá una mejor idea de los nuevos usos de la cantera, que en este caso serán dos: 1-.Diseño de un circuito de motocross, e implantación del mismo intentando aprovechar la topografía del terreno (idea surgida a partir de la proximidad del circuito de pruebas automovilísticas de la Idiada, en L´Albornar). 2-.Recuperación ambiental total o parcial, dependiendo de si el relleno de la superficie explotada se va a realizar mediante elementos naturales propios de la zona (sustratos geológicos, hidrológicos y ecológicos) o mediante materiales de aportación (residuos inertes, es decir, usándola como vertedero). Todo ello conlleva un estudio minucioso, tanto en el diseño e implantación del circuito como en la mejora de los accesos al mismo, así como un detallado cálculo de los volúmenes de aportación para su restauración ambiental. Así pues se realizará un estudio de impacto medioambiental con el fin de maximizar la integración del nuevo entorno con su futura ubicación

Near-Field Beamfocusing with Polarized Antennas

One of the most relevant challenges in future 6G wireless networks is how to support a massive spatial multiplexing of a large number of user terminals. Recently, extremely large antenna arrays (ELAAs), also referred to as extra-large MIMO (XL-MIMO), have emerged as an potential enabler of this type of spatially multiplexed transmission. These massive configurations substantially increase the number of available spatial degrees of freedom (transmission modes) while also enabling to spatially focus the transmitted energy into a very small region, thanks to the properties of near-field propagation and the large number of transmitters. This work explores whether multiplexing of multiple orthogonal polarizations can enhance the system performance in the near-field. We concentrate on a simple scenario consisting of a Uniform Linear Array (ULA) and a single antenna element user equipment (UE). We demonstrate that the number of spatial degrees of freedom can be as large as 3 in the near-field of a Line of Sight (LoS) channel when both transmitter and receiver employ three orthogonal linear polarizations. In the far-field, however, the maximum number of spatial degrees of freedom tends to be only 2, due to the fact that the equivalent MIMO channel becomes rank deficient. We provide an analytical approximation to the achievable rate, which allows us to derive approximations to the optimal antenna spacing and array size that maximize the achievable rateComment: submitted for conference publicatio

On the Resolution Probability of Conditional and Unconditional Maximum Likelihood DoA Estimation

After decades of research in Direction of Arrival (DoA) estimation, today Maximum Likelihood (ML) algorithms still provide the best performance in terms of resolution capabilities. At the cost of a multidimensional search, ML algorithms achieve a significant reduction of the outlier production mechanism in the threshold region, where the number of snapshots per antenna and/or the signal to noise ratio (SNR) are low. The objective of this paper is to characterize the resolution capabilities of ML algorithms in the threshold region. Both conditional and unconditional versions of the ML algorithms are investigated in the asymptotic regime where both the number of antennas and the number of snapshots are large but comparable in magnitude. By using random matrix theory techniques, the finite dimensional distributions of both cost functions are shown to be Gaussian distributed in this asymptotic regime, and a closed form expression of the corresponding asymptotic covariance matrices is provided. These results allow to characterize the asymptotic behavior of the resolution probability, which is defined as the probability that the cost function evaluated at the true DoAs is smaller than the values that it takes at the positions of the other asymptotic local minima

Large information plus noise random matrix models and consistent subspace estimation in large sensor networks

In array processing, a common problem is to estimate the angles of arrival of $K$ deterministic sources impinging on an array of $M$ antennas, from $N$ observations of the source signal, corrupted by gaussian noise. The problem reduces to estimate a quadratic form (called "localization function") of a certain projection matrix related to the source signal empirical covariance matrix. Recently, a new subspace estimation method (called "G-MUSIC") has been proposed, in the context where the number of available samples $N$ is of the same order of magnitude than the number of sensors $M$. In this context, the traditional subspace methods tend to fail because the empirical covariance matrix of the observations is a poor estimate of the source signal covariance matrix. The G-MUSIC method is based on a new consistent estimator of the localization function in the regime where $M$ and $N$ tend to $+\infty$ at the same rate. However, the consistency of the angles estimator was not adressed. The purpose of this paper is to prove the consistency of the angles of arrival estimator in the previous asymptotic regime. To prove this result, we show the property that the singular values of M x N Gaussian information plus noise matrix escape from certain intervals is an event of probability decreasing at rate O(1/N^p) for all p. A regularization trick is also introduced, which allows to confine these singular values into certain intervals and to use standard tools as Poincar\'e inequality to characterize any moments of the estimator. These results are believed to be of independent interest

Visual Summary of Egocentric Photostreams by Representative Keyframes

Building a visual summary from an egocentric photostream captured by a lifelogging wearable camera is of high interest for different applications (e.g. memory reinforcement). In this paper, we propose a new summarization method based on keyframes selection that uses visual features extracted by means of a convolutional neural network. Our method applies an unsupervised clustering for dividing the photostreams into events, and finally extracts the most relevant keyframe for each event. We assess the results by applying a blind-taste test on a group of 20 people who assessed the quality of the summaries.Comment: Paper accepted in the IEEE First International Workshop on Wearable and Ego-vision Systems for Augmented Experience (WEsAX). Turin, Italy. July 3, 201