142 research outputs found

    Data driven joint sensor fusion and regression based on geometric mean squared error

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    This paper explores the problem of estimating a temporal series measured from multiple independent sensors with unequal and stationary measurement errors with unknown variances. By formulating the data fusion problem as a joint Maximum Likelihood estimation of sensor covariances and a fusion rule, a batch data driven method is derived involving a residual covariance determinant minimization of a diagonal matrix. It is shown that yielding useful learning from data with good generalization properties in the joint regression and fusion approach requires the assumption of some structure on the sensor noises and/or on the temporal series to be estimated. An efficient data driven algorithm is proposed to obtain the best linear sensor combiner, whose performance is numerically analyzed and compared with the Cramer-Rao Lower Bound of the estimated parameters.This work has been supported by the Spanish Ministry of Science and Innovation through project RODIN (PID2019-105717RB-C22 / AEI / 10.13039/501100011033) and by the Catalan Government (AGAUR) under grant 2017 SGR 578.Peer ReviewedPostprint (author's final draft

    On the estimation of Tsallis entropy and a novel information measure based on its properties

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    This letter explores a plug-in estimator of second-order Tsallis entropy based on Kernel Density Estimation (KDE) and its implicit regularization process. First, it is shown that the expected value of the estimator corresponds to the entropy of an Additive White Gaussian Noise (AWGN) model. Then, we prove various relevant properties of the Tsallis entropy: It is monotonically non-decreasing under random variables addition, its derivative with respect to the Gaussian noise power is monotonically non-increasing, and it is concave in the additive noise power. From these, we derive an information metric that provides an alternative to the strategy of regularization.This work was supported in part by the Spanish Ministry of Science and Innovation project RODIN under Grant PID2019-105717RB-C22, in part by Generalitat de Catalunya under Grant 2021 SGR 01033, in part by Fellowship 2019 FI 00620 and Fellowship 2023 FI “Joan Oró” 00050 by the Generalitat de Catalunya and the European Social Fund, and in part by Fellowship 2022 FPI-UPC 028 by the Universitat Politècnica de Catalunya and Banc de Santander. The associate editor coordinating the review of this manuscript and approving it for publication was Prof. Giuseppe Thadeu Freitas de AbreuPeer ReviewedPostprint (published version

    Regularized estimation of information via canonical correlation analysis on a finite-dimensional feature space

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    This paper aims to estimate the information between two random phenomena by using consolidated second-order statistics tools. The squared-loss mutual information, a surrogate of the Shannon mutual information, is chosen due to its property of being expressed as a second-order moment. We first review the rationale for i.i.d. discrete sources, which involves mapping the data onto the simplex space, and we highlight the links with other well-known related concepts in the literature based on local approximations of information-theoretic measures. Then, the problem is translated to analog sources by mapping the data onto the characteristic space, focusing on the adaptability between the discrete and the analog case and its limitations. The proposed approach gains interpretability and scalability for its use on large data sets, providing a unified rationale for the free regularization parameters. Moreover, the structure of the proposed mapping allows resorting to Szegö’s theorem to reduce the complexity for high dimensional mappings, exhibiting a strong duality with spectral analysis. The performance of the developed estimators is analyzed using Gaussian mixtures.This work has been supported by the Spanish Ministry of Science and Innovation through project RODIN (PID2019-105717RB- C22/MCIN/AEI/10.13039/501100011033), by the grant 2021 SGR 01033 (AGAUR, Generalitat de Catalunya), and fellowship FI 2019 by the Secretary for University and Research of the Generalitat de Catalunya and the European Social Fund.Peer ReviewedPostprint (author's final draft

    Context-aware lossless and lossy compression of radio frequency signals

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    We propose an algorithm based on linear prediction that can perform both the lossless and near-lossless compression of RF signals. The proposed algorithm is coupled with two signal detection methods to determine the presence of relevant signals and apply varying levels of loss as needed. The first method uses spectrum sensing techniques, while the second one takes advantage of the error computed in each iteration of the Levinson–Durbin algorithm. These algorithms have been integrated as a new pre-processing stage into FAPEC, a data compressor first designed for space missions. We test the lossless algorithm using two different datasets. The first one was obtained from OPS-SAT, an ESA CubeSat, while the second one was obtained using a SDRplay RSPdx in Barcelona, Spain. The results show that our approach achieves compression ratios that are 23% better than gzip (on average) and very similar to those of FLAC, but at higher speeds. We also assess the performance of our signal detectors using the second dataset. We show that high ratios can be achieved thanks to the lossy compression of the segments without any relevant signal.This work was (partially) funded by the European Space Agency (ESA) Contract No. 4000137290, the Spanish Ministry of Science and Innovation projects PID2019-105717RB-C22 (RODIN) and PID2021-122842OB-C21, the ERDF (a way of making Europe) by the European Union, the Institute of Cosmos Sciences University of Barcelona (ICCUB, Unidad de Excelencia María de Maeztu) through grant CEX2019-000918-M, grant 2021 SGR 1033 by Generalitat de Catalunya (AGAUR), and fellowship FPI-UPC 2022 by Universitat Politècnica de Catalunya and Banc de Santander.Postprint (published version

    A test for conditional correlation between random vectors based on weighted u-statistics

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    This article explores U-Statistics as a tool for testing conditional correlation between two multivariate sources with respect to a potential confounder. The proposed approach is effectively an instance of weighted U-Statistics and does not impose any statistical model on the processed data, in contrast to other well-known techniques that assume Gaussianity. By avoiding determinants and inverses, the method presented displays promising robustness in small-sample regimes. Its performance is evaluated numerically through its MSE and ROC curves.Peer ReviewedPostprint (author's final draft

    Sparse-aware approach for covariance conversion in FDD systems

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    This paper proposes a practical way to solve the Uplink-Downlink Covariance Conversion (UDCC) problem in a Frequency Division Duplex (FDD) communication system. The UDCC problem consists in the estimation of the Downlink (DL) spatial covariance matrix from the prior knowledge of the Uplink (UL) spatial covariance matrix without the need of a feedback transmission from the User Equipment (UE) to the Base Station (BS). Estimating the DL sample spatial covariance matrix is unfeasible in current massive Multiple-Input Multiple-Output (MIMO) deployments in frequency selective or fast fading channels due to the required large training overhead. Our method is based on the application of sparse filtering ideas to the estimation of a quantized version of the so-called Angular Power Spectrum (APS), being the common factor between the UL and DL spatial channel covariance matrices.This work has been supported by the Spanish Ministry of Science and Innovation through project RODIN (PID2019-105717RB-C22 / AEI / 10.13039/501100011033) and by the Catalan Government (AGAUR) under grant 2017 SGR 578.Peer ReviewedPostprint (author's final draft

    On infinite past predictability of cyclostationary signals

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    This paper explores the asymptotic spectral decomposition of periodically Toeplitz matrices with finite summable elements. As an alternative to polyphase decomposition and other approaches based on Gladyshev representation, the proposed route exploits the Toeplitz structure of cyclic autocorrelation matrices, thus leveraging on known asymptotic results and providing a more direct link to the cyclic spectrum and spectral coherence. As a concrete application, the problem of cyclic linear prediction is revisited, concluding with a generalized Kolmogorov-Szeg theorem on the predictability of cyclostationary signals. These results are finally tested experimentally in a prediction setting for an asynchronous mixture of two cyclostationary pulse-amplitude modulation signals.This work has been supported by the Spanish Ministry of Science and Innovation through project RODIN (PID2019-105717RB-C22 / MCIN / AEI / 10.13039/501100011033). Authors are within Signal Processing and Communications group (SPCOM) (Signal Theory and Communications Department) at Technical University of Catalonia (UPC).Peer ReviewedPostprint (author's final draft

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    Resolved2021/202

    Affine projection subspace tracking

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    © 2021 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works.In this paper, we consider the problem of estimating and tracking an R-dimensional subspace with relevant information embedded in an N-dimensional ambient space, given that N>>R. We focus on a formulation of the signal subspace that interprets the problem as a least squares optimization. The approach we present relies on the geometrical concepts behind the Affine Projection Algorithms (APA) family to obtain the Affine Projection Subspace Tracking (APST) algorithm. This on-line solution possesses various desirable tracking capabilities, in addition to a high degree of configurability, making it suitable for a large range of applications with different convergence speed and computational complexity requirements. The APST provides a unified framework that generalises other well-known techniques, such as Oja’s rule and stochastic gradient based methods for subspace tracking. This algorithm is finally tested in a few synthetic scenarios against other classical adaptive methods.This work has been supported by the Spanish Ministry of Science and Innovation through project RODIN (PID2019-105717RB-C22 / AEI / 10.13039/501100011033) and by the Catalan Government (AGAUR) under grant 2017 SGR 578.Peer ReviewedPostprint (author's final draft
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