Balanced least squares: estimation in linear systems with noisy inputs and multiple outputs

This paper revisits the linear model with noisy inputs, in which the performance of the total least squares (TLS) method is far from acceptable. Under the assumption of Gaussian noises, the maximum likelihood (ML) estimation of the system response is reformulated as a general balanced least squares (BLS) problem. Unlike TLS, which minimizes the trace of the product between the empirical and inverse theoretical covariance matrices, BLS promotes solutions with similar values of both the empirical and theoretical error covariance matrices. The general BLS problem is reformulated as a semidefinite program with a rank constraint, which can be relaxed in order to obtain polynomial time algorithms. Moreover, we provide new theoretical results regarding the scenarios in which the relaxation is tight, as well as additional insights on the performance and interpretation of BLS. Finally, some simulation results illustrate the satisfactory performance of the proposed method.This work has been supported by the Spanish Government, Ministerio de Ciencia e Innovación, under project RACHEL (TEC2013-47141-C4-3-R

Balanced Least Squares: Linear model estimation with noisy inputs

This paper focuses on a linear model with noisy inputs in which the performance of the conventional Total Least Squares (TLS) approach is (maybe surprisingly) far from satisfactory. Under the typical Gaussian assumption, we obtain the maximum likelihood (ML) estimator of the system response. This estimator promotes a reasonable balance between the empirical and theoretical variances of the residual errors, which suggests the name of Balanced Least Squares (BLS). The solution of the associated optimization problem is based on its reformulation as a rank constrained semidefinite program (SDP), for which we show that the relaxation is tight with probability one. Both TLS and BLS can be seen as regularized LS estimators, but the (possibly negative) regularization in BLS is softer than its TLS counterpart, which avoids the inconsistency of TLS in our particular model.This work has been supported by the Spanish Government, Ministerio de Ciencia e Innovación, under project RACHEL (TEC2013-47141-C4-3-R)

Adaptive EM-based algorithm for cooperative spectrum sensing in mobile environments

In this work we propose a new adaptive algorithm for cooperative spectrum sensing in dynamic environments where the channels are time varying. We assume a cooperative sensing procedure based on the soft fusion of the signal energy levels measured at the sensors. The detection problem is posed as a composite hypothesis testing problem. Then, we consider the Generalized Likelihood Ratio Test approach where the maximum likelihood estimate of the unknown parameters (which are the signal-to-noise ratio under the different hypotheses) are obtained from the most recent energy levels at the sensors by means of the Expectation-Maximization algorithm. We derive simple closed-form expressions for both, the E and the M steps. The algorithm can operate even when only a subset of sensors report their energy estimates, which makes it suited to be used with any sensor selection strategy (active sensing). Simulation results show the feasibility and efficiency of the method in realistic slow-fading environments.This work has been funded by SODERCAN and Programa Operativo FEDER under grant CAIMAN - 12.JU01.64661, and by the Ministerio de Economía, Industria y Competitividad (MINECO) of Spain, and AEI/FEDER funds of the E.U., under grants TEC2017-86921-C2-1-R (CAIMAN), TEC2013-47141-C4-R (RACHEL) and TEC2016-75067- C4-4-R (CARMEN)

Adaptive kernel canonical correlation analysis algorithms for nonparametric identification of Wiener and Hammerstein systems

This paper treats the identification of nonlinear systems that consist of a cascade of a linear channel and a nonlinearity, such as the well-known Wiener and Hammerstein systems. In particular, we follow a supervised identification approach that simultaneously identifies both parts of the nonlinear system. Given the correct restrictions on the identification problem, we show how kernel canonical correlation analysis (KCCA) emerges as the logical solution to this problem.We then extend the proposed identification algorithm to an adaptive version allowing to deal with time-varying systems. In order to avoid overfitting problems, we discuss and compare three possible regularization techniques for both the batch and the adaptive versions of the proposed algorithm. Simulations are included to demonstrate the effectiveness of the presented algorithm

Code combination for blind channel estimation in general MIMO-STBC systems

The problem of blind channel estimation under space-time block coded (STBC) transmissions is addressed. Firstly, a blind channel estimation criterion that generalizes previous works is proposed. The technique is solely based on second-order statistics (SOS) and if the channel is identifiable, the estimate is obtained as the main eigenvector of a generalized eigenvalue problem (GEV). Secondly, a new transmission technique is proposed to solve the indeterminacies associated to the blind channel estimation problem. The technique is based on the combination of different STBCs, and it can be reduced to a nonredundant precoding consisting in the rotation or permutation of the transmit antennas. Unlike other previous approaches, the proposed technique does not imply a penalty in the transmission rate or capacity of the STBC system, while it is able to avoid the ambiguities in many practical cases, which is illustrated by means of some simulation examples

Modeling Biomass Production in Seasonal Wetlands Using MODIS NDVI Land Surface Phenology

Plant primary production is a key driver of several ecosystem functions in seasonal marshes, such as water purification and secondary production by wildlife and domestic animals. Knowledge of the spatio-temporal dynamics of biomass production is therefore essential for the management of resources—particularly in seasonal wetlands with variable flooding regimes. We propose a method to estimate standing aboveground plant biomass using NDVI Land Surface Phenology (LSP) derived from MODIS, which we calibrate and validate in the Doñana National Park’s marsh vegetation. Out of the different estimators tested, the Land Surface Phenology maximum NDVI (LSP-Maximum-NDVI) correlated best with ground-truth data of biomass production at five locations from 2001–2015 used to calibrate the models (R2 = 0.65). Estimators based on a single MODIS NDVI image performed worse (R2 ≤ 0.41). The LSP-Maximum-NDVI estimator was robust to environmental variation in precipitation and hydroperiod, and to spatial variation in the productivity and composition of the plant community. The determination of plant biomass using remote-sensing techniques, adequately supported by ground-truth data, may represent a key tool for the long-term monitoring and management of seasonal marsh ecosystems.We acknowledge support by the CSIC Open Access Publication Initiative through its Unit of Information Resources for Research (URICI).David Aragonés, Isabel Afán, Ricardo Díaz-Delgado and Diego García Díaz (EBD-LAST) provided support for remote-sensing and LSP analyses. Alfredo Chico, José Luis del Valle and Rocío Fernández Zamudio (ESPN, ICTS-RBD) provided logistic support and taxonomic expertise during the field work (validation dataset). Ernesto García and Cristina Pérez assisted with biomass harvesting and processing (calibration dataset). Gerrit Heil provided support in the project design. This study received funding from Ministerio de Medio Ambiente-Parque Nacional de Doñana, Consejeria de Medio Ambiente, Junta de Andalucia (1999–2000): RNM118 Junta de Andalucia (2003); the European Union’s Horizon 2020 Research and Innovation Program under grant agreement No. 641762 to ECOPOTENTIAL project; and the Spanish Ministry of Economy, Plan Estatal de I+D+i 2013–2016, under grant agreement CGL2016-81086-R to GRAZE project

Passive detection of rank-one signals with a multiantenna reference channel

In this work we consider a two-channel passive detection problem, in which there is a surveillance array where the presence/absence of a target signal is to be detected, and a reference array that provides a noise-contaminated version of the target signal. We assume that the transmitted signal is an unknown rank-one signal, and that the noises are uncorrelated between the two channels, but each one having an unknown and arbitrary spatial covariance matrix. We show that the generalized likelihood ratio test (GLRT) for this problem rejects the null hypothesis when the largest canonical correlation of the sample coherence matrix between the surveillance and the reference channels exceeds a threshold. Further, based on recent results from random matrix theory, we provide an approximation for the null distribution of the test statistic.The work of I. Santamaría was supported by the Spanish Government through grants PRX14/0028 (Estancias de Movilidad de Profesores, Ministerio de Educación) and by project RACHEL (TEC2013-47141-C4-3-R) funded by the Ministerio de Economía y Competitividad (MINECO). The work of L. Scharf and D. Cochran was supported in part by a sub-contract with Matrix Research for research sponsored by the Air Force Research Laboratory under contract FA8650-14-D-1722

A GLRT approach for detecting correlated signals in white noise in two MIMO channels

In this work, we consider a second-order detection problem where rank-p signals are structured by an unknown, but common, p-dimensional random vector and then received through unknown M x p matrices at each of two M-element arrays. The noises in each channel are independent with identical variances. We derive generalized likelihood ratio (GLR) tests for this problem when the noise variance is either known or unknown. The resulting detection problems may be phrased as two-channel factor analysis problems.The work of I. Santamaría and J. Vía has been supported by the Ministerio de Economía, Industria y Competitividad (MINECO) of Spain, and AEI/FEDER funds of the E.U., under grants TEC2013-47141-C4-R (RACHEL), TEC2016-75067-C4-4-R (CARMEN), and TEC2016-81900- REDT (KERMES)

Conformación ciega de haz mediante regresión con máquinas de vectores soporte

Blind beamforming is a common problem in wireless communications, where an array of antennas receives a number of signals from distinct locations at the same frequency and at the same time. In this paper the problem of blind beamforming for multiple constant modulus (CM) signals separation is solved using support vector machine (SVM) techniques. The CM property of the signal is used to formulate a regression problem which can be adapted to the SVM scheme, leading to an iterative reweighted algorithm. Once a signal is recovered, its contribution to the original observations is removed and the iterative procedure can be applied again to extract another CM signal. Simulation results show that this SVM-based algorithm offers better performance than the algebraic constant modulus algorithm (ACMA), mainly when only a small number of snapshots is available

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