Optimal Linear Precoding Strategies for Wideband Non-Cooperative Systems based on Game Theory-Part I: Nash Equilibria

In this two-parts paper we propose a decentralized strategy, based on a game-theoretic formulation, to find out the optimal precoding/multiplexing matrices for a multipoint-to-multipoint communication system composed of a set of wideband links sharing the same physical resources, i.e., time and bandwidth. We assume, as optimality criterion, the achievement of a Nash equilibrium and consider two alternative optimization problems: 1) the competitive maximization of mutual information on each link, given constraints on the transmit power and on the spectral mask imposed by the radio spectrum regulatory bodies; and 2) the competitive maximization of the transmission rate, using finite order constellations, under the same constraints as above, plus a constraint on the average error probability. In Part I of the paper, we start by showing that the solution set of both noncooperative games is always nonempty and contains only pure strategies. Then, we prove that the optimal precoding/multiplexing scheme for both games leads to a channel diagonalizing structure, so that both matrix-valued problems can be recast in a simpler unified vector power control game, with no performance penalty. Thus, we study this simpler game and derive sufficient conditions ensuring the uniqueness of the Nash equilibrium. Interestingly, although derived under stronger constraints, incorporating for example spectral mask constraints, our uniqueness conditions have broader validity than previously known conditions. Finally, we assess the goodness of the proposed decentralized strategy by comparing its performance with the performance of a Pareto-optimal centralized scheme. To reach the Nash equilibria of the game, in Part II, we propose alternative distributed algorithms, along with their convergence conditions.Comment: Paper submitted to IEEE Transactions on Signal Processing, September 22, 2005. Revised March 14, 2007. Accepted June 5, 2007. To be published on IEEE Transactions on Signal Processing, 2007. To appear on IEEE Transactions on Signal Processing, 200

Evolutionary and variable step size strategies for multichannel filtered-x affine projection algorithms

This study is focused on the necessity to improve the performance of the affine projection (AP) algorithm for active noise control (ANC) applications. The proposed algorithms are evaluated regarding their steady-state behaviour, their convergence speed and their computational complexity. To this end, different strategies recently applied to the AP for channel identification are proposed for multichannel ANC. These strategies are based either on a variable step size, an evolving projection order, or the combination of both strategies. The developed efficient versions of the AP algorithm use the modified filtered-x structure, which exhibits faster convergence than other filtering schemes. Simulation results show that the proposed approaches exhibit better performance than the conventional AP algorithm and represent a meaningful choice for practical multichannel ANC applications.This work was supported by a grant of the Romanian National Authority for Scientific Research, CNCS-UEFISCDI, project number PN-II-ID-PCE-2011-3-0097, Spanish Ministerio de Ciencia e Innovacion TEC2009-13741 and Generalitat Valenciana PROMETEO 2009/2013.Gonzalez, A.; Albu, F.; Ferrer Contreras, M.; Diego Antón, MD. (2013). Evolutionary and variable step size strategies for multichannel filtered-x affine projection algorithms. IET Signal Processing. 7(6):471-476. https://doi.org/10.1049/iet-spr.2012.0213S47147676Shin, H.-C., Sayed, A. H., & Song, W.-J. (2004). Variable Step-Size NLMS and Affine Projection Algorithms. IEEE Signal Processing Letters, 11(2), 132-135. doi:10.1109/lsp.2003.821722Paleologu, C., Benesty, J., & Ciochina, S. (2008). A Variable Step-Size Affine Projection Algorithm Designed for Acoustic Echo Cancellation. IEEE Transactions on Audio, Speech, and Language Processing, 16(8), 1466-1478. doi:10.1109/tasl.2008.2002980Shin, H.-C., & Sayed, A. H. (2004). Mean-Square Performance of a Family of Affine Projection Algorithms. IEEE Transactions on Signal Processing, 52(1), 90-102. doi:10.1109/tsp.2003.820077Kong, S.-J., Hwang, K.-Y., & Song, W.-J. (2007). An Affine Projection Algorithm With Dynamic Selection of Input Vectors. IEEE Signal Processing Letters, 14(8), 529-532. doi:10.1109/lsp.2007.891325Seong-Eun Kim, Se-Jin Kong, & Woo-Jin Song. (2009). An Affine Projection Algorithm With Evolving Order. IEEE Signal Processing Letters, 16(11), 937-940. doi:10.1109/lsp.2009.2027638Kim, K.-H., Choi, Y.-S., Kim, S.-E., & Song, W.-J. (2011). An Affine Projection Algorithm With Periodically Evolved Update Interval. IEEE Transactions on Circuits and Systems II: Express Briefs, 58(11), 763-767. doi:10.1109/tcsii.2011.2168023Bouchard, M. (2003). Multichannel affine and fast affine projection algorithms for active noise control and acoustic equalization systems. IEEE Transactions on Speech and Audio Processing, 11(1), 54-60. doi:10.1109/tsa.2002.805642Kong, N., Shin, J., & Park, P. (2011). A two-stage affine projection algorithm with mean-square-error-matching step-sizes. Signal Processing, 91(11), 2639-2646. doi:10.1016/j.sigpro.2011.06.003MoonSoo Chang, NamWoong Kong, & PooGyeon Park. (2010). An Affine Projection Algorithm Based on Reuse Time of Input Vectors. IEEE Signal Processing Letters, 17(8), 750-753. doi:10.1109/lsp.2010.2053355Arablouei, R., & Doğançay, K. (2012). Affine projection algorithm with selective projections. Signal Processing, 92(9), 2253-2263. doi:10.1016/j.sigpro.2012.02.018Gonzalez, A., Ferrer, M., de Diego, M., & Piñero, G. (2012). An affine projection algorithm with variable step size and projection order. Digital Signal Processing, 22(4), 586-592. doi:10.1016/j.dsp.2012.03.00

Structure-Based Bayesian Sparse Reconstruction

Sparse signal reconstruction algorithms have attracted research attention due to their wide applications in various fields. In this paper, we present a simple Bayesian approach that utilizes the sparsity constraint and a priori statistical information (Gaussian or otherwise) to obtain near optimal estimates. In addition, we make use of the rich structure of the sensing matrix encountered in many signal processing applications to develop a fast sparse recovery algorithm. The computational complexity of the proposed algorithm is relatively low compared with the widely used convex relaxation methods as well as greedy matching pursuit techniques, especially at a low sparsity rate.Comment: 29 pages, 15 figures, accepted in IEEE Transactions on Signal Processing (July 2012

Optimal scaling of the ADMM algorithm for distributed quadratic programming

This paper presents optimal scaling of the alternating directions method of multipliers (ADMM) algorithm for a class of distributed quadratic programming problems. The scaling corresponds to the ADMM step-size and relaxation parameter, as well as the edge-weights of the underlying communication graph. We optimize these parameters to yield the smallest convergence factor of the algorithm. Explicit expressions are derived for the step-size and relaxation parameter, as well as for the corresponding convergence factor. Numerical simulations justify our results and highlight the benefits of optimally scaling the ADMM algorithm.Comment: Submitted to the IEEE Transactions on Signal Processing. Prior work was presented at the 52nd IEEE Conference on Decision and Control, 201

Hyperspectral Super-Resolution with Coupled Tucker Approximation: Recoverability and SVD-based algorithms

We propose a novel approach for hyperspectral super-resolution, that is based on low-rank tensor approximation for a coupled low-rank multilinear (Tucker) model. We show that the correct recovery holds for a wide range of multilinear ranks. For coupled tensor approximation, we propose two SVD-based algorithms that are simple and fast, but with a performance comparable to the state-of-the-art methods. The approach is applicable to the case of unknown spatial degradation and to the pansharpening problem.Comment: IEEE Transactions on Signal Processing, Institute of Electrical and Electronics Engineers, in Pres

Sampling of graph signals via randomized local aggregations

Sampling of signals defined over the nodes of a graph is one of the crucial problems in graph signal processing. While in classical signal processing sampling is a well defined operation, when we consider a graph signal many new challenges arise and defining an efficient sampling strategy is not straightforward. Recently, several works have addressed this problem. The most common techniques select a subset of nodes to reconstruct the entire signal. However, such methods often require the knowledge of the signal support and the computation of the sparsity basis before sampling. Instead, in this paper we propose a new approach to this issue. We introduce a novel technique that combines localized sampling with compressed sensing. We first choose a subset of nodes and then, for each node of the subset, we compute random linear combinations of signal coefficients localized at the node itself and its neighborhood. The proposed method provides theoretical guarantees in terms of reconstruction and stability to noise for any graph and any orthonormal basis, even when the support is not known.Comment: IEEE Transactions on Signal and Information Processing over Networks, 201

A New Surrogating Algorithm by the Complex Graph Fourier Transform (CGFT)

[EN] The essential step of surrogating algorithms is phase randomizing the Fourier transform while preserving the original spectrum amplitude before computing the inverse Fourier transform. In this paper, we propose a new method which considers the graph Fourier transform. In this manner, much more flexibility is gained to define properties of the original graph signal which are to be preserved in the surrogates. The complex case is considered to allow unconstrained phase randomization in the transformed domain, hence we define a Hermitian Laplacian matrix that models the graph topology, whose eigenvectors form the basis of a complex graph Fourier transform. We have shown that the Hermitian Laplacian matrix may have negative eigenvalues. We also show in the paper that preserving the graph spectrum amplitude implies several invariances that can be controlled by the selected Hermitian Laplacian matrix. The interest of surrogating graph signals has been illustrated in the context of scarcity of instances in classifier training.This research was funded by the Spanish Administration and the European Union under grant TEC2017-84743-P.Belda, J.; Vergara Domínguez, L.; Safont Armero, G.; Salazar Afanador, A.; Parcheta, Z. (2019). A New Surrogating Algorithm by the Complex Graph Fourier Transform (CGFT). Entropy. 21(8):1-18. https://doi.org/10.3390/e21080759S118218Schreiber, T., & Schmitz, A. (2000). Surrogate time series. Physica D: Nonlinear Phenomena, 142(3-4), 346-382. doi:10.1016/s0167-2789(00)00043-9Miralles, R., Vergara, L., Salazar, A., & Igual, J. (2008). Blind detection of nonlinearities in multiple-echo ultrasonic signals. IEEE Transactions on Ultrasonics, Ferroelectrics and Frequency Control, 55(3), 637-647. doi:10.1109/tuffc.2008.688Mandic, D. ., Chen, M., Gautama, T., Van Hulle, M. ., & Constantinides, A. (2008). 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Higher-order spectral analysis of stray flux signals for faults detection in induction motors

[EN] This work is a review of current trends in the stray flux signal processing techniques applied to the diagnosis of electrical machines. Initially, a review of the most commonly used standard methods is performed in the diagnosis of failures in induction machines and using stray flux; and then specifically it is treated and performed the algorithms based on statistical analysis using cumulants and polyspectra. In addition, the theoretical foundations of the analyzed algorithms and examples applications are shown from the practical point of view where the benefits that processing can have using HOSA and its relationship with stray flux signal analysis, are illustrated.This work has been supported by Generalitat Valenciana, Conselleria d'Educació, Cultura i Esport in the framework of the "Programa para la promoción de la investigación científica, el desarrollo tecnológico y la innovación en la Comunitat Valenciana", Subvenciones para grupos de investigación consolidables (ref: AICO/2019/224). J. Alberto Conejero is also partially supported by MEC Project MTM2016-75963-P.Iglesias Martínez, ME.; Antonino Daviu, JA.; Fernández De Córdoba, P.; Conejero, JA. (2020). Higher-order spectral analysis of stray flux signals for faults detection in induction motors. Applied Mathematics and Nonlinear Sciences. 5(2):1-14. https://doi.org/10.2478/amns.2020.1.00032S11452H. Akçay and E. Germen. 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