{"id":79,"date":"2015-08-17T22:34:52","date_gmt":"2015-08-17T22:34:52","guid":{"rendered":"http:\/\/grupo.us.es\/gapsc\/?page_id=79"},"modified":"2019-10-29T07:38:55","modified_gmt":"2019-10-29T07:38:55","slug":"gaussian-processes-in-digital-communications","status":"publish","type":"page","link":"https:\/\/grupo.us.es\/gapsc\/gaussian-processes-in-digital-communications\/","title":{"rendered":"Gaussian Processes and Kernel Methods"},"content":{"rendered":"

Overview<\/h2>\n

Gaussian processes are non-parametric kernel based Bayesian tools to perform inference. Non-parametric kernel solutions are based on providing a new solution for some new input by using the set of training data. This set is included in the so-called kernel matrix.<\/p>\n

Gaussian processes for regression (GPR) are useful tool to perform prediction or even detection. It exhibits three\u00a0major advantages. First, the formulation is analytic and so it is its solution. This solution can be cast as a “non-linear” version of the linear minimum mean square error (MMSE) estimator with extra regularization term. Second, the hyper-parameter learning can be performed in a principled way, rather than using cross-validation. Third, it does not only provides a predicted or estimated value, but a probabilistic information on it. Its counterpart for classification, GP for classification (GPC), exhibits the same features but that of being analytic.<\/p>\n

Since MMSE has been a quite extended tool in digital communications, we forecasted that GPR and GPC\u00a0would be\u00a0useful there were the linear MMSE failed. Both, in the inversion of linear and non-linear systems. We proved its good features in the multiuser detection and channel equalization. Furthermore, we exploited its output being probabilistic to feed them to modern channel decoders, quite improving the overall performance.<\/p>\n

In some other applications we found it a competitive tool. As in the prediction of tax incomes in Brazil, where we collaborated with the University of Brazilia.<\/p>\n

Lately, and given the interest to develop non-parametric tools for complex-valued signals, we are working on the formulation of GPR for both, proper and non-proper complex signals. With application, among others, to channel equalization.<\/p>\n

Involved Members<\/h2>\n

Juan J. Murillo-Fuentes,\u00a0Fernando P\u00e9rez-Cruz, Rafael Boloix-Tortosa, Pablo M. Olmos, Javier Pay\u00e1n-Somet, Eva Arias de Reyna.<\/p>\n

Publications<\/h2>\n

Journals<\/h3>\n
    \n
  1. R. Boloix-Tortosa, J.J. Murillo-Fuentes S.A. Tsaftaris. (2019). “The Generalized Complex Kernel Least-Mean-Square Algorithm” IEEE Transactions on Signal Processing<\/em>, Vol. 67, no. 20, pp. 5213 – 5222. Oct.15, 2019. DOI 10.1109\/TSP.2019.2937289<\/a>, https:\/\/arxiv.org\/abs\/1902.08692<\/a><\/li>\n
  2. Santos, J.J. Murillo-Fuentes, P. M. Djuric. (2019). Recursive Estimation of Dynamic RSS Fields Based on Crowdsourcing and Gaussian Processes. IEEE Transactions on Signal Processing.<\/em> 2019. EEE (2017) Q1, 32\/260. DOI 10.1109\/TSP.2018.2889987<\/a>, https:\/\/arxiv.org\/abs\/1806.02530<\/a>.<\/li>\n
  3. R. Boloix-Tortosa, J. J. Murillo-Fuentes, F. J. Pay\u00e1n-Somet and F. P\u00e9rez-Cruz, “Complex Gaussian Processes for Regression,” in\u00a0<\/span>IEEE Transactions on Neural Networks and Learning Systems<\/em>, vol. 29, no. 11, pp. 5499-5511, Nov. 2018.\u00a0DOI:\u00a0<\/span>10.1109\/TNNLS.2018.2805019<\/a> https:\/\/arxiv.org\/abs\/1511.05710<\/a><\/li>\n
  4. R. Boloix-Tortosa, J. J. Murillo-Fuentes, I. Santos and F. P\u00e9rez-Cruz, (2017) “Widely Linear Complex-Valued Kernel Methods for Regression,” in IEEE Transactions on Signal Processing<\/em>, vol. 65, no. 19, pp. 5240-5248, Oct.1, 1 2017. Paper<\/a>, also in IEEE TSP<\/a>,\u00a0arxiv.org<\/a><\/li>\n
  5. F. P\u00e9rez-Cruz, S. Van Vaerenbergh, J. J. Murillo-Fuentes, M. L\u00e1zaro-Gredilla and I. Santamar\u00eda.\u00a0”Gaussian Processes for Nonlinear Signal Processing”<\/a>. IEEE Signal Processing Magazine<\/i>. Vol.30, no.4. 2013.<\/li>\n
  6. P. M. Olmos, J. J. Murillo-Fuentes and F. P\u00e9rez-Cruz, (2010). ”Joint Nonlinear Channel Equalization and Soft LDPC Decoding with\u00a0Gaussian Processes”<\/a>. IEEE Transactions on Signal Processing<\/i>, Vol. 58, N. 3, pp. 1183 – 1192, March 2010.<\/li>\n
  7. J. J. Murillo-Fuentes and F. P\u00e9rez-Cruz, (2009). ”Gaussian Process Regressors for Multiuser Detection in DS-CDMA\u00a0Systems”. <\/a>IEEE Transactions on Communications<\/i>,
    \n57(8):2339-2347, August 2009.<\/li>\n
  8. F. P\u00e9rez-Cruz, J. J. Murillo-Fuentes and S. Caro, (2008). ”Nonlinear Channel Equalization with Gaussian Processes for\u00a0Regression”<\/a>. IEEE Transactions on Signal Processing<\/i>, 56(10-2):5283-5286, October 2008.<\/li>\n
  9. F. P\u00e9rez-Cruz and J. J. Murillo-Fuentes, (2008). ”Digital Communication Receivers Using Gaussian Processes for\u00a0Machine Learning”. Journal on Advances in Signal Processing<\/i>. Vol 2008. doi:10.1155\/2008\/491503.<\/li>\n<\/ol>\n

    Book Chapters<\/h3>\n