Group-Lasso on splines for spectrum cartography

Juan Andrés Bazerque, Gonzalo Mateos, Georgios B. Giannakis

Research output: Contribution to journalArticlepeer-review

111 Scopus citations

Abstract

The unceasing demand for continuous situational awareness calls for innovative and large-scale signal processing algorithms, complemented by collaborative and adaptive sensing platforms to accomplish the objectives of layered sensing and control. Towards this goal, the present paper develops a spline-based approach to field estimation, which relies on a basis expansion model of the field of interest. The model entails known bases, weighted by generic functions estimated from the field's noisy samples. A novel field estimator is developed based on a regularized variational least-squares (LS) criterion that yields finite-dimensional (function) estimates spanned by thin-plate splines. Robustness considerations motivate well the adoption of an overcomplete set of (possibly overlapping) basis functions, while a sparsifying regularizer augmenting the LS cost endows the estimator with the ability to select a few of these bases that better explain the data. This parsimonious field representation becomes possible, because the sparsity-aware spline-based method of this paper induces a group-Lasso estimator for the coefficients of the thin-plate spline expansions per basis. A distributed algorithm is also developed to obtain the group-Lasso estimator using a network of wireless sensors, or, using multiple processors to balance the load of a single computational unit. The novel spline-based approach is motivated by a spectrum cartography application, in which a set of sensing cognitive radios collaborate to estimate the distribution of RF power in space and frequency. Computer simulations and tests on real data corroborate that the estimated power spectrum density atlas yields the desired RF state awareness, since the maps reveal spatial locations where idle frequency bands can be reused for transmission, even when fading and shadowing effects are pronounced.

Original languageEnglish (US)
Article number5934611
Pages (from-to)4648-4663
Number of pages16
JournalIEEE Transactions on Signal Processing
Volume59
Issue number10
DOIs
StatePublished - Oct 2011

Bibliographical note

Funding Information:
Manuscript received October 08, 2010; revised March 21, 2011 and June 11, 2011; accepted June 16, 2011. Date of publication June 27, 2011; date of current version September 14, 2011. The associate editor coordinating the review of this manuscript and approving it for publication was Prof. Patrick Flandrin. Work in this paper was supported by the NSF grants CCF-0830480 and ECCS-0824007; and by QNRF-NPRP award 09-341-2-128. This paper appeared in part in the Proceedings of the 43rd Asilomar Conference on Signals, Systems, and Computers, Pacific Grove, CA, November 1–4, 2009.

Keywords

  • (group-) Lasso
  • Cognitive radio sensing
  • field estimation
  • optimization
  • sparsity
  • splines

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