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This paper presents a novel approach for cooperative spectrum sensing and mapping using nonparametric basis pursuit methods. By employing a Basis Expansion Model (BEM), we aim to generate a spatial map of the power spectrum density (PSD) that allows for the identification of idle bands for reuse and enhances handoff operations in cognitive radio networks. The proposed method utilizes cooperation among sensors to improve performance through spatial interpolation and sparsity-aware PSD estimation. The resulting estimates from real RF data offer insights into spectrum utilization and primary user activity localization.
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Basis Pursuit for Spectrum Cartography Juan A. Bazerque, Gonzalo Mateos, and Georgios B. Giannakis ECE Department, University of Minnesota Acknowledgments: NSF grants no. CCF-0830480, 1016605 EECS-0824007, 1002180 May 25, 2011
Goal: find s.t. is the spectrum at position Cooperative spectrum sensing • Idea: collaborate to form a spatial map of the spectrum • Cooperation improves performance, e.g., [Quan et al’08] • Approach: • Basis expansion model (BEM) for • Nonparametric basis pursuit
Power spectrum density (PSD) maps envisioned for: • Identification of idle bands reuse and handoff operation • Localization and tracking of primary user (PU) activity • Cross-layer design of CR networks Motivation & prior art • Approaches to spectrum cartography • Spatial interpolation via Kriging [Alaya-Feki et al’08][Kim et al’09] • Sparsity-aware PSD estimation [Bazerque-Giannakis‘08] • Decentralized signal subspace projections [Barbarossa et al’09] • Basis pursuit [Chen et al’98], LASSO [Tibshirani’94] • Scalar vs. functional coefficient selection in overcomplete BEM • Specific models: COSSO [Lin-Zhang’06], SpAM [Ravikumar’09]
PSD of Tx source is Basis expansion in frequency • Basis functions • Accommodate prior knowledge raised-cosine • Sharp transitions (regulatory masks) rectangular, non-overlapping • Overcomplete basis set (large ) robustness Frequency basis expansion
Spatial loss function Unknown • Per sub-band factorization in space and frequency (indep. of ) • Goal: estimate PSD atlas as Spatial PSD model • BEM:
Available data: location of CRsmeasured frequencies (I) Observations • Nonparametric basis selection ( not selected) Nonparametric basis pursuit • Twofold regularization of variational LS estimator • Avoid overfitting by promoting smoothness
Q1: How to estimate based on ? Thin-plate splines solution Proposition 1: Estimates in (I) are thin-plate splines [Duchon’77] where is the radial basis function , and • Unique, closed-form, finitely-parameterized minimizers! • Q2: How does (I) perform basis selection?
Matrices ( and dependent) i) ii) iii) Proposition 2: Minimizers of (I) are fully determined by w/ as • Remark: group Lasso encourages sparse factors • Full-rank mapping: Lassoing bases • (I) equivalent to group Lasso estimator [Yuan-Lin’06]
Simulated test • sensing CRs, sampling frequencies • sources; raised cosine pulses • bases; (roll off x center frequency x bandwidth) frequency (Mhz) basis index Original Estimated S P E C T R U M M A P
Real RF data CRs -60 -50 -40 -20 (dBi) -30 -10 1 2 3 • IEEE 802.11 WLAN activity sensed 4 5 6 7 8 9 10 11 12 13 14 • Maps recovered and extrapolated Frequency bases identified 10
PSD estimation as regularized nonparametric regression • Thin-plate regularization effects smoothness • Bi-dimensional splines arise in the solution • Sparsity-encouraging penalty basis selection via group Lasso Concluding Summary • Cooperative PSD map estimation • Fundamental task in cognitive radio networks • (Overcomplete) BEM for the power map in frequency/space • Computer simulations and real RF data for testing • PSD atlas reveal (un-)occupied bands across space • Source localization and identification of Tx parameters
