basis pursuit for spectrum cartography
DESCRIPTION
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. - PowerPoint PPT PresentationTRANSCRIPT
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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
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Cooperative spectrum sensing Cooperation improves performance, e.g., [Quan et al’08]
Goal: find s.t. is the spectrum at position
Approach: Basis expansion model (BEM) for
Nonparametric basis pursuit
Idea: collaborate to form a spatial map of the spectrum
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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]
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
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]
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Frequency basis expansion 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
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Spatial PSD model Spatial loss function Unknown
Per sub-band factorization in space and frequency (indep. of )
BEM:
Goal: estimate PSD atlas as
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Twofold regularization of variational LS estimator
(I)
Nonparametric basis pursuit Available data:
location of CRs
measured frequencies
Observations
Avoid overfitting by promoting smoothness
Nonparametric basis selection ( not selected)
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Thin-plate splines solution
Unique, closed-form, finitely-parameterized minimizers!
Proposition 1: Estimates in (I) are thin-plate splines [Duchon’77]
where is the radial basis function , and
Q2: How does (I) perform basis selection?
Q1: How to estimate based on ?
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Lassoing bases (I) equivalent to group Lasso estimator [Yuan-Lin’06]
Matrices ( and dependent)
i) ii) iii)
Remark: group Lasso encourages sparse factors Full-rank mapping:
Proposition 2:
as
w/
Minimizers of (I) are fully determined by
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Simulated test
SPECTRUM MAP
basis index frequency (Mhz)
sources; raised cosine pulses sensing CRs, sampling frequencies bases; (roll off x center frequency x bandwidth)
Original Estimated
1010
Real RF data
Frequency bases identified Maps recovered and extrapolated
IEEE 802.11 WLAN activity sensed
CRs
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-50-60 -40 -30 -20 -10 (dBi)
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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
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