IEEE TRANSACTIONS ON SIGNAL PROCESSING, VOL. 58, NO. 3, MARCH 2010 1847 Distributed Spectrum Sensing for Cognitive Radio Networks by Exploiting Sparsity Juan Andrés Bazerque, Student Member, IEEE, and Georgios B. Giannakis, Fellow, IEEE Abstract—A cooperative approach to the sensing task of wire- less cognitive radio (CR) networks is introduced based on a basis expansion model of the power spectral density (PSD) map in space and frequency. Joint estimation of the model parameters enables identification of the (un)used frequency bands at arbitrary loca- tions, and thus facilitates spatial frequency reuse. The novel scheme capitalizes on two forms of sparsity: the first one introduced by the narrow-band nature of transmit-PSDs relative to the broad swaths of usable spectrum; and the second one emerging from sparsely lo- cated active radios in the operational space. An estimator of the model coefficients is developed based on the Lasso algorithm to ex- ploit these forms of sparsity and reveal the unknown positions of transmitting CRs. The resultant scheme can be implemented via distributed online iterations, which solve quadratic programs lo- cally (one per radio), and are adaptive to changes in the system. Simulations corroborate that exploiting sparsity in CR sensing re- duces spatial and frequency spectrum leakage by 15 dB relative to least-squares (LS) alternatives. Index Terms—Cognitive radios, compressive sampling, cooper- ative systems, distributed estimation, parallel network processing, sensing, sparse models, spectral analysis. I. INTRODUCTION S PECTRUM sensing is a critical prerequisite in envisioned applications of wireless cognitive radio (CR) networks which promise to resolve the perceived bandwidth scarcity versus under-utilization dilemma. Creating an interference map of the operational region plays an instrumental role in enabling spatial frequency reuse and allowing for dynamic spectrum allocation in a hierarchical access model comprising primary (licensed) and secondary (opportunistic) users [21], [22]. The non-coherent energy detector has been widely used to this end because it is simple and obviates the need for synchroniza- tion with unknown transmitted signals; see e.g., [11], [12], [14], and [17]. Power information (or other statistics [8], [9]) collected locally per CR is fused centrally by an access point Manuscript received January 12, 2009; accepted November 09, 2009. First published December 11, 2009; current version published February 10, 2010. The associate editor coordinating the review of this manuscript and approving it for publication was Prof. Daniel Palomar. Prepared through collaborative participation in the Communications and Networks Consortium sponsored by the U.S. Army Research Laboratory under the Collaborative Technology Alliance Program, Cooperative Agreement DAAD19-01-2-0011. The U.S. Government is authorized to reproduce and distribute reprints for Government purposes notwithstanding any copyright notation thereon. Results from this paper were presented in the Forty-Second Asilomar Conference on Signals, Systems and Computers, Pacific Grove, CA, October 26–29, 2008,. The authors are with the Department of Electrical and Computer Engi- neering, University of Minnesota, Minneapolis, MN 55414 USA (e-mail: bazer002@umn.edu; georgios@umn.edu). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TSP.2009.2038417 in order to decide absence or presence of a primary user per frequency band. At the expense of commensurate communi- cation overhead [12], these cooperative sensing and detection schemes have been shown to increase reliability, reduce the average detection time, cope with fading propagation effects, and improve throughput [9], [11], [14], [17]. Recently, the possibility of spatial reuse has received growing attention. It was noticed that even if a frequency band is occupied, there could be locations where the transmitted power is low enough so that these frequencies can be reused without suffering from or causing harmful interference to the primary system. These opportunities are discussed in [15], and a statistical model for the transmitters’ spatial distribution is advocated in [16]. The present paper goes in the direction of sensing these reusable zones, by means of a collaborative scheme whereby receiving CRs cooperate to estimate the distribution of power in space and frequency as well as localize, as a byproduct, the positions of transmitting CRs. The main contribution is a distributed online approach to estimating a map of the power spectral density (PSD) at arbitrary locations in space. This is particularly useful in wide area ad-hoc networks, where the power transmitted by primary users reaches only a small subset of CRs. Knowing the spectrum at any location allows remote CRs to reuse dynamically idle bands. It also enables secondary users to adapt their transmit-power so as to minimally interfere with primary users. In this context, the threshold for deciding occupancy of a frequency band is not set according to the prob- ability of false alarms, but through comparing PSD estimates with minimum power levels prescribed by the primary users. The goal of estimating the power distribution in space and fre- quency is admittedly very ambitious. The PSD estimate sought however, does not need to be super accurate but precise enough to identify (un)used bands. This relaxed objective motivates the proposed PSD estimator using a parsimonious basis expansion model. The general setup includes receiving CRs willing to cooperate in estimating the location of transmitting ra- dios as well as the frequency bands used for transmission. Upon constructing a basis expansion model of the PSD map , in spatial location and frequency , the novel cooperative scheme amounts to estimating the basis expansion coefficients of based on PSD frequency samples collected at re- ceiving CRs located at positions . These coefficients are in- herently sparse given the narrow-band individual transmissions compared to the overall band scanned, as well as the scarce dis- tribution of active transmitters in the area. Sparsity is then ex- ploited as prior information to improve estimation performance by suitably modifying the least-absolute shrinkage and selection operator (Lasso) in [20]. The novel distributed algorithm termed D-Lasso implements Lasso using an ad-hoc network of nodes. It does not require 1053-587X/$26.00 © 2010 IEEE Authorized licensed use limited to: University of Minnesota. Downloaded on February 8, 2010 at 19:22 from IEEE Xplore. Restrictions apply.