IEEE COMMUNICATIONS LETTERS, VOL. 15, NO. 1, JANUARY 2011 19 Gradient-Based Threshold Adaptation for Energy Detector in Cognitive Radio Systems Deepak R. Joshi, Student Member, IEEE, Dimitrie C. Popescu, Senior Member, IEEE, and Octavia A. Dobre, Senior Member, IEEE Abstract—Cognitive Radio (CR) systems have been proposed to enable flexible use of the frequency spectrum in future generations of wireless networks. These are expected to detect spectrum bands that are not actively used by licensed (primary) users and provide unlicensed (secondary) users access to these bands. In this context it is important for the CR systems to promptly react to changes in the operating environment and to adapt to the changing patterns of spectrum use. This motivates the work presented in this paper, which studies adaptation of the detection threshold for energy-based spectrum sensing in dynamic scenarios under constraints imposed on the probabilities of missed detection and false alarm. Index Terms—Cognitive radio, energy detector, threshold adaptation. I. I NTRODUCTION C OGNITIVE radio represents an emerging technology designed to enable dynamic access to the frequency spectrum under the condition that no harmful interference be caused to the incumbent licensed users of the spectrum [1]. CR systems are expected to enable reuse of licensed frequencies through efficient and reliable sensing of the electromagnetic environment, which includes estimation of the spectrum used by licensed radio systems that operate as Primary Users (PU). Various methods have been proposed for spectrum sensing in CR systems, which include the multitaper method [2], the use of pilot signals and matched filtering [3], cyclostationarity- based methods [4]–[6], and the use of polyphase filter banks [7]. These methods have been developed and investigated in static scenarios, where the spectrum usage and background noise statistics do not vary in time. However, in practical sys- tems, spectrum usage changes in time as the number of active transmissions and/or their corresponding parameters change, while the background noise varies due to temperature changes, ambient interference, etc. This motivates the work presented in this letter, which studies energy-based spectrum sensing in dynamic scenarios and proposes a gradient-based algorithm for sensing threshold adaptation. We note that energy detection is a suitable spectrum sensing technique when the CR has no knowledge on the active PU signals [8] and its applicability will be enhanced when an adaptive sensing threshold that changes in dynamic scenarios is employed. The rest of the paper is organized as follows: in Section II we introduce the system model and formally state the problem. Manuscript received April 20, 2010. The associate editor coordinating the review of this letter and approving it for publication was R. Nabar. D. R. Joshi and D. C. Popescu are with the Department of Electrical and Computer Engineering, Old Dominion University, 231 Kaufman Hall, Norfolk, VA 23529 (e-mail: {djosh002, dpopescu}@odu.edu). O. A. Dobre is with the Faculty of Engineering and Applied Science, Memorial University of Newfoundland, 300 Prince Phillip Dr., St. John’s, NL, A1B 3X5, Canada (e-mail: odobre@mun.ca). Digital Object Identifier 10.1109/LCOMM.2010.11.100654 | | 2 Average samples M x(n) Y H \ H 0 1 RF front end x(t) ADC CR front end Threshold y(n) Adaptation Threshold Fig. 1. Block diagram of energy detector system for spectrum sensing. In Section III we discuss how the variance of the PU signal and of the background noise are estimated from the noisy signal received by the CR. In Section IV we present a gradient-based sensing threshold adaptation procedure and we formally state the proposed algorithm, which is illustrated with numerical results obtained from simulations in Section V. We present final remarks and conclusions in Section VI. II. SYSTEM MODEL AND PROBLEM STATEMENT We consider spectrum sensing using the energy detec- tor, which is described schematically in Fig. 1 [3]. After performing the front end processing along with the analog to digital conversion (ADC), the received signal is expressed as ()= ()+ (), (1) with () being the active radio signal at the location of the CR system, and () the additive white Gaussian noise (AWGN) corrupting the active signal with zero mean and variance 2 . Under the assumption of non-coherent detection, the samples of the active radio signal () may also be modeled as a Gaussian random process with variance 2 [3]. We note that both 2 and 2 are estimated from the received signal (), as it will be described in Section III. The decision statistic for the energy detector is expressed as the time average [3], [8] ()= ∑ =− ∣ () ∣ 2 . (2) This provides information on the active signal spectrum at time instant and can be used for detecting the presence of active PU in the tested spectrum band. A binary hypothesis testing is performed to identify the presence of active PU: at a given time instant the frequency band is considered to be vacant if only noise is detected, while the band is considered to be occupied by an active PU if a PU signal and noise are detected. Thus, the following binary hypothesis testing is performed at time instant to determine whether the frequency band is used by an active PU [3], [8] ℋ 0 : ()= () ℋ 1 : ()= ()+ (), (3) 1089-7798/11$25.00 c ⃝ 2011 IEEE