How often and how long should a cognitive radio sense the spectrum? Nader Moayeri and Hui Guo National Institute of Standards and Technology Gaithersburg, MD 20899-8920, USA Email: {moayeri,hguo}@nist.gov Abstract—This paper presents a Bayesian framework and a disasters or when national security is at risk, these concerns pricing structure for a secondary wireless user that opportunis- are trumped by more important priorities and opportunistic use N tically uses a RF channel licensed to a network of primary of any spectrum is justified. However, in the absence of such users. The secondary user operates in a time-slotted fashion, where each time slot consists of observing the channel for D conditions, there has to be a balance between empowering seconds followed by possibly using it for W seconds depending unlicensed users to use an underutilized RF band and not on the decision the user makes after observing the channel. The noticeably degrading the radio communications of the licensed paper assumes the secondary user observes the on-off Markov users. In fact, this is by far the most major obstacle to viability process modeling the primary user activity corrupted by additive of OSA and deployment of CRNs. white Gaussian noise, and it employs a decision rule that is a time- averager followed by a threshold device. The pricing structure There has been some work on developing techniques for includes rewards for the secondary user when it uses the channel unlicensed, henceforth called secondary, users to characterize, without interfering with the primary users and penalties when quantify, and manage interference to the licensed, henceforth it does so and it interferes. The paper derives a formula for the called primary, users when a secondary user (SU) decides average per unit time net profit of the secondary user. Numerical to opportunistically use the licensed spectrum. This problem results are presented that show the behavior of the maximum profit of the secondary user, its throughput, and the resulting is trivial in certain scenarios. For example, a SU could in level of interference to the primary users as functions of various principle use the spectrum allocated for television broadcasting network parameters. when TV is off air, because TV broadcast schedules in a given geographic region are well known and widely advertised. I. INTRODUCTION This is an example of spatial OSA. Although technically more The volume of wireless communications has dramatically challenging, a SU might be allowed to transmit over the TV increased over the past two decades and this trend is ex- bands even when TV broadcasting is on, and this is the subject pected to continue with new and increasingly bandwidth- of a recent FCC ruling on the use of the so-called “white hungry mobile applications and services introduced every day. spaces” by unlicensed users [6]. The problem would then Wireless service providers typically argue that they need more be that of detecting the presence of TV sets (receivers) in radio frequency (RF) spectrum and lobby spectrum regulatory the vicinity of a prospective secondary transmitter. An early agencies to release more spectrum so that they can cope with work on this topic [7] uses the RF energy leaked from TV rising data traffic demands. On the other hand, there is ample local oscillators to detect their presence. Temporal OSA is evidence [1] that suggests that much of the licensed spectrum the other type of OSA that arises when SUs try to exploit is underutilized. Of course, the degree of underutilization a licensed spectrum during very short periods of time when varies greatly depending on the frequency band, location, primary users (PUs) are not using the spectrum. This problem and time, but it appears that at most locations at any given is in general quite challenging, because there is usually no time opportunities exist to use some underutilized frequency coordination between PUs and SUs. At best, the latter have bands. These observations and the increasing importance of a statistical characterization of the primary system traffic. software-defined radios led Mitola and Maguire [2] to propose Hidden and exposed terminal problems, shadowing, fading, the concept of a cognitive radio network (CRN) in 1999. A and other types of RF propagation effects [8] are some of number of survey papers on the subject have been published the problems that have to be dealt with. Yet, a number since then ([3], [4], [5]) that cover the progress made in this of researchers have worked on this problem under various field as well as open problems and challenges. settings. [9] classifies classic detection problems that could be The license holders of any frequency band that might be used for spectrum sensing into three categories: matched filter, regarded as a good candidate for opportunistic spectrum access energy detector, and feature detector. One example of spectrum (OSA) are understandably concerned that any opportunistic sensing using feature detection is [10]. A more promising use of their spectrum would lead to a degradation of their approach is collaborative / cooperative spectrum sensing where radio communications or wireless services they provide over all users in a secondary network sense the licensed spectrum that band. Perhaps in certain circumstances, e.g. emergency and arrive at a more reliable picture of spectrum occupancy response in the aftermath of large-scale natural or man-made through use of centralized or preferably distributed detection algorithms [11], [12]. Naturally, these techniques require more solution consists of choosing in the first step a spectrum resources and have a higher overhead. sensor (operating point on ROC curves for various channel Of more relevance to our work are papers that consider not sensors) and an access strategy (probabilities of use for various just the spectrum sensing aspect but also the benefit to the channels depending on sensing operation recommendations) SU as a result of using the spectrum. Some work has been to maximize the instantaneous SU throughput subject to a done on pricing, economic models, and applications of game collision constraint (limit on interference caused to the PUs) theory to CRNs. For example, [13] proposes a game-theoretic and in the second step a sensing strategy (which channels to model for analyzing the behavior and dynamics of a CRN. sense) to maximize the overall throughput. It turns out that a [14] uses game theory to analyze a scenario where multiple general separation principle does not exist in the case where primary service providers compete with each other to offer the secondary user is allowed to sense multiple channels in spectrum opportunities to SUs with the goal of maximizing each time slot. As an example, the paper considers a case their profits subject to constraints on the quality of service where the PU signal is assumed to be a white Gaussian (QoS) they provide to their own PUs. [15] is an application noise process that is corrupted by an additive white Gaussian of stochastic control theory to the MAC layer protocol design noise (AWGN) process, in which case an energy detector for CRNs. Specifically, the paper considers N data channels, is optimal under the NP criterion. In a departure from the which both the PUs and SUs use in a time-slotted fashion. At time-slotted operation assumption for the PUs, [19] consid- the beginning of certain time slots, a SU selects one channel ers a continuous-time Markov chain (CTMC) model for PU to sense and it transmits over that channel for L time slots activity. Specifically, the PU occupancy of the i’th channel, if it finds it idle. The SU gets a reward of L units if the i =0, 1, ···,N − 1, is modeled by a homogeneous CTMC transmissions are successful and a reward of −αL if any of the with exponential sojourn times with parameters λ i and μi transmissions fail due to a collision with the PUs. The paper for the idle and busy states, respectively. The SU senses a designs a channel selection policy for the SUs by taking a single channel at the beginning of each time slot and decides stochastic control approach and maximizing a discounted sum if and over which channel, again not necessarily the one that of expected rewards over an infinite horizon. was sensed, to transmit. This leads to a constrained Markov Along similar lines, Markov decision theory has been used decision process (CMDP) problem in which the SU average to optimize the SU spectrum sensing operation under the a throughput over an infinite horizon is maximized subject to periodic sensing assumption. Specifically, it is assumed that a an upper bound on the average interference caused for the SU senses one or more licensed channels at the beginning of PUs. The paper solves for the optimal policy via a linear a time slot and then may decide to use one of the licensed program. Finally, [20] extends the results of [18] to the case channels, not necessarily one of those that were sensed. The of an unslotted primary system under certain conditions on the goal of the SU is to maximize its own throughput subject to false alarm probability of the spectrum sensor. limits on interference caused to the PUs. The papers described There are some other papers on OSA with periodic sensing below assume error-free spectrum sensing and/or sensing and that are relevant to our paper. [21] considers a CTMC model PU activity detection schemes that could suffer from errors. for PU activity. In each cycle, an SU monitors the channel Whenever the latter is considered, the papers start from the for Tmonitor seconds and uses an energy detector to decide assumption that the receiver operating curve (ROC) for the whether there is PU activity on the channel sensed.