Prediction of Exponentially Distributed Primary User Traffic for Dynamic Spectrum Access Chun-Hao Liu, Wesam Gabran, and Danijela Cabric Department of Electrical Engineering University of California, Los Angeles Email: {liuch37, wgabran, danijela}@ee.ucla.edu Abstract—In order to fully exploit the availability of primary users’ (PUs) unused spectrum by secondary users, traffic predic- tion can be used to increase system throughput. In this paper we propose a PU traffic prediction algorithm based on estimated PU traffic state transition probabilities. The probabilities are obtained via constrained-time PU traffic parameters estimation assuming exponentially distributed PU ON/OFF channel utiliza- tion intervals. Moreover, we define prediction regions for the estimated parameters where optimal traffic prediction is possible. Finally, we theoretically quantify the prediction confidence as a function of the prediction time, the total estimation time period and the number of samples used for estimation. Index Terms—Dynamic spectrum access, traffic estimation, traffic prediction, prediction region, prediction confidence. I. I NTRODUCTION Cognitive radio networks provide a solution for spectrum scarcity by exploiting vacant licensed spectral bands. Sec- ondary (unlicensed) users (SUs) can access the primary (li- censed) channels to increase the spectrum utilization. Mean- while, SUs need to perform spectrum sensing in order to avoid collision with primary users (PUs) [1]–[3]. The PU traffic is a stochastic process where the traffic randomness, together with the imperfections in the spectrum sensing process, may cause collisions between the SUs and PUs and limit the achievable throughput by the SUs. Accordingly, modeling and predicting the PU traffic by the SUs can improve the performance of cognitive radio networks. The most notable work that considers PU traffic prediction can be found in [4]–[7]. In [4], an energy-minimization framework is presented based on predicting the PU traffic. The authors assume perfect prediction in order to reduce both transmission and switching energy. Achievable throughput optimization based on the correlation of different channels has been discussed in [5] with a single SU and multiple PUs in a slotted-transmission mode using spectrum usage prediction. The authors in [6] adopt multi-carrier techniques to flexibly allocate channel resources over a wide bandwidth. The prediction is performed across a number of frequency bands where subcarrier allocation is achieved considering collision minimization. A Markov-based prediction method has been proposed in [7], which is a form of the universal predictor, that allows SUs to sense the channels with most available probability. In the aforementioned work, however, the authors either assume perfect channel prediction or rely on algorithm-based prediction methods that do not fully exploit the PU traffic char- acteristics. Furthermore, theoretical analysis that quantifies the prediction accuracy has not been addressed. In this paper, we propose a prediction algorithm for PUs assuming perfect sensing with exponentially distributed traffic. The contribution of this work is twofold: a) Prediction Algorithm: In [8], we study the accuracy of PU traffic estimation in terms of the mean squared error of the traffic parameter estimates. Here, we propose an algorithm that predicts the PU traffic based on the PU traffic parameter estimates in contrary to prior works that assume perfect knowledge of traffic parameters. b) Analysis of Prediction Confidence: We further define a number of regions which are functions of the PU traffic parameters and for each region we derive conditions re- quired to achieve minimum prediction error rate. Moreover, we quantify the prediction confidence for different regions based on the accuracy of the estimated traffic parameters. The confidence serves as a guideline for determining the required estimation accuracy needed to meet a given prediction error rate constraint. The paper is organized as follows. The system model is presented in Section II. In Section III, we define the predic- tion regions, quantify the prediction error, and analyze the prediction confidence in terms of the parameter estimation error. Section IV shows numerical results comparing different prediction schemes, and discusses the prediction confidence. Finally, Section V concludes this paper. II. SYSTEM MODEL FOR TRAFFIC PREDICTION This section describes the models used for traffic estimation and prediction. We consider a single channel randomly ac- cessed by a single PU, where the traffic of the PU is assumed to be stationary. Moreover, the PU ON/OFF intervals are assumed to be exponentially distributed [9]–[11], where the probability density function of the interval, t, is given by f λ (t)=  λe -λt for t ≥ 0, 0 otherwise, (1) with λ = λ n and λ = λ f for the ON and OFF periods, respectively. As a property of exponential distributions, the means of the ON and OFF intervals equal the reciprocals of λ n and λ f , respectively. The duty cycle u is defined by u = λ f λ f +λ n , indicating the fraction of time with the presence of