A Stackelberg Game for Cooperative Transmission and Random Access in Cognitive Radio Networks Xiaolei Hao, Man Hon Cheung, Vincent W.S. Wong, and Victor C.M. Leung Department of Electrical and Computer Engineering The University of British Columbia, Vancouver, Canada e-mail: {xiaoleih, mhcheung, vincentw, vleung}@ece.ubc.ca Abstract— In cognitive radio networks, the secondary users (SUs) can be selected as the cooperative relays to assist the transmission of the primary user (PU). In order to increase the utility, the PU needs to consider whether it is beneficial to use cooperative transmission and which SU should be chosen as the cooperative relay. In addition, if the PU selects a secondary relay, it needs to allocate time resources for cooperative transmission. Then, the SUs need to determine their strategies of random access when the licensed spectrum of the PU is available. In this paper, we first establish a model for cooperative cognitive radio networks with one PU and multiple SUs. We then propose a cooperative transmission and random access (CTRA) scheme. Based on the sequential structure of the decision-making, we study the cooperative cognitive radio network and determine the equilibrium strategies for both the PU and the SUs using the Stackelberg game. Simulation results show that both the PU and the SUs obtain higher utilities when compared with the noncooperative transmission and random access (NTRA) scheme. I. I NTRODUCTION Spectrum resources are scarce and the demand for the radio spectrum has been increasing in recent years. According to the report released by the Federal Communications Commission [1], fixed spectrum allocation may not always be efficient and the licensed spectrum may remain unoccupied for a long pe- riod of time. This motivates the concept of cognitive radio [2], which allows the secondary users (SUs) to dynamically access the licensed spectrum allocated to the primary users (PUs) when the licensed spectrum is not being utilized temporarily. Therefore, the efficiency of spectrum usage can be increased. Motivated by the physical layer cooperative communication technique [3], cooperative cognitive radio networks are new cognitive radio paradigm. In [4], Jia et al. exploited a new research direction for cognitive radio networks by utilizing cooperative relay to assist the transmission and improve spec- trum efficiency. In [5], the system enables cooperation between a primary cluster and a cognitive cluster in order to maintain the target primary throughput and provide more transmission opportunities to the SUs. In [6], Simeone et al. proposed and analyzed a framework, where a PU can lease its spectrum to an ad hoc network of secondary nodes in exchange for cooperation in the form of distributed space-time coding. The framework is modeled as a Stackelberg game [7]. In [8], Zhang et al. proposed a coopera- tive cognitive radio framework. Both the PU and the SUs target at maximizing their utilities in terms of their transmission rate and revenue. This model is formulated as a Stackelberg game and a unique Nash equilibrium is characterized. In [9]. Yi et al. considered multiple PUs and SUs in the system model, and analyzed the optimal strategies on the relay selection and the price for spectrum leasing by a Stackelberg game. In [10], Kasbekar et al. formulated the price competition in a cognitive radio network as a game by taking into account both bandwidth uncertainty and spatial reuse. Niyato et al. studied the problem of spectrum trading with multiple PUs selling spectrum opportunities to multiple SUs in [11]. They modeled the dynamic behavior of the SUs using the theory of evolutionary game [12]. An algorithm of the evolution process implementation for the SUs was proposed. In general, when the licensed spectrum is idle, all the SUs should have the opportunities to access the spectrum. The system models in [6], [8], [9] assumed the SUs access the licensed spectrum in a time division multiple access (TDMA) mode. Moreover, the system model in [10] assumed the PU who has unused bandwidth in a time slot can lease it to a SU for the duration of the whole slot. Therefore, the results of [6], [8]–[10] cannot be extended to the situation where the SUs can access the licensed spectrum in a random access manner. In this paper, we consider both cooperative transmission and random access in cognitive radio networks. The problem is to find the optimal strategies for both the PU and the SUs in order to maximize their own utilities. The PU needs to determine whether it is beneficial to use cooperative transmission and which SU should be chosen as the cooperative relay. If the PU selects a secondary relay, it also needs to determine its strategy on time resource allocation for cooperative transmission. The SUs need to decide the transmission probability in random access. In this paper, we establish a model for cooperative cognitive radio networks and analyze the behaviour of the PU and the SUs using game theory. The contributions of our work are summarized as follows: • We propose a cooperative transmission and random ac- cess (CTRA) scheme for cognitive radio networks. The PU is responsible for relay selection and resource allo- cation. The SUs serve as relays and transmit their own data using random access. • We propose a game-theoretic model to study the pro- posed cooperative cognitive radio system. We describe the strategies available for both the PU and the SUs. In order to maximize their own utilities, we analyze the