We consider a situation where wireless service providers compete for heterogenous wireless users. The users differ in their willingness to pay as well as in their individual channel gains. We prove existence and uniqueness of the Nash equilibrium for the competition of two service providers, for a generic channel model. Interestingly, the competition of two providers leads to a globally optimal outcome. We extend some of the results to the case where more than two providers are competing. Finally, we provide numerical examples that illustrate the effects of various parameters on the Nash equilibrium.
Until recently, the heterogeneity of the users was largely ignored. The first work that explicitly takes into account the channel differences for different users is @cite_10 . To our knowledge, our work is the first one to consider the pricing competition of providers for users who are heterogenous in both willingness to pay and the channel quality for arbitrary channel coefficients. Also, most previous work considered nonatomic users, i.e., each user's influence on the network is small and negligible @cite_2 . This assumption may not be realistic in practice, which motivates us to study the atomic user case that involves resource splitting among networks (see Section for details).
@cite_10 @cite_2
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In this paper, the problem of joint multichannel cooperative sensing and resource allocation is investigated. A cognitive radio network with multiple potential channels and multiple secondary users is considered. Each secondary user carries out wideband spectrum sensing to get a test statistic for each channel and transmits the test statistic to a coordinator. After collecting all the test statistics from secondary users, the coordinator makes the estimation as to whether primary users are idle or not in the channels. When a channel is estimated to be free, secondary users can get access to the channel with assigned bandwidth and power. An optimization problem is formulated, which maximizes the weighted sum of secondary users' throughputs while guaranteeing a certain level of protection for the activities of primary users. Although the problem is nonconvex, it is shown that the problem can be solved by bilevel optimization and monotonic programming. This paper is also extended to cases with consideration of proportional and max-min fairness. We explore the performance tradeoff between opportunistic and regulated access inherent in the design of multiuser cognitive radio networks. We consider a multichannel cognitive radio system with sensing limits at the secondary users and interference tolerance limits at the primary and secondary users. Our objective is to determine the optimal amount of spectrum sharing, i.e., the number of secondary users that maximizes the total deliverable throughput in the network.We begin with the case of perfect primary user detection and zero interference tolerance at each of the primary and secondary nodes. With identical primary and secondary traffic statistics, we find that the optimal fraction of licensed users lies between the two extremes of fully opportunistic and fully licensed operation and is equal to the traffic duty cycle. When the secondary users can vary their transmission probabilities based on the number of active primary users, we find that the optimal number of opportunistic users is equal to the average number of unoccupied channels. We then consider the more involved case of imperfect sensing and non-zero interference tolerance constraints. We provide numerical simulation results to study the tradeoff between licensing and autonomy and the impact of primary user sensing and interference tolerance on the deliverable throughput for two different subchannel selection strategies at the secondary users. This paper tackles the problem of joint users’ uplink transmission power and data rate allocation in multi-service two-tier femtocell networks. Each user—either macrocell (MUE) or femtocell user equipment (FUE)—is associated with a two-variable utility function that represents his perceived satisfaction with respect to his allocated resources (i.e., power and rate). User's utility function is differentiated based both on the tier that the user belongs to and the service he requests. The joint resource allocation problem is directly confronted as a two-variable optimization problem and formulated as a non-cooperative game. The theory of supermodular games is utilized towards treating the two-variable optimization problem and the inherent multidimensional competition that arises among the users. The existence of proposed game's Nash Equilibrium (NE) point is analytically shown, while game's convergence to its NE point is proven. A distributed and iterative algorithm for computing the desired NE is introduced, where the optimal values of each user's uplink transmission power and data rate are simultaneously updated at the same step. The performance of the proposed approach is evaluated via modeling and simulation and its superiority compared to other state of the art approaches is illustrated. We consider a wireless collision channel, shared by a finite number of users who transmit to a common base station. Users are self-optimizing, and each wishes to minimize its average transmission rate (or power investment), subject to minimum- throughput demand. The channel quality between each user and the base station is time-varying, and partially observed by the user in the form of channel state information (CSI) signals. We assume that each user can transmit at a fixed power level and that its transmission decision at each time slot is stationary in the sense that it can depend only on the current CSI. We are interested in properties of the Nash equilibrium of the resulting game between users. We define the feasible region of user's throughput demands, and show that when the demands are within this region, there exist exactly two Nash equilibrium points, with one strictly better than the other (in terms of invested power) for all users. We further provide some lower bounds on the channel capacity that can be obtained, both in the symmetric and non-symmetric case. Finally, we show that a simple greedy mechanism converges to the best equilibrium point without requiring any coordination between the users.