Abstract—We address the problem of spectrum pricing in a cognitive radio network where multiple primary service providers compete with each other to offer spectrum access opportunities to the secondary users. By using an equilibrium pricing scheme, each of the primary service providers aims to maximize its profit under quality of service (QoS) constraint for primary users. We formulate this situation as an oligopoly market consisting of a few firms and a consumer. The QoS degradation of the primary services is considered as the cost in offering spectrum access to the secondary users. For the secondary users, we adopt a utility function to obtain the demand function. With a Bertrand game model, we analyze the impacts of several system parameters such as spectrum substitutability and channel quality on the Nash equilibrium (i.e., equilibrium pricing adopted by the primary services). We present distributed algorithms to obtain the solution for this dynamic game. The stability of the proposed dynamic game algorithms in terms of convergence to the Nash equilibrium is studied. However, the Nash equilibrium is not efficient in the sense that the total profit of the primary service providers is not maximized. An optimal solution to gain the highest total profit can be obtained. A collusion can be established among the primary services so that they gain higher profit than that for the Nash equilibrium. However, since one or more of the primary service providers may deviate from the optimal solution, a punishment mechanism may be applied to the deviating primary service provider. A repeated game among primary service providers is formulated to show that the collusion can be maintained if all of the primary service providers are aware of this punishment mechanism, and therefore, properly weight their profits to be obtained in the future. Index Terms—Spectrum sharing, cognitive radio, pricing scheme, game theory, Nash equilibrium, distributed adaptation, collusion. I.

Two tier cellular networks, comprising of a central macrocell underlaid with short range femtocell hotspots offer an economical way to improve cellular capacity. With shared spectrum and lack of coordination between tiers, cross-tier interference limits overall capacity. To quantify near-far effects with universal frequency reuse, this paper derives a fundamental relation providing the largest feasible macrocell Signal-to-Interference-Plus-Noise Ratio (SINR), given any set of feasible femtocell SINRs. A distributed utility-based SINR adaptation at femtocells is proposed in order to alleviate cross-tier interference at the macrocell from overlaid femtocell infrastructure. The Foschini-Miljanic (FM) algorithm is a special case of the adaptation. Each femtocell maximizes its individual utility consisting of a SINR based reward less an incurred cost (interference to the macrocell). Numerical results show greater than 30 % improvement in mean femtocell SINRs relative to FM. In the event that cross-tier interference prevents a macro-user from obtaining its SINR target, an algorithm is proposed that adaptively curtails transmission powers of the strongest femtocell interferers. The algorithm ensures that a macrouser achieves its SINR target even with 100 femtocells/cell-site, and requires a worst case SINR reduction of only 16 % at femtocells. These results motivate design of power control schemes requiring minimal network overhead in two-tier networks with shared spectrum.

A game-theoretic model is proposed to study the cross-layer problem of joint power and rate control with quality of service (QoS) constraints in multiple-access networks. In the proposed game, each user seeks to choose its transmit power and rate in a distributed manner in order to maximize its own utility while satisfying its QoS requirements. The user’s QoS constraints are specified in terms of the average source rate and an upper bound on the average delay where the delay includes both transmission and queuing delays. The utility function considered here measures energy efficiency and is particularly suitable for wireless networks with energy constraints. The Nash equilibrium solution for the proposed noncooperative game is derived and a closed-form expression for the utility achieved at equilibrium is obtained. It is shown that the QoS requirements of a user translate into a “size ” for the user which is an indication of the amount of network resources consumed by the user. Using this competitive multiuser framework, the tradeoffs among throughput, delay, network capacity and energy efficiency are studied. In addition, analytical expressions are given for users ’ delay profiles and the delay performance of the users at Nash equilibrium is quantified.

Abstract—This paper proposes distributed joint power and admission control algorithms for the management of interfer-ence in two-tier femtocell networks, where the newly-deployed femtocell users (FUEs) share the same frequency band with the existing macrocell users (MUEs) using code-division multiple access (CDMA). As the owner of the licensed radio spectrum, the MUEs possess strictly higher access priority over the FUEs; thus, their quality-of-service (QoS) performance, expressed in terms of the prescribed minimum signal-to-interference-plus-noise ratio (SINR), must be maintained at all times. For the lower-tier FUEs, we explicitly consider two different design objectives, namely, throughput-power tradeoff optimization and soft QoS provisioning. With an effective dynamic pricing scheme combined with admission control to indirectly manage the cross-tier interference, the proposed schemes lend themselves to distributed algorithms that mainly require local information to offer maximized net utility of individual users. The approach employed in this work is particularly attractive, especially in view of practical implementation under the limited backhaul network capacity available for femtocells. It is shown that the proposed algorithms robustly support all the prioritized MUEs with guar-anteed QoS requirements whenever feasible, while allowing the FUEs to optimally exploit the remaining network capacity. The convergence of the developed solutions is rigorously analyzed, and extensive numerical results are presented to illustrate their potential advantages. Index Terms—Femtocell, macrocell, CDMA, power control, admission control, QoS protection, distributed interference man-agement. I.

Abstract — A systematic approach to solve seemingly nonconvex resource allocation problems in wireless cellular networks is studied in this paper. By revealing and exploiting the hidden convexity in the problem formulations, we obtain solutions that can tackle a variety of objective functions, provide robustness to resource allocations such as power, and be obtained often through distributed algorithms. The advantages of such flexibility and robustness are demonstrated through comparisons with the state-of-the-art in recent research literature. First we show how to distributively solve a variety of resource allocation problems in FDMA and interference limited CDMA channels with quality of service constraints, such as meeting min-imum queueing delay or energy per bit requirement. Then, for uplink transmission in a CDMA cellular network, we propose an optimal power control scheme with congestion-aware active link protection. In particular, the tradeoff between power expenditure and the protection margin of the SIR-balancing power algorithm is optimized.

Abstract — In the seminal paper by Foschini and Miljanic in 1993, a distributed power control algorithm was developed to meet SIR targets with minimal powers in cellular network uplinks. Since the SIR on an active link may dip below the SIR target during the transient after a new user enters the cell, Bambos et al. proposed an active link protection algorithm to provide robustness, at the expense of higher energy consumption. This paper examines the tradeoff between energy and robustness. An optimization problem is formulated where robustness is captured in the constraint and the price of robustness penalized in the objective function. A distributed algorithm is developed to solve this problem. Local convergence and optimality of equilibrium are proved for the algorithm. The objective function modulates the tradeoff between energy and robustness, and between energy and speed of admission, as illustrated through a series of numerical experiments. A parameterized family of objective functions is constructed to control the transient and equilibrium properties of robust distributed power control.

This paper summarizes and explains the main results on signal-to-interference (SIR) based power control algorithms, which are used to increase network capacity, extend battery life, and improve quality of service in cellular wireless radio systems. The classic works of Aein, Meyerhoff, and Nettleton and Alavi attracted considerable attention in the nineties. The modern approach to the power balancing control problem in wireless networks, formulated by Zander in 1992, matured in the papers of Foschini and Yates and their coworkers in the latter part of the nineties. However, the field is still wide open for research as is indicated by the increasing number of papers published in the area each year. The most recent approaches to solving the mobile power distribution problem in wireless networks use Kalman filters, dynamic estimators, and noncooperative Nash game theory.

Abstract—Distributed power control is investigated for cognitive radio networks (CRNs) based on a cooperative gametheoretic framework. Taking into consideration both network efficiency and user fairness, a cooperative Nash bargaining powercontrol game (NBPCG) model is formulated, where interference power constraints (IPCs) are imposed to protect the primary users ’ (PUs’) transmissions, and minimum signal-to-interferenceplus-noise ratio (SINR) requirements are employed to provide reliable transmission opportunities to secondary cognitive users. An SINR-based utility function is designed for this game model, which not only reflects the spectrum efficiency of the CRN but also complies with all the axioms in the Nash theorem and, hence, facilitates efficient algorithmic development. The existence, uniqueness, and fairness of this game solution are proved analytically. To deal with the IPCs where the power-control decisions of all users are coupled, these IPCs are properly transformed into a pricing function in the objective utility. Accordingly, a Kalai–Smorodinsky (KS) bargaining solution and a Nash bargaining solution (NBS) are developed, which result in Pareto-optimal solutions to the NBPCG problem with different user-fairness policies. Theoretical analysis and simulations are provided to testify the effectiveness of the proposed cooperative game algorithms for efficient and fair power control in CRNs. Index Terms—Cognitive radio networks (CRNs), cooperative game theory, fairness, Kalai–Smorodinsky (KS) bargaining game, Nash bargaining game, power control. I.

Abstract—This paper proposes two Pareto-optimal power con-trol algorithms for a two-tier network, where newly-deployed femtocell user equipments (FUEs) operate in the licensed spec-trum owned by an existing macrocell. Different from homoge-neous network settings, the inevitable requirement of robustly protecting the quality-of-service (QoS) of all prioritized macrocell user equipments (MUEs) here lays a major obstacle that hinders the successful application of any available solutions. Directly tar-geting at this central issue, the first algorithm jointly maximizes the total utility of both user classes. Specifically, we adopt the log-barrier penalty method to effectively enforce the minimum signal-to-interference-plus-noise ratios (SINRs) imposed by the macrocell, paving the way for the adaptation of load-spillage solution framework. On the other hand, the second algorithm is applied to the scenario where only the sum utility of all FUEs needs to be maximized. At optimality, we show that the MUEs ’ prescribed SINR constraints are met with equality in this case. With the search space for Pareto-optimal SINRs substantially reduced, the second algorithm features scalability, low computational complexity, short converging time, and stable performance. We prove that the two developed algorithms converge to their respective global optima, and more importantly, they can be implemented in a distributive manner at individual links. Effective mechanisms are also available to flexibly designate the access priority to MUEs and FUEs, as well as to fairly share radio resources among users. Numerical results confirm the merits of the devised approaches. Index Terms—Convex optimization, global optimality, hetero-geneous network, interference management, Pareto optimality, power control, QoS protection, SINR optimization, utility maxi-mization. I.

Abstract—Next generation wireless systems will be required to support heterogeneous services with different transmission rates that include real time multimedia transmissions, as well as non-real time data transmissions. In order to provide such flexible transmission rates, efficient use of system resources in next generation systems will require control of both data transmission rate and power for mobile terminals. In this paper we formulate the problem of joint transmission rate and power control for the uplink of a single cell CDMA system as a non-cooperative game. We assume that the utility function depends on both transmission rates and powers and show the existence of Nash equilibrium in the non-cooperative joint transmission rate and power control game (NRPG). We include numerical results obtained from simulations that compare the proposed algorithm with a similar one which is also based on game theory and it also updates the transmission rates and powers simultaneously in a single step. Index Terms—Power control, rate control, non-cooperative games, Nash equilibrium. I.