Abstract—A major challenge in the operation of wireless communications systems is the efficient use of radio resources. One important component of radio resource management is power control, which has been studied extensively in the context of voice communications. With the increasing demand for wireless data services, it is necessary to establish power control algorithms for information sources other than voice. We present a power control solution for wireless data in the analytical setting of a game theoretic framework. In this context, the quality of service (QoS) a wireless terminal receives is referred to as the utility and distributed power control is a noncooperative power control game where users maximize their utility. The outcome of the game results in a Nash equilibrium that is inefficient. We introduce pricing of transmit powers in order to obtain Pareto improvement of the noncooperative power control game, i.e., to obtain improvements in user utilities relative to the case with no pricing. Specifically, we consider a pricing function that is a linear function of the transmit power. The simplicity of the pricing function allows a distributed implementation where the price can be broadcast by the base station to all the terminals. We see that pricing is especially helpful in a heavily loaded system. Index Terms—Game theory, Pareto efficiency, power control, pricing, wireless data. I.

In this pape we introduce powe r control as a solution tothe multiple accel proble in conte tion-base wiren-b ad-hocne works.The motivation for this study is two fold, limiting multi-use intej- toincre single hop throughput, andrej powe r consumption to increj batte life We focus onne ne bor transmissions whes node are rej tose information packe - tothe re e e re e sub jej to a constraint on the signal-to-inteal-to-injj- ratio.The multiple acce - proble is solve via twoaltej- phase name schej and powe r control.The sche algorithm isej tial to coordinate the transmissions ofinde ede t use inorde toejj strong intej- (e.g selfinterference) that can not be ove by powe r control. On the othe hand, powe r control isej in adistribute fashion to dej- the admissible powe r ve ifone ene that can be use bythe sche use to satisfy thei singlej transmissionrensmissi ts. This isdone for two type s ofne works, namej TDMA and TDMA/CDMA wire/CD ad-hocne works.

In this paper we consider distributed power control in a multicell wireless data system and study the effect of pricing transmit power. Drawing on our earlier work in [1], we formulate the QoS of a data user via a utility function measured in bits per Joule. We consider distributed power control, modeled as a non-cooperative game, where users maximize their utilities in a multicell system. Base station assignment based on received signal strength as well as received signal-to-interference ratio (SIR) are considered jointly with power control. Our results indicate that for both assignment schemes, such a procedure results in an ine#cient operating point (Nash equilibrium) for the entire system. We introduce pricing of transmit power as a mechanism for influencing data user behavior and our results show that the distributed power control based on maximizing the net utility (utility minus the price) results in improving the Pareto efficiency of the resulting operating point. Variations of pricing based on global and local loading in cells are considered as a means of improving the efficiency of wireless data networks. Finally, we discuss the improvement in utilities through a centralized scheme where each base station (BS) calculates the best SIR to be targeted by the terminals it is assigned.

In this paper, we provide a theoretical framework for cross-layer optimization for orthogonal frequency division multiplexing (OFDM) wireless networks. The utility is used in our study to build a bridge between the physical layer and the media ac-cess control (MAC) layer and to balance the efficiency and fairness of wireless resource allocation. We formulate the cross-layer optimization problem as one that maximizes the average utility of all active users subject to certain conditions, which are determined by adaptive resource allocation schemes. We present necessary and sufficient conditions for utility-based optimal subcarrier assignment and power allocation and discuss the convergence properties of optimization. Numerical results demonstrate a significant performance gain for the cross-layer optimization and the gain increases with the number of active users in the networks.

Distributed power-control algorithms for systems with hard signal-to-interference ratio (SIR) constraints may diverge when infeasibility arises. In this paper, we present a powercontrol framework called utility-based power control (UBPC) by reformulating the problem using a softened SIR requirement (utility) and adding a penalty on power consumption (cost). Under this framework, the goal is to maximize the net utility, defined as utility minus cost. Although UBPC is still noncooperative and distributed in nature, some degree of cooperation emerges: a user will automatically decrease its target SIR (and may even turn off transmission) when it senses that traffic congestion is building up. This framework enables us to improve system convergence and to satisfy heterogeneous service requirements (such as delay and bit error rate) for integrated networks with both voice users and data users. Fairness, adaptiveness, and a high degree of flexibility can be achieved by properly tuning parameters in UBPC.

Abstract—A game-theoretic model for studying power control in multicarrier code-division multiple-access systems is proposed. Power control is modeled as a noncooperative game in which each user decides how much power to transmit over each carrier to maximize its own utility. The utility function considered here measures the number of reliable bits transmitted over all the carriers per joule of energy consumed and is particularly suitable for networks where energy efficiency is important. The multidimensional nature of users ’ strategies and the nonquasi-concavity of the utility function make the multicarrier problem much more challenging than the single-carrier or throughput-based-utility case. It is shown that, for all linear receivers including the matched filter, the decorrelator, and the minimum-mean-square-error detector, a user’s utility is maximized when the user transmits only on its “best ” carrier. This is the carrier that requires the least amount of power to achieve a particular target signal-to-interference-plus-noise ratio at the output of the receiver. The existence and uniqueness of Nash equilibrium for the proposed power control game are studied. In particular, conditions are given that must be satisfied by the channel gains for a Nash equilibrium to exist, and the distribution of the users among the carriers at equilibrium is characterized. In addition, an iterative and distributed algorithm for reaching the equilibrium (when it exists) is presented. It is shown that the proposed approach results in significant improvements in the total utility achieved at equilibrium compared with a single-carrier system and also to a multicarrier system in which each user maximizes its utility over each carrier independently. Index Terms—Energy efficiency, game theory, multicarrier code-division multiple-access (CDMA), multiuser detection, Nash equilibrium, power control, utility function. I.

Abstract not found

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.

Abstract — Game theory is a set of tools developed to model interactions between agents with conflicting interests, and is thus well-suited to address some problems in communications systems. In this paper we present some of the basic concepts of game theory and show why it is an appropriate tool for analyzing some communication problems and providing insights into how communication systems should be designed. We then provided a detailed example in which game theory is applied to the power control problem in a CDMA-like system. I.

Distributed power control algorithms for systems with hard SIR constraints may diverge when infeasibility arises. In this paper, we present a power control framework called utility-based power control (UBPC) by reformulating the problem using a softened SIR requirement (utility) and adding a penalty on power consumption (cost). Under this framework, the goal is to maximize the net utility, defined as utility minus cost. Although UBPC is still non-cooperative and distributed in nature, some degree of cooperation emerges: a user will automatically decrease its target SIR (and may even turn off transmission) when it senses that traffic congestion is building up. This framework enables us to improve system convergence and to satisfy heterogeneous service requirements (such as delay and bit error rate) for integrated networks with both voice users and data users. Fairness, adaptiveness, and a high degree of flexibility can be achieved by properly tuning parameters in UBPC. Keywords--- Signal-to-interference ratio (SIR), wireless, cellular system, power control, utility function, distributed algorithm. I.