Efficient power control via pricing in wireless data networks

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 (1951) 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     

Pricing and power control in a multicell wireless data network

We consider distributed power control in a multicell wireless data system and study the effect of pricing transmit power. Drawing on the earlier work of Goodman and Mandayam (see IEEE Personal Commun. Mag., vol.7, p.48-54, 2000), 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 noncooperative 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 inefficient 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     

Distributed Scheduling and Dynamic Pricing in a Communication Network

This paper studies dynamic resource allocation in a decentralized communication network. The temporal aspect in the decentralized resource allocation problem presents new challenges, e.g., in optimizing the delay-throughput trade-off under user-specific delay costs. A dynamic bandwidth allocation game modelling an agent-based network is presented. The dynamic noncooperative game achieves Pareto-efficient bandwidth allocation that can be implemented by a greedy algorithm with pricing. Optimal dynamic pricing is discussed for the efficient sharing of network resources. An ad hoc wireless network is an example of such self-organizing decentralized system: the mobile nodes need not be directly connected to a base station. Another application of the model is to consider distributed uplink scheduling, based on local information, in a WCDMA network. The discretized control variable of a mobile node is either the received power/QoS-level or the binary decision on packet transmission.     

Price‐based interference management in dense femtocell systems

Femtocell technology has been drawing considerable attention as a cost‐effective means of improving cellular coverage and capacity. However, under co‐channel deployment, femtocell system in dense environment may incur high uplink interference to existing macrocells and experiences strong inter‐cell interference at the same time. To manage the uplink interference to macrocell, as well as the inter‐cell interference, this paper proposes a price‐based uplink interference management scheme for dense femtocell systems. Specifically, on the one hand, to guarantee the macrocell users' quality of service, the macrocell base station prices the interference from femtocell users (FUEs) subject to a maximum tolerable interference power constraint. On the other hand, the inter‐cell interference is also taken into consideration. Moreover, a Stackelberg game model is adopted to jointly study the utility maximization of the macrocell base station and FUEs. Then, in order to reduce the amount of information exchange, we design a distributed power allocation algorithm for FUEs. In addition, admission control is adopted to protect the active FUEs' performance. Numerical results show that the price‐based interference management scheme is effective. Meanwhile, it is shown that the distributed power allocation combined with admission control is capable of robustly protecting the performance of all the active FUEs. Copyright © 2013 John Wiley & Sons, Ltd.     

A Radio Resource Management Framework for Multi-User Multi-Cell OFDMA Networks Based on Game Theory

This work proposes a radio resource management framework employing game theoretic concepts for orthogonal frequency division multiple access, the most prevalent multiple access technique for the next generation wireless networks. The subcarrier allocation problem is encountered as a combinatorial auction, where the base station auctions the subcarriers and the users bid for and buy bundles of subcarriers, aiming at minimising their required transmit power. Subsequently, each allocated subcarrier is loaded with a number of bits, decided by each user independently, and the power control process is set up as a non-cooperative game. Each user responds to the interference sensed in his environment and, through a best responses process, the game converges to the unique, Pareto optimal, Nash equilibrium. In order to guarantee convergence, a limit is imposed to the maximum modulation level for each subcarrier. Simulation results show that the auction algorithm follows closely the performance of the optimal algorithm, whereas it is of lower computational complexity and requires less feedback information. Similarly, the proposed distributed bit loading and power control scheme achieves lower transmit power per offered bit rate unit. However, the distributed nature of the algorithm results in lower total offered bit rate, because of the partial knowledge and exploitation of channel state information.     

Utility-based power control for a two-cell CDMA data network

Power allocation across users in two adjacent cells is studied for a code-division multiple access (CDMA) data service. The forward link is considered and cells are modeled as one-dimensional with uniformly distributed users and orthogonal signatures within each cell. Each user is assumed to have a utility function that describes the user's received utility, or willingness to pay, for a received signal-to-interference-plus-noise ratio (SINR). The objective is to allocate the transmitted power to maximize the total utility summed over all users subject to power constraints in each cell. It is first shown that this optimization can be achieved by a pricing scheme in which each base station announces a price per unit transmitted power to the users, and each user requests power to maximize individual surplus (utility minus cost). Setting prices to maximize total revenue over both cells is also considered, and it is shown that, in general, the solution is different from the one obtained by maximizing total utility. Conditions are given for which independent optimization in each cell, which leads to a Nash equilibrium (NE), is globally optimal. It is shown that, in general, coordination between the two cells is needed to achieve the maximum utility or revenue.     

Distributed interference compensation for wireless networks

We consider a distributed power control scheme for wireless ad hoc networks, in which each user announces a price that reflects compensation paid by other users for their interference. We present an asynchronous distributed algorithm for updating power levels and prices. By relating this algorithm to myopic best response updates in a fictitious game, we are able to characterize convergence using supermodular game theory. Extensions of this algorithm to a multichannel network are also presented, in which users can allocate their power across multiple frequency bands.     

基于多天线波束赋形的CRN分布式上行功率控制算法

针对工作于underlay模式的认知无线网络（CRN,Cognitive Radio Network）上行功率控制问题,本文提出一种基于多天线波束赋形,由认知基站和认知用户联合优化的分布式上行功率控制算法.联合优化的具体步骤为认知基站通过求解最大广义特征值问题完成多天线波束赋形优化;认知用户先将非线性功率优化问题转换为几何规划凸优化问题,再使用梯度法完成分布式发送功率优化;认知基站和认知用户交替优化,实现网络效用最大化.数值仿真显示,同只优化认知用户功率的上行功率控制算法相比,认知基站和认知用户联合优化的上行功率控制算法不仅能得到更大的网络效用值,而且对主用户的干扰具有鲁棒性.     

Asynchronous Iterative Water-Filling for Gaussian Frequency-Selective Interference Channels

This paper considers the maximization of information rates for the Gaussian frequency-selective interference channel, subject to power and spectral mask constraints on each link. To derive decentralized solutions that do not require any cooperation among the users, the optimization problem is formulated as a static noncooperative game of complete information. To achieve the so-called Nash equilibria of the game, we propose a new distributed algorithm called asynchronous iterative water-filling algorithm. In this algorithm, the users update their power spectral density (PSD) in a completely distributed and asynchronous way: some users may update their power allocation more frequently than others and they may even use outdated measurements of the received interference. The proposed algorithm represents a unified framework that encompasses and generalizes all known iterative water-filling algorithms, e.g., sequential and simultaneous versions. The main result of the paper consists of a unified set of conditions that guarantee the global converge of the proposed algorithm to the (unique) Nash equilibrium of the game.     

Joint random access and power control game in ad hoc networks with noncooperative users

We consider a distributed joint random access and power control scheme for interference management in wireless ad hoc networks. To derive decentralized solutions that do not require any cooperation among the users, we formulate this problem as noncooperative joint random access and power control game, in which each user minimizes its average transmission cost with a given rate constraint. Using supermodular game theory, the existence and uniqueness of Nash equilibrium are established. Furthermore, we present an asynchronous distributed algorithm to compute the solution of the game based on myopic best response updates, which converges to Nash equilibrium globally. Finally, a link admission algorithm is carried out to guarantee the reliability of the active users. Performance evaluations via simulations show that the game-theoretical based cross-layer design achieves high performance in terms of energy consumption and network stability.     

CDMA Uplink Power Control as a Noncooperative Game

We present a game-theoretic treatment of distributed power control in CDMA wireless systems. We make use of the conceptual framework of noncooperative game theory to obtain a distributed and market-based control mechanism. Thus, we address not only the power control problem, but also pricing and allocation of a single resource among several users. A cost function is introduced as the difference between the pricing and utility functions, and the existence of a unique Nash equilibrium is established. In addition, two update algorithms, namely, parallel update and random update, are shown to be globally stable under specific conditions. Convergence properties and robustness of each algorithm are also studied through extensive simulations.     

CR系统中基于微分博弈的功率控制算法

该文针对认知无线电系统动态性的特点,将微分博弈理论应用在认知无线电系统的功率控制中,建立了功率控制的非合作微分博弈模型,提出了一种基于微分博弈的分布式非合作功率控制算法。该算法在满足认知用户平均功率门限和QoS需求的基础上,实现了分布式动态功率控制,获得了反馈纳什均衡解析解。仿真结果表明,该算法可有效控制各认知用户的发射功率,增加系统吞吐量,提高系统性能。     

Power Control Based on Maximum Power Adaptation in Two-Tier Femtocell Networks

In recent years, femtocells are receiving considerable attention in mobile communication as a cost-effective means of improving indoor coverage and capacity. A significant technical challenge in the deployment of a large number of femtocells is the management of interference from the underlay of femtocells onto the overlay of macrocell. In this paper, a reasonable and effective interference suppression scheme based on the adaptive adjustment of femtocell users’ maximum transmission power is proposed. The highlight of the scheme is the joint design of macrocell users’ uplink communication protection and femtocell users’ optimal power allocation. The scheme restricts the cross-tier interference at macrocell base station below a given threshold and ensures the optimization of femtocell users’ power allocation at each adjustment phase. Last, admission control is also considered, aiming to exploit the network resources more effectively. Simulation results show the superiority of the proposed scheme over the scheme based on the Signal-to-Interference-Plus-Noise Ratio adaptation. We also give some reference on utility function selection by setting different coefficients in the utility function, and show the effectiveness of admission control in both fixed and random network topologies.     

A coalitional game‐based relay load balancing and power allocation scheme in decode‐and‐forward cellular relay networks

In this paper, a game theoretic relay load balancing and power allocation scheme is proposed for downlink transmission in a decode‐and‐forward orthogonal frequency division multiple access‐based cellular relay network. A system with a base station communicating with multiple users via multiple relays is considered. The relays have limited power, which must be divided among the users they support. In traditional scheme, each relay simply divides its transmit power equally among all its users. Moreover, each user selects the relay with the highest channel gain. In this work, we do not apply the traditional relay scheme. It is because the users are distributed randomly, and by applying the traditional relay selection scheme, it may happen that some relays have more users connected to them than other relays, which results in having unbalanced load among the relays. In order to avoid performance degradation, achieve relay load balancing, and maximize the total data rate of the network, a game theoretic approach is proposed, which efficiently assigns the users to relays. The power of each relay is wisely distributed among users by the efficient power allocation scheme. Simulation results indicate that the proposed game‐based scheme can considerably improve the average sum‐spectral efficiency. Moreover, it shows that by applying the game, users who can connect to uncongested relays join them as opposed to connecting to congested relays. Copyright © 2015 John Wiley & Sons, Ltd.     

异构蜂窝网络中基于Stackelberg博弈的能效优化算法

设备到设备(Device To Device,D2D)通信允许移动终端无需通过基站而进行直接通信。为提高蜂窝系统能效,引入D2D通信共享频谱资源形成异构蜂窝网络。本文将D2D通信的能效优化问题转化为博弈收益最大化问题,并提出了一种基于Stackelberg博弈的分布式功率控制算法。针对系统模型中存在的跨层干扰以及层内干扰,该算法建立了干扰价格系数与D2D对发送功率之间的函数关系,并求解出给定干扰价格系数下D2D对最佳发送功率的闭合表达式。仿真结果表明所提算法能够在最大化基站端蜂窝用户收益的基础上有效提高D2D对的总能效。      

Joint network-centric and user-centric radio resource management in a multicell system

A pricing mechanism to mediate (and allocate resources) between conflicting user and network objectives has been recently proposed by the authors in a single-cell system. Here, we extend the results to a multicell system, where the autonomous base station assignment and power control are formulated as a noncooperative game among users. The network prices the resources using two strategies: global pricing that maximizes the revenue, and minimax pricing that trades off the revenue for a more even resource allocation.     

Power allocation games in wireless networks of multi-antenna terminals

We consider wireless networks that can be modeled by multiple access channels in which all the terminals are equipped with multiple antennas. The propagation model used to account for the effects of transmit and receive antenna correlations is the unitary-invariant-unitary model, which is one of the most general models available in the literature. In this context, we introduce and analyze two resource allocation games. In both games, the mobile stations selfishly choose their power allocation policies in order to maximize their individual uplink transmission rates; in particular they can ignore some specified centralized policies. In the first game considered, the base station implements successive interference cancellation (SIC) and each mobile station chooses his best space-time power allocation scheme; here, a coordination mechanism is used to indicate to the users the order in which the receiver applies SIC. In the second framework, the base station is assumed to implement single-user decoding. For these two games a thorough analysis of the Nash equilibrium is provided: the existence and uniqueness issues are addressed; the corresponding power allocation policies are determined by exploiting random matrix theory; the sum-rate efficiency of the equilibrium is studied analytically in the low and high signal-to-noise ratio regimes and by simulations in more typical scenarios. Simulations show that, in particular, the sum-rate efficiency is high for the type of systems investigated and the performance loss due to the use of the proposed suboptimum coordination mechanism is very small.     

Power allocation for downlink multiuser hybrid NOMA‐OMA systems: An auction game approach

Nonorthogonal multiple access (NOMA) is viewed as one of the key enabling candidate for the fifth‐generation systems. The effectiveness of such networks heavily relies on the power allocation. This paper addresses the problem of power allocation in a downlink multiuser hybrid NOMA‐orthogonal multiple access (OMA) network, where NOMA is integrated into OMA. Users with strong channel conditions are paired up with the users having weak channel conditions based on a random mechanism. Further, user pairs compete in an auction game for the transmit power being sold by the base station. Bids are placed iteratively by each user pair such that it maximizes their own utility. The existence of a unique Nash equilibrium has been proved theoretically. Simulation results show that the proposed scheme achieves higher average sum rate of users in comparison with that of the existing algorithms.     

Hierarchical SIR and rate control on the forward link for CDMA datausers under delay and error constraints

We study the signal-to-interference ratio (SIR) and rate control for code division multiple access (CDMA) data users on the forward link under average or peak power constraints. The quality of service (QoS) for data users is specified by delay and error rate constraints as well as a family of utility functions representing the throughput and fairness among the data users. It is found that the optimal SIR and rate control algorithm has a hierarchical structure which can be easily implemented in a distributed manner. The SIR targets can be adjusted independently by the mobiles using information specific to the individual users. The data rates can be adjusted jointly by the base station based on limited feedback from the mobiles. We also propose a two-level iteration algorithm for both the mobile and the base station to efficiently compute the SIR and data rates. Our results show that a flexible tradeoff between total system throughput (sum of rates achieved) and fairness (similarity in data rates) can be achieved by choosing appropriate utility functions used in this scheme     

基于总能效最优化的终端匹配设计和实现

终端直通通信技术(Device-to-Device communication,D2D)是指相距较近的用户设备(user equipment,UE)可不借助于基站而直接进行通信,它可以有效提高传输速率和频谱利用率.受限于电池的容量,基站调度上应尽可能使终端的续航时间更长.为此,本文旨在追求单位能量的传输比特率最大化,即能效最大化目标.本文在构建蜂窝用户与D2D用户资源复用场景下的能效模型基础上,将目标实现分为两个步骤:1)终端最优发射功率的设置,利用准凸函数的性质,通过最优化的方法迭代求解蜂窝和D2D用户各自的最优功率,使得复杂度大为降低;2)利用KM算法实施蜂窝用户与D2D对的配对.通过仿真验证,使用本文提出的算法相对于以最大功率发送的情况下可以获得约40％左右的增益.