Competitive Resource Sharing Based on Game Theory in Cooperative Relay Networks

This letter considers the problem of resource sharing among a relay and multiple user nodes in cooperative transmission networks. We formulate this problem as a sellers’ market competition and use a noncooperative game to jointly consider the benefits of the relay and the users. We also develop a distributed algorithm to search the Nash equilibrium, the solution of the game. The convergence of the proposed algorithm is analyzed. Simulation results demonstrate that the proposed game can stimulate cooperative diversity among the selfish user nodes and coordinate resource allocation among the user nodes effectively.     

基于非合作博弈论的多小区OFDMA系统动态资源分配算法研究

该文采用非合作博弈论的方法研究了多小区OFDMA系统中的动态资源分配问题,首先将各基站的发射功率平均分配给各子载波,然后由所有小区在每个子载波上独立地进行资源分配博弈,给出了用户调度与功率分配联合博弈框架。为了进一步简化,将用户调度和资源分配分开完成,通过将信道增益引入到定价函数中,提出了一种新的定价机制,建立了用户确定时的非合作功率分配博弈模型,分析了其纳什均衡的存在性和唯一性,并设计了具体的博弈算法。仿真结果表明,所提算法在保证吞吐量性能的同时,进一步提升了系统的公平性。     

Multiradio Channel Allocation in Multihop Wireless Networks

Channel allocation was extensively investigated in the framework of cellular networks, but it was rarely studied in the wireless ad hoc networks, especially in the multihop networks. In this paper, we study the competitive multiradio multichannel allocation problem in multihop wireless networks in detail. We first analyze that the static noncooperative game and Nash equilibrium (NE) channel allocation scheme are not suitable for the multihop wireless networks. Thus, we model the channel allocation problem as a hybrid game involving both cooperative game and noncooperative game. Within a communication session, it is cooperative; and among sessions, it is noncooperative. We propose the min-max coalition-proof Nash equilibrium (MMCPNE) channel allocation scheme in the game, which aims to maximize the achieved data rates of communication sessions. We analyze the existence of MMCPNE and prove the necessary conditions for MMCPNE. Furthermore, we propose several algorithms that enable the selfish players to converge to MMCPNE. Simulation results show that MMCPNE outperforms NE and coalition-proof Nash equilibrium (CPNE) schemes in terms of the achieved data rates of multihop sessions and the throughput of whole networks due to cooperation gain.     

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。     

Optimal power control for wireless cooperative relay networks: a cooperative game theoretic approach

Wireless nodes operating on batteries are always assumed to be selfish to consume their energy solely to maximize their own benefits. Thus, the two network objectives, that is, system efficiency and user fairness should be considered simultaneously. To this end, we propose two game theoretic mechanisms, that is, the signal‐to‐noise ratio (SNR) game and the data‐rate game to stimulate cooperation among selfish user nodes for cooperative relaying. Considering one node could trade its transmission power for its partner's relaying directly, the strategy of a node is defined as the amount of power that it is willing to contribute for relaying purpose. In the SNR game, selfish nodes are willing to achieve SNR increases at their receivers, while in the data‐rate game the nodes are willing to achieve data‐rate gains. We prove that each of the games has a unique Nash bargaining solution. Simulation results show that the Nash bargaining solution lead to fair and efficient resource allocation for both the cooperative partner nodes in the Pareto optimal sense, that is, both the nodes could experience better performance than they work independently and the degree of cooperation of a node only depends on how much contribution its partner can make to improve its own performance. Copyright © 2012 John Wiley & Sons, Ltd.     

Dynamic theoretic proactive caching placement game for energy saving in H‐CRAN

Edge caching is an effective feature of the next 5G network to guarantee the availability of the service content and a reduced time response for the user. However, the placement of the cache content remains an issue to fully take advantage of edge caching. In this paper, we address the proactive caching problem in Heterogeneous Cloud Radio Access Network (H‐CRAN) from a game theoretic point of view. The problem is formulated as a bargaining game where the remote radio heads (RRHs) dynamically negotiate and decide which content to cache in which RRH under energy saving and cache capacity constraints. The Pareto optimal equilibrium is proved for the cooperative game by the iterative Nash bargaining algorithm. We compare between cooperative and noncooperative proactive caching games and demonstrate how the selfishness of different players can affect the overall system performance. We also showed that our cooperative proactive caching game improves the energy consumption of 40% as compared with noncooperative game and of 68% to no‐game strategy. Moreover, the number of satisfied requests at the RRHs with the proposed cooperative proactive caching scheme is significantly increased.     

Dense femtocell networks power self‐optimization: an exact potential game approach

Femtocell is regarded as a promising technology to enhance indoor coverage and improve network capacity. However, highly dense and self‐organized femtocells in urban environment will result in serious inter‐femtocell interference. To solve this problem, this paper proposes a distributed power self‐optimization scheme for the downlink operation of dense femtocell networks. First, a novel convex pricing mechanism is presented to price the transmit power of femtocells and construct the utility function of femtocells. Then, a noncooperative game framework for power self‐optimization of femtocells in dense femtocell networks is established on the basis of the exact potential game theory, which is demonstrated to converge to a pure and unique Nash equilibrium. Finally, combined with firefly algorithm, an effective power self‐optimization algorithm with guaranteed convergence is proposed to achieve the Nash equilibrium of the proposed game. With practical LTE parameters and a 3GPP dual‐strip femtocell model, simulation results show that the proposed game with convex pricing mechanism increases the femtocell network throughput by 7% and reduces the average transmit power of femtocells by 50% in dense femtocell networks, with respect to the compared schemes. Copyright © 2014 John Wiley & Sons, Ltd.     

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.     

Distributed multiuser power control for digital subscriber lines

This paper considers the multiuser power control problem in a frequency-selective interference channel. The interference channel is modeled as a noncooperative game, and the existence and uniqueness of a Nash equilibrium are established for a two-player version of the game. An iterative water-filling algorithm is proposed to efficiently reach the Nash equilibrium. The iterative water-filling algorithm can be implemented distributively without the need for centralized control. It implicitly takes into account the loop transfer functions and cross couplings, and it reaches a competitively optimal power allocation by offering an opportunity for loops to negotiate the best use of power and frequency with each other. When applied to the upstream power backoff problem in very-high bit-rate digital subscriber lines and the downstream spectral compatibility problem in asymmetric digital subscriber lines, the new power control algorithm is found to give a significant performance improvement when compared with existing methods     

多小区无线数据网络中基于最佳等信干比的功率控制

指出多小区无线数据系统中基于非合作博弈的功率控制算法的纳什均衡不是帕累托最优的。提出一种新的适用于多小区无线数据网络的基于最佳等信干比的功率控制算法,使系统中每个小区的终端都工作在最佳等信干比下。仿真结果表明,该算法明显提高了系统的性能,使系统终端具有相对较高的效用和较低的发射功率,并使得无线网络资源的使用更加合理和公平。     

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.     

A game approach for cooperative spectrum sharing in cognitive radio networks

We consider the problem of cooperative spectrum sharing among primary users (PUs) and secondary users (SUs) in cognitive radio networks. In our system, each PU selects a proper set of SUs to serve as the cooperative relays for its transmission and in return, leases portion of channel access time to the selected SUs for their own transmission. PU decides how to select SUs and how much time it would lease to SUs, and the cooperative SUs decide their respective power levels in helping PU's transmission, which are proportional to their access times. We assume that both PUs and SUs are rational and selfish. In single‐PU scenario, we formulate the problem as a noncooperative game and prove that it converges to a unique Stackelberg equilibrium. We also propose an iterative algorithm to achieve the unique equilibrium point. We then extend the proposed cooperative mechanism to a multiple‐PU scenario and develop a heuristic algorithm to assign proper SUs to each PU considering both performance and fairness. The simulation results show that when the competition among SUs is fierce, the performance gap between our heuristic algorithm and the optimal one is smaller than 3%. Copyright © 2013 John Wiley & Sons, Ltd.     

Optimal Power Control in Cooperative Relay Networks Based on a Differential Game

In this paper, the optimal power control problem in a cooperative relay network is investigated and a new power control scheme is proposed based on a non‐cooperative differential game. Optimal power allocated to each node for a relay is formulated using the Nash equilibrium in this paper, considering both the throughput and energy efficiency together. It is proved that the non‐cooperative differential game algorithm is applicable and the optimal power level can be achieved.     

Performance analysis of multi-user diversity in heterogeneous cooperative communication systems

The heterogeneous cooperative relaying technique can be utilized to complete the hierarchical convergence for the multi-radio access networks, where the single heterogeneous cooperative relay is selected and the maximal-ratio combining (MRC) scheme is utilized to achieve the cooperative diversity gain. In order to evaluate performances of the hierarchical convergence mechanism, this paper theoretically investigates the key factors of the multi-user diversity (MUD) gain, the heterogeneous cooperative diversity gain and the large scale fading of the first and second links. The tight closed-form expressions in terms of the outage probability and the average symbol error rate are derived for evaluating how and with what factors impact on the system performance. The analytical and simulation results show that the number of heterogeneous cooperative relay nodes (HCRNs)M and the number of destination stations (DSs)K have great impacts on performances, and the order of outage probability is (M + 1)K. The large scale fading ratio of the first hop to the second hop also has a big impact on performances. Thus in the real network, we can utilize advanced radio resource management schemes to achieve a high multi-user diversity, instead of configuring too many HCRNs for the heterogeneous cooperative diversity gain. Furthermore, we can guarantee the transmission quality between the BS and HCRNs via the network planning to optimize the overall network performance.     

基于合作目标与非合作目标的一体化空间配准新算法

针对移动平台雷达同时探测到合作目标与非合作目标怎样进行空间配准的问题,提出了一种一体化的空间配准算法,将基于合作目标的雷达系统偏差估计结果作为附加条件输入到基于非合作目标建立的线性方程组中,一起采用递推最小二乘法（RLS）重新估计两平台的系统偏差大小。仿真结果表明该新方法切实可行,合理地利用了合作目标信息与共同量测的非合作目标信息,提高了雷达量测系统偏差估计的准确性和最终目标航迹的配准精度,相信在多机协同探测领域具有一定的应用价值。     

Joint Rate-and-Power Allocation for Multi-channel Spectrum Sharing Networks with Balanced QoS Provisioning and Power Saving

In this paper we study the joint rate-and-power allocation for multi-channel spectrum sharing networks with balanced QoS provisioning and power saving. We formulate this cross-layer optimization problem as a non-cooperative game G _JRPA in which each user has a coupled two-tuple strategy, i.e., simultaneous rate and multi-channel power allocations. A multi-objective cost function is proposed to represent user’s awareness of both QoS provisioning and power saving. We analyze the properties of Nash equilibrium (N.E.) for our G _JRPA , including its existence, and properties of QoS provisioning and power saving. Furthermore, we derive a layered structure by applying the Lagrangian dual decomposition to G _JRPA and design a distributed algorithm to find the N.E.. Simulation results are presented to show the validity of our game theoretic formulation and the performance of our proposed algorithm. Detailed studies on the performance tradeoff between QoS provisioning and power saving are also carried out.

A Generalized Iterative Water-Filling Algorithm for Distributed Power Control in the Presence of a Jammer

Consider a scenario in which $K$ users and a jammer share a common spectrum of $N$ orthogonal tones. Both the users and the jammer have limited power budgets. The goal of each user is to allocate its power across the $N$ tones in such a way that maximizes the total sum rate that he/she can achieve, while treating the interference of other users and the jammer's signal as additive Gaussian noise. The jammer, on the other hand, wishes to allocate its power in such a way that minimizes the utility of the whole system; that being the total sum of the rates communicated over the network. For this noncooperative game, we propose a generalized version of the existing iterative water-filling algorithm whereby the users and the jammer update their power allocations in a greedy manner. We study the existence of a Nash equilibrium of this noncooperative game as well as conditions under which the generalized iterative water-filling algorithm converges to a Nash equilibrium of the game. The conditions that we derive in this paper depend only on the system parameters, and hence can be checked a priori. Simulations show that when the convergence conditions are violated, the presence of a jammer can cause the, otherwise convergent, iterative water-filling algorithm to oscillate.      

MIMO-CDMA系统中一种基于博弈方式的分布式功率控制

针对MIMO-CDMA系统中的无线数据业务,本文研究了分布式非合作功率控制博弈。对MIMO-CDMA系统中的无线数据业务建立了收益函数,该收益函数对功率效率和频谱效率都进行了考虑,并能够反映系统中无线数据用户对服务质量(QoS)的满意程度。以收益函数为基础,建立了两种非合作功率控制博弈模型,并对模型纳什均衡的存在性和唯一性进行了推导。另外,还研究了两种代价函数机制。最后,给出了一种获得纳什均衡的算法,数值仿真结果表明该算法具有良好的性能,有效地控制了各用户的发射功率。     

Dynamic multicast sharing protection algorithm based on fuzzy game in multi-domain optical network

Aiming at the problem of dynamic multicast service protection in multi-domain optical network, this paper proposes a dynamic multicast sharing protection algorithm based on fuzzy game in multi-domain optical network. The algorithm uses the minimum cost spanning tree strategy and fuzzy game theory. First, it virtualizes two planes to calculate the multicast tree and the multicast protection tree respectively. Then, it performs a fuzzy game to form a cooperative alliance to optimize the path composition of each multicast tree. Finally, it generates a pair of optimal multicast work tree and multicast protection tree for dynamic multicast services. The time complexity of the algorithm is O(k3m2n), where n represents the number of nodes in the networks, k represents the number of dynamic multicast requests, and m represents the number of destination nodes for each multicast request. The experimental results show that the proposed algorithm reduces significantly the blocking rate of dynamic multicast services, and improves the utilization of optical network resources within a certain number of dynamic multicast request ranges.     

A joint subcarrier selection and power allocation scheme using variational inequality in OFDM‐based cognitive relay networks

Introducing orthogonal frequency division multiplexing (OFDM) into cognitive radio (CR) can potentially increase the spectrum efficiency, but it also leads to further challenges for the resource allocation of CR networks. In OFDM‐based cognitive relay networks, two of the most significant research issues are subcarrier selection and power allocation. In this paper, a non‐cooperative game model is proposed to maximize the system throughput by jointly optimizing subcarrier selection and power allocation. First, taking the direct and relay links into consideration, an equivalent channel gain is presented to simplify the cooperative relay model into a non‐relay model. Then, a variational inequality method is utilized to prove the existence and uniqueness of the Nash equilibrium solution of the proposed non‐cooperative game. Moreover, to compute the solution of the game, a suboptimal algorithm based on the Lagrange function and distributed iterative water‐filling algorithm is proposed. The proposed algorithm can jointly optimize the process of subcarrier selection and power allocation. Finally, simulation results are shown to demonstrate the effectiveness of the proposed joint subcarrier selection and power allocation scheme. Copyright © 2015 John Wiley & Sons, Ltd.