蜂窝小区干扰抑制与性能增强技术研究
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摘要
正交频分多址(OFDMA)技术将成为未来蜂窝移动通信系统的关键技术之一。由于在小区内部子载波相互正交,小区内干扰将得到有效地降低,而子载波在不同小区的复用将使得小区间干扰问题变得更加严重。在这种背景下,如何抑制小区间干扰和提高小区用户性能就显得日益紧迫。本论文主要研究了蜂窝小区干扰抑制与性能增强技术,其研究工作可分为小区间干扰抑制策略和小区性能增强策略两大部分。
其中,小区间干扰抑制策略的研究分别包含干扰协调、干扰预测和干扰消除三方面：
1、小区间干扰协调主要涉及频率协调和功率协调。针对频率协调,本文分析了现有频率复用方案的研究现状,分别从图论原理、代数解析原理和可拓原理三方面阐述了小区频率协调的理论基础,并介绍了一种软分数频率复用方案,推导了该方案的频率复用系数。仿真结果表明该方案较之软频率复用方案有效提高了小区边缘用户的传输速率。针对功率协调,本文分析了功率控制算法的研究现状,提出了小区间功率控制的思想以及指数迭代的功率控制核心方程,较之通常的算术迭代核心方程,其迭代收敛速度更快。在此基础上,将基于指数迭代的小区间功率控制算法与通常的DPC、DB算法进行了性能比较,仿真结果表明该算法有效改善了用户的SINR,提高了小区中心用户的吞吐量,同时降低了边缘用户的阻塞率。
2、本文提出了主动式的干扰抑制方法——小区间干扰预测的思想,阐述了干扰预测的理论基础——最优估计理论,分别从时间序列和最优滤波估计两角度进行了理论分析,并结合相干时间与预测时间延迟对预测精度的影响分析了干扰预测的有效性。此外,本文还通过采集移动网实测信号,借助时间序列的AR模型、MA模型以及ARIMA模型分析了实测信号的变化趋势,分析结果证实采用时间序列模型可有效预测并跟踪无线信号变化。
3、针对小区间干扰消除技术,本文首先叙述了现有小区间干扰技术的两种技术方法,即空间干扰抑制技术和干扰重构／减去技术。同时基于盲源分离中的独立分量(ICA)技术,提出了一种半盲状态下的Max-SINR ICA干扰消除算法。该算法以提高输出信噪比为目标,优化初始迭代分离矩阵。仿真结果表明,Max-SINR ICA算法的收敛速度快于传统的Fast-ICA算法。此外,通过固定处理帧长和固定热噪声强度两种情况下输入SINR和输出SNR的变化情况比较分析,采用Max-SINR ICA算法可在半盲状态下消除小区间干扰,以及在较低输入SINR,较高输入SNR和较长处理帧长的情况下有效提高输出SNR。
此外,小区性能增强策略的研究包括多小区资源分配、多小区选择优化以及协作多点传输三方面的内容：
1、在现有的多小区资源分配算法中,其普遍特征是当前的资源分配算法通常都依据当前的信道状态信息,然而随着信道状态的变化,基于当前信道状态信息的资源分配方法难以在下一时刻达到设置的优化目标。针对这种问题,本文提出了一种基于预测信息的资源分配方法,以消除基于当前信道状况分配的滞后性。本文以Kalman滤波为例,给出了基于滤波预测的多小区子载波分配方法,基于下一时刻的信道状况最优预测值进行多小区间的子载波分配。该方法通过检测获取不同子载波对用户当前的增益干扰比(GIR),进而采用Kalman滤波估计得到下一时刻的GIR预测值大小,并以该预测值作为子载波分配的依据。与时间序列和维纳滤波预测方法相比,Kalman滤波方法降低了预测算法的复杂度。
2、针对多小区选择优化策略,本文分析了多小区选择的理论基础,介绍了层次分析法(AHP)和灰色关联分析(GRA)原理以及在多目标小区选择中的应用,同时针对小区选择中评判准则过于单-缺乏灵活性和公平性的问题,提出了一种基于多目标优化的新型小区选择算法。该算法借助可拓理论,构造了一种小区性能QoE参数评价的映射表,并将实际参数映射到对应的标度区间,然后计算待评小区的实际分析值。在此基础之上,采用模糊层次分析的方法构造出判断矩阵,并检验其一致性。最后根据权重向量大小对计算出的各小区总效益函数值排序,找到最优的小区选择策略。仿真分析表明,小区性能因子的权重影响到总效益函数值的大小。与现有的小区选择算法相比,该算法在增加一定算法复杂度的情况下,实现了小区性能参数评判的全面性,降低了用户的阻塞率,提高了用户的吞吐量。
3、针对协作多点传输技术,本文首先分析了协作多点传输架构的四种应用场景,即小区内单用户、小区内多用户、小区间单用户和小区间多用户,同时提出了滑动协作小区簇的构造模型。针对原有的频率复用方案基于干扰规避而不支持小区间协作的状况,本文提出了一种支持协作的频率复用方案,仿真结果表明该频率复用方案通过小区间干扰协调以及协作多点传输,有利于提高小区边缘用户吞吐量。另外,针对协作环境下的功率协调问题,本文还提出了一种基于博弈论的协作小区功率分配算法,建立了该环境下的功率分配博弈模型,并证明了纳什均衡的存在性和唯一性,给出了非合作博弈的功率分配算法。仿真结果表明该算法有效提高了小区中心和边缘的吞吐量,降低了边缘用户的阻塞率。
Orthogonal frequency division multiple access (OFDMA) becomes a key technology in the future cellular mobile communication systems. For the sub-carriers in the intra-cell are orthogonal with each other, the intra-cell interference can be avoided efficiently. However, the inter-cell interference problems may become serious since many co-frequency sub-carriers are reused among different cells. Under this background, how to mitigate inter-cell interference and improve the performance for cellular users become more urgent. In this dissertation, the critical technologies about cellular interference mitigation and performance enhancement are researched. The work can be divided into two parts: inter-cell interference mitigation strategies and cellular performance enhancement strategies.
Especially, the inter-cell interference mitigation strategies include three schemes, which respectively are interference coordination, interference prediction and interference cancellation.
1. Frequency coordination and power coordination play important roles in the inter-cell interference coordination. For frequency coordination, the current research about frequency reuse schemes are analyzed, and its theoretical basis are explained from the point of the graph theory, the algebraic analysis theory and the extension theory. Moreover, a novel frequency reuse scheme is introduced in this dissertation, called as soft fractional frequency reuse. Also we derive its frequency reuse factor. By this scheme, simulation results show the throughputs in cell-edge are efficiently improved compared with soft frequency reuse scheme. For power coordination, the current research about power control are analyzed. On this basis, both the inter-cell power control method and the exponential iterative kernel equation are proposed. Compared with the usual arithmetic iterative equation, the convergence speed is faster for the exponential iterative kernel equation. Simulation results show such inter-cell power control algorithm improves the users' SINR, improve the throughputs for cell-center users and reduce the blocking rate for cell-edge users, which shows better performance than DPC and DB algorithm.
2. The inter-cell interference prediction is proposed in this dissertation, which is an active interference mitigation method. Moreover, we give its theoretical basis, which is the optimal estimation theory. It includes two parts:time series and the optimal filter estimation. Besides, the reliability is also analyzed by means of prediction accuracy, which is based on the relationship of the coherent time and the time delay. In addition, we analyze change trend for the actual measured radio signals, with AR model, MA model and ARIMA model. The analytical results show time series model can efficiently predict the radio signals change.
3. For inter-cell interference cancellation, two major technologies are described in this dissertation, which respectively are space interference suppression and interference reconstruction/subtraction. Based on the independent component analysis (ICA) technology in blind source separation, a semi-blind interference cancellation algorithm is proposed, written as Max-SINR ICA, which aims to improve the output SNR and optimize the innitial iterative separation matrix. Simulation results show that the iterative convergence speed for Max-SINR ICA algorithm is faster than the traditional Fast-ICA algorithm. Besides, we consider the input SINR and the output SNR in two scenarios, respectively fix the processing frame and fix the thermal noise. By the Max-SINR ICA algorithm, the inter-cell interference can be efficiently cancelled in a semi-blind state, especially with lower input SINR, higher input SNR and longer processing frame.
On the other hand, the cellular performance enhancement strategies also include three parts, which respectively are multi-cell resource allocation, multi-cell selection optimization and coordinated multi-point transmission.
1. For many existing multi-cell resource allocation algorithms, the resource allocation usually depends on current channel state information (CSI). However, as the CSI varying, such resource allocation method may hardly reach to the optimal object at the next time slot. According to this problem, a novel resource allocation based on prediction information is proposed to eliminate such time lag. Take Kalman filter as example, it allocates the sub-carriers based on the optimal estimated CSI in the next timeslot by filter prediction. Specially, we detect the gain to interference ratio (GIR), and predict the GIR in the next timeslot by Kalman filter, then allocate the sub-carriers according to the predicted GIR. Compared with time series and Wiener filter, Kalman filter reduces the complexity.
2. For multi-cell selection optimization strategy, this dissertation analyzes the theoretical basis of multi-cell selection, then introduces the AHP and GRA principle, and applys such priciples into multi-cell selection. Considering the criteria for Fast Cell Selection (FCS) usually depend on single factor, which is lack of flexibility and fairness. In order to improve FCS performance, a novel algorithm is proposed. Based on extension theory, a flexible mapping table is constructed for Quality of Experience (QoE) evaluation parameters, and some actual performance parameters are mapped into corresponding calibration interval. Then the mapping values are calculated. On this basis, a judgment matrix is constructed by means of Fuzzy Analytic Hierarchy Process (FAHP) analysis, and its consistency is tested. Finally, the total utility function values of each cell are calculated by the weight vectors. According to such values, the optimal FCS scheme can be found. Simulation analysis shows that the weight factors in each cell have a directly effect on utility function. Compared with the existing algorithms, the proposed algorithm makes the judgment of performance parameters to be comprehensive with the proper increase of computing complexity, which reduces the blocking rate and raises the throughputs.
3. For coordinated multi-point transmission technology, this dissertation analyzes four senarios:intra-cell single user, intra-cell multi-users, inter-cell single user and inter-cell multi-users. Moreover, we propose a slide coordinated cell cluster model. Considering the existing frequency reuse schemes aims to interference avoidance while hardly supports inter-cell coordination, we also give a novel frequency reuse scheme supporting coordination. Simulation results show that this scheme enables to improve the throughputs in cell-edge. On the other hand, in order to solve power coordination problem in coordinated scenario, a new power allocation algorithm is presented for coordinated cell, which is based on game theory. Specially, we establish the power allocation game model, prove the existence and uniqueness of Nash equilibrium, and gives a non-cooperative game power allocation algorithm. Simulation results show that the proposed algorithm improves the throughputs in cell-center and cell-edge, and reduces the blocking rate for cell-edge users.
其中,小区间干扰抑制策略的研究分别包含干扰协调、干扰预测和干扰消除三方面：
1、小区间干扰协调主要涉及频率协调和功率协调。针对频率协调,本文分析了现有频率复用方案的研究现状,分别从图论原理、代数解析原理和可拓原理三方面阐述了小区频率协调的理论基础,并介绍了一种软分数频率复用方案,推导了该方案的频率复用系数。仿真结果表明该方案较之软频率复用方案有效提高了小区边缘用户的传输速率。针对功率协调,本文分析了功率控制算法的研究现状,提出了小区间功率控制的思想以及指数迭代的功率控制核心方程,较之通常的算术迭代核心方程,其迭代收敛速度更快。在此基础上,将基于指数迭代的小区间功率控制算法与通常的DPC、DB算法进行了性能比较,仿真结果表明该算法有效改善了用户的SINR,提高了小区中心用户的吞吐量,同时降低了边缘用户的阻塞率。
2、本文提出了主动式的干扰抑制方法——小区间干扰预测的思想,阐述了干扰预测的理论基础——最优估计理论,分别从时间序列和最优滤波估计两角度进行了理论分析,并结合相干时间与预测时间延迟对预测精度的影响分析了干扰预测的有效性。此外,本文还通过采集移动网实测信号,借助时间序列的AR模型、MA模型以及ARIMA模型分析了实测信号的变化趋势,分析结果证实采用时间序列模型可有效预测并跟踪无线信号变化。
3、针对小区间干扰消除技术,本文首先叙述了现有小区间干扰技术的两种技术方法,即空间干扰抑制技术和干扰重构／减去技术。同时基于盲源分离中的独立分量(ICA)技术,提出了一种半盲状态下的Max-SINR ICA干扰消除算法。该算法以提高输出信噪比为目标,优化初始迭代分离矩阵。仿真结果表明,Max-SINR ICA算法的收敛速度快于传统的Fast-ICA算法。此外,通过固定处理帧长和固定热噪声强度两种情况下输入SINR和输出SNR的变化情况比较分析,采用Max-SINR ICA算法可在半盲状态下消除小区间干扰,以及在较低输入SINR,较高输入SNR和较长处理帧长的情况下有效提高输出SNR。
此外,小区性能增强策略的研究包括多小区资源分配、多小区选择优化以及协作多点传输三方面的内容：
1、在现有的多小区资源分配算法中,其普遍特征是当前的资源分配算法通常都依据当前的信道状态信息,然而随着信道状态的变化,基于当前信道状态信息的资源分配方法难以在下一时刻达到设置的优化目标。针对这种问题,本文提出了一种基于预测信息的资源分配方法,以消除基于当前信道状况分配的滞后性。本文以Kalman滤波为例,给出了基于滤波预测的多小区子载波分配方法,基于下一时刻的信道状况最优预测值进行多小区间的子载波分配。该方法通过检测获取不同子载波对用户当前的增益干扰比(GIR),进而采用Kalman滤波估计得到下一时刻的GIR预测值大小,并以该预测值作为子载波分配的依据。与时间序列和维纳滤波预测方法相比,Kalman滤波方法降低了预测算法的复杂度。
2、针对多小区选择优化策略,本文分析了多小区选择的理论基础,介绍了层次分析法(AHP)和灰色关联分析(GRA)原理以及在多目标小区选择中的应用,同时针对小区选择中评判准则过于单-缺乏灵活性和公平性的问题,提出了一种基于多目标优化的新型小区选择算法。该算法借助可拓理论,构造了一种小区性能QoE参数评价的映射表,并将实际参数映射到对应的标度区间,然后计算待评小区的实际分析值。在此基础之上,采用模糊层次分析的方法构造出判断矩阵,并检验其一致性。最后根据权重向量大小对计算出的各小区总效益函数值排序,找到最优的小区选择策略。仿真分析表明,小区性能因子的权重影响到总效益函数值的大小。与现有的小区选择算法相比,该算法在增加一定算法复杂度的情况下,实现了小区性能参数评判的全面性,降低了用户的阻塞率,提高了用户的吞吐量。
3、针对协作多点传输技术,本文首先分析了协作多点传输架构的四种应用场景,即小区内单用户、小区内多用户、小区间单用户和小区间多用户,同时提出了滑动协作小区簇的构造模型。针对原有的频率复用方案基于干扰规避而不支持小区间协作的状况,本文提出了一种支持协作的频率复用方案,仿真结果表明该频率复用方案通过小区间干扰协调以及协作多点传输,有利于提高小区边缘用户吞吐量。另外,针对协作环境下的功率协调问题,本文还提出了一种基于博弈论的协作小区功率分配算法,建立了该环境下的功率分配博弈模型,并证明了纳什均衡的存在性和唯一性,给出了非合作博弈的功率分配算法。仿真结果表明该算法有效提高了小区中心和边缘的吞吐量,降低了边缘用户的阻塞率。
Orthogonal frequency division multiple access (OFDMA) becomes a key technology in the future cellular mobile communication systems. For the sub-carriers in the intra-cell are orthogonal with each other, the intra-cell interference can be avoided efficiently. However, the inter-cell interference problems may become serious since many co-frequency sub-carriers are reused among different cells. Under this background, how to mitigate inter-cell interference and improve the performance for cellular users become more urgent. In this dissertation, the critical technologies about cellular interference mitigation and performance enhancement are researched. The work can be divided into two parts: inter-cell interference mitigation strategies and cellular performance enhancement strategies.
Especially, the inter-cell interference mitigation strategies include three schemes, which respectively are interference coordination, interference prediction and interference cancellation.
1. Frequency coordination and power coordination play important roles in the inter-cell interference coordination. For frequency coordination, the current research about frequency reuse schemes are analyzed, and its theoretical basis are explained from the point of the graph theory, the algebraic analysis theory and the extension theory. Moreover, a novel frequency reuse scheme is introduced in this dissertation, called as soft fractional frequency reuse. Also we derive its frequency reuse factor. By this scheme, simulation results show the throughputs in cell-edge are efficiently improved compared with soft frequency reuse scheme. For power coordination, the current research about power control are analyzed. On this basis, both the inter-cell power control method and the exponential iterative kernel equation are proposed. Compared with the usual arithmetic iterative equation, the convergence speed is faster for the exponential iterative kernel equation. Simulation results show such inter-cell power control algorithm improves the users' SINR, improve the throughputs for cell-center users and reduce the blocking rate for cell-edge users, which shows better performance than DPC and DB algorithm.
2. The inter-cell interference prediction is proposed in this dissertation, which is an active interference mitigation method. Moreover, we give its theoretical basis, which is the optimal estimation theory. It includes two parts:time series and the optimal filter estimation. Besides, the reliability is also analyzed by means of prediction accuracy, which is based on the relationship of the coherent time and the time delay. In addition, we analyze change trend for the actual measured radio signals, with AR model, MA model and ARIMA model. The analytical results show time series model can efficiently predict the radio signals change.
3. For inter-cell interference cancellation, two major technologies are described in this dissertation, which respectively are space interference suppression and interference reconstruction/subtraction. Based on the independent component analysis (ICA) technology in blind source separation, a semi-blind interference cancellation algorithm is proposed, written as Max-SINR ICA, which aims to improve the output SNR and optimize the innitial iterative separation matrix. Simulation results show that the iterative convergence speed for Max-SINR ICA algorithm is faster than the traditional Fast-ICA algorithm. Besides, we consider the input SINR and the output SNR in two scenarios, respectively fix the processing frame and fix the thermal noise. By the Max-SINR ICA algorithm, the inter-cell interference can be efficiently cancelled in a semi-blind state, especially with lower input SINR, higher input SNR and longer processing frame.
On the other hand, the cellular performance enhancement strategies also include three parts, which respectively are multi-cell resource allocation, multi-cell selection optimization and coordinated multi-point transmission.
1. For many existing multi-cell resource allocation algorithms, the resource allocation usually depends on current channel state information (CSI). However, as the CSI varying, such resource allocation method may hardly reach to the optimal object at the next time slot. According to this problem, a novel resource allocation based on prediction information is proposed to eliminate such time lag. Take Kalman filter as example, it allocates the sub-carriers based on the optimal estimated CSI in the next timeslot by filter prediction. Specially, we detect the gain to interference ratio (GIR), and predict the GIR in the next timeslot by Kalman filter, then allocate the sub-carriers according to the predicted GIR. Compared with time series and Wiener filter, Kalman filter reduces the complexity.
2. For multi-cell selection optimization strategy, this dissertation analyzes the theoretical basis of multi-cell selection, then introduces the AHP and GRA principle, and applys such priciples into multi-cell selection. Considering the criteria for Fast Cell Selection (FCS) usually depend on single factor, which is lack of flexibility and fairness. In order to improve FCS performance, a novel algorithm is proposed. Based on extension theory, a flexible mapping table is constructed for Quality of Experience (QoE) evaluation parameters, and some actual performance parameters are mapped into corresponding calibration interval. Then the mapping values are calculated. On this basis, a judgment matrix is constructed by means of Fuzzy Analytic Hierarchy Process (FAHP) analysis, and its consistency is tested. Finally, the total utility function values of each cell are calculated by the weight vectors. According to such values, the optimal FCS scheme can be found. Simulation analysis shows that the weight factors in each cell have a directly effect on utility function. Compared with the existing algorithms, the proposed algorithm makes the judgment of performance parameters to be comprehensive with the proper increase of computing complexity, which reduces the blocking rate and raises the throughputs.
3. For coordinated multi-point transmission technology, this dissertation analyzes four senarios:intra-cell single user, intra-cell multi-users, inter-cell single user and inter-cell multi-users. Moreover, we propose a slide coordinated cell cluster model. Considering the existing frequency reuse schemes aims to interference avoidance while hardly supports inter-cell coordination, we also give a novel frequency reuse scheme supporting coordination. Simulation results show that this scheme enables to improve the throughputs in cell-edge. On the other hand, in order to solve power coordination problem in coordinated scenario, a new power allocation algorithm is presented for coordinated cell, which is based on game theory. Specially, we establish the power allocation game model, prove the existence and uniqueness of Nash equilibrium, and gives a non-cooperative game power allocation algorithm. Simulation results show that the proposed algorithm improves the throughputs in cell-center and cell-edge, and reduces the blocking rate for cell-edge users.
引文
[1]Foschini GJ., et al. A simple distributed autonomous power control algorithm and its convergence. IEEE Trans. on Vehicular Technology.1993,42(4):641-646.
[2]Boudreau G, Panicker J., Guo N. et al. Interference coordination and cancellation for 4G networks, IEEE Communications Magazine,2009,47(4):74-81.
[3]3GPP Rl-050738, Interference mitigation considerations and results on frequency reuse. Siemens, Sept 2005.
[4]3GPP R1-050507, Soft frequency reuse scheme for UTRAN LTE. Huawei, May 2005.
[5]3GPP R1-050896, Description and simulations of interference management technique for OFDMA based E-UTRA downlink evaluation, Qualcomm,2005.
[6]3GPP TR 25.912. Feasibility Study for Evolved UTRA and UTRAN, August 2007.
[7]Racz A., Reider N., Fodor G. On the impact of inter-cell interference in LTE. IEEE GLOBECOM,2008, (1):1-6.
[8]Simonsson A., Frequency reuse and intercell interference coordination in E-UTRA, Dublin: IEEE VTC 2007-Spring, Apr.2007, (1):3091-3095.
[9]W K Hale. Frequency assignment:theory and applications. Proc. of The IEEE,1980,68 (12):1497-1514.
[10]杜鹃,张玉清.重图的T-染色.河北省科学院学报,2006,23(3)：1-4.
[11]IMT-A_LTE+_09229 Inter-cell Interference Coordination for DL CoMP, June 2009.
[12]蔡文,杨春燕,何斌.可拓逻辑初步.北京：科学出版社,2003：69-77.
[13]3GPP R1-050738, Interference mitigation considerations and results on frequency reuse. Siemens, Sept 2005.
[14]3GPP R1-050764, Inter-cell interference handling for E-UTRA, Ericsson, Sep.2005.
[15]3GPP R1-050407, Interference coordination in new OFDM DL air interface, Alcatel, May 2005.
[16]3GPP R1-083569, Further Discussion on Inter-Cell Interference Mitigation through Limited Coordination, Samsung, Sep.2008.
[17]3GPP2 C30-20060911-064R1, Soft Fractional Frequency Reuse,2006.
[18]Necker M.. Interference Coordination in Cellular OFDMA Networks. IEEE Network,2008, 22(6):12-19.
[19]Necker M.C., Local interference coordination in cellular 802.16e networks. IEEE VTC 2007-Fall, Baltimore, Oct.2007.
[20]3GPP TR25.814, Physical layer aspects for evolved UTRA,2006.
[21]3GPP TS36.213, Evolved Universal Terrestrial Radio Access Network (E-UTRAN):Physical layer procedures,2006.
[22]Zhang Hui, Xu Xiaodong, Li Jingya, et al. Performance of power control in inter-cell interference coordination. Journal of Chinese Universities of Posts and Telecommunications, 2010,17(1):37-43.
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[1]3GPP TR 36.814, Further Advancements for E-UTRA Physical Layer Aspects (Release 9), May 2009.
[2]3GPP R1-082024, A discussion on some technology components for LTE-Advanced, May 2008.
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[11]3GPP TR25.814, Physical layer aspects for evolved UTRA,2006.
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[3]3GPP Rl-050738, Interference mitigation considerations and results on frequency reuse. Siemens, Sept 2005.
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[5]3GPP R1-050896, Description and simulations of interference management technique for OFDMA based E-UTRA downlink evaluation, Qualcomm,2005.
[6]3GPP TR 25.912. Feasibility Study for Evolved UTRA and UTRAN, August 2007.
[7]Racz A., Reider N., Fodor G. On the impact of inter-cell interference in LTE. IEEE GLOBECOM,2008, (1):1-6.
[8]Simonsson A., Frequency reuse and intercell interference coordination in E-UTRA, Dublin: IEEE VTC 2007-Spring, Apr.2007, (1):3091-3095.
[9]W K Hale. Frequency assignment:theory and applications. Proc. of The IEEE,1980,68 (12):1497-1514.
[10]杜鹃,张玉清.重图的T-染色.河北省科学院学报,2006,23(3)：1-4.
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[12]蔡文,杨春燕,何斌.可拓逻辑初步.北京：科学出版社,2003：69-77.
[13]3GPP R1-050738, Interference mitigation considerations and results on frequency reuse. Siemens, Sept 2005.
[14]3GPP R1-050764, Inter-cell interference handling for E-UTRA, Ericsson, Sep.2005.
[15]3GPP R1-050407, Interference coordination in new OFDM DL air interface, Alcatel, May 2005.
[16]3GPP R1-083569, Further Discussion on Inter-Cell Interference Mitigation through Limited Coordination, Samsung, Sep.2008.
[17]3GPP2 C30-20060911-064R1, Soft Fractional Frequency Reuse,2006.
[18]Necker M.. Interference Coordination in Cellular OFDMA Networks. IEEE Network,2008, 22(6):12-19.
[19]Necker M.C., Local interference coordination in cellular 802.16e networks. IEEE VTC 2007-Fall, Baltimore, Oct.2007.
[20]3GPP TR25.814, Physical layer aspects for evolved UTRA,2006.
[21]3GPP TS36.213, Evolved Universal Terrestrial Radio Access Network (E-UTRAN):Physical layer procedures,2006.
[22]Zhang Hui, Xu Xiaodong, Li Jingya, et al. Performance of power control in inter-cell interference coordination. Journal of Chinese Universities of Posts and Telecommunications, 2010,17(1):37-43.
[1]. G.J. Foschini, et al. A simple distributed autonomous power control algorithm and its convergence. IEEE Trans. on Vehicular Technology.1993,42(4):641-646.
[2].沈嘉.3GPP长期演进(LTE)技术原理与系统设计,人民邮电出版社,2008.
[3].3GPP. TR25.814, Physical layer aspects for evolved UTRA,2006.
[4].3GPP. R1-050896, Description and simulation of interference management technique for OFDMA based EUTRA downlink evaluation,2005.
[5]. J. Zander, Performance of optimum transmitter power control in cellular radio systems. IEEEE Transactions on Vehicular Technology,1992,41(1):57-62.
[6]. J. Zander, Distributed cochannel interference control in cellular radio systems. IEEE Transactions on Vehicular Technology,1992,41(3):305-311.
[7]. V.Shah, N.B.Mandayam, D.J.Goodman, Power control for wireless data based on utility and pricing. IEEE International Symposium on Personal, Indoor and Mobile Radio Communications,1998,3(3):1427-1432.
[8]. V. Hasu, H.N. Koivo, A block MIMO PI-power control algorithm for cellular systems. IEEE Vehicular Technology Conference, Atlantic City, NJ, USA,2001, (3):1927-1931.
[9]. Z. Uykan, R. Jantti, A PI-power control algorithm for cellular radio systems. IEEE Sixth International Symposium on Spread Spectrum Techniques and Applications,2000, (2): 782-785.
[10].S.A.Grandhi, J. Zander, Constrained power control in cellular radio systems. Stockholm: IEEE Vehicular Technology Conference, Jun.1994, (2):824-828.
[11].Y. Leung. Power control in cellular networks subject to measurement error. IEEE Transactions on Communications, Jul.1996,44(7):772-775.
[12]1.赵琳.CDMA系统中改进的功率控制算法.北京邮电大学学报,2007,30(3)：96-99.
[13]. Goodman D.J., Mandayam N.B.. Power control for wireless data. IEEE Wireless Communications,2000,7(2):48-54.
[14].Saraydar C.U., Mandayam N.B., Goodman D.J. Efficient power control via pricing in wireless data networks. IEEE Transactions on Communications,2002,50(2):291-303.
[15].Saraydar C.U., Mandayam N.B., Goodman D.J. Pricing and power control in a multicell wireless data network. IEEE Journal on Selected Areas in Communications,2001, 19(10):1883-1892.
[16].Koskie S., Gajic Z. A Nash game algorithm for SIR-based power control in 3G wireless CDMA networks. IEEE/ACM Transactions on Networking,2005,13(5):1017-1026.
[17].俞的雄,等.CDMA系统中一种新的分布式博弈功率控制算法.电子与信息学报,2008,30(2)：443-446.
[18].Kivanc D., et al, Computationally efficient bandwidth allocation and power control for OFDMA. IEEE Transactions on Wireless Communications,2003,2(6):1150-1158.
[19].Wang Lan, Niu Zhisheng. Adaptive power control in multi-cell OFDM systems:a noncooperative game with power unit based utility. IEICE Transactions on Communication,2006, E89-B (6):1951-1954.
[20]. Song G., Li Y. (G), Cross-layer optimization for OFDM wireless networks:Algorithm development. IEEE Transactions on Wireless Communications,2005,4(5):625-634.
[21].程世伦,等.新的认知无线电功率控制博弈算法.通信学报,2007,28(3)：100-107.
[22].张天魁,等.基于博弈论的OFDMA系统多小区功率分配协调算法.通信学报,2008,29(1)：22-29.
[23].张天魁,等.用于多小区OFDM系统的分布式上行功率控制算法.北京工业大学学报,2008,34(6)：561-566.
[24].李中年,等.一种基于IoT控制的小区间功率控制方法.电子与信息学报,2009,31(11)：2703-2707.
[25].Zhang Hui, Xu Xiaodong, Li Jingya, Tao Xiaofeng. Performance of power control in inter-cell interference coordination. Journal of Chinese Universities of Posts and Telecommunications,2010,17(1):37-43.
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