基于定向天线的Ad Hoc网络拓扑控制算法研究
|
摘要
随着通信技术、嵌入式计算技术和传感器技术的迅速发展,Ad Hoc网络作为一种新型无线网络通信模式成为了近年来学术界的主要研究热点之一,网络的随机部署、自组织、环境自适应等特性推进了实现在任意环境下自由通信的进程,同时也为军事通信、灾难救助和临时通信等诸多领域提供了有效的解决方案。
在Ad Hoc网络中,网络节点大多是体积微小的嵌入式设备,只能依靠电池作为其能量来源,且通常工作在较为复杂、危险的地理区域,节点的电池得不到更换或能量的补充,如果所有节点都以最大发射功率工作,节点有限的能量将被通信部件快速耗尽,影响节点的无线通信质量,从而降低网络生命周期。并且,网络中每个节点的无线信号将覆盖其它大量节点,造成无线信号冲突频繁,降低网络吞吐量。另外,在生成的网络拓扑中将存在大量的边,导致网络拓扑信息量大、路由计算复杂。如何有效的平衡节点能耗和降低节点之间的干扰,是目前AdHoc网络研究的关键问题之一。
拓扑控制技术是Ad Hoc网络的重要组成部分,在保证网络连通的前提下,通过调整节点发射功率和建立合适的相邻关系,形成优化的拓扑结构,达到延长网络生命周期,提高网络吞吐量的目的。本文的主要工作如下：
(1)对现有的几种典型的拓扑控制算法进行了简要的算法分析,并实现了几种拓扑控制算法的模拟器。实验表明经过拓扑控制算法后减小了节点的度和传输范围,提高了网络的节能性和抗干扰性。
(2)针对自适应波束定向天线节能与抗干扰的优点,提出了一种基于自适应波束天线的局部优化拓扑控制算法-SLTC(Steered beam directional antenna based Local optimal Topology Control algorithm)算法,通过OPNET网络仿真工具搭建算法性能仿真平台,分析了不同网络负载,不同拓扑控制算法生成的拓扑结构的网络吞吐量、平均端到端延时和路由开销等参数。实验结果表明,SLTC算法减小了节点的度和传输范围,提高了网络吞吐量,减小了网络延迟和路由开销。
(3)在SLTC算法的基础上进行均衡节点能耗控制。改进算法以均衡网络能耗为主要目的,考虑到网络中节点能量不均衡的情况,通过选取剩余能量最大的节点担任区域头节点,并周期性的感知邻居节点能量变化,重建网络拓扑,均衡网络能耗,实验表明改进算法减少了死亡节点数量。
With the rapid development of communication technology, embedded computing technology and sensor technology, Ad Hoc networks, as a new type of wireless network communication mode, have become one of the main academia research focuses in recent years. The characteristics of stochastic laid, self-organization and adaptation to the environment have promoted the process of free communications in any environment, and have provided effective solutions for military communications, disaster relief, interim communications, etc.
In Ad Hoc networks, network nodes are mostly small volume embedded equipments can only take battery as the source of energy and usually exist in the complicated and dangerous geographic areas; and the battery of nodes can't be replaced or recharged. If all nodes work with the maximum transmit power, the limited energy of the nodes will be depleted quickly by communications components, which will affect the quality of wireless communications and lower the network life cycle. At the same time, the wireless signals of every node in the network will cover other large number of nodes, which will make the wireless signals conflict very frequently and lower the network throughput. Besides, a large number of edges existed in the generated network topology make the amount of network topology information large and make the routing calculation complicated. How to balance the node energy consumption effectively and lower the interference between nodes is one of the key issues in Ad Hoc network research.
Topology control technology is the important part of Ad Hoc network. In the premise of ensuring network connectivity, topology control technology forms optimized topology through adjusting the transmit power of nodes and building appropriate adjacent relationship to extend the network life cycle and improve the network throughput. The main works of the thesis are as follows:
(1) Analyse several existing classical topology control algorithms and get some simulators of them.the result shows that the alogorithms reduce the average node'degree and transmission range,which can improved the capacity of economizing on energy and the capacity of anti-jamming.
(2) Advance a topology control algorithm-SLTC(Steered beam directional antenna based Local optimal Topology Control algorithm) for local optimization based on the steered beam directional antennas according to the advantages of energy conservation and resistance to interference of the steered beam directional antennas. To build SLTC algorithm performance simulation platform through OPNET network simulation tools and analyze various loads, the network throughput of diverse topologies generated by different topology control algorithm and the parameters of average end-to-end delay and routing overhead, etc. The results of simulation experiments show that the proposed algorithm has reduced the average node'degree and transmission range, boosted the capacity of network throughput,reduced the delay and routing overhead.
(3) Control the dissipative of node energy based on the SLTC algorithm. The main aim of the algorithm is to balance network energy, which has considered the circumstance of node energy imbalance in the network. To extend the network life cycle through selecting the node with the largest residual energy as the arehead and apperceiving the change of neighbors'energy periodically to rebuild the network topology and balance network energy.the result shows that the new algorithm reduces the number of the dead node.
在Ad Hoc网络中,网络节点大多是体积微小的嵌入式设备,只能依靠电池作为其能量来源,且通常工作在较为复杂、危险的地理区域,节点的电池得不到更换或能量的补充,如果所有节点都以最大发射功率工作,节点有限的能量将被通信部件快速耗尽,影响节点的无线通信质量,从而降低网络生命周期。并且,网络中每个节点的无线信号将覆盖其它大量节点,造成无线信号冲突频繁,降低网络吞吐量。另外,在生成的网络拓扑中将存在大量的边,导致网络拓扑信息量大、路由计算复杂。如何有效的平衡节点能耗和降低节点之间的干扰,是目前AdHoc网络研究的关键问题之一。
拓扑控制技术是Ad Hoc网络的重要组成部分,在保证网络连通的前提下,通过调整节点发射功率和建立合适的相邻关系,形成优化的拓扑结构,达到延长网络生命周期,提高网络吞吐量的目的。本文的主要工作如下：
(1)对现有的几种典型的拓扑控制算法进行了简要的算法分析,并实现了几种拓扑控制算法的模拟器。实验表明经过拓扑控制算法后减小了节点的度和传输范围,提高了网络的节能性和抗干扰性。
(2)针对自适应波束定向天线节能与抗干扰的优点,提出了一种基于自适应波束天线的局部优化拓扑控制算法-SLTC(Steered beam directional antenna based Local optimal Topology Control algorithm)算法,通过OPNET网络仿真工具搭建算法性能仿真平台,分析了不同网络负载,不同拓扑控制算法生成的拓扑结构的网络吞吐量、平均端到端延时和路由开销等参数。实验结果表明,SLTC算法减小了节点的度和传输范围,提高了网络吞吐量,减小了网络延迟和路由开销。
(3)在SLTC算法的基础上进行均衡节点能耗控制。改进算法以均衡网络能耗为主要目的,考虑到网络中节点能量不均衡的情况,通过选取剩余能量最大的节点担任区域头节点,并周期性的感知邻居节点能量变化,重建网络拓扑,均衡网络能耗,实验表明改进算法减少了死亡节点数量。
With the rapid development of communication technology, embedded computing technology and sensor technology, Ad Hoc networks, as a new type of wireless network communication mode, have become one of the main academia research focuses in recent years. The characteristics of stochastic laid, self-organization and adaptation to the environment have promoted the process of free communications in any environment, and have provided effective solutions for military communications, disaster relief, interim communications, etc.
In Ad Hoc networks, network nodes are mostly small volume embedded equipments can only take battery as the source of energy and usually exist in the complicated and dangerous geographic areas; and the battery of nodes can't be replaced or recharged. If all nodes work with the maximum transmit power, the limited energy of the nodes will be depleted quickly by communications components, which will affect the quality of wireless communications and lower the network life cycle. At the same time, the wireless signals of every node in the network will cover other large number of nodes, which will make the wireless signals conflict very frequently and lower the network throughput. Besides, a large number of edges existed in the generated network topology make the amount of network topology information large and make the routing calculation complicated. How to balance the node energy consumption effectively and lower the interference between nodes is one of the key issues in Ad Hoc network research.
Topology control technology is the important part of Ad Hoc network. In the premise of ensuring network connectivity, topology control technology forms optimized topology through adjusting the transmit power of nodes and building appropriate adjacent relationship to extend the network life cycle and improve the network throughput. The main works of the thesis are as follows:
(1) Analyse several existing classical topology control algorithms and get some simulators of them.the result shows that the alogorithms reduce the average node'degree and transmission range,which can improved the capacity of economizing on energy and the capacity of anti-jamming.
(2) Advance a topology control algorithm-SLTC(Steered beam directional antenna based Local optimal Topology Control algorithm) for local optimization based on the steered beam directional antennas according to the advantages of energy conservation and resistance to interference of the steered beam directional antennas. To build SLTC algorithm performance simulation platform through OPNET network simulation tools and analyze various loads, the network throughput of diverse topologies generated by different topology control algorithm and the parameters of average end-to-end delay and routing overhead, etc. The results of simulation experiments show that the proposed algorithm has reduced the average node'degree and transmission range, boosted the capacity of network throughput,reduced the delay and routing overhead.
(3) Control the dissipative of node energy based on the SLTC algorithm. The main aim of the algorithm is to balance network energy, which has considered the circumstance of node energy imbalance in the network. To extend the network life cycle through selecting the node with the largest residual energy as the arehead and apperceiving the change of neighbors'energy periodically to rebuild the network topology and balance network energy.the result shows that the new algorithm reduces the number of the dead node.
引文
[1]郑少仁,王海涛,赵志峰.Ad Hoc网络技术.北京：人民邮电出版社,2005,2-4
[2]田乐,谢东亮,韩冰等.无线传感器网络中瓶颈节点的研究.软件学报,2006,17(4)：830-837
[3]Liu G, Li Z G, Zhou X S. Transmission power control for wireless Sensor networks In:Proc of International Conference on Wireless Communications Networking and Mobile Computing, WiCOM. Shanghai,2007,2596-2599
[4]Santi P. Topology Control in Wireless Ad Hoc and Sensor Networks. ACM Computing Surveys,2005,37(2):164-194
[5]Huang Z C, Shen C C, S. Srisathapornphat, et al. Topology control for Ad hoc networks with directional antennas. In:Proc of IEEE ICCCN. Istanbul,2002, 16-21
[6]Uesh K, Himanshu G, Samir R D. A topology control approach to using directional antennas in wireless mesh networks. In:Proc of IEEE ICC. Istanbul, 2006,4083-4088
[7]朱思明.无线Ad Hoc网络拓扑控制算法仿真和研究：[西安电子科技大学硕士学位论文].西安：西安电子科技大学,2006,2-4
[8]张学,陆桑璐,陈贵海等.无线传感器网络的拓扑控制.软件学报,2007,18(4)：943-954
[9]Rodoplu V, Meng T H. Minimum energy mobile wireless networks. IEEE Journal on Selected Areas in Communications,1999,17(8):1333-1344
[10]Dan Y, Hui L. On the definition of ad hoc network connectivity. In:Proc of International Conference on Communication Technology. Beijing,2003,990-994
[11]Tao Y, Papadias D, Sun J. The TPR*-Tree:An Optimized Spatio-Temporal Access Method for Predictive Queries. In:Proc of VLDB. Berlin,2003,790-801
[12]Amis A D, Prakash R, Vuong T H P, et al. Max-Min D-Cluster formation in wireeless Ad. Hoc networks. In:Proc of IEEE Conf on Comptuer Commnunications. TelAviv,1999,32-41
[13]Kubish M, Karl H, Wolisz A, et al. Distributed algorithms for transmission power control in wireless sensor networks. In:Proc of IEEE WCNC, New Orleans, Louisiana,2003,35-42
[14]Feng X, Kumar P R. The Number of Neighbors Needed for Connectivity of Wireless Networks. Wireless Networks,2004,10(2):169-181
[15]Douglas M B, Mauro L, Giovanni R, et al. The K-Neigh protocol for Symmetric Topology Control in Ad Hoc Networks. In:Proc of ACM Mobile Ad Hoc, New York,2003,141-152
[16]Ram R, Regina R H. Topology Control of Multihop Wireless Networks using Transmit Power Adjustment. In:Proc of IEEE INFOCOM. Tel-Aviv,2000, 404-413
[17]Li L, Halpern J Y, Bahl P, etal. A cone-based distributed topology-control algorithm for wireless multi-hop networks. IEEE/ACM Transactions on Networking,2005,13(1):147-159
[18]Li L, Hou J C, Bahl P. Analysis of a cone-based distributed topology control algorithm for wireless multi-hop networks. ACM Symp on Principles of Distributed Computing, Newport, RI, May,2001,6(8):26-42
[19]Godfried T. Toussaint. The relative neighborhood graph of a finite planar set. Pattern Recognition,1980,12(4):261-268
[20]Gabriel K R, Robert R S. A new statistical approach to geographic variation analysis. Systematic Zoology,1969,18(3):259-278
[21]Jie G, Leonidas J G. John H, et al. Geometric spanner for routing in mobile networks. In:Proc of Proceedings of the 2nd ACM symposium on mobile ad hoc networking & computing. Long Beach,2001,45-55
[22]Tamas L. New Results on Geometric Spanners and Their Applications: [dissertation]. Paderborn:University of Paderborn,1999,19-27
[23]Rajmohan R. Topology control and routing in ad hoc networks. A survey. SIGACT News,2002,33(2):60-73
[24]Xiang Y L, Peng J W, Yu W. Power efficient and sparse spanner for wireless ad hoc networks. In:Proc of IEEE Int Conf on Computer Communications and Networks (ICCCN01). Chicago,2001,564-567
[25]Xiang Y L. Algorithmic, Geometric and Graphs Issues in Wireless Networks. Wireless Comm. and Mobile Computing,2003,3(2):119-140
[26]Ning L, Jennifer C H, Lui S. Design and Analysis of an MST-Based Topology Control Algorithm. In:Proc of IEEE INFOCOM'03. San Francisco,2003, 1702-1712
[27]Ning L, Jennifer C H. Topology control in heterogeneous wireless networks: Porblems and Soltuions. In:Proc of 23th Joint Conf on IEEE Computer and Communications Socielies. Hong Kong,2004,232-243
[28]Heinzelman W R, Chandrakasan A, Balakrishnan H. An application-specific protocol architecture for wireless microsensor networks. IEEE Transactions on Wireless Communications,2002,1(4):660-670
[29]Younis O, fahmy S. HEED:A hybrid, energy-efficient; distributed clustering approach for ad hoc sensor networks. IEEE Trans. on Mobile Computing,2004, 3(4):600-669
[30]Xu Y, Heidemann J, Estrin D. Geography-Informed energy conservation for ad hoc routing. In:Proc of Rose C, ed. Proc. of the ACM Int'l Conf. on Mobile Computing and Networking. New York,2001,70-85
[31]Ram. R. On the performance of Ad hoc networks using beamforming antennas. In: Proc of ACM Mobile ad hoc. Long Beach,2001,95-105
[32]Su Y, Yong P, Shivkumar K. On the capacity improvement of Ad hoc wireless networks using directional antennas. In:Proc of Proceedings of the 4th ACM international symposium on Mobile Ad hoc Networking and Computing. Annapolis,2003,108-116
[33]Salvatore B, Jeffrey F, Ravi G, et al. Smart Antenna System Analysis, Integration and Performance for Mobile Ad-Hoc Networks(MANETs). In:Proc of IEEE Transactions on Antennas and Propagation. New York,2002,571-581
[34]Carl B. Dietrich, Jr. Adaptive Arrays and Diversity Antenna Configurations for Handheld Wireless Communication Terminals:[dissertation]. Virginia: Blacksburg, Virginia,2000,30-51
[35]Richard B. Ertel Antenna array systemsp ropagation and performance: [dissertation]. Virginia:Blacksburg, Virginia,1999,23-41
[36]Vikash S. A Smart Antennas & Power Management in Wireless Networks: [dissertation]. Virginia:Blacksburg, Virginia,2002,27-45
[37]Bellofiore, S Balanis, C A Smart-antenna system for mobile communication network. IEEE Antennas and Propagation Magazine,2002,44 (3):145-154
[38]Balanis C A. Antenna Theory Analysis and Design. New York:Harper and Row, Publishers,1982,805-807
[39]Vinod N, Li. X G, Ramakrishna J. Power efficienttopology control for wireless networks with switched beam directional antennas. In:Proc of IEEE MASS'05. Washington, DC,2005,3-11
[40]贺鹏,李建东,陈彦辉等.Ad Hoc网络中基于方向性天线的分布式拓扑控制算法.软件学报,2007,18(6)：1308-1318
[41]Gentian J, Wenjie L, Srikanth V K. An integrated neighbor discovery and MAC protocol for Ad hoc networks using directional antennas. In:Proc of IEEE WoW-MoM. Taormina, Italy,2007,11-21
[42]王东,陈文斌,胡婷等.自组网中基于自适应波束天线的拓扑控制算法.计算机研究与发展,2010,47(3)：407-415
[43]邢云冰,史浩山.基于备用节点的无线传感器网络LEACH协议的改进.传感技术学报,2007,20(7)：1592-1596
[44]Bahramgiri M, Hajiaghayi M T, Mirrokni V S. Fault-Tolerant and 3-dimensional distributed topology control algorithms in wireless multihop networks. Wireless Networks,2006(4):179-188
[45]Kawadia. V. Protocols and architecture for wireless ad hoc networks: [dissertation]. University of Urbana-Champaign,2004,35-42
[2]田乐,谢东亮,韩冰等.无线传感器网络中瓶颈节点的研究.软件学报,2006,17(4)：830-837
[3]Liu G, Li Z G, Zhou X S. Transmission power control for wireless Sensor networks In:Proc of International Conference on Wireless Communications Networking and Mobile Computing, WiCOM. Shanghai,2007,2596-2599
[4]Santi P. Topology Control in Wireless Ad Hoc and Sensor Networks. ACM Computing Surveys,2005,37(2):164-194
[5]Huang Z C, Shen C C, S. Srisathapornphat, et al. Topology control for Ad hoc networks with directional antennas. In:Proc of IEEE ICCCN. Istanbul,2002, 16-21
[6]Uesh K, Himanshu G, Samir R D. A topology control approach to using directional antennas in wireless mesh networks. In:Proc of IEEE ICC. Istanbul, 2006,4083-4088
[7]朱思明.无线Ad Hoc网络拓扑控制算法仿真和研究：[西安电子科技大学硕士学位论文].西安：西安电子科技大学,2006,2-4
[8]张学,陆桑璐,陈贵海等.无线传感器网络的拓扑控制.软件学报,2007,18(4)：943-954
[9]Rodoplu V, Meng T H. Minimum energy mobile wireless networks. IEEE Journal on Selected Areas in Communications,1999,17(8):1333-1344
[10]Dan Y, Hui L. On the definition of ad hoc network connectivity. In:Proc of International Conference on Communication Technology. Beijing,2003,990-994
[11]Tao Y, Papadias D, Sun J. The TPR*-Tree:An Optimized Spatio-Temporal Access Method for Predictive Queries. In:Proc of VLDB. Berlin,2003,790-801
[12]Amis A D, Prakash R, Vuong T H P, et al. Max-Min D-Cluster formation in wireeless Ad. Hoc networks. In:Proc of IEEE Conf on Comptuer Commnunications. TelAviv,1999,32-41
[13]Kubish M, Karl H, Wolisz A, et al. Distributed algorithms for transmission power control in wireless sensor networks. In:Proc of IEEE WCNC, New Orleans, Louisiana,2003,35-42
[14]Feng X, Kumar P R. The Number of Neighbors Needed for Connectivity of Wireless Networks. Wireless Networks,2004,10(2):169-181
[15]Douglas M B, Mauro L, Giovanni R, et al. The K-Neigh protocol for Symmetric Topology Control in Ad Hoc Networks. In:Proc of ACM Mobile Ad Hoc, New York,2003,141-152
[16]Ram R, Regina R H. Topology Control of Multihop Wireless Networks using Transmit Power Adjustment. In:Proc of IEEE INFOCOM. Tel-Aviv,2000, 404-413
[17]Li L, Halpern J Y, Bahl P, etal. A cone-based distributed topology-control algorithm for wireless multi-hop networks. IEEE/ACM Transactions on Networking,2005,13(1):147-159
[18]Li L, Hou J C, Bahl P. Analysis of a cone-based distributed topology control algorithm for wireless multi-hop networks. ACM Symp on Principles of Distributed Computing, Newport, RI, May,2001,6(8):26-42
[19]Godfried T. Toussaint. The relative neighborhood graph of a finite planar set. Pattern Recognition,1980,12(4):261-268
[20]Gabriel K R, Robert R S. A new statistical approach to geographic variation analysis. Systematic Zoology,1969,18(3):259-278
[21]Jie G, Leonidas J G. John H, et al. Geometric spanner for routing in mobile networks. In:Proc of Proceedings of the 2nd ACM symposium on mobile ad hoc networking & computing. Long Beach,2001,45-55
[22]Tamas L. New Results on Geometric Spanners and Their Applications: [dissertation]. Paderborn:University of Paderborn,1999,19-27
[23]Rajmohan R. Topology control and routing in ad hoc networks. A survey. SIGACT News,2002,33(2):60-73
[24]Xiang Y L, Peng J W, Yu W. Power efficient and sparse spanner for wireless ad hoc networks. In:Proc of IEEE Int Conf on Computer Communications and Networks (ICCCN01). Chicago,2001,564-567
[25]Xiang Y L. Algorithmic, Geometric and Graphs Issues in Wireless Networks. Wireless Comm. and Mobile Computing,2003,3(2):119-140
[26]Ning L, Jennifer C H, Lui S. Design and Analysis of an MST-Based Topology Control Algorithm. In:Proc of IEEE INFOCOM'03. San Francisco,2003, 1702-1712
[27]Ning L, Jennifer C H. Topology control in heterogeneous wireless networks: Porblems and Soltuions. In:Proc of 23th Joint Conf on IEEE Computer and Communications Socielies. Hong Kong,2004,232-243
[28]Heinzelman W R, Chandrakasan A, Balakrishnan H. An application-specific protocol architecture for wireless microsensor networks. IEEE Transactions on Wireless Communications,2002,1(4):660-670
[29]Younis O, fahmy S. HEED:A hybrid, energy-efficient; distributed clustering approach for ad hoc sensor networks. IEEE Trans. on Mobile Computing,2004, 3(4):600-669
[30]Xu Y, Heidemann J, Estrin D. Geography-Informed energy conservation for ad hoc routing. In:Proc of Rose C, ed. Proc. of the ACM Int'l Conf. on Mobile Computing and Networking. New York,2001,70-85
[31]Ram. R. On the performance of Ad hoc networks using beamforming antennas. In: Proc of ACM Mobile ad hoc. Long Beach,2001,95-105
[32]Su Y, Yong P, Shivkumar K. On the capacity improvement of Ad hoc wireless networks using directional antennas. In:Proc of Proceedings of the 4th ACM international symposium on Mobile Ad hoc Networking and Computing. Annapolis,2003,108-116
[33]Salvatore B, Jeffrey F, Ravi G, et al. Smart Antenna System Analysis, Integration and Performance for Mobile Ad-Hoc Networks(MANETs). In:Proc of IEEE Transactions on Antennas and Propagation. New York,2002,571-581
[34]Carl B. Dietrich, Jr. Adaptive Arrays and Diversity Antenna Configurations for Handheld Wireless Communication Terminals:[dissertation]. Virginia: Blacksburg, Virginia,2000,30-51
[35]Richard B. Ertel Antenna array systemsp ropagation and performance: [dissertation]. Virginia:Blacksburg, Virginia,1999,23-41
[36]Vikash S. A Smart Antennas & Power Management in Wireless Networks: [dissertation]. Virginia:Blacksburg, Virginia,2002,27-45
[37]Bellofiore, S Balanis, C A Smart-antenna system for mobile communication network. IEEE Antennas and Propagation Magazine,2002,44 (3):145-154
[38]Balanis C A. Antenna Theory Analysis and Design. New York:Harper and Row, Publishers,1982,805-807
[39]Vinod N, Li. X G, Ramakrishna J. Power efficienttopology control for wireless networks with switched beam directional antennas. In:Proc of IEEE MASS'05. Washington, DC,2005,3-11
[40]贺鹏,李建东,陈彦辉等.Ad Hoc网络中基于方向性天线的分布式拓扑控制算法.软件学报,2007,18(6)：1308-1318
[41]Gentian J, Wenjie L, Srikanth V K. An integrated neighbor discovery and MAC protocol for Ad hoc networks using directional antennas. In:Proc of IEEE WoW-MoM. Taormina, Italy,2007,11-21
[42]王东,陈文斌,胡婷等.自组网中基于自适应波束天线的拓扑控制算法.计算机研究与发展,2010,47(3)：407-415
[43]邢云冰,史浩山.基于备用节点的无线传感器网络LEACH协议的改进.传感技术学报,2007,20(7)：1592-1596
[44]Bahramgiri M, Hajiaghayi M T, Mirrokni V S. Fault-Tolerant and 3-dimensional distributed topology control algorithms in wireless multihop networks. Wireless Networks,2006(4):179-188
[45]Kawadia. V. Protocols and architecture for wireless ad hoc networks: [dissertation]. University of Urbana-Champaign,2004,35-42