基于可变长Markov链的无线衰落信道认知方法研究
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摘要
与传统以基础设施为中心的无线通信网络设计思想相比,认知无线电更加关注于以用户为中心、以目标驱动为框架的理念,因此,从认知终端可观测的角度考虑局部电波传播环境的变化及快速适应问题,将复杂电波传播机制和认知方法进行有效融合,有利于提高认知终端对于无线环境局部特征的认知能力；另外,与频谱密切相关的信道状态估计在无线环境解析中是不可忽略的,面向动态环境复杂的衰落信道,认知终端具有一定的信道参数预测能力,以便根据环境变化实时调整操作参数,为提高频谱利用率提供更为直观准确的依据。
本文从认知终端角度出发,研究面向无线信道衰落特征的认知问题；利用可变长Markov链(VLMC, Variable Length Markov Chain)技术,对无线信道的衰落状态信息进行学习、分析与推理,通过理解信道记忆信息,对无线衰落信道进行建模,识别衰落统计特征,并构建信道状态预测方法,实现感知结果与实际环境的高度匹配。具体贡献及创新点如下：
1、VLMC的衰落信道建模：在衰落参数样本的基础上,利用VLMC技术,建立衰落信道模型,其中包含两个重点与难点：最优衰落分区问题及最优VLMC信道模型的选择问题；文中还给出基于先验知识(分区个数及状态转移概率个数)的快速VLMC信道建模算法。
2、衰落信道统计特征参数识别：利用VLMC信道模型推导衰落特征参数的统计计算方法,研究由VLMC模型处理后的信道统计特性与局部动态衰落信道参数之间的对应关系,通过识别无线衰落信道的统计特性来表征局部信道质量。
3、信道衰落状态预测：通过上述模型建立局部的电波传播特征库,面向具体的衰落信道参数,利用已知的认知信息来预测无线传播环境中未来信道状态信息,实现具有局部环境认知能力的无线信道状态预测。
4、仿真实现与性能评估：通过仿真结果,评估了利用VLMC技术进行无线衰落信道认知的准确度和有效性；结果还表明,基于VLMC的衰落信道认知方法在精确度和复杂度方面做了更好的权衡。
Compared with the traditional wireless communication design which is based on a central infrastructure, the basic idea of cognitive radio are mainly the user-centered and goal-driven. Therefore, through the research on the dynamic propagation characteristics and fast adaptation from the cognitive terminals, the sensing capacity in local dynamic wireless environment of those terminals can be improved, that is very helpful to the research on the kernel theory and technology of Cognitive Radio.
A new cognitive method for fading characteristics in the local wireless channel from the cognitive terminals is proposed in this paper. This method takes VLMC (Variable-Length Markov Chain) technology to characterize the fading channel, extract the statistical characteristics and predict the future states of the local dynamic wireless environment.
The main contribution and innovation of this paper are as follows:
1. Based on the received data, a model that optimally represents a fading channel with VLMC is proposed. This model consists of two main components:1) the optimal fading partition under the constraint of a transmission policy and2) the derivation of the best VLMC representation. The VLMC modeling based on the prior knowledge is also described.
2. A statistic computing method of local fading channel characteristics is derived. The statistical characteristics treated by VLMC are mapped to local dynamic fading channel parameters to explore the fading characteristics under different wireless environments further.
3. On a basis of learning and recognizing the statistic characteristics of the VLMC model, the future fading states of the channel parameters are predicted.
4. The simulation is carried out to evaluate the performance of the proposed cognitive method. The results demonstrate that the cognitive method using VLMC can provide an optimal tradeoff between accuracy and complexity.
本文从认知终端角度出发,研究面向无线信道衰落特征的认知问题；利用可变长Markov链(VLMC, Variable Length Markov Chain)技术,对无线信道的衰落状态信息进行学习、分析与推理,通过理解信道记忆信息,对无线衰落信道进行建模,识别衰落统计特征,并构建信道状态预测方法,实现感知结果与实际环境的高度匹配。具体贡献及创新点如下：
1、VLMC的衰落信道建模：在衰落参数样本的基础上,利用VLMC技术,建立衰落信道模型,其中包含两个重点与难点：最优衰落分区问题及最优VLMC信道模型的选择问题；文中还给出基于先验知识(分区个数及状态转移概率个数)的快速VLMC信道建模算法。
2、衰落信道统计特征参数识别：利用VLMC信道模型推导衰落特征参数的统计计算方法,研究由VLMC模型处理后的信道统计特性与局部动态衰落信道参数之间的对应关系,通过识别无线衰落信道的统计特性来表征局部信道质量。
3、信道衰落状态预测：通过上述模型建立局部的电波传播特征库,面向具体的衰落信道参数,利用已知的认知信息来预测无线传播环境中未来信道状态信息,实现具有局部环境认知能力的无线信道状态预测。
4、仿真实现与性能评估：通过仿真结果,评估了利用VLMC技术进行无线衰落信道认知的准确度和有效性；结果还表明,基于VLMC的衰落信道认知方法在精确度和复杂度方面做了更好的权衡。
Compared with the traditional wireless communication design which is based on a central infrastructure, the basic idea of cognitive radio are mainly the user-centered and goal-driven. Therefore, through the research on the dynamic propagation characteristics and fast adaptation from the cognitive terminals, the sensing capacity in local dynamic wireless environment of those terminals can be improved, that is very helpful to the research on the kernel theory and technology of Cognitive Radio.
A new cognitive method for fading characteristics in the local wireless channel from the cognitive terminals is proposed in this paper. This method takes VLMC (Variable-Length Markov Chain) technology to characterize the fading channel, extract the statistical characteristics and predict the future states of the local dynamic wireless environment.
The main contribution and innovation of this paper are as follows:
1. Based on the received data, a model that optimally represents a fading channel with VLMC is proposed. This model consists of two main components:1) the optimal fading partition under the constraint of a transmission policy and2) the derivation of the best VLMC representation. The VLMC modeling based on the prior knowledge is also described.
2. A statistic computing method of local fading channel characteristics is derived. The statistical characteristics treated by VLMC are mapped to local dynamic fading channel parameters to explore the fading characteristics under different wireless environments further.
3. On a basis of learning and recognizing the statistic characteristics of the VLMC model, the future fading states of the channel parameters are predicted.
4. The simulation is carried out to evaluate the performance of the proposed cognitive method. The results demonstrate that the cognitive method using VLMC can provide an optimal tradeoff between accuracy and complexity.
引文
[1]FCC. Facilitating opportunities for flexible, efficient and reliable spectrum use employing cognitive radio technologies:notice of proposed rule making and order [R]. Washington, D. C.:FCC ET Docket,2003:04-100.
[2]Q. Q. Zhang, S. Kota, V. Lau, et al. Introduction to the issue on cooperative communication and signal processing in cognitive radio systems [J]. IEEE Journal of Selected Topics in Signal Processing, Dec.2010,5(1):1-4.
[3]B. B. Wang and K. J. R. Liu. Advances in cognitive radio networks:a survey [J]. IEEE Journal on Selected Topics in Signal Processing, Nov.2011,5(1):5-23.
[4]J. Mitola and G.Q. Maguire. Cognitive radios:making software radios more personal [J]. IEEE Personal Communications Magazine, Aug.1999,6(4):13-18.
[5]S. Haykin. Cognitive radio:brain-empowered wireless communications [J]. IEEE Journal on Selected Areas in Communications, Feb.2005,23(2):201-220.
[6]A. S. Cacciapuoti, I. F. Akyildiz, L. Paura. Correlation-aware user selection for cooperative spectrum sensing in cognitive radio ad hoc networks [J]. IEEE Journal on Selected Areas in Communications, Feb.2012,30(2):297-306.
[7]T. Clancy. Achievable capacity under the interference temperature model [C].26th IEEE International Conference Computer Communications,2007:794-802.
[8]Z. Han, K. J. R. Liu. Resource allocation for wireless networks:basics techniques, and applications [M]. Cambridge:Cambridge University Press,2008.
[9]M. F. Hanif, P. J. Smith. On the statistics of cognitive radio capacity in shadowing and fast fading environments [J]. IEEE Transactions on Wireless Communications, Feb.2010,9(2): 844-852.
[10]J. Poutanen, J. Salmi, K. Haneda, et al. Angular and shadowing characteristics of dense multipath components in indoor radio channels [J]. IEEE Transactions on Antennas and Propagation, Jan.2011,59(1):1-9.
[11]A. Konrad, B. Y. Zhao, A. Joseph, et al. A Markov-based channel model algorithm for wireless networks [J]. Wireless Networks, May 2003,9(3):28-36.
[12]W. H. Tranter, K. S. Shanmugan, T. S. Rappaport等著,肖明波,杨光松,许芳,等译.通信系统仿真原理与无线应用[M],北京：机械工业出版社,2005.
[13]E. N. Gilbert. Capacity of a burst-noise channel [J]. Bell System Technical Journal, Jan.1960, 39(1):1253-1266.
[14]E. O. Elliott. Estimates of error rates for codes on burst-noise channels [J]. Bell System Technical Journal, Sep.1963,42(9):1977-1997.
[15]H. S. Wang, N. Moayeri. Finite-state Markov channel:a useful model for radio communication channels [J]. IEEE Transactions on Vehicular Technology, Feb.1995,45(1): 163-171.
[16]C. Tan, N. Beaulieu. On first-order Markov modeling for the Rayleigh fading channel [J]. IEEE Transactions on Communications, Dec.2000,48(12):2032-2040.
[17]F. Babich, G. Lombardi. A Markov model for the mobile propagation channel [J]. IEEE Transactions on Vehicular Technology, Jan.2000,49(1) 63-73.
[18]S. Sivaprakasam, K. S. Shanmugan. An equivalent Markov model for burst errors in digital channels [J], IEEE Transactions on Communications, Feb.1995,43(2),1347-1355.
[19]T. Yucek and H. Arslan. A survey of spectrum sensing algorithms for cognitive radio applications [J]. IEEE Communications Surveys & Tutorials, Jan.2009,11(1):116-130.
[20]J. Cai, A. S. Alfa, Optimal channel sensing in wireless communication networks with cognitive radio [C]. IEEE International Conference on Communications,2009:1-5.
[21]H. Chen, C. K. Tse, F. Zhao. Optimal quantisation bit budget for a spectrum sensing scheme in bandwidth-constrained cognitive sensor networks [J].Wireless Sensor Systems, Sep.2011, 3(1):144-150.
[22]V. K. Tumuluru, P. Wang, D. Niyato. A neural network based spectrum prediction scheme for cognitive radio [C]. IEEE International Conference on Communications,2010:1-5.
[23]L. Gavrilovska, V. Atanasovski. Spectrum sensing framework for cognitive radio networks [J]. Wireless Personal Communications, Feb.2011,59(3):447-469.
[24]S. H. Huang, X. Liu, Z. Ding. Decentralized cognitive radio control based on inference from primary link control information [J]. IEEE Journal on Selected Areas in Communications, Feb.2011,29(2):394-406.
[25]G. Taricco. Optimization of linear cooperative spectrum sensing for cognitive radio networks [J]. IEEE Journal on Selected Topics in Signal Processing, Jun.2010,5(1):77-86.
[26]Y. Ephraim, N. Merhav. Hidden Markov processes [J]. IEEE Transactions on Information Theory, Jun.2002,48(6):1518-1569.
[27]J. Meng, W. T. Yin, H. S. Li, et al. Collaborative spectrum sensing from sparse observations in cognitive radio networks [J]. IEEE Journal on Selected Areas in Communications, Feb. 2011,29(2):327-337.
[28]K. Bakowski, K. Wesolowski. Change the channel:A new model for the IMT-advanced system [J]. IEEE Vehicular Technology Magazine, Jul.2011,6(2):82-91.
[29]A. Goldsmith, S. Chua. Variable-rate variable-power MQAM for fading channels [J]. IEEE Transactions on Communications, Oct.1997,45(10):1218-1230.
[30]P. Buhlmann, A. J. Wyner. Variable length Markov chains [J]. Annals of Statistics, Apr.1999, 27(2):480-513.
[31]M. Machler, P. Buhlmann. Variable length Markov chains:methodology, computing, and software [J]. Journal of Computational and Graphical Statistics, Jan.2004,13(2):435-455.
[32]M. Girolami, C. He. Probability density estimation from optimally condensed data samples [J]. IEEE Transactions on Pattern Analysis and Machine Intelligence, Oct.2003,25(10): 1253-1264.
[33]W. Kumwilaisak, J. Kuo. Fading channel modeling via variable length Markov chain technique [J]. IEEE Transactions on Vehicular Technology, May 2008,57(3):1338-1358.
[34]T. M. Cover, J. A. Thomas. Elements of information theory [M]. New York:Wiley,2006.
[35]S. Boyd, L. Vandenberghe. Convex optimization [M]. Cambridge:Cambridge University Press,2004.
[36]G. L. Stuber. Principles of mobile communication [M]. Boston:Kluwer,1996
[37]X. Cheng, C. X. Wang, H. M. Wang, et al. Cooperative MIMO channel modeling and multi-link spatial correlation properties [J], IEEE Journal on Selected Areas in Communications, Feb.2012,30(2):388-396.
[38]杨大成,等著.移动传播环境理论基础：分析方法和建模技术[M].北京：机械工业出版,2003.
[39]H. Celebi, I. Guvenc, S.Gezoco. Cognitive-radio systems for spectrum, location, and environmental awareness [J]. IEEE Antennas and Propagation Magazine, Aug.2010,52(4): 41-61.
[40]R. Bhagavatula, C. Oestges. A new double-directional channel model including antenna patterns, array orientation, and depolarization [J]. IEEE Transactions on Vehicular Technology, Jun.2010,59(5):2219-2231.
[41]C. Xiao, Y. R. Zheng, N. C. Beaulieu. Novel sum-of-sinusoids simulation models for Rayleigh and Rician fading channels [J], IEEE Transactions on Wireless Communications, Dec.2006,5(12):3667-3679.
[42]A. S. Alfa, V. Pla, J. Martinez-Bauset, et al. Discrete time analysis of cognitive radio networks with saturated source of secondary users [C]. IFIP TC 6th International Conference on Networking,2011:3-12.
[43]D. Katsaros, Y. Manolopoulos. Prediction in wireless networks by Markov chains [J]. IEEE Wireless Communications, Apr.2009,16(1):56-64.
[44]R. Begleiter, R. El-yaniv, G. Yona. On prediction using variable order Markov models [J]. Journal of Artificial Intelligence Research, Jan.2004,22(1):385-421.
[45]Z. Chen, N. Guo, Z. Hu, et al. Experimental validation of channel state prediction considering delays in practical cognitive radio [J]. IEEE Transactions on Vehicular Technology, May 2011, 60(4),1314-1325.
[46]L. Shen, H. Q. Wang, W. Zhang, et al. Blind spectrum sensing for cognitive radio channels with noise uncertainty [J]. IEEE Transactions on Wireless Communications, Jun.2011,10(6): 1721-1724.
[47]A. Aragon-Zavala, B. Belloul, V. Nikolopoulos, et al. Accuracy evaluation analysis for indoor measurement-based radio wave propagation predictions [C]. IEEE Proceedings on Microwaves, Antennas and Propagation,2006:67-74.
[48]Z. Y. Zhang, H. Y. Luo, J. M. Zhang, et al. Cognitive radio transmission strategies exploiting the primary-link adaptively [J]. IEEE Transactions on Vehicular Technology, Oct.2011, 60(8):3805-3813.
[49]L. Gavrilovska, V. Atanasovski. Spectrum sensing framework for cognitive radio networks [J]. Wireless Personal Communications, Feb.2011,59(3):447-469.
[50]Y. Pei, Y. C. Liang, K. C. Teh, et al. Energy-efficient design of sequential channel sensing in cognitive radio networks:optimal sensing strategy, power allocation, and sensing order [J]. IEEE Journal on Selected Areas in Communications, Sep.2011,29(8):1648-1659.
[51]H. Jiang, L. Lai, R. F. Fan, et al. Optimal selection of channel sensing order in cognitive radio [J]. IEEE Transactions on Wireless Communications, Jan.2009,8(1):297-307.
[52]H. T. Cheng, W. H. Zhuang, Simple channel sensing order in cognitive radio networks [J]. IEEE Journal on Selected Areas in Communications, Apr.2011,29(4):676-688.
[2]Q. Q. Zhang, S. Kota, V. Lau, et al. Introduction to the issue on cooperative communication and signal processing in cognitive radio systems [J]. IEEE Journal of Selected Topics in Signal Processing, Dec.2010,5(1):1-4.
[3]B. B. Wang and K. J. R. Liu. Advances in cognitive radio networks:a survey [J]. IEEE Journal on Selected Topics in Signal Processing, Nov.2011,5(1):5-23.
[4]J. Mitola and G.Q. Maguire. Cognitive radios:making software radios more personal [J]. IEEE Personal Communications Magazine, Aug.1999,6(4):13-18.
[5]S. Haykin. Cognitive radio:brain-empowered wireless communications [J]. IEEE Journal on Selected Areas in Communications, Feb.2005,23(2):201-220.
[6]A. S. Cacciapuoti, I. F. Akyildiz, L. Paura. Correlation-aware user selection for cooperative spectrum sensing in cognitive radio ad hoc networks [J]. IEEE Journal on Selected Areas in Communications, Feb.2012,30(2):297-306.
[7]T. Clancy. Achievable capacity under the interference temperature model [C].26th IEEE International Conference Computer Communications,2007:794-802.
[8]Z. Han, K. J. R. Liu. Resource allocation for wireless networks:basics techniques, and applications [M]. Cambridge:Cambridge University Press,2008.
[9]M. F. Hanif, P. J. Smith. On the statistics of cognitive radio capacity in shadowing and fast fading environments [J]. IEEE Transactions on Wireless Communications, Feb.2010,9(2): 844-852.
[10]J. Poutanen, J. Salmi, K. Haneda, et al. Angular and shadowing characteristics of dense multipath components in indoor radio channels [J]. IEEE Transactions on Antennas and Propagation, Jan.2011,59(1):1-9.
[11]A. Konrad, B. Y. Zhao, A. Joseph, et al. A Markov-based channel model algorithm for wireless networks [J]. Wireless Networks, May 2003,9(3):28-36.
[12]W. H. Tranter, K. S. Shanmugan, T. S. Rappaport等著,肖明波,杨光松,许芳,等译.通信系统仿真原理与无线应用[M],北京：机械工业出版社,2005.
[13]E. N. Gilbert. Capacity of a burst-noise channel [J]. Bell System Technical Journal, Jan.1960, 39(1):1253-1266.
[14]E. O. Elliott. Estimates of error rates for codes on burst-noise channels [J]. Bell System Technical Journal, Sep.1963,42(9):1977-1997.
[15]H. S. Wang, N. Moayeri. Finite-state Markov channel:a useful model for radio communication channels [J]. IEEE Transactions on Vehicular Technology, Feb.1995,45(1): 163-171.
[16]C. Tan, N. Beaulieu. On first-order Markov modeling for the Rayleigh fading channel [J]. IEEE Transactions on Communications, Dec.2000,48(12):2032-2040.
[17]F. Babich, G. Lombardi. A Markov model for the mobile propagation channel [J]. IEEE Transactions on Vehicular Technology, Jan.2000,49(1) 63-73.
[18]S. Sivaprakasam, K. S. Shanmugan. An equivalent Markov model for burst errors in digital channels [J], IEEE Transactions on Communications, Feb.1995,43(2),1347-1355.
[19]T. Yucek and H. Arslan. A survey of spectrum sensing algorithms for cognitive radio applications [J]. IEEE Communications Surveys & Tutorials, Jan.2009,11(1):116-130.
[20]J. Cai, A. S. Alfa, Optimal channel sensing in wireless communication networks with cognitive radio [C]. IEEE International Conference on Communications,2009:1-5.
[21]H. Chen, C. K. Tse, F. Zhao. Optimal quantisation bit budget for a spectrum sensing scheme in bandwidth-constrained cognitive sensor networks [J].Wireless Sensor Systems, Sep.2011, 3(1):144-150.
[22]V. K. Tumuluru, P. Wang, D. Niyato. A neural network based spectrum prediction scheme for cognitive radio [C]. IEEE International Conference on Communications,2010:1-5.
[23]L. Gavrilovska, V. Atanasovski. Spectrum sensing framework for cognitive radio networks [J]. Wireless Personal Communications, Feb.2011,59(3):447-469.
[24]S. H. Huang, X. Liu, Z. Ding. Decentralized cognitive radio control based on inference from primary link control information [J]. IEEE Journal on Selected Areas in Communications, Feb.2011,29(2):394-406.
[25]G. Taricco. Optimization of linear cooperative spectrum sensing for cognitive radio networks [J]. IEEE Journal on Selected Topics in Signal Processing, Jun.2010,5(1):77-86.
[26]Y. Ephraim, N. Merhav. Hidden Markov processes [J]. IEEE Transactions on Information Theory, Jun.2002,48(6):1518-1569.
[27]J. Meng, W. T. Yin, H. S. Li, et al. Collaborative spectrum sensing from sparse observations in cognitive radio networks [J]. IEEE Journal on Selected Areas in Communications, Feb. 2011,29(2):327-337.
[28]K. Bakowski, K. Wesolowski. Change the channel:A new model for the IMT-advanced system [J]. IEEE Vehicular Technology Magazine, Jul.2011,6(2):82-91.
[29]A. Goldsmith, S. Chua. Variable-rate variable-power MQAM for fading channels [J]. IEEE Transactions on Communications, Oct.1997,45(10):1218-1230.
[30]P. Buhlmann, A. J. Wyner. Variable length Markov chains [J]. Annals of Statistics, Apr.1999, 27(2):480-513.
[31]M. Machler, P. Buhlmann. Variable length Markov chains:methodology, computing, and software [J]. Journal of Computational and Graphical Statistics, Jan.2004,13(2):435-455.
[32]M. Girolami, C. He. Probability density estimation from optimally condensed data samples [J]. IEEE Transactions on Pattern Analysis and Machine Intelligence, Oct.2003,25(10): 1253-1264.
[33]W. Kumwilaisak, J. Kuo. Fading channel modeling via variable length Markov chain technique [J]. IEEE Transactions on Vehicular Technology, May 2008,57(3):1338-1358.
[34]T. M. Cover, J. A. Thomas. Elements of information theory [M]. New York:Wiley,2006.
[35]S. Boyd, L. Vandenberghe. Convex optimization [M]. Cambridge:Cambridge University Press,2004.
[36]G. L. Stuber. Principles of mobile communication [M]. Boston:Kluwer,1996
[37]X. Cheng, C. X. Wang, H. M. Wang, et al. Cooperative MIMO channel modeling and multi-link spatial correlation properties [J], IEEE Journal on Selected Areas in Communications, Feb.2012,30(2):388-396.
[38]杨大成,等著.移动传播环境理论基础：分析方法和建模技术[M].北京：机械工业出版,2003.
[39]H. Celebi, I. Guvenc, S.Gezoco. Cognitive-radio systems for spectrum, location, and environmental awareness [J]. IEEE Antennas and Propagation Magazine, Aug.2010,52(4): 41-61.
[40]R. Bhagavatula, C. Oestges. A new double-directional channel model including antenna patterns, array orientation, and depolarization [J]. IEEE Transactions on Vehicular Technology, Jun.2010,59(5):2219-2231.
[41]C. Xiao, Y. R. Zheng, N. C. Beaulieu. Novel sum-of-sinusoids simulation models for Rayleigh and Rician fading channels [J], IEEE Transactions on Wireless Communications, Dec.2006,5(12):3667-3679.
[42]A. S. Alfa, V. Pla, J. Martinez-Bauset, et al. Discrete time analysis of cognitive radio networks with saturated source of secondary users [C]. IFIP TC 6th International Conference on Networking,2011:3-12.
[43]D. Katsaros, Y. Manolopoulos. Prediction in wireless networks by Markov chains [J]. IEEE Wireless Communications, Apr.2009,16(1):56-64.
[44]R. Begleiter, R. El-yaniv, G. Yona. On prediction using variable order Markov models [J]. Journal of Artificial Intelligence Research, Jan.2004,22(1):385-421.
[45]Z. Chen, N. Guo, Z. Hu, et al. Experimental validation of channel state prediction considering delays in practical cognitive radio [J]. IEEE Transactions on Vehicular Technology, May 2011, 60(4),1314-1325.
[46]L. Shen, H. Q. Wang, W. Zhang, et al. Blind spectrum sensing for cognitive radio channels with noise uncertainty [J]. IEEE Transactions on Wireless Communications, Jun.2011,10(6): 1721-1724.
[47]A. Aragon-Zavala, B. Belloul, V. Nikolopoulos, et al. Accuracy evaluation analysis for indoor measurement-based radio wave propagation predictions [C]. IEEE Proceedings on Microwaves, Antennas and Propagation,2006:67-74.
[48]Z. Y. Zhang, H. Y. Luo, J. M. Zhang, et al. Cognitive radio transmission strategies exploiting the primary-link adaptively [J]. IEEE Transactions on Vehicular Technology, Oct.2011, 60(8):3805-3813.
[49]L. Gavrilovska, V. Atanasovski. Spectrum sensing framework for cognitive radio networks [J]. Wireless Personal Communications, Feb.2011,59(3):447-469.
[50]Y. Pei, Y. C. Liang, K. C. Teh, et al. Energy-efficient design of sequential channel sensing in cognitive radio networks:optimal sensing strategy, power allocation, and sensing order [J]. IEEE Journal on Selected Areas in Communications, Sep.2011,29(8):1648-1659.
[51]H. Jiang, L. Lai, R. F. Fan, et al. Optimal selection of channel sensing order in cognitive radio [J]. IEEE Transactions on Wireless Communications, Jan.2009,8(1):297-307.
[52]H. T. Cheng, W. H. Zhuang, Simple channel sensing order in cognitive radio networks [J]. IEEE Journal on Selected Areas in Communications, Apr.2011,29(4):676-688.