基于Fano译码复杂度和隐马尔科夫模型的信道建模和预测
|
摘要
无线通信信道的模型研究是无线通信领域的关键技术之一。相对于波形信道,离散信道模型(DCM,Discrete Channel Model)一般采用马尔科夫链(MarkovChains)进行描述,具有更高的计算效率,由于它把信道划分成不同的离散状态,在不同的状态下可以选择不同的自适应调制编码技术,这也是目前无线通信发展的趋势之一。在信道模型建立的条件下,准确的信道预测是信道自适应的另一个关键问题。
本文从三个方面进行深入研究:
(1)分别研究了信道信噪比和瑞利衰落信道多普勒频扩与Fano译码复杂度之间的对应关系。从统计意义上说,低信噪比条件下的Fano译码复杂度要大于高信噪比条件下的Fano译码复杂度,高多普勒频扩条件下的Fano译码复杂度要大于低多普勒频扩条件下的Fano译码复杂度,所以用Fano译码复杂度衡量信道条件是可行的。
(2)研究了基于Fano译码复杂度和隐马尔科夫模型的离散信道建模。本文以量化的Fano译码的复杂度作为观测值,采用HMM中的Baum-Welch算法训练信道参数,并且在得到训练参数后用Viterbi译码算法来估计离散信道模型状态。最后采用随机松弛(SR,Stochastic Relaxation)优化算法改进传统的Baum-Welch算法,提高了离散信道模型参数估计精度,信道状态估计的准确率达到90%以上。
(3)在离散信道隐马尔科夫模型建立的基础上,研究基于马尔科夫链转移概率矩阵的信道状态预测。首先通过滑动窗方法(Sliding Window)截取一定长度的观测值序列进行Viterbi译码得到当前时刻的信道状态;然后采用隐马尔科夫模型的状态转移概率矩阵进行信道状态的单步和多步预测,其中一步预测的效果非常好,多步预测因为误差累计的原因效果逐渐下降。
The research on the model of wireless channel is one of the key technologies in the field of wireless communications. Compared to wave channels, discrete channel models usually adopt Markov model, which has higher computational efficiency. And because the Markov model divides the channel into different discrete states, we can choose different adaptive technology, which is also the trend in the wireless communication development. Another core problem of adaptive technology is the accurate prediction of channels.
This thesis focuses on three aspects:
Firstly, the relationship between the complexity of Fano sequential decoding, signal-to-noise ratio (SNR) in a mobile channel and Doppler spread in Rayleigh fading channels is disscussed. We found that when SNR is higher, the complexity of Fano sequential decoding is lower, and when Doppler spread is lower, the complexity of Fano sequential decoding is lower. So it is reasonable to use the complexity of Fano sequential decoding as a measure of the condition of channels.
Secondly, Model-building of the discrete channel, using the complexity of Fano sequential decoding and HMM, is discussed. In this thesis, measured Fano decoding complexity is used as observation value, Baum-Welch algorithm is employed to obtain an optimal estimate of the HMM model parameters, and then the maximum likelihood hidden state sequence is found by using the Viterbi algorithm. After optimized Baum-Welch algorithm by Stochastic Relaxation algorithm, accuracy of the Discrete Channel Model estimate is improved and estimates accuracy rate of the channel state is over of 90 percent.
Thirdly, research on the channel prediction with the state transition probability matrix of Markov model, based on discrete channel models by HMM is discussed. First, by using Sliding Window algorithm to obtain a sequence of measured values before performing Viterbi decoding, the instantaneous state of channel is achieved; Then using HMM's state transition probability matrix to predict one step and many steps of channel states. One step of prediction has achieved good results; while, because of accumulated error, the result of prediction of many steps fails.
本文从三个方面进行深入研究:
(1)分别研究了信道信噪比和瑞利衰落信道多普勒频扩与Fano译码复杂度之间的对应关系。从统计意义上说,低信噪比条件下的Fano译码复杂度要大于高信噪比条件下的Fano译码复杂度,高多普勒频扩条件下的Fano译码复杂度要大于低多普勒频扩条件下的Fano译码复杂度,所以用Fano译码复杂度衡量信道条件是可行的。
(2)研究了基于Fano译码复杂度和隐马尔科夫模型的离散信道建模。本文以量化的Fano译码的复杂度作为观测值,采用HMM中的Baum-Welch算法训练信道参数,并且在得到训练参数后用Viterbi译码算法来估计离散信道模型状态。最后采用随机松弛(SR,Stochastic Relaxation)优化算法改进传统的Baum-Welch算法,提高了离散信道模型参数估计精度,信道状态估计的准确率达到90%以上。
(3)在离散信道隐马尔科夫模型建立的基础上,研究基于马尔科夫链转移概率矩阵的信道状态预测。首先通过滑动窗方法(Sliding Window)截取一定长度的观测值序列进行Viterbi译码得到当前时刻的信道状态;然后采用隐马尔科夫模型的状态转移概率矩阵进行信道状态的单步和多步预测,其中一步预测的效果非常好,多步预测因为误差累计的原因效果逐渐下降。
The research on the model of wireless channel is one of the key technologies in the field of wireless communications. Compared to wave channels, discrete channel models usually adopt Markov model, which has higher computational efficiency. And because the Markov model divides the channel into different discrete states, we can choose different adaptive technology, which is also the trend in the wireless communication development. Another core problem of adaptive technology is the accurate prediction of channels.
This thesis focuses on three aspects:
Firstly, the relationship between the complexity of Fano sequential decoding, signal-to-noise ratio (SNR) in a mobile channel and Doppler spread in Rayleigh fading channels is disscussed. We found that when SNR is higher, the complexity of Fano sequential decoding is lower, and when Doppler spread is lower, the complexity of Fano sequential decoding is lower. So it is reasonable to use the complexity of Fano sequential decoding as a measure of the condition of channels.
Secondly, Model-building of the discrete channel, using the complexity of Fano sequential decoding and HMM, is discussed. In this thesis, measured Fano decoding complexity is used as observation value, Baum-Welch algorithm is employed to obtain an optimal estimate of the HMM model parameters, and then the maximum likelihood hidden state sequence is found by using the Viterbi algorithm. After optimized Baum-Welch algorithm by Stochastic Relaxation algorithm, accuracy of the Discrete Channel Model estimate is improved and estimates accuracy rate of the channel state is over of 90 percent.
Thirdly, research on the channel prediction with the state transition probability matrix of Markov model, based on discrete channel models by HMM is discussed. First, by using Sliding Window algorithm to obtain a sequence of measured values before performing Viterbi decoding, the instantaneous state of channel is achieved; Then using HMM's state transition probability matrix to predict one step and many steps of channel states. One step of prediction has achieved good results; while, because of accumulated error, the result of prediction of many steps fails.
引文
1. John G. Proakis. Digital Communications. 4~(th) edition. 北京：电子工业出版社, 2001.10.
2. A.F.molisch. Wideband Wireless Digital Communications. Pearson Education, Inc., 2001.
3. Steven M.Kay. Fundamentals of Statistical Signal Processing, Volume 1: Estimation Theory. 北京: 电子工业出版社, 2006.
4. M.C.Jeruchim, P.Balaban, and K.S.Shanmugan. Simulation of Communications Systems, 2~(nd) ed. New York: Kluwer Academic/Plenum Publishers, 2000
5. W.Turin and M.M.Sondhi. Modeling Error Sources in Digital Channels. IEEE Journal on Selected Areas in Communications, Vol.11, No.3, April 1993, pp. 340-347
6. E.O.Ellott. Estimates of error rates for codes on burst-noise channel. System.Tech.J. vol.42.pp.1977-1997, Sep 1963
7. M.Mushkin and I.Bar-David. Capacity and coding for Gilbert-Elliott channels. IEEE Trans.Info.Theory, vol.35, pp.1277-1290, Nov.1989
8. S.Perreau, L.B.White. Channel estimation and symbol detection for multiuser CDMA receivers using HMMs. Statistical Signal and Array Processing, 1998. Proceedings, Ninth IEEE SP Workshop on 14-16 Sept. 1998 pp.272-275
9. Anwer A.Khan. Iterative Decoding and Channel Estimation over Hidden Markov Fading Channels. Submitted to the Faculty of the Virginia Polytechnic Institute and State University in partial fulfillment of the requirement for the degree of Master of Science in Electrical Engineering, [Online], Available: http://scholar.lib.vt.edu/theses/ available/etd-05102000-13390004/unrestricted/AAKhan.pdf
10. W.Pan. Variable complexity algorithms and adaptive computation control in video coding and communications. Ph.D.thesis, the University of Southern California,2002
11. G.L.Stuber. Principles of Mobile Communication, Kluwer Academic Press, 1996
12. H.Bischl and E.Luts. Packet error rate in the non-interleaved Rayleigh channe. IEEE Trans.on Communication, vol.43, no.2/3/4.pp.1375-1282. Feb-April 1995
13. W.Turin and R.van Nobelen. Hidden Markov modeling of flat fading channels. IEEE Journal on Selected Areas in communication, vol.16, no.9.pp.1809-1817, Dec 1998
14.J M Wozencraft,Kennedy.R.Modulation and demodulation for probabilistic coding.Infeimation Theory,IEEE Transactions on Volume 12,issue 3,July 1966Page(s):291-297
15.Lebrow.I,McHugh.P,Parker.A,J M Wozencraft.Information Theory,IEEE Transactions on Volume 9,issue 2,Apr 1963 Page(s):124-126
16.R.M.Fano,A heuristic discussion of probabilistic decoding,IEEE Trans.Information Theory,vol.IT-9,pp.66-74,April 1963
17.A.J.Viterbi and J.K.Omura.Principles of digital communication and coding,McGraw-Hill,1979
18.W.Pan and A.Ortega.Buffer control for variable complexity fano decoders.IEEE Global Telecommunication Conference.San Antonio,Texas,November 2001.pp.176-180
19.P.Orten and A.Svensson.Sequential decoding of convolutional codes for Rayleigh fading channels.Submitted to Kluwer,Wireless Personal Communications,July 1999
20.S.Lin and D.J.Costello(Jr).Error control coding:fundamentals and applications,Prentice-Hall,1983
21.David Wendi Pan,Seong-Moo Yoo and Reza Adhami.Prediction of Rayleigh Fading Channels based on Hidden Markov Modeling of Sequential Channel Decoding Complexity System Theory,2003.Proceedings of the 35th Southeastern Symposium on 16-18 March 2003 Page(s):304-307
22.Bahl L.R.Brown P F et al.Maximum Information Estimation of Hidden Markov Parameters for Speech Recognition.IEEE Proc.ICASSP.1986.49-52
23.Bahl L.R.A New Algorithm for the Estimation of Hidden Markov Parameters.IEEE Proc.ICASSP.1988,493-496
24.杨行峻,迟惠生等.语音信号数字处理.北京:电子工业出版社,1995,
25.Chau C W,Kwong S,Diu C K.Optimization of HMM by a Genetic Algorithm.1997年声学,语音及信号文集 1727-1730
26.孙敬,胡光锐,徐雄.利用基因算法训练连续隐马尔科夫模型的语音识别 上海交通大学学报 1998 32(6)19-22
27.Geman W S.Stochastic Relaxatio.Gibbs distributions and Bayessan restoration of images.IEEE Trans.PAMI-6,Nov.1984:721-741
28.T.S.Rappaport.Wireless Communication principles and practice.2nd Edition.北京:电子工业出版社,2006.7.
29.束锋.OFDM和MIMO-OFDM系统中同步误差分析与信道估计研究.东南大学博士后出站报告,2005.10.
30.杨大成.移动传播环境:理论基础、分析方法和建模技术.北京:机械工业出版社,2003.8.
31.R.S.Liptser and A.N.Shiryayev.Statistics of Random Processes.New York:Sp ringer-Verlag,1977
32.严加安.测度论讲义.北京:科学出版社,2000
33.数学模型讲义.北京大学数学科学学院.2000
34.苑诗松,王静龙,淮晓龙.高等数理统计 北京:高等教育出版社,1998.7
35.Steffen Michalek,Mirko WAGNER,Jens TIMMER.A new approximate likelihood estimator for ARMA-filtered hidden Markov models.Signal Processing,IEEE Transactions on[see also Acoustics,Speech,and Signal Processing,IEEE Transactions on]Volume 48,Issue 6,June 2000 Page(s):1537-1547
36.Vikram Krishnamurthy,Gang George Yin.Recursive algorithms for estimation of hidden Markov models and autoregressive models with Markov regime.IEEE Transactions on Information Theory 48(2):458-476(2002)
37.Peter M.Djuric,Senior Member IEEE and Joon-Hwa Chun.An MCMC Sampling to Estimation of HMMs.IEEE Trans.Signal Processing,Vol.50,no.5,2002,pp.1113-1123
38.Janez Kaiser.University of Maribor,Faculty of Electrical Engineering and Computer Science,Smetanora 17 Maribor slovenia.trainin of HMM with GA.w ww.dsplab.uni-mb.si/Clanki/janez/ast98.pdf
39.丁建立,陈增强,袁著扯.遗传算法与蚂蚁算法的融合.计算机研究与发展,2003,40卷,第9期
40.韩广军,罗强,李兵.基于DCPM-FGA的隐马氏模型的参数训练.国防科技大学学报,2004,第26卷,第4期
41.Yariv Ephraim,David Malah.Speech Enhancement based upon Hidden Markov Modeling.Acoustics,Speech,and Signal Processing,1989.ICASSP-89,1989International Conference on 23-26 May 1989 Page(s):353-356 vol.1
42.Enzo Baccarelli and Robert Cusani.Recuursive Kahnan-type optimal estimation and detection of Hidden Markov chains.Signal Processing,1996
43.易克初,田斌,付强.语音信号处理.北京:国防工业出版社,2000
44.Booker L.B.,Goldberg D.E.,and Holland J.H.Classifier System and Application.Fuzzy Sets and Systems,1994(61):129-136
45.谢锦辉.隐Markov模型(HMM)及其在语音处理中的应用.武汉:华中理工大学出版社1995年
46.韦岗、邱伟.现代信号处理理论与技术.广州:华南理工大学出版社 1994
47.L.R.Rabiner.A Tutorial on Hidden Markov Models and Selected Application in Speech Recognition.IEEE Trans.ASSP,vol.77,No2.,Feb 1989.257-286
48.S.E.Levinson,L.R.Rabiner,and M.M.Sondhi.An Introduction to the Application of the Theory of Probabilistic Functions of a Markov Process to Automatic Speech Recognition.Bell System Tech.J.,April 1983 1035-1074
49.B.Mericldo.Phonetic Recognition Using Hidden Markov Models and Maximum Mutual Information Training.Proc.ICASSP-88,:111-114
50.杨国亮,王志良,刘翼伟等.基于改进MMI的HMM训练算法及其在面部表情识别中的应用.北京科技大学学报,2007年04期
51.W.Turin.Digital Transmission Systems:Performance,Analysis and Modeling,2nd ed.,NewYork:McGraw-Hill,1999
52.L.R.Rabiner and B.H.Juang.An Introduction to Hidden Markov.IEEE ASSP Magzine,January 1986,pp.4-16
53.R.A.Hoeard.Dynamic Probability System,Vol.Ⅰ:Markov Models.New York:Wiley,1971
54.R.A.Hoeard.Dynamic Probability System,Vol.Ⅱ:SemiMarkov and Decision Processes.New York:Wiley,1971
55.H.S.Wang and N.Moayeri.Finite-State Markov Channel-A Useful Model for Radio Communications Channels.IEEE Transactions on Vehicular Technology,Vol.44,February 1995,pp.163-171
56.S.Sivaprakasam and K.S.Shanmugan.An Equivalent Model for Burst Errors in Digital Channels.IEEE Transactions on Communications,Vol.43,No.2/3/4,February/March/April 1995,pp.1347-1355
57.H.S.Wang and P.-C.Chang.On Verifying the First-Order Markovian Assumption for a Rayleigh Channel Model.IEEE Transactions on Vehicular Technology,Vol.45,May 1996,pp.353-357
58.W.Turin and R.van Nobelen.Hidden Markov Modeling of Flat Fading Channels.IEEE Journal on Selected Areas in Communications,Vol.16,No.9,December 1998,pp.1809-1817
59.F.Babich,O.E.Kelly,and G.Lombardi.Generalized Markov Modeling for Flat Fading.IEEE Transactions on Communications,Vol.48,No.4,April 2000,pp.347-351
60.M.Zorzi,R.R.Rao,and L.B.Milstein.A Markov Model for Block Errors on Fading Channels.PIMRC'96 Conference Record,October 1996
61.E.N.Gilbert.Capacity of a Burst-Noise Channel.Bell System Technical Journal,Vol.39,September 1960,pp.1253-1266
62.B.D.Fritchman.A Binary Characterization Using Partitioned Markov Chains.IEEE Transactions on Information Theory,Vol.IT-13,No.2,April 1967,pp.221-227
63.P.Elias.Coding for Noisy Channel.IRE Conv.Rec.,p.4:37-47,1955
64.J M Wozencraft.Sequential Decoding for Reliable Communication.IRE Conv.REC.5(pt.2):11-25,1957
65.J M Wozencraft and B.Reiffen.Sequential Decoding.MIT Press,Cambridge,1961
66.Shu Lin,Daniel J.Costello著.差错控制编码(原书第二版).北京:机械工业出版社 2007.6
67.Masse.J.L.Threshold Decoding,The MIT Press.Cambridge,Mass.1963
68.Viterbi.A.J.Error Bounds for convolutinal Codes and an Asymptotically Optimum Decoding Algorithm.IEEE Trans.Inf.Theory,vol.IT13,pp.260-269,April,1967
69.R.Johannesson and K.S.Zigangorov.Fundamentals of Convolutional Coding.IEEE Press,Piscataway,1999
70.J A Heller and I M Jacobs.Viterbi Decoding for Satellite and Space Communication.IEEE Trans.Commun.Techol.COM-19:835-48
71.Juang B H.A Probabilistic Distance Measure for Hidden Markov Models.AT&T.Technical Journal.Feb 1985,64(2).391-408
72.F.Swarts and H.C.Ferreira.Markov Characterization of Digital Fading Mobiling.VHF Channels.IEEE Trans.Veh.Technol,1994;43(4):977-985
73.王京,王跃科.低轨卫星信道隐马尔科夫仿真模型研究.计算机仿真2007年1月
74.惠晓威,马飞.GSM移动信道特性的仿真研究 辽宁工程技术大学学报 2002年6月
75.ETSI TR 125 943 V5.1.0(2002-06)
76.Gao Jiang,Ding Xiaoqing,Wu Youshou.A segmenta-tion algorithm for handwritten chinese characterstrings[A][M].Proc 6th Int Conf Document Analysisand Recognition[C];1999年
77.杜世平,李海.Second-order Hidden Markov Models and Its Application to Computatonal Linguistics.四川大学学报(自然科学版)Journal of Sichuan University(Namral Science Edition)
78.Burshtein D.Robust parametric modeling of duration in hidden markov models.IEEE Trans on Speech & Audio Processing,1996,4(3):240-242
79.J.Gehrke,F.Kom,D.Srivastava.On Computing Correlated Aggregates over Continual Data Streams.In SIGMOD,2001,pp.13-24
80.袁东风,张立.MARKOV模型在移动信道中的应用.Radio Engineering 1999.Vol.29 No.4
2. A.F.molisch. Wideband Wireless Digital Communications. Pearson Education, Inc., 2001.
3. Steven M.Kay. Fundamentals of Statistical Signal Processing, Volume 1: Estimation Theory. 北京: 电子工业出版社, 2006.
4. M.C.Jeruchim, P.Balaban, and K.S.Shanmugan. Simulation of Communications Systems, 2~(nd) ed. New York: Kluwer Academic/Plenum Publishers, 2000
5. W.Turin and M.M.Sondhi. Modeling Error Sources in Digital Channels. IEEE Journal on Selected Areas in Communications, Vol.11, No.3, April 1993, pp. 340-347
6. E.O.Ellott. Estimates of error rates for codes on burst-noise channel. System.Tech.J. vol.42.pp.1977-1997, Sep 1963
7. M.Mushkin and I.Bar-David. Capacity and coding for Gilbert-Elliott channels. IEEE Trans.Info.Theory, vol.35, pp.1277-1290, Nov.1989
8. S.Perreau, L.B.White. Channel estimation and symbol detection for multiuser CDMA receivers using HMMs. Statistical Signal and Array Processing, 1998. Proceedings, Ninth IEEE SP Workshop on 14-16 Sept. 1998 pp.272-275
9. Anwer A.Khan. Iterative Decoding and Channel Estimation over Hidden Markov Fading Channels. Submitted to the Faculty of the Virginia Polytechnic Institute and State University in partial fulfillment of the requirement for the degree of Master of Science in Electrical Engineering, [Online], Available: http://scholar.lib.vt.edu/theses/ available/etd-05102000-13390004/unrestricted/AAKhan.pdf
10. W.Pan. Variable complexity algorithms and adaptive computation control in video coding and communications. Ph.D.thesis, the University of Southern California,2002
11. G.L.Stuber. Principles of Mobile Communication, Kluwer Academic Press, 1996
12. H.Bischl and E.Luts. Packet error rate in the non-interleaved Rayleigh channe. IEEE Trans.on Communication, vol.43, no.2/3/4.pp.1375-1282. Feb-April 1995
13. W.Turin and R.van Nobelen. Hidden Markov modeling of flat fading channels. IEEE Journal on Selected Areas in communication, vol.16, no.9.pp.1809-1817, Dec 1998
14.J M Wozencraft,Kennedy.R.Modulation and demodulation for probabilistic coding.Infeimation Theory,IEEE Transactions on Volume 12,issue 3,July 1966Page(s):291-297
15.Lebrow.I,McHugh.P,Parker.A,J M Wozencraft.Information Theory,IEEE Transactions on Volume 9,issue 2,Apr 1963 Page(s):124-126
16.R.M.Fano,A heuristic discussion of probabilistic decoding,IEEE Trans.Information Theory,vol.IT-9,pp.66-74,April 1963
17.A.J.Viterbi and J.K.Omura.Principles of digital communication and coding,McGraw-Hill,1979
18.W.Pan and A.Ortega.Buffer control for variable complexity fano decoders.IEEE Global Telecommunication Conference.San Antonio,Texas,November 2001.pp.176-180
19.P.Orten and A.Svensson.Sequential decoding of convolutional codes for Rayleigh fading channels.Submitted to Kluwer,Wireless Personal Communications,July 1999
20.S.Lin and D.J.Costello(Jr).Error control coding:fundamentals and applications,Prentice-Hall,1983
21.David Wendi Pan,Seong-Moo Yoo and Reza Adhami.Prediction of Rayleigh Fading Channels based on Hidden Markov Modeling of Sequential Channel Decoding Complexity System Theory,2003.Proceedings of the 35th Southeastern Symposium on 16-18 March 2003 Page(s):304-307
22.Bahl L.R.Brown P F et al.Maximum Information Estimation of Hidden Markov Parameters for Speech Recognition.IEEE Proc.ICASSP.1986.49-52
23.Bahl L.R.A New Algorithm for the Estimation of Hidden Markov Parameters.IEEE Proc.ICASSP.1988,493-496
24.杨行峻,迟惠生等.语音信号数字处理.北京:电子工业出版社,1995,
25.Chau C W,Kwong S,Diu C K.Optimization of HMM by a Genetic Algorithm.1997年声学,语音及信号文集 1727-1730
26.孙敬,胡光锐,徐雄.利用基因算法训练连续隐马尔科夫模型的语音识别 上海交通大学学报 1998 32(6)19-22
27.Geman W S.Stochastic Relaxatio.Gibbs distributions and Bayessan restoration of images.IEEE Trans.PAMI-6,Nov.1984:721-741
28.T.S.Rappaport.Wireless Communication principles and practice.2nd Edition.北京:电子工业出版社,2006.7.
29.束锋.OFDM和MIMO-OFDM系统中同步误差分析与信道估计研究.东南大学博士后出站报告,2005.10.
30.杨大成.移动传播环境:理论基础、分析方法和建模技术.北京:机械工业出版社,2003.8.
31.R.S.Liptser and A.N.Shiryayev.Statistics of Random Processes.New York:Sp ringer-Verlag,1977
32.严加安.测度论讲义.北京:科学出版社,2000
33.数学模型讲义.北京大学数学科学学院.2000
34.苑诗松,王静龙,淮晓龙.高等数理统计 北京:高等教育出版社,1998.7
35.Steffen Michalek,Mirko WAGNER,Jens TIMMER.A new approximate likelihood estimator for ARMA-filtered hidden Markov models.Signal Processing,IEEE Transactions on[see also Acoustics,Speech,and Signal Processing,IEEE Transactions on]Volume 48,Issue 6,June 2000 Page(s):1537-1547
36.Vikram Krishnamurthy,Gang George Yin.Recursive algorithms for estimation of hidden Markov models and autoregressive models with Markov regime.IEEE Transactions on Information Theory 48(2):458-476(2002)
37.Peter M.Djuric,Senior Member IEEE and Joon-Hwa Chun.An MCMC Sampling to Estimation of HMMs.IEEE Trans.Signal Processing,Vol.50,no.5,2002,pp.1113-1123
38.Janez Kaiser.University of Maribor,Faculty of Electrical Engineering and Computer Science,Smetanora 17 Maribor slovenia.trainin of HMM with GA.w ww.dsplab.uni-mb.si/Clanki/janez/ast98.pdf
39.丁建立,陈增强,袁著扯.遗传算法与蚂蚁算法的融合.计算机研究与发展,2003,40卷,第9期
40.韩广军,罗强,李兵.基于DCPM-FGA的隐马氏模型的参数训练.国防科技大学学报,2004,第26卷,第4期
41.Yariv Ephraim,David Malah.Speech Enhancement based upon Hidden Markov Modeling.Acoustics,Speech,and Signal Processing,1989.ICASSP-89,1989International Conference on 23-26 May 1989 Page(s):353-356 vol.1
42.Enzo Baccarelli and Robert Cusani.Recuursive Kahnan-type optimal estimation and detection of Hidden Markov chains.Signal Processing,1996
43.易克初,田斌,付强.语音信号处理.北京:国防工业出版社,2000
44.Booker L.B.,Goldberg D.E.,and Holland J.H.Classifier System and Application.Fuzzy Sets and Systems,1994(61):129-136
45.谢锦辉.隐Markov模型(HMM)及其在语音处理中的应用.武汉:华中理工大学出版社1995年
46.韦岗、邱伟.现代信号处理理论与技术.广州:华南理工大学出版社 1994
47.L.R.Rabiner.A Tutorial on Hidden Markov Models and Selected Application in Speech Recognition.IEEE Trans.ASSP,vol.77,No2.,Feb 1989.257-286
48.S.E.Levinson,L.R.Rabiner,and M.M.Sondhi.An Introduction to the Application of the Theory of Probabilistic Functions of a Markov Process to Automatic Speech Recognition.Bell System Tech.J.,April 1983 1035-1074
49.B.Mericldo.Phonetic Recognition Using Hidden Markov Models and Maximum Mutual Information Training.Proc.ICASSP-88,:111-114
50.杨国亮,王志良,刘翼伟等.基于改进MMI的HMM训练算法及其在面部表情识别中的应用.北京科技大学学报,2007年04期
51.W.Turin.Digital Transmission Systems:Performance,Analysis and Modeling,2nd ed.,NewYork:McGraw-Hill,1999
52.L.R.Rabiner and B.H.Juang.An Introduction to Hidden Markov.IEEE ASSP Magzine,January 1986,pp.4-16
53.R.A.Hoeard.Dynamic Probability System,Vol.Ⅰ:Markov Models.New York:Wiley,1971
54.R.A.Hoeard.Dynamic Probability System,Vol.Ⅱ:SemiMarkov and Decision Processes.New York:Wiley,1971
55.H.S.Wang and N.Moayeri.Finite-State Markov Channel-A Useful Model for Radio Communications Channels.IEEE Transactions on Vehicular Technology,Vol.44,February 1995,pp.163-171
56.S.Sivaprakasam and K.S.Shanmugan.An Equivalent Model for Burst Errors in Digital Channels.IEEE Transactions on Communications,Vol.43,No.2/3/4,February/March/April 1995,pp.1347-1355
57.H.S.Wang and P.-C.Chang.On Verifying the First-Order Markovian Assumption for a Rayleigh Channel Model.IEEE Transactions on Vehicular Technology,Vol.45,May 1996,pp.353-357
58.W.Turin and R.van Nobelen.Hidden Markov Modeling of Flat Fading Channels.IEEE Journal on Selected Areas in Communications,Vol.16,No.9,December 1998,pp.1809-1817
59.F.Babich,O.E.Kelly,and G.Lombardi.Generalized Markov Modeling for Flat Fading.IEEE Transactions on Communications,Vol.48,No.4,April 2000,pp.347-351
60.M.Zorzi,R.R.Rao,and L.B.Milstein.A Markov Model for Block Errors on Fading Channels.PIMRC'96 Conference Record,October 1996
61.E.N.Gilbert.Capacity of a Burst-Noise Channel.Bell System Technical Journal,Vol.39,September 1960,pp.1253-1266
62.B.D.Fritchman.A Binary Characterization Using Partitioned Markov Chains.IEEE Transactions on Information Theory,Vol.IT-13,No.2,April 1967,pp.221-227
63.P.Elias.Coding for Noisy Channel.IRE Conv.Rec.,p.4:37-47,1955
64.J M Wozencraft.Sequential Decoding for Reliable Communication.IRE Conv.REC.5(pt.2):11-25,1957
65.J M Wozencraft and B.Reiffen.Sequential Decoding.MIT Press,Cambridge,1961
66.Shu Lin,Daniel J.Costello著.差错控制编码(原书第二版).北京:机械工业出版社 2007.6
67.Masse.J.L.Threshold Decoding,The MIT Press.Cambridge,Mass.1963
68.Viterbi.A.J.Error Bounds for convolutinal Codes and an Asymptotically Optimum Decoding Algorithm.IEEE Trans.Inf.Theory,vol.IT13,pp.260-269,April,1967
69.R.Johannesson and K.S.Zigangorov.Fundamentals of Convolutional Coding.IEEE Press,Piscataway,1999
70.J A Heller and I M Jacobs.Viterbi Decoding for Satellite and Space Communication.IEEE Trans.Commun.Techol.COM-19:835-48
71.Juang B H.A Probabilistic Distance Measure for Hidden Markov Models.AT&T.Technical Journal.Feb 1985,64(2).391-408
72.F.Swarts and H.C.Ferreira.Markov Characterization of Digital Fading Mobiling.VHF Channels.IEEE Trans.Veh.Technol,1994;43(4):977-985
73.王京,王跃科.低轨卫星信道隐马尔科夫仿真模型研究.计算机仿真2007年1月
74.惠晓威,马飞.GSM移动信道特性的仿真研究 辽宁工程技术大学学报 2002年6月
75.ETSI TR 125 943 V5.1.0(2002-06)
76.Gao Jiang,Ding Xiaoqing,Wu Youshou.A segmenta-tion algorithm for handwritten chinese characterstrings[A][M].Proc 6th Int Conf Document Analysisand Recognition[C];1999年
77.杜世平,李海.Second-order Hidden Markov Models and Its Application to Computatonal Linguistics.四川大学学报(自然科学版)Journal of Sichuan University(Namral Science Edition)
78.Burshtein D.Robust parametric modeling of duration in hidden markov models.IEEE Trans on Speech & Audio Processing,1996,4(3):240-242
79.J.Gehrke,F.Kom,D.Srivastava.On Computing Correlated Aggregates over Continual Data Streams.In SIGMOD,2001,pp.13-24
80.袁东风,张立.MARKOV模型在移动信道中的应用.Radio Engineering 1999.Vol.29 No.4