FIR-MIMO系统可盲均衡信道矩阵的特征分解研究
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摘要
通信的目的是进行信息的传输，对于一个无线通信系统来说，多址干扰和码间干扰的存在影响了信息的传输以及信号的检测和恢复，在某种程度上，多址干扰可通过多用户检测技术来克服，而均衡技术则可以减弱因信道的非理想特性造成的码间干扰。显然，无线信道的均衡能力将直接影响和决定无线信道的传输能力和利用率。为了提高信道带宽利用率，“盲均衡”方法应运而生，该方法仅利用接收序列本身及其先验信息即可对信道进行均衡。
FIR-MIMO无线信道的可盲均衡条件是学者们研究的重要问题之一，随着研究的深入，该条件得到了不断地扩展，从最初要求信道矩阵H(z)不可约的极其苛刻的条件扩展到可逆条件，后又扩展为半可逆条件。本文从理论上推导出了FIR-MIMO系统信道矩阵在不可约、可逆、半可逆三种可盲均衡条件下信道矩阵分解的统一形式H(z) =H_1(z)D(z)Q，并证明了：不可约条件是可逆条件的一种特例，而半可逆条件包含了前两者，是三种条件下适用范围最广的可盲均衡条件。另外，从信道矩阵的特征分析中还能看出，不可约的信道矩阵是一个基础，可盲均衡条件的扩展在数学上可等价的表现为在不可约信道系统上级联一个特殊的系统，级联系统的不同性质就对应了相应的可盲均衡范围。
作为前述理论的一个应用，以半可逆条件下的可盲均衡理论为基础，实现FIR-MIMO系统下QPSK复信号的高效、快速盲检测，本文通过矩阵变换的方法把实信道下QPSK复信号的盲多用户检测问题转化为一个二值约束的二次规划问题，在求解此二次规划时使用复杂度仅为多项式级别的e近似算法，最后进行实例仿真。仿真结果表明：该算法在FIR-MIMO信道可含公零点的情况下，扩大了适用范围，降低了计算复杂度。
本文共有五章内容，首先介绍的是本课题的研究背景和意义；第二章概述了通信系统盲均衡技术；第三章详细描述了FIR-MIMO系统模型，并说明了在该模型下的三种可盲均衡条件，分析了不同条件下信道矩阵的特征，然后以上述模型和理论为基础，在传输信号属于有限字符集的条件下，研究含公零点系统的盲均衡问题，给出了该系统下复传输信号的直接盲检测方法；第四章给出了具体的仿真实验；第五章是对全文工作的总结及展望。
The objective of communications is to transfer the messages. For a wireless communicationsystem, the existence of the multiple access interference and the presence of inter-symbolinterference affects the transformation of the messages, detection and recovery of signals. Insome content, multiple access interference can be decreased by multi-user detection, whileequalization can used to eliminate the inter-symbol interference caused by the non-idealcharacteristics of channels. Apparently, the balance capability of the wireless channel willdirectly affect and determine the transmission of wireless channel capacity and utilization. Inorder to improve the channel bandwidth utilization, "blind equalization" method came into being,the method using only the received sequence itself and the priori information to balance thechannel.
The conditions guarantee the FIR-MIMO wireless channel to be blindly equalizable is oneof the important hot topics investigated by researchers in the literature. The concrete conditionsare continuously extended by the research scholars, from the initially extremely harsh conditionsto the reversible conditions, and later to the semi-reversible condition. In this thesis, based on theprevious research, we investigate the channel matrix. Using the polynomial matrix theory, wegive the universal factorization H(z) =H_1(z)D(z)Q for the channel matrix under differentequalizable conditions. In addition, analysis on the channel matrix characteristic factorizationalso prove in theory that: the irreducible condition is a special case of reversible conditions,while the former two ones are included in the third one, semi-reversible conditions, which is ablandly equalizable condition and can be applied to the most widest range. It can be seen fromthe characteristics of the channel matrix that the irreducible channel matrix is just a basis, theextension of the conditions to be blindly equalizable is mathematically equivalent to be cascadeda special system. Different properties of the cascaded systems correspond to a system which canbe applied to a different equalizable range area.
As an application of the former theory, based on the blind equalizable theory under thesemi-reversible conditions, to detect the QPSK complex signal efficiently for the FIR-MIMOsystems, this thesis transform the problems of the blind multiuser detection into a quadraticprogramming optimization problem subjecting to some relatively simple binary constraints usingthe matrix transformation. The complexity of solving the approximation algorithms is onlypolynomial. Simulation results indicate that: in the case of the FIR-MIMO channels withcommon zeros, comparing with the subspace method, the algorithm in this thesis is suitable for awider range with better performance.
This thesis consists of five chapters, the first introduces the research background andsignificance of this topic; the second chapter provides an overview of the blind equalization ofcommunication systems; the third chapter describes in detail the FIR-MIMO system model andpresents universal factorization of the channel matrix under three blindly equalizable conditions.Moreover, using the above-mentioned models and it’s theories, under the conditions that thetransmission signal belongs to a finite alphabet set and the channel having common zeros, wegive the method of directly signal detection of the system. The fourth chapter gives the specificsimulation of the directly blindly detection of the complex transmission signal. The fifth chapteris a summary of the full text of the work and discussion of the future work.
FIR-MIMO无线信道的可盲均衡条件是学者们研究的重要问题之一，随着研究的深入，该条件得到了不断地扩展，从最初要求信道矩阵H(z)不可约的极其苛刻的条件扩展到可逆条件，后又扩展为半可逆条件。本文从理论上推导出了FIR-MIMO系统信道矩阵在不可约、可逆、半可逆三种可盲均衡条件下信道矩阵分解的统一形式H(z) =H_1(z)D(z)Q，并证明了：不可约条件是可逆条件的一种特例，而半可逆条件包含了前两者，是三种条件下适用范围最广的可盲均衡条件。另外，从信道矩阵的特征分析中还能看出，不可约的信道矩阵是一个基础，可盲均衡条件的扩展在数学上可等价的表现为在不可约信道系统上级联一个特殊的系统，级联系统的不同性质就对应了相应的可盲均衡范围。
作为前述理论的一个应用，以半可逆条件下的可盲均衡理论为基础，实现FIR-MIMO系统下QPSK复信号的高效、快速盲检测，本文通过矩阵变换的方法把实信道下QPSK复信号的盲多用户检测问题转化为一个二值约束的二次规划问题，在求解此二次规划时使用复杂度仅为多项式级别的e近似算法，最后进行实例仿真。仿真结果表明：该算法在FIR-MIMO信道可含公零点的情况下，扩大了适用范围，降低了计算复杂度。
本文共有五章内容，首先介绍的是本课题的研究背景和意义；第二章概述了通信系统盲均衡技术；第三章详细描述了FIR-MIMO系统模型，并说明了在该模型下的三种可盲均衡条件，分析了不同条件下信道矩阵的特征，然后以上述模型和理论为基础，在传输信号属于有限字符集的条件下，研究含公零点系统的盲均衡问题，给出了该系统下复传输信号的直接盲检测方法；第四章给出了具体的仿真实验；第五章是对全文工作的总结及展望。
The objective of communications is to transfer the messages. For a wireless communicationsystem, the existence of the multiple access interference and the presence of inter-symbolinterference affects the transformation of the messages, detection and recovery of signals. Insome content, multiple access interference can be decreased by multi-user detection, whileequalization can used to eliminate the inter-symbol interference caused by the non-idealcharacteristics of channels. Apparently, the balance capability of the wireless channel willdirectly affect and determine the transmission of wireless channel capacity and utilization. Inorder to improve the channel bandwidth utilization, "blind equalization" method came into being,the method using only the received sequence itself and the priori information to balance thechannel.
The conditions guarantee the FIR-MIMO wireless channel to be blindly equalizable is oneof the important hot topics investigated by researchers in the literature. The concrete conditionsare continuously extended by the research scholars, from the initially extremely harsh conditionsto the reversible conditions, and later to the semi-reversible condition. In this thesis, based on theprevious research, we investigate the channel matrix. Using the polynomial matrix theory, wegive the universal factorization H(z) =H_1(z)D(z)Q for the channel matrix under differentequalizable conditions. In addition, analysis on the channel matrix characteristic factorizationalso prove in theory that: the irreducible condition is a special case of reversible conditions,while the former two ones are included in the third one, semi-reversible conditions, which is ablandly equalizable condition and can be applied to the most widest range. It can be seen fromthe characteristics of the channel matrix that the irreducible channel matrix is just a basis, theextension of the conditions to be blindly equalizable is mathematically equivalent to be cascadeda special system. Different properties of the cascaded systems correspond to a system which canbe applied to a different equalizable range area.
As an application of the former theory, based on the blind equalizable theory under thesemi-reversible conditions, to detect the QPSK complex signal efficiently for the FIR-MIMOsystems, this thesis transform the problems of the blind multiuser detection into a quadraticprogramming optimization problem subjecting to some relatively simple binary constraints usingthe matrix transformation. The complexity of solving the approximation algorithms is onlypolynomial. Simulation results indicate that: in the case of the FIR-MIMO channels withcommon zeros, comparing with the subspace method, the algorithm in this thesis is suitable for awider range with better performance.
This thesis consists of five chapters, the first introduces the research background andsignificance of this topic; the second chapter provides an overview of the blind equalization ofcommunication systems; the third chapter describes in detail the FIR-MIMO system model andpresents universal factorization of the channel matrix under three blindly equalizable conditions.Moreover, using the above-mentioned models and it’s theories, under the conditions that thetransmission signal belongs to a finite alphabet set and the channel having common zeros, wegive the method of directly signal detection of the system. The fourth chapter gives the specificsimulation of the directly blindly detection of the complex transmission signal. The fifth chapteris a summary of the full text of the work and discussion of the future work.
引文
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[2] Benveniste A,Goursat M, Ruget G. Robust Identification of A Nonminimum PhaseSystem:Blind Adjustment of A Linear Equalizer In Data Communications[J]. IEEE Trans.Automatic Control, 1980, 25:385-399.
[3] Bernard Widrow, Samuel D. Stearns,王永德,龙宪惠.自适应信号处理[M].北京:机械工业出版社, 2008.
[4] Constantinos B. P., Arogyaswami J. P.. A Constant Modulus Algorithm for Multi-UserSignal Separation in Presence of Delay Spread Using Antenna Arrays[J]. IEEE SignalProcessing Letters, 1997, 4(6):178-181.
[5] Daniel Y., Boaz P.. Blind Identification of FIR Systems Excited by Discrete AlphabetInput[J]. IEEE Trans. Signal Processing. 1993, 41(3):1331-1339.
[6] Gardner W. A.. A New Method of Channel Identification[J]. IEEE Trans. Communication,1991, COM-39:813-817.
[7] Giannakis G. B., Hua Y., Stoica P., et al. Signal Processing Advances in Wireless andMobile Communications, Volume 1: Trends in Channel Estimation and Equalization[M].Pearson Education, Inc, 2002.
[8] Girolami M.. A Nonlinear Model of The Binaural Cocktail Party Effect[J]. NeuralComputation, 1998, 22(1-3):201-215.
[9] Gorokhov A., Loubaton P. Subspace Based Techniques for Second Order Blind Separationof Convolutive Mixtures With Temporally Correlated Sources[J]. IEEE Trans. CircuitsSyst. I, 1997, 44:813-820.
[10]顾雯. MIMO系统中基于e近似的直接盲多用户检测算法研究[D].南京:南京邮电大学硕士学位论文, 2007.
[11]韩彬.含公零点FIR-MIMO信道的盲均衡[D].南京:南京邮电大学硕士学位论文,2010.
[12]何振亚.自适应信号处理[M].北京:科学出版社, 2002.
[13] Inouye Y, Ruey W L. A System-Thoertic Foundation for Blind Equalization of An FIRMIMO Channel System [J]. IEEE Trans. Circults and Systems. 2002, 49(4): 425- 436.
[14]纪迪. MIMO系统的盲均衡算法研究[D].哈尔滨:哈尔滨工程大学硕士学位论文,2008.
[15] Kechriotis G, Zervas E. Using Recurrent Neural Network for Adaptive CommunicationChannel Equalization[J]. IEEE Trans on Neural Network, 1994, 5:267-278.
[16] Kenendy R A, Ding Z. Blind Adaptive Equalizers for Quadrature Amplitude ModulatedCommunication Systems Based on Convex Cost Function[J]. Optical Engineering, 1992,31(6):1189-1199.
[17] Klein A., Baier P. W.. Simultaneous Cancellation of Cross Interference and ISI in CDMAMobile Radio Communications[A]. Proceedings of the 3rd IEEE International Symposiumon PIMRC, 1992, 10:118-122.
[18]雷震洲.从移动通信的演进轨迹看创新[J].移动通信, 2010, 19: 10-14.
[19]梁启联,周正.基于多层神经网络的盲均衡算法[J].北京邮电大学学报, 1996,19(3):27-32.
[20]梁启联,周正,刘泽民.基于递归神经网络的盲均衡算法的改进[J].北京邮电大学学报, 1997, 20(4):6-11.
[21] Liu H, Xu G, Tong L, Kailath T. Recent Developments in Blind Channel Equalization:From Cyclostationarity to Subspsces, Sig. Proc. 1996:1-17.
[22]刘琚,何振亚.盲源分离和盲反卷积[J].电子学报, 2002, 30(4): 570-576.
[23]马建仓,牛奕龙,陈海洋.盲信号处理[M].北京:国防工业出版社. 2006.
[24] Mo S, Shafai B. Blind Equalization Using Higher Order Cumulants and Neural Network[J].IEEE Trans on Signal Processing, 1994, 42:3209-3217.
[25] Moulines E, Duhamel P, Cardoso J, Mayrargue S. Subspace Methods for BlindIdentification of Multichannel FIR Filters[J]. IEEE Trans. Signal Processing, 1995,43:516-525.
[26] Picchi G, Prati G. Blind Equalization and Carrier Recovery Using 'Stop-and-Go'Decision-Directed Algorithm[J]. IEEE Trans on Communication, 1987, 35(9):877-887.
[27] Sato Y. A Method of Self-Recovering Equalization for Multiple Amplitude ModulationSchemes[J]. IEEE Trans on Communication, 1975, 23:679-682.
[28] Shalvi O, Weinstein E. New Criteria for Blind Deconvolution of Nonminimum PhaseSystems(Channels)[J]. IEEE Trans On Signal Processing, 1990, 36: 312-321.
[29]史鹍. MIMO系统均衡算法及其应用的研究[D].北京:清华大学硕士学位论文, 2005.
[30]孙鹏杰,张文爱.浅析盲反卷积算法及其进展[J].太原科技,2009, 5: 48-52.
[31]孙守宇.盲信号处理基础及其应用[M].北京:国防工业出版社, 2010.
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