子带技术研究及其在宽带信号处理中的应用
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摘要
近年来，随着多媒体技术和通信前端接收技术的不断发展，无线通信的速率越来越高，可接收的信号带宽也越来越宽。宽带通信系统在提高通信容量的同时，也使得某些传统窄带信号处理技术在宽带信号处理上遇到了困难和挑战，单载波宽带信号的均衡处理与宽带多通道信道化接收就是其中较为突出的两个问题。一方面，宽带传输信道的冲激响应比较长，如果采用传统全频带均衡技术则要求均衡器的阶数很高。高阶均衡器收敛性能差、计算复杂度高，且难以工程实现。因此如何有效实现宽带信号的信道均衡已经成为提高宽带通信系统解调性能的关键问题之一。另一方面，随着接收机接收带宽的不断增加，宽带接收数据中信号的数量和种类越来越多。传统采用独立数字下变频技术的多通道信道化方法硬件耗费大、计算量大，且不能灵活地适应动态信道化接收。如何高效地实现宽带多通道信道化接收是提高宽带接收系统性能的另一个关键问题。
子带技术可以将宽带数据进行分解和重构，避免了直接进行宽带信号处理的困难，为宽带信号接收处理提供了新的途径。深入研究子带系统的基本理论，并将其推广应用到宽带信号接收处理中，对解决宽带通信系统面临的难题具有重要的理论和现实意义。本文首先研究了均匀子带滤波器组和非均匀子带滤波器组的设计方法，在保证子带系统重构特性满足要求的同时，尽可能地简化了设计复杂度；然后重点研究了子带技术在单载波宽带信号均衡和宽带多通道信道化接收两方面的应用，改进了现有方法的不足，提高了宽带信号处理的性能和效率。
本文的创新点主要包括以下4个方面。
1、在均匀子带滤波器组设计方面，针对现有迭代设计方法中原型滤波器阶数过高、混叠误差较大等问题，提出了一种改进的原型滤波器迭代设计算法。该方法通过在代价函数中添加一阶混叠项因子，更好地抑制了系统混叠误差，放松了对原型滤波器阻带衰减特性和阶数的要求。本文将新的代价函数表示成滤波器系数的二次函数形式，并推导出其闭合解的数学表达式，利用迭代的方式逐渐逼近极值点，避免了直接求解高维非线性代价函数的困难。此外，本文将改进的原型滤波器迭代算法与内插思想相结合，提出了一种高效的均匀子带调制滤波器组迭代设计方法，可进一步减小优化算法中目标参数的个数、降低计算复杂度。
2、在非均匀子带滤波器组设计方面，针对现有间接设计方法优化求解困难的问题，提出了一种基于两级合并的非均匀子带滤波器组迭代设计方法。该方法采用内外层滤波器分步优化的设计思路，以抑制系统误差项为准则构造代价函数，并通过化简将高维非线性代价函数转换成滤波器系数向量的二次函数形式，推导出其极值解的解析表达式，利用迭代逼近的方法得到最优解。该方法基于普遍意义建立代价函数，对抽样因子没有特别限制，相对传统直接优化求解设计方法具有易收敛、计算复杂度相对较低的优点。
3、在单载波宽带信号子带均衡方面，给出了均匀子带与非均匀子带划分的实现方法，定义了子带划分的性能评估参数，推导了子带均衡系统中均衡权系数矩阵为对角阵的条件，分析了子带均衡并行结构的误差来源。针对子带均衡并行结构在抽样因子较大的系统中存在较大混叠误差的问题，提出了一种添加权值临近项的子带均衡结构。该结构利用均衡权系数矩阵次对角线上的临近项更好地抑制了系统的混叠误差，放松了对子带滤波器组阻带衰减特性和系统抽样因子的要求，改善了子带均衡的效果。实验证明本文添加权值临近项的子带均衡结构比子带均衡并行结构具有更快的收敛速度和更小的稳态误差。
4、在宽带多通道信道化接收方面，针对现有非均匀子带信道化技术存在子带合并方法适用性有限以及对所关注信号信道化效率不高等问题，提出了一种基于子带信号特征的非均匀子带信道化结构。该结构利用子带编号匹配的综合滤波器进行非均匀合并，消除了对子带通道数目与抽样速率的取值限制。在子带信号特征提取方面，建立了单载波信号子带信道化输出的数学模型，推导给出了基于子带信号的波特率、载波频率参数估计算法。本文基于子带信号特征的非均匀子带信道化结构仅合并输出所关注的重要信号，可有效提高对所关注重点信号宽带信道化的效率，其子带特征提取算法对其它频谱失真情况下的信号参数估计也具有指导意义。
In the recent years, with the rapid development of multimedia and communicationreceiving technology, the rate of wireless communication is higher and higher, the band ofreceiving signal is wider and wider. While the communication capability is increasing, sometraditional narrowband signal processing technologies are challenged by the widebandprocessing. The equalization of single carrier wideband singal and wideband multi-channelreceiving are the two outstanding problems. On the one hand, because of the long impulseresponse of the wideband transmission channel, the equalizer order should be high using thetraditional equalization technologies. The high order equalizer has bad convergenceperformance and huge calculation complexity, which made it hard to be realization. How toeffectively realize the equalization of wideband signal becomes one of the key questions toimprove the demodulation performance in wideband communication systems. On the otherhand, the quantity and type of signals included in the wideband data become more and moreas the increasing of the receiving bandwidth. Parallel digital down conversion is used by thetraditional multi-channel channelization method, which has huge computation and can’t adaptin dynamic channelization. How to effectively realize wideband multi-channel receivingbecomes another key question to improve the performance of wideband receiving systems.
Subband technology can avoid the wideband processing difficulties by decompositionand reconstruction of the wideband data. It provides a new solution for wideband signalprocessing. It has significant theoretic and practical meaning to research the subbandtechnology and its applications. This paper gives out the design methods of subband filterbanks. It can decrease the design complexity and meet the reconstruction performance of thesubband system. Then the paper focuses on the subband applications in wideband signalequalization and channelization. Some new methods are proposed which can improve theperformance and efficiency of the wideband signal processing.
The innovation points of the thesis include the following four aspects.
1. The design methods for uniform subband filter banks are researched. The prototypefilters generally have high order and bad alias error performance using trandition iterativedesign methods. In order to resolve this problem, a modified iterative design method forprototype filter is proposed. The new method can decrease the alias error and the length of thefilter by adding the first-order alias term for the cost function. The cost function is formulatedas a quadratic function of prototype filter coefficients. A mathematics closed-form solution isdeduced for the new cost function. Its minimum point is obtained by iterative approach avoiding the difficulty of direct solution. This modified iterative method and the interpolationdesign method are combined in order to decease the parameter number of the optimizationalgorithm. Therefore it can greatly decrease the computation in the iterative design process.
2. The indirect design methods of nonuniform subband filter are usually difficult toobtain its optimum solution. Aiming at this problem, a new iterative design method fornonuniform subband filterbank is proposed based on two-stage merging processing. In thismethod, the outside basic filter banks are designed firstly, then the inner merging filter banksare designed. The cost function is constructed by suppressing of alias terms. The nonlinearcost function is predigested and expressed by a quadratic function of the prototype filtercoefficient vector. Then the closed form solution of the cost function is deduced so that theoptimal solution can be achieved by iterative approach. The new iterative method has nospecial limitation on the decimation rate. As to the traditional design methods, it has betterconvergence performance and lower computation complexity.
3. The realization methods are given out for the uniform and nonuniform subbandpartition, which are used in the subband equalization. Two parameters for partitionperformance evaluation are defined. The condition is deduced when the equalizer coefficientmatrix is diagonal-matrix. The error analyse is carried out for subband equalization withparallel structure. A new subband equalization scheme with adding adjacent term is proposedto decease the alias error when the decimation rate is large. The new method can suppress thealias error and loose the limitations for the stopband attenuation performance of the subbandfilter banks. Simulation results prove that the new subband equalization structure has betterconvergence performance compared with the subband equalization parallel structure.
4. Aiming at the problems of the conventional subband channelization structure, a newnonuniform subband channelization scheme based on the features of subband signals isproposed. This new scheme uses the matched suband filters to merge the subbands. Iteliminates the limitations on the decimation rate. Moreover, its subband combination processis carried out only for the subbands which have the special features. So the new scheme canimprove the channelization efficiency for special signals. The subband signal model for singlecarrier signal is established. The baud rate and carrier frequency estimation methods arededuced based on the subband signal. The above estimation methods can be consulted byother parameter estimation questions under spectrum distortion conditions.
子带技术可以将宽带数据进行分解和重构，避免了直接进行宽带信号处理的困难，为宽带信号接收处理提供了新的途径。深入研究子带系统的基本理论，并将其推广应用到宽带信号接收处理中，对解决宽带通信系统面临的难题具有重要的理论和现实意义。本文首先研究了均匀子带滤波器组和非均匀子带滤波器组的设计方法，在保证子带系统重构特性满足要求的同时，尽可能地简化了设计复杂度；然后重点研究了子带技术在单载波宽带信号均衡和宽带多通道信道化接收两方面的应用，改进了现有方法的不足，提高了宽带信号处理的性能和效率。
本文的创新点主要包括以下4个方面。
1、在均匀子带滤波器组设计方面，针对现有迭代设计方法中原型滤波器阶数过高、混叠误差较大等问题，提出了一种改进的原型滤波器迭代设计算法。该方法通过在代价函数中添加一阶混叠项因子，更好地抑制了系统混叠误差，放松了对原型滤波器阻带衰减特性和阶数的要求。本文将新的代价函数表示成滤波器系数的二次函数形式，并推导出其闭合解的数学表达式，利用迭代的方式逐渐逼近极值点，避免了直接求解高维非线性代价函数的困难。此外，本文将改进的原型滤波器迭代算法与内插思想相结合，提出了一种高效的均匀子带调制滤波器组迭代设计方法，可进一步减小优化算法中目标参数的个数、降低计算复杂度。
2、在非均匀子带滤波器组设计方面，针对现有间接设计方法优化求解困难的问题，提出了一种基于两级合并的非均匀子带滤波器组迭代设计方法。该方法采用内外层滤波器分步优化的设计思路，以抑制系统误差项为准则构造代价函数，并通过化简将高维非线性代价函数转换成滤波器系数向量的二次函数形式，推导出其极值解的解析表达式，利用迭代逼近的方法得到最优解。该方法基于普遍意义建立代价函数，对抽样因子没有特别限制，相对传统直接优化求解设计方法具有易收敛、计算复杂度相对较低的优点。
3、在单载波宽带信号子带均衡方面，给出了均匀子带与非均匀子带划分的实现方法，定义了子带划分的性能评估参数，推导了子带均衡系统中均衡权系数矩阵为对角阵的条件，分析了子带均衡并行结构的误差来源。针对子带均衡并行结构在抽样因子较大的系统中存在较大混叠误差的问题，提出了一种添加权值临近项的子带均衡结构。该结构利用均衡权系数矩阵次对角线上的临近项更好地抑制了系统的混叠误差，放松了对子带滤波器组阻带衰减特性和系统抽样因子的要求，改善了子带均衡的效果。实验证明本文添加权值临近项的子带均衡结构比子带均衡并行结构具有更快的收敛速度和更小的稳态误差。
4、在宽带多通道信道化接收方面，针对现有非均匀子带信道化技术存在子带合并方法适用性有限以及对所关注信号信道化效率不高等问题，提出了一种基于子带信号特征的非均匀子带信道化结构。该结构利用子带编号匹配的综合滤波器进行非均匀合并，消除了对子带通道数目与抽样速率的取值限制。在子带信号特征提取方面，建立了单载波信号子带信道化输出的数学模型，推导给出了基于子带信号的波特率、载波频率参数估计算法。本文基于子带信号特征的非均匀子带信道化结构仅合并输出所关注的重要信号，可有效提高对所关注重点信号宽带信道化的效率，其子带特征提取算法对其它频谱失真情况下的信号参数估计也具有指导意义。
In the recent years, with the rapid development of multimedia and communicationreceiving technology, the rate of wireless communication is higher and higher, the band ofreceiving signal is wider and wider. While the communication capability is increasing, sometraditional narrowband signal processing technologies are challenged by the widebandprocessing. The equalization of single carrier wideband singal and wideband multi-channelreceiving are the two outstanding problems. On the one hand, because of the long impulseresponse of the wideband transmission channel, the equalizer order should be high using thetraditional equalization technologies. The high order equalizer has bad convergenceperformance and huge calculation complexity, which made it hard to be realization. How toeffectively realize the equalization of wideband signal becomes one of the key questions toimprove the demodulation performance in wideband communication systems. On the otherhand, the quantity and type of signals included in the wideband data become more and moreas the increasing of the receiving bandwidth. Parallel digital down conversion is used by thetraditional multi-channel channelization method, which has huge computation and can’t adaptin dynamic channelization. How to effectively realize wideband multi-channel receivingbecomes another key question to improve the performance of wideband receiving systems.
Subband technology can avoid the wideband processing difficulties by decompositionand reconstruction of the wideband data. It provides a new solution for wideband signalprocessing. It has significant theoretic and practical meaning to research the subbandtechnology and its applications. This paper gives out the design methods of subband filterbanks. It can decrease the design complexity and meet the reconstruction performance of thesubband system. Then the paper focuses on the subband applications in wideband signalequalization and channelization. Some new methods are proposed which can improve theperformance and efficiency of the wideband signal processing.
The innovation points of the thesis include the following four aspects.
1. The design methods for uniform subband filter banks are researched. The prototypefilters generally have high order and bad alias error performance using trandition iterativedesign methods. In order to resolve this problem, a modified iterative design method forprototype filter is proposed. The new method can decrease the alias error and the length of thefilter by adding the first-order alias term for the cost function. The cost function is formulatedas a quadratic function of prototype filter coefficients. A mathematics closed-form solution isdeduced for the new cost function. Its minimum point is obtained by iterative approach avoiding the difficulty of direct solution. This modified iterative method and the interpolationdesign method are combined in order to decease the parameter number of the optimizationalgorithm. Therefore it can greatly decrease the computation in the iterative design process.
2. The indirect design methods of nonuniform subband filter are usually difficult toobtain its optimum solution. Aiming at this problem, a new iterative design method fornonuniform subband filterbank is proposed based on two-stage merging processing. In thismethod, the outside basic filter banks are designed firstly, then the inner merging filter banksare designed. The cost function is constructed by suppressing of alias terms. The nonlinearcost function is predigested and expressed by a quadratic function of the prototype filtercoefficient vector. Then the closed form solution of the cost function is deduced so that theoptimal solution can be achieved by iterative approach. The new iterative method has nospecial limitation on the decimation rate. As to the traditional design methods, it has betterconvergence performance and lower computation complexity.
3. The realization methods are given out for the uniform and nonuniform subbandpartition, which are used in the subband equalization. Two parameters for partitionperformance evaluation are defined. The condition is deduced when the equalizer coefficientmatrix is diagonal-matrix. The error analyse is carried out for subband equalization withparallel structure. A new subband equalization scheme with adding adjacent term is proposedto decease the alias error when the decimation rate is large. The new method can suppress thealias error and loose the limitations for the stopband attenuation performance of the subbandfilter banks. Simulation results prove that the new subband equalization structure has betterconvergence performance compared with the subband equalization parallel structure.
4. Aiming at the problems of the conventional subband channelization structure, a newnonuniform subband channelization scheme based on the features of subband signals isproposed. This new scheme uses the matched suband filters to merge the subbands. Iteliminates the limitations on the decimation rate. Moreover, its subband combination processis carried out only for the subbands which have the special features. So the new scheme canimprove the channelization efficiency for special signals. The subband signal model for singlecarrier signal is established. The baud rate and carrier frequency estimation methods arededuced based on the subband signal. The above estimation methods can be consulted byother parameter estimation questions under spectrum distortion conditions.
引文
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