【作者】 潘进；

【导师】 焦李成；

【作者基本信息】 西安电子科技大学 ， 电路与系统， 2001， 博士

【摘要】 本文围绕多子波分析及其在CDMA中的应用展开研究。主要进行了以下几个方面的工作： 1．研究了利用遗传算法确定短序列正交多子波的方法。确定多尺度函数所生成的多子波是灵活运用多子波理论的一个重要环节，在一定的条件下，它可以等价地转化为一个高维空间中的优化问题。遗传算法是模拟自然进化过程的全局性鲁棒优化算法，利用遗传算法来确定由短序列正交多尺度函数所生成的正交多子波，使确定多子波的思路变得清晰而简单。 2．建立了利用矩阵特征值和特征向量构造短序列正交多子波的方法。理论分析表明，在一定的条件下，多子波系统的子波序列可由尺度序列所构成的矩阵的特征值和特征向量构造出来。这种构造方法的优点在于不受多子波重数的限制。 3．提出了多子波神经网络的概念和模型，并对其逼近性能进行了研究。随着子波理论研究的不断深入，尺度函数的诸多特性以及用不同层级的尺度空间去匹配被逼近信号的思想，已经在神经网络的研究中有了一些成功的应用。网络权值和隐层节点数目的初始值选取是进行网络训练时的难点。多子波神经网络由于有子波理论的指导，因此可以在训练前对这两个值给出较好的估计 按尺度空间的增大方式来进行网络训练，使多子波网络具有更快的收敛速度。 4．提出了一种多子波神经网络的预处理方法。初始化问题是多子波神经网络的一个基本问题，网络初始值的选取直接影响着网络的逼近性能和收敛速度。虽然在子波理论的指导下可以得到多子波神经网络初始值的较好估计，但本文的预处理方法在此基础上给出了更为接近最佳权值的初始值，从而更进一步地提高了网络的收敛速度。 5．提出了一种基于多子波神经网络的多用户检测器。多子波神经网络具有逼近性能好、收敛速度快的特点，因此，多子波神经网络检测器与以前的神经网络检测器相比，也有其独特的性能。另外，本文中所提出的绛维预处理对于提高多子波神经网络检测器的性能也起到了重要的作用。 6．提出了CDMA通信系统中激活用户及时延的联合估计方法。基于多子波神经网络的多用户检测方法是在已知激活用户数和时延等信道参数的假设下提出来的，但是在通信过程中这些参数都是随时间变化的，因此必须对这些参数进行实时地估计。本文利用子空间方法将接收信号的自相关矩阵分解为信号子空间和噪声子空间，并根11 多子汲分折及其在mMA中的应用据信号子空间与噪声子空间的正交性估计出期望用户的广义特征向量，进而求解出期望用户的信道参数及时延。这种方法的特点是算法简单、可进行动态估计并且不需要训练序列。 7．提出了多子波CDMA多址框架并研究了其抗噪性能。目前所使用的直接序列扩频CDMA系统，具有软容量和抗干扰等诸多优点。多址干扰、多径干扰、远近效应和环境噪声是这种系统的主要问题。在抑制多址干扰的同时增加用户容量是提高系统性能的关键。多子波分析滤波器可将信号投影到线性无关的子空间上进行处理使得CDMA中的特征码可以重复使用；时间上重叠的多个子波及其平移相互正交使得单位时间内可传输更多的PN码；优化设计的多子波时－频特性使得频带的利用更为有效。因此，本文所提出的多子波CDMA多址方案可以很好地抑制多址干扰和环境噪声，并且其解码计算相当简单。 8．提出了基于Haar子波低通滤波器的多子波CDMA。由于经过解码后的期望用户信号与多址千扰和噪声属干不同的Haar子波空间，故使用Haar子波分析滤波器可以滤除干扰和噪奇 基于这一原理，本文将多子波的分析滤波器、预滤波、平衡化等方面的最新研究成果以及单子波的Haar子波滤波器应用于通信须域，提出了基于Haar分析滤波器的多子波码分多址系统的理论框架。更多还原

【Abstract】 Multiwavelet analysis and its applications in CDMA systems are investigated in detail in this dissertation. The main work can be summarized as follows.1. A method for determining the associated multiwavelets from a class of multi-scaling functions using the genetic algorithm is proposed. It is important to determine the associated multiwavelet generated by a multi-scaling function for the flexible application of the multiwavelet analysis, and this can be converted equivalently into a problem of optimization in a high dimensional space under some conditions. The genetic algorithm, which simulates the evolutional process of the nature, is a global and robust algorithm, and the construction of orthogonal multiwavelets via genetic algorithm makes the guideline to determine multiwavelets clear and simple.2. A method for determining the associated multiwavelets from a class of multi-scaling functions using eigenvalues and eigenvectors of matrices is proposed. The theoretical analysis shows that under some conditions the associated wavelet sequence of a multiwavelet system can be constructed by eigenvalues and eigenvectors consisting of the scaling sequence of the multiwavelet system. This construction method is not restricted by the multiplicity of multiwavelets.3. The concept and the model of the multiwavelet neural network is proposed. Its universal and L: approximation properties as well as its consistency are proved, and the convergence rates associated with these properties are given. The theoretical analyses show-that multiwavelet networks can have more rapid convergence rate than wavelets, but wavelet networks can have better choice of initial values. To make a comparison between both networks experiments are carried out with GHM multiwavelet network and Daubechies 2 wavelet network.4. A method for the preprocessing of multiwavelet neural networks is presented. Initialization is a crucial problem in the application of multiwavelets, and the selection of initial weight affects directly the approximation performance and convergence rate of a multiwavelet neural network. The preprocessing method presented here gives a better scheme for the selection of initial weights of multiwavelet neural networks.5. The multiuser detection based on multiwavelet neural networks is proposed. Themultiwavelet neural network is characterized by high approximation performance and rapid convergence, and so the multiuser detector based on a multiwavelet neural network possesses its advantages over existing neural network-based multiuser detectors. Moreover, the dimension-reducing preprocessing presented in the thesis improves the performance of the multiwavelet neural network detector.6. Based on the method of subspace, the problems of the estimation of active users and timing in asynchronous CDMA systems are studied, the algorithms of the estimation of active user and timing are given, and the performances are analyzed. Furthermore, the problems of the estimation of channel parameters and timing are discussed in multipath fading asynchronous CDMA communication system. Combing the method of subspace with output energy minimum criterion, we give the estimated values of the channel parameters and timing of the desired user, and many computer simulations show the efficiency of the proposed methods in the case of different SNR and different SIR.7. A multiwavelet-based code-division multiple-access (MW-CDMA) scheme is presented based on the application of recent results in multiwavelet analysis filter, preprocessing and balancing to communications area. In MW-CDMA. at first, the received signal is decomposed into the components in the orthogonal wavelet spaces, and then the multiuser demodulation is implemented in each wavelet space. Theoretical analyses and experimental results show that MW-CDMA systems suppress multiple-access interference and ambient noise well. Moreover, the scheme gives a new guideline of thought to reduce the computation for demodulating.8. Multi更多还原