基于小波和分形理论的多径衰落信号分析

首次将小波理论和分形理论相结合来分析多径衰落信号，从多径衰落信号产生的动力学机制出发，指出了多径衰落信号具有分形的特征，进一步研究多径衰落信道的多重分形特性，分析并指出了多重分形维数是描述无线信道传播特性的重要参数，根据多径衰落信道参数突变，首次指出了多径衰落信号具有局部奇异性，其局部奇异性对信道参数估计和信号重构有着重要的作用，中提出了短时网格分形维数的定义和给出了其计算的详细算法，用Lipschitz指数来表征局部奇异性，利用小波检测多径衰落信号奇异性和信号重构。仿真实验结果表明：小波重构后信号具有很好去噪性能；多径衰落信号不同尺度下小波变换系数具有自相似性，论证了多径衰落信号的分形特性，不同移动速度时多径衰落信号的多重分形特性仿真实验表明：随着移动速度增大，其短时网格分形维数也变大。

Multipath Fading Signal Analysis with Wavelet and Fractal Theories

This paper applies wavelet and fractal theories to analyze multipath fading signal in mobile radio communications for the first time. Multipath fading signal has fractal characteristic according to dynamics mechanism of multipath fading signal. Multifractal characteristics of multipath fading signal are studied furtherscribing the signal propogation in wireless channnels. The local singularity exists in multipath fading signal according to the suddenly changed channel parameters in the multipath fading channel. Singularity plays an important role in the channel estimation and signal reconstruction. Singularity shows local mutation of multipath fading signal, and multifractal shows self-similarity between local and whole. Short-duration grille fractal dimension is defined and the algorithm of its calculation is discussed in detail. Mathematics model of singularity is expressed with Lipschitz expenont. The singularity can be detected with wavelet and signal can be reconstructed through wavelet transform. Simulation results reveal that the reconstructed signal with wavelet can denoise. The wavelet coefficients under the different scales have self-similarity, which proves that multipath fading signal has fractal characteristic. The multifractal characteristics under different mobile speeds are studied and find that its short-duration grille fractal dimension gets larger with speed increasing.