Slepian半小波基函数及其在无线通讯信号概率密度估计中的应用

文[20]引进了Slepian半小波基函数并讨论了这组基在概率度估计核方法中的应用[21]，Slepian半小波基函数具有极好的性质．包括多重尺度结构和局部非负性．更值得指出的是．与Gauss核不同，Slepian函数是与无线信号类似的具有平滑谱的有限带宽函数．在所有相同带宽的函数中．Slepian函数在特定的时同区域上具有最大能量．在逼近具有平滑谱的无线信号中．这些特性使得Slepian半小波核与Gauss核以及其他小波基相比具有潜在的优越性．美中不足的是．和其他核密度估计一样．Slepian核密度估计的算法设计具有一定的挑战性．幸运的是．我们注意到Slepian核可以被表示成卷积形式．这一观察具有重要的计算意义．本文主要讨论Slephn核密度估计的应用及其计算．我们首先设计了基于离散卷积的算法并讨论了这一算法的有效性．在文章的结尾，以Slepian核密度估计作为具有平滑谱的远程信号的衰减包络的模型为例．我们考查了Slepian核及其算法的性质．为了尝试数学理论与应用的紧密联系，本文的数值试验不仅采用了模拟数据而且包括了从无线通讯用户的硬件直接采集的实际数据．

Slepian Semi Wavelets and Their use in Density Estimation for Wireless Signals

The Slepian semi wavelet kernel density estimator, originally developed in [21], has a few magnificent properties including multiscale structure and local positivity. Unlike the Gaussian kernel, Slepian functions are bandlimited functions with flat spectral in frequency domain similar to wireless signals. Unfortunately, like any other kernel density estimators, the implementation is a challenging task since it is computational intensive. Fortunately, the Slepian kernel can be approximated by a convolution type kernel. This observation bears important computational advantages. In this article, we will restrict our attention to the applications of the density estimators. We introduced an algorithm based on discrete convolution which can be used to compute the density estimator effectively. To test the capability, the kernel density estimator is used to model fading envelop of long range fading signals with flat spectral. Both simulated data and field data are used in the numerical experiments.