对称 alpha 稳定分布的两段曲线逼近算法

摘要

The symmetric alpha stable (SaS) was used to model a non-Gaussian, heavy tail and impulsive noise of com-munication channels. However, explicit expressions for the probability density functions (PDF) in terms of elementary functions are still unknown except for some special cases, which limits the application of the SaS distribution in practice, which the bi-region separated by the triple divergence was proposed. Specially, within the triple divergence, a simple exponential function with two special parameters was constructed, and the two parameters were determined by using Taylor serial expansion. Compared with conventional algorithms using the series expansion, the proposed algorithm avoids the selecting the number of the series items and the risk of series expansion divergence. Moreover, numerical re-sults verify that the proposed approximation is closer to the actual SaS PDF than the conventional Cauchy-Gaussian mixture approximation.%　　针对描述通信信道中存在的非高斯、重拖尾脉冲噪声的对称稳定(SS)分布模型，其概率密度函数不存在解析表达式，在信号检测和信道迭代译码等应用场合不易分析和处理的问题，提出了一种以3倍散度为界的两段曲线逼近算法。首先，确定两段曲线的分界点；其次，在3倍散度之外，确定了前3项级数来逼近；最后，在3倍散度之内，构造了一个简洁的双参数指数函数，并用泰勒级数展开的方法确定指数函数中的2个参数。所提出的两段曲线逼近法避免了已有级数逼近法中存在的级数项项数的选择问题和级数发散的问题。数值计算结果表明，与传统的柯西高斯混合逼近算法相比，提出的逼近算法更接近真实的 SS 分布。