α稳定噪声中基于双参数CGM模型的Rao检测

摘要

Aimed at the problem that a-stable distribution has no closed form expression for the probability density function (PDF) ,an approximate expression is suggested. Such model is a mixture of Gaussian and Cauchy with bi-parameter. The mixture ratio is determined by fractional low order moment (FLOM). Proposed model has a complete closed form and provides analytical convenience. Based on such model, this paper further proposes a Rao statistical test method for the detection of sine signal under the a-stable noise environment. We illustrate the detection performances of the proposed Rao test for various a,and compare them with the Rao test that based on Gaussian assumption. Simulation results show that the proposed Rao detector distinctively outperforms the Rao detector that based on Gaussian assumption.%针对α稳定分布概率密度函数无闭式表达的问题,给出了一种解析的近似模型,该模型采用双参数的柯西和高斯混合形式.由分数低阶矩,给出了混合比率的解析表达式.同传统的柯西-高斯混合模型和高斯混合模型相比,该模型具有完全的解析形式.基于该模型,导出了a稳定噪声条件下正弦信号的Rao检测统计量.通过仿真给出了不同特征指数α时Rao检测的性能,并同基于高斯假设的Rao检测进行了比较.仿真结果表明,该检测器在α稳定分布噪声条件下对信号的检测性能明显优于基于高斯假设的Rao检测.