The performance of telecommunication systems is significantly subject to scattered signals superposed at the receivers. Notably, if the superposed scattered signals are impulsive in nature, this leads to burst effect on the communicated symbols. Thus, attaining an accurate estimate of the parameters of the underlying statistical model of the aggregate scattered signals becomes more important. More specifically, in the case of radar applications, finding efficient estimators for the amplitude distribution has been found to be of highly importance. In this article, the Bayesian approach has been adopted for parameter estimation of the amplitude distribution. To this end, within a Gibbs sampling framework, this would be done by the sampling from four full conditionals which can be performed in a straightforward manner. Depending on the size of sample, two types of priors, i.e. Jeffreys (small size) and conjugate (non-small size), are considered for the scale parameter of the amplitude distribution. While using the conjugate prior, hyperparameters can be found through the empirical Bayes. For the purpose of validation of the proposed approach, performance of the adopted Bayesian paradigm will be demonstrated through the simulation study. Furthermore, analysis through real datasets of radar signals reveals that the proposed Bayesian approach outperforms the known moment and log-moment estimators of the amplitude distribution and works better than the maximum likelihood estimator when sample size is small.

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幅度分布的贝叶斯推断及其在雷达杂波中的应用

电信系统的性能很大程度上受到接收器处叠加的散射信号的影响。值得注意的是，如果叠加的散射信号本质上是脉冲信号，则这会导致对通信符号的突发效应。因此，获得对聚合散射信号的基础统计模型的参数的准确估计变得更加重要。更具体地说，在雷达应用中，发现有效的幅度分布估计器非常重要。在本文中，采用贝叶斯方法进行幅度分布的参数估计。为此，在吉布斯采样框架内，这将通过从四个完整条件中采样来完成，这可以以简单的方式执行。根据样本的大小，振幅分布的尺度参数考虑两种类型的先验，即Jeffreys（小尺寸）和共轭（非小尺寸）。使用共轭先验时，可以通过经验贝叶斯找到超参数。为了验证所提出的方法，将通过模拟研究来证明所采用的贝叶斯范式的性能。此外，通过对雷达信号的真实数据集进行分析表明，所提出的贝叶斯方法优于已知的幅度分布矩和对数矩估计器，并且在样本量较小时比最大似然估计器效果更好。