论文标题
混合物伽马变体产品与应用与无线通信的比率
Ratio of Products of Mixture Gamma Variates with Applications to Wireless Communications
论文作者
论文摘要
在本文中，首先提供了独立和非分布的混合物伽马（MG）随机变量（RV）的量产物的统计特性。具体而言，概率密度函数（PDF），累积分布函数（CDF）和力矩生成函数（MGF）的简单精确闭合形式表达式是根据单变量Meijer的$ G $ function得出的。然后得出MG变量产物比率分布的统计特征。这些统计数据用于分析中断概率（OP），不同调制方案的平均误差概率，通信系统的有效速率（ER）以及接收器工作特性下的平均面积（AUC）在级联褪色通道上的能量检测曲线（AUC）。此外，通过利用该产品的统计量，研究了安全概率（SOP $^l $）的下限和具有解释性（DF）继电器协议和共同渠道干扰（CCI）的MultiHop通信系统的非零秘密容量（PNSC）的概率，并利用该产品的统计量来研究。派生的性能指标适用于Beaulieu-XIE和$α-λ-η-$阴影褪色通道，这些通道尚未在文献中进行研究。因此，给出了上述通道的Mg分布的等效参数。给出了数值结果与蒙特卡洛模拟之间的比较，以验证我们的分析的验证。
In this paper, the statistical properties of the product of independent and non-identically distributed mixture Gamma (MG) random variables (RVs) are provided first. Specifically, simple exact closed-form expressions for the probability density function (PDF), cumulative distribution function (CDF), and moment generating function (MGF) are derived in terms of univariate Meijer's $G$-function. The statistical characterisations of the distribution of the ratio of products of MG variates are then derived. These statistics are used to analyse the outage probability (OP), the average error probability for different modulation schemes, the effective rate (ER) of communications systems and the average area under the receiver operating characteristics (AUC) curve of energy detection over cascaded fading channels. Additionally, the lower bound of secure outage probability (SOP$^L$) and probability of non-zero secrecy capacity (PNSC) of the physical layer and the OP of the multihop communications systems with decode-and-forward (DF) relaying protocol and co-channel interference (CCI) are studied by utilising the statistics of the ratio of the products. The derived performance metrics are applied for the Beaulieu-Xie and $α-λ-η-μ$ shadowed fading channels that have not been yet investigated in the literature. Accordingly, the equivalent parameters of a MG distribution for the aforementioned channels are given. A comparison between the numerical results and the Monte Carlo simulations is presented to verify the validation of our analysis.
