已知copula 模型可以用來配適聯合分佈，而在通訊應用中的衰褪通道(fading channel)上，大多使用聯合韋伯分佈。在分析上，要求得衰褪通道(fading channel)中的數據，必須得知其聯合密度函數 (p.d.f) 和累積分佈函數 (c.d.f)。再來計算三種不同接收系統下的中斷機率，分別為選擇結合(SC)，相等獲取結合(EGC)，和最大比率結合(MRC)。在 Sagias (2005)中，分別在三個不同的系統，使用聯合韋伯分佈去求得中斷機率。在此篇論文中，則使用聯合copula 模型得到近似的聯合韋伯分佈之後，分別在三個不同的系統求得中斷機率，願能使計算上能更簡化些。

關鍵字: 選擇結合，相等獲取結合，最大比率結合

In this work, copula models for fitting bivariate response data with Weibull marginal distributions are studied, which are motivated by the need of model fading channels in signal applications. The analytical expressions for the joint probability density function
(p.d.f.), and joint cumulative distribution function (c.d.f.) are utilized as the bivariate distribution of the fading channels data with not necessarily identical fading parameters and average powers. The performances of outage probability employing diversity receivers, called as selection combining (SC), equal-gain combining (EGC), and maximal-ratio combining (MRC) of two diversity receivers under bivariate copula models with Weibull marginal distributions are presented. They are also compared with the results in Sagias (2005) where the data assumed to follow the bivariate Weibull distribution. It will be demonstrated that the copula models can approximate the bivariate Weibull distribution used in Sagias (2005) very closely with suitable copula model, and the computations for
obtaining the performances of outage probability under SC are much simplified.
Keywords and phrases: equal-gain combining, maximal-ratio combining, selection combining

Abstract 1
1 Introduction 1
2 Review of wireless telecommunication processing 2
2.1 Outage probability...................................................... 3
2.2 Diversity receivers...................................................... 3
3 Copula models 5
3.1 Sklar's theorem......................................................... 5
3.2 Some bivariate copula models................................5
3.3 Probability-integral transform...................................6
4 Outage probability under bivariate copula models with Weibull marginal distributions 8
4.1 The bivariate copula model with Weibull marginal distribution........................................................................... 9
5 Conclusion 16
References 18

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