In this paper, we derive exact closed-form expressions for the bivariateNakagami-$m$ cumulative distribution function (CDF) with positive integerfading severity index $m$ in terms of a class of hypergeometric functions.Particularly, we show that the bivariate Nakagami-$m$ CDF can be expressed as afinite sum of elementary functions and bivariate confluent hypergeometric$\Phi_3$ functions. Direct applications which arise from the proposedclosed-form expression are the outage probability (OP) analysis of adual-branch selection combiner in correlated Nakagami-$m$ fading, or thecalculation of the level crossing rate (LCR) and average fade duration (AFD) ofa sampled Nakagami-$m$ fading envelope.
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机译：在本文中，我们根据一类超几何函数推导了具有正整数衰落严重性指数$ m $的双变量Nakagami- $ m $累积分布函数（CDF）的精确闭式表达式。特别是，我们证明了双变量Nakagami- $ m $ CDF可以表示为基本函数和双变量合一超几何$ \ Phi_3 $函数的总和。提议的闭式表达式产生的直接应用是相关Nakagami- $ m $衰落中的分支选择合并器的中断概率（OP）分析，或水平交叉速率（LCR）和平均衰落持续时间（AFD）的计算抽取的Nakagami- $ m $衰落信封样本。
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