We evaluate the outage probability (OP) for $L-$ branch equal gain combining (EGC) receivers operating over fading channels, i.e., equivalently the cumulative distribution function (CDF) of the sum of the $L$ channel envelopes. In general, closed form expressions of OP values are out of reach. The use of Monte Carlo (MC) simulations is not a good alternative as it requires a large number of samples for small values of OP. In this paper, we use the concept of importance sampling (IS), being known to yield accurate estimates using fewer simulation runs. Our proposed IS scheme is based on sample rejection where the IS density is the truncation of the underlying density over the $L$ dimensional sphere. It assumes the knowledge of the CDF of the sum of the $L$ channel gains in closed-form. Such an assumption is not restrictive since it holds for various challenging fading models. We apply our approach to the case of independent Rayleigh, correlated Rayleigh, and independent and identically distributed Rice fading models. Next, we extend our approach to the interesting scenario of generalised selection combining receivers combined with EGC under the independent Rayleigh environment. For each case, we prove the desired bounded relative error property. Finally, we validate these theoretical results through some selected experiments.

中文翻译：

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具有等增益组合的中断概率的精确样本拒绝估计器

我们评估以下情况的中断概率（OP） $ L- $ 在衰落信道上工作的分支等增益合并（EGC）接收器，即等效地，总和的累积分布函数（CDF） $ L $ 频道信封。通常，OP值的闭式表达式无法使用。蒙特卡洛（MC）模拟的使用不是一个很好的选择，因为它需要大量的样本来获得较小的OP值。在本文中，我们使用重要性抽样（IS）的概念，众所周知，它可以使用较少的模拟运行来产生准确的估计。我们提出的IS方案基于样品剔除，其中IS密度是在 $ L $ 尺寸球。它假定CDF的总和的知识 $ L $ 封闭形式的渠道收益。这种假设不是限制性的，因为它适用于各种具有挑战性的衰落模型。我们将我们的方法应用于独立瑞利，相关瑞利以及独立且分布均匀的莱斯衰落模型的情况。接下来，我们将方法扩展到在独立瑞利环境下将接收器与EGC相结合的广义选择组合的有趣场景。对于每种情况，我们证明所需的有界相对误差属性。最后，我们通过一些选定的实验验证了这些理论结果。