Wireless channels exhibit time, frequency, and spatial correlation. Models in literature that study four-branch diversity receivers make assumptions such as independence, constant correlation, exponential correlation, or some other kind between received signals at each antenna. However, these models are not accurate in many scenarios. Addressing this issue, we provide novel results for the moments, moment-generating function, probability density function, and cumulative distribution function of the quadrivariate Rayleigh distribution with an arbitrary correlation model. To the best of our knowledge, our model is the most comprehensive and the only one that can incorporate the 3GPP suggested spatial correlation structure. We use our new results to derive an analytical expression for the moments of the output signal-to-noise ratio of the four-branch equal gain combining receiver and the four-branch maximal ratio combining receiver. We provide original insight about their output signal-to-noise ratio distributions through their higher order moments in different scenarios. Our expressions are valid for all moments.

中文翻译：

---

四元瑞利分布的矩及其在分集接收机中的应用

无线信道显示时间，频率和空间相关性。研究四分支分集接收机的文献模型在每个天线的接收信号之间做出了诸如独立性，恒定相关，指数相关或其他某种类型的假设。但是，这些模型在许多情况下都不准确。针对此问题，我们提供了具有任意相关性模型的四变量瑞利分布的矩，矩生成函数，概率密度函数和累积分布函数的新颖结果。据我们所知，我们的模型是最全面的模型，也是唯一可以纳入3GPP建议的空间相关结构的模型。我们使用新的结果来推导四分支相等增益组合接收器和四分支最大比率组合接收器的输出信噪比矩的解析表达式。我们通过它们在不同情况下的高阶矩来提供有关其输出信噪比分布的原始见解。我们的表达在任何时候都是有效的。