Abstract

An approximation method for the cumulative distribution function (CDF) of a signal envelope at the output of an arbitrary radio channel based on the gamma distribution is proposed. The well-known Nakagami approximation method is a special case of the proposed approach. In contrast to the Nakagami method, the convergence of the CDF of some arbitrary non-negative statistics to the proposed asymptotic CDF is presented strictly in the paper and the conditions for this convergence are determined. In addition, the proposed method allows us to take into account the type of the receiving device processing. The use of the proposed approximation is illustrated by the example of a memoryless channel with additive white Gaussian noise, although the possibilities of its application are much wider. We show, that the specificity of a channel model is reduced to a single parameter, called the channel scintillation index. The values of scintillation index for several channel models are calculated, and the error analysis of the proposed CDF approximation is carried out on the basis of them. In the analysis we show, that in the practically significant range of CDF ≥ 0.5, the relative approximation error is within a few percent. The possibility of a relatively simple statistical description of new channel models is illustrated, because their traditional description has significant mathematical difficulties. In particular, a multipath generalization of a TWDP channel model is proposed, called as a MWDP channel.

中文翻译：

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具有任意散射的无线电信道中信号包络的累积分布近似

摘要

提出了一种基于伽马分布的任意无线电信道输出处信号包络的累积分布函数（CDF）的近似方法。众所周知的Nakagami近似方法是该方法的特例。与Nakagami方法相反，本文严格提出了一些任意非负统计量的CDF收敛到所提出的渐近CDF的方法，并确定了收敛的条件。另外，提出的方法允许我们考虑接收设备处理的类型。通过具有加性高斯白噪声的无记忆通道的示例来说明所建议的近似方法的使用，尽管其应用的可能性要广泛得多。我们展示 通道模型的特异性降低到单个参数，称为通道闪烁指数。计算了几种通道模型的闪烁指数值，并在此基础上对所提出的CDF近似进行了误差分析。在分析中我们发现，在CDF≥0.5的实际有效范围内，相对逼近误差在百分之几以内。由于新的信道模型的传统描述具有明显的数学困难，因此说明了相对简单的统计描述新信道模型的可能性。特别地，提出了TWDP信道模型的多路径概括，称为MWDP信道。在此基础上进行了建议的CDF近似的误差分析。在分析中我们发现，在CDF≥0.5的实用范围内，相对逼近误差在百分之几以内。由于新的信道模型的传统描述具有明显的数学困难，因此说明了相对简单的统计描述新信道模型的可能性。特别地，提出了TWDP信道模型的多路径概括，称为MWDP信道。在此基础上进行了建议的CDF近似的误差分析。在分析中我们发现，在CDF≥0.5的实际有效范围内，相对逼近误差在百分之几以内。由于新的信道模型的传统描述具有明显的数学困难，因此说明了相对简单的统计描述新信道模型的可能性。特别地，提出了TWDP信道模型的多路径概括，称为MWDP信道。因为它们的传统描述存在很大的数学困难。特别地，提出了TWDP信道模型的多路径概括，称为MWDP信道。因为它们的传统描述存在很大的数学困难。特别地，提出了TWDP信道模型的多路径概括，称为MWDP信道。