Cumulative distribution approximation of signal envelope in radio channels with arbitrary scattering
Keywords:statistical channel model, mobile communication system, cumulative distribution of envelope, gamma distribution, Nakagami approximation, AWGN channel, channel scintillation index, Rayleigh channel, Rice channel, TWDP channel, approximation error, MWDP channel
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.
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