Global positioning system is an important space information network for location service. However, the satellite signal is\nattenuated or even blocked in indoor environment. To make up for the defect of global positioning system, IEEE 802.11\nwireless local area network (Wi-Fi) infrastructure is proposed to relay the task of positioning in indoor scenario with\ntheir superiority of being widely deployed. In Wi-Fi indoor localization application, received signal strength indicator is\nthe most prevalent parameter. From the former literature, it was supposed to be Gaussian distribution. In this article,\nwe first formulate the received signal in a multipath channel based on the IEEE 802.11 standard, then we derive the probability\ndensity function of received signal strength indicator and it is proved to be a noncentral Chi-square distribution.\nFinally, the correctness of the distribution is verified from the aspect of noncentral parameter in an experiment system.
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