Theoretical Data on Support of a Unified Indoor Geolocation Channel Model

In this paper we present theoretical data in support of the unified indoor geolocation channel model namely (1) path loss and (2) multipath distribution models. First, the path loss model is currently accepted to be a function of the transmitter and receiver geometry and frequency of operation. Second, the most widely used and accepted indoor channel multipath distribution models are Nakagami with m degrees of freedom, Rayleigh, Rician, and lognormal. The purpose of this paper is two fold: (1) to provide a better interpretation of the sets of theoretical data for the indoor channel model and (2) to be able to explain the lack of fit of the well-known multipath distribution models from the previous measurement data sets reported in the literature; thus, providing support for the unified indoor channel model theory. The unified path loss model consists of an approach for linking together the path loss models of the three geolocation systems (macrocellular, microcellular, and indoor) with the distance between the transmitter and receiver, R, and the frequency of operation, f. The path loss caused by increase of the transmitter receiver distance is much more severe than the path loss caused by the path loss caused by increase of the frequency of operation. The bottom line here is that we need to design future receivers or propose a signal structure that will account for 40 to 80 dB of signal degradation indoors. The unified multipath distribution consists of a linear transformation of the well-known multipath distribution models such as Nakagami with m degrees of freedom, Rayleigh, Rician, and lognormal. While it is rather straight forward to prove the unified geolocation multipath distribution model when only the contributing individual distributions are Rayleigh, Rician, and lognormal, if we assume that we have a fourth distribution such as Nakagami with m degrees then the process is not straight forward any more. We will investigate this and report the results in the future. The main purpose of the unified multipath distribution model is to enable the calculations of reflections’ gain. Assuming that the channel is composed of individual distributions such as Rayleigh, Rician, and Lognormal we have perform reflection gain calculations. From the theoretical data it appears that reflections with gain 3dB or higher than the LOS gain are on the order of 1 out of 6.2 days. On the other hand, reflections with gain 5dB greater than the LOS gain are of the order of 1 out of ~6072 years. And this is the most important conclusion of this work that for simulation or implementation purposes we should never consider reflections with gains greater than equal to 5 dB greater than the LOS gain.