Impact of Position Errors on Path Loss Model Estimation for Device-to-Device Channels

Many wireless applications require a propagation model that describes the attenuation of the transmitted signal as a function of the distance between devices. Such channel models are derived commonly from signal strength measurements, and assume that the true distances between wireless terminals are known. In practice, however, the true distances may be unavailable or difficult to obtain, for instance in mobile scenarios or in the absence of line-of-sight. These conditions typically occur in forested environments, urban areas, etc. This paper addresses the problem of path loss model parameter estimation in presence of erroneous distance measurements, such as the ones derived from the GPS positions. We provide a model for the uncertainties, and study the impact of distance errors on the estimation of a log-distance channel model. Our main conclusion is that the path loss model can be estimated with a reasonable accuracy from unreliable distances, provided that the measurements are taken at distances beyond a few standard deviations of the GPS positioning error. In case the maximum communication range does not allow such large distances, we provide a method to correct the erroneous channel model. Real-world measurements are used in order to validate our approach.