Application of Friis Transmission Equation for the Power Delay Profile in Gaussian Scattering

Power delay profile (PDP) of a wireless channel has been widely studied using different approaches and measurements. In this paper we take a new approach by applying Friis transmission equation to derive the PDP in a Gaussian scattering scenario. Using this approach we notice that if the scattering spread is large or the distance between the base station and the mobile station is small, the PDP has a peak at a delay greater than the line of sight delay. The obtained PDP is able to explain the peak reported in measurements and is consistent with the delay probability density function. Further, the profile comes closer to the PDP reported in the literature when either the distance between the base station and mobile station is large or the scattering spread is small.