A closed-form expression for the received power through the usage of the Dirac-Delta functions with nonlinear argument

Abstract

We present a closed-form expression for the received power through parametrized Dirac-Delta functions inside the framework of input and output integrals. This expression is derived from the 'spike' property of the Dirac-Delta function which was generalized to the case where the argument might depend on a polynomial function containing an infinity number of free parameters. These nonlinear Dirac-Delta integrals can be interpreted as the convolution of a physical observable that falls to distance such as power intensity. This methodology is applied to extract values of the emitted power by a base station antenna inside a zone that contains inhomogeneous buildings and others obstacles. In order to identify the system parameters, the Monte Carlo method was used. It has served to identify up to 12 free parameters which would give information about the power intensity values with a precision of 8 ± 3 m.