On the solution of scatter density in geometry-based channel models

Assuming a single bounce scattering geometric channel model with circularly symmetric scatter density we deduce a general integral relation between angle of arrival (AOA) and scatter density function. Then we show that this relation can be expressed in terms of an integral equation that admits an accurate numerical solution provided that AOA is known. Furthermore, we show that similar integral equation relation between time of arrival (TOA) and scatter density function can be efficiently solved numerically for a given TOA. Results indicate that the scatter density can be numerically computed for a given AOA or TOA. Since these marginal distributions can be directly fit in channel measurements, the method provides means to adjust the applied geometrical channel model through field measurements. Hence, we follow the idea of inverse scattering theory where the far field pattern of scattered waves is known and the aim is to define the structure of the scattering medium. We consider two example AOA distributions, Gaussian and Student's t-distribution, found in literature. Our results show that scatter densities as well as the corresponding TOAs greatly vary depending on the assumed AOA.