Random phase and time of arrival statistics for circular disk scattering model

Fading simulators are tested by verifying the statistics of channel created by multipath environment. These statistics are an angle of arrival (AoA), time of arrival (ToA), and angle of deviation (AoD). In literature, fading simulators statistics are analysed by joint probability density function (pdf) of AoA and ToA and/or joint pdf of AoA and AoD. The multipath environment has been represented by various geometrical models. These fading simulators assume independency of random phase and angle of arrival. Continuously changing phase of multipath components affect the statistics which in turn causes fading. Because of this continuously changing phase of multipath components, at receiver side demodulator has to adjust the phase by trial and error method to recover the original time variant signal which is a tedious process. In this paper the circular disk scattering model is analysed by marginal pdf of ToA and random phase and it is proved that ToA is negative exponential and random phase is uniformly distributed which proves the dependency of ToA on random phase. Later, the simple relation has been derived between AoD and random phase which can directly help at receiver side for adjusting the deviation occurred in transmitted signal for all wireless applications.