A modified synthesis procedure for first order stochastic differential equations for the simulation of baseband random processes

An extra condition is added in the synthesis procedure of first order stochastic differential equations so that the hitting time statistics of the actual process are simulated as well, along with the actual process’ first- and second-order statistics. The hitting time is a random variable which resembles the well known fade and inter-fade duration. The aforementioned new condition is motivated by the operation mechanism of control-loops often applied in radio frequency channels. It is expected that this extra condition could lead to a stochastic differential equation that better reproduces the generation mechanism of the actual process. Besides, to make our synthesis procedure applicable, analytical or semi-analytical methods are demonstrated for the calculation of both second order and hitting time statistics for the case of a first order stochastic differential equation. The first method (which has been used in the past) concerns second-order statistics and it is presented here for the first time in detail. The second method, which is novel, is significantly better than the first in terms of computational complexity for the calculation of second-order statistics. Finally, the modified synthesis procedure is applied for the simulation of rain attenuation affecting a satellite link operating in Athens, Greece. Results indicate that this extra condition contributes towards the more accurate reproduction of the generation mechanism belonging to the particular actual process.