Asymptotic Expansion of the Reciprocity Integral in a Bidirectional Ray-Tracing Approach

摘要

Bidirectional ray-tracing launches rays from both the transmitter and the receiver sites, where the transfer function between the antennas can be computed by evaluating a reciprocity interaction integral. In this work, an asymptotic expansion approach for the evaluation of this interaction integral is introduced and discussed. By using an oscillatory integral representation and high-frequency assumptions, it is shown that the stationary phase approximation yields a simple algebraic expression for the result of the integral. Thus, the evaluation of the reciprocity integral becomes much more straightforward without any significant decline in terms of accuracy. The strong dependency between computation time and operating frequency is mostly avoided, in contrast to the traditional integration approaches. As a result, substantial speed-up factors can be achieved. Numerical results demonstrate the merits of this approach.