Efficient ultrawideband propagation modelling by using the cubic B-spline function in ray tracing calculations

In site-specific ultrawideband propagation modelling, electromagnetic field calculations need to be performed by ray tracing at numerous frequencies of the band in order to properly include the frequency variations of the propagation mechanisms and antenna patterns. This is computationally intensive especially in calculating the coverage map or finding the statistics of the channel parameters where field calculations need to be carried out at a lot of receiver locations. In this study, the cubic B-spline function is incorporated in ray tracing to increase the computational efficiency of site-specific ultrawideband propagation modelling. This function can accurately reconstruct a signal from a few samples at a low-computational cost. By calculating the electromagnetic fields at a few frequency samples followed by cubic B-spline reconstruction, a lot of unnecessary calculations of the post-processing stage are suppressed without degrading the accuracy of the results. The study develops a systematic procedure for determining the number of required frequency samples according to the geometrical and electromagnetic properties of the walls, frequency variations of the antenna patterns and characteristics of the cubic B-spline function. The proper functionality of the proposed method is verified by numerical results where the simulation time is reduced several times for a typical indoor environment.