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

Efficient and reliable ray tracing, some challenges and proposed solutions

“…Time-domain and frequency-domain formulations can be found in the literature for electromagnetic field calculations in ultrawideband channels [12], [13]. Time-domain methods assume closed form frequency variation of dielectric constants and derive (semi-)analytical formulas for the reflection, transmission and diffraction coefficients.…”

“…A brilliant idea based on using the cubic B-spline function has been presented in [13] to reduce the computational burden of field calculations. The cubic B-spline function is a piecewise polynomial function of the third degree defined as…”

“…Then, the cubic B-spline function is used to reconstruct the electromagnetic fields in a dense frequency mesh in the whole bandwidth of the channel. The number of required frequency samples can be systematically determined according to the material properties and thicknesses of the walls [13]. However, less than 100 samples uniformly distributed in the 7.5 GHz bandwidth of the UWB channel are usually sufficient.…”

“…However, less than 100 samples uniformly distributed in the 7.5 GHz bandwidth of the UWB channel are usually sufficient. Due to low computational complexity involved in the cubic B-spline reconstruction, a significant speedup of several times can be achieved in typical indoor environments as reported in [13].…”

Indoor ultrawideband propagation modelling using Chebyshev interpolation in 60 GHz band based on ray tracing technique

“…To include the effects of multipath components with late times of arrival which have considerable amount of energy, a lot of time will be wasted, especially where the number of receiving points is relatively large; for example in analysis of statistics of the channel like channel parameter statistics. In this paper to enhance the calculation and degrade the computational cost, the idea that has published in [5] is used. The authors of [5] show that, fields at the receiver can be computed at a few frequency samples and then interpolating the results by using cubic B-spline function must be done.…”