Numerical Transformation of Power Azimuth Spectrum into Normalized Doppler Spectrum

A power azimuth spectrum (PAS) and Doppler spectrum (DS) are one of the most popular channel characteristics. The former is used to describe a dispersion of a signal reception angle. The second one illustrates the received signal dispersion in a frequency domain. Usually, estimation methods based on measurements and modeling methods for these channel characteristics are definitely different. This is due to the fact that the PAS reflect a static situation related to one or several measurement points, while the DS corresponds to a dynamic situation obtained during a movement of objects (transmitter or receiver) at a specified route. Despite these differences, a close relationship exists between these characteristics because the Doppler frequency shift is associated with the angle of arrival. In this paper, this relationship and the numerical transformation of the PAS to DS are shown. The presented transformation allows for a quick estimation of the normalized DS shape based on the measured or modeled PAS. The proposed transformation is universal and allows determining the shapes of many DSs depending on the analyzed directions of the object movement based on one PAS only.