Impact of path-loss on the Doppler spectrum for the geometrically based single bounce vector channel models

It has been shown that the Doppler spectrum can be related to the distribution of power over the angle of arrival at the mobile. A slightly more general expression is found which shows that the Doppler spectrum may be expressed as the product of the Doppler frequency probability density function and the conditional expected value of the power given the Doppler frequency (i.e. the average received power given the Doppler frequency). The derived relationship is used to find the Doppler spectrum for the elliptical geometrically based vector channel model, without ignoring the dependence of the received signal power on the angle of arrival which results from the distance dependent path-loss