A generalized Doppler power spectrum for wireless environments

We provide a direct derivation of a generalized Doppler power spectrum of the signal received by a mobile station traveling at a constant velocity. The derivation uses the three-dimensional (3-D) incident radiation intensity and the receiving antenna pattern to obtain an expression for the generalized power spectrum which is useful in environments where the 3-D propagation characteristics of wireless signals must be taken into consideration. A special case of radiation confined to a plane is considered to obtain the power spectrum given in the book written by Jakes (1974).