  With the advent of 5G cellular systems there is an increased interest in
exploring higher frequency bands above 6 GHz. At these frequencies, beamforming
appears as a straightforward solution to overcome higher path loss thereby
altering the Doppler characteristics of the received waves. Higher frequencies
can suffer from strong Doppler impairments because of the linear dependency of
Doppler shift with carrier frequency, which makes them challenging to use in
high-mobility scenarios, particularly Vehicular-to-Infrastructure (V2I)
communications. Therefore, the impact of beamforming on the Doppler
characteristics of the received signals is of utter importance for future V2I
systems. This paper presents a theoretical analysis of the Doppler power
spectrum in the presence of beamforming at the transmit and/or the receive
sides. Further approximations are made for the resulting Doppler spread and
Doppler shift when the receive beam width is sufficiently small, and a possible
design solution is presented to control the Doppler spread in V2I systems. The
results can be of key importance in waveform and air interface design for V2I
systems.
