## Doppler shift

#### The Doppler shift introduced into a signal between transmitter and receiver units, or moving reflectors, is a function of their relative motion, the angle of arrival of the signal, and the operating frequency or wavelength. These parameters are related as follows:
Doppler shift (Hz) = v.f.cos(x) / c
where v is the relative speed of transmitter and receiver units in m/s, f is the carrier frequency in Hz, c = 3 x 108 m/s and x is the relative angle of arrival in degrees.
For example, the Doppler shift experienced by a cellular phone within a car travelling at 70 mph directly away from a base-station transmitter, operating on the DCS1800 system (carrier frequency 1.8 GHz) is 189 Hz. The Doppler shift for a person walking along the street at 4 mph is, however, much smaller at only 11 Hz.
A typical spectrum of a signal received at a mobile terminal when moving within a multipath environment with several reflectors each giving different angles of arrival and hence different Doppler shift is shown below. The source was a single tone at the carrier frequency.

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