Doppler–frequency–shift is a deviation in the signal frequency due to a change in the path length between the transmitter and receiver. This can be due to movement of any or all of the following: the transmitter, the receiver, or reflective surfaces along the path. The Doppler frequency shift is given by the following equation:

where v is the rate of change in path length between the transmit and receive antenna, c is the speed of light, fc is the carrier frequency of the signal, and fd is the Doppler frequency shift. The carrier frequency is shifted from fc to fc + fd.

Figure 1 shows four signal paths, all of which have the same path length between the transmitter and receiver. In this example, the receiver is moving in a direction away from the transmitter. As one can see, the angle of signal arrival at the mobile receiver has a direct bearing on the rate of change in the path length. Path 1 will show the greatest rate of change in path length, whereas, path 4 will show the smallest rate of change in path length. This is due to the angle of signal arrival in relation to the direction of movement of the receiver. Note that path 3 will show a positive frequency shift, whereas paths 1 and 2 will show a negative frequency shift.

For the example shown in Figure 1, there are four different signal paths, all of the same length, which show different Doppler frequency shifts. Because there are frequency differences between the four different paths, the resulting summation of the different signals from the four different paths causes fluctuations in amplitude of the delay component, seen over a period of time. The fluctuations in amplitude, of a particular delay component, can be analyzed for frequency components to separate out the different Doppler shifts corresponding to the different paths. This is accomplished by performing complex fourier analysis over a period of time for each delay component. This results in a three dimensional plot called a scatter plot. An example scatter plot is shown. This plot was created from measurement data acquired while an omni directional receive antenna was moved a specified speed in one direction. The vertical axis shows relative amplitude of the received signal. One of the horizontal axes shows the delay time in microseconds and represents signal travel time for different path lengths between the transmitter and receiver. The other horizontal axis shows the Doppler frequency in Hz, representing the rate of change in path length between the transmitter and receiver. It can be seen that, at each delay, there are sometimes multiple points with different Doppler frequency shifts. Each of the points, associated with the same delay, represents reflections with the same path length but different angles of arrival in relation to the path of travel. A contour plot of the same data can also be seen. In this plot, each enclosed set of lines represents a discrete reflective surface (resolvable within a hemisphere).