Bistatic Doppler shift

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Bistatic Doppler shift is a specific example of the Doppler effect that is observed by a radar or sonar system with a separated transmitter and receiver. The Doppler shift is due to the component of motion of the object in the direction of the transmitter, plus the component of motion of the object in the direction of the receiver. Equivalently, it can be considered as proportional to the rate of change of bistatic range.

The Doppler effect is the change in frequency or wavelength of a wave in relation to an observer who is moving relative to the wave source. It is named after the Austrian physicist Christian Doppler, who described the phenomenon in 1842.

Bistatic range

Bistatic range refers to the basic measurement of range made by a radar or sonar system with separated transmitter and receiver. The receiver measures the time difference of arrival of the signal from the transmitter directly, and via reflection from the target. This defines an ellipse of constant bistatic range, called an iso-range contour, on which the target lies, with foci centred on the transmitter and receiver. If the target is at range Rrx from the receiver and range Rtx from the transmitter, and the receiver and transmitter are a distance L apart, then the bistatic range is Rrx+Rtx-L. Motion of the target causes a rate of change of bistatic range, which results in bistatic Doppler shift.

In a bistatic radar with wavelength λ, where the distance between transmitter and target is Rtx and distance between receiver and target is Rrx, the received bistatic Doppler frequency shift is calculated as:

Note that objects moving along the line connecting the transmitter and receiver will always have 0 Hz Doppler shift, as will objects moving around an ellipse of constant bistatic range.

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