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Radar Equation
The power Pr returning to the receiving antenna is given by the radar equation:
where
- Pt = transmitter power
- Gt = gain of the transmitting antenna
- Ar = effective aperture (area) of the receiving antenna
- σ = radar cross section, or scattering coefficient, of the target
- F = pattern propagation factor
- Rt = distance from the transmitter to the target
- Rr = distance from the target to the receiver.
In the common case where the transmitter and the receiver are at the same location, Rt = Rr and the term Rt² Rr² can be replaced by R4, where R is the range. This yields:
This shows that the received power declines as the fourth power of the range, which means that the reflected power from distant targets is very, very small.
The equation above with F = 1 is a simplification for vacuum without interference. The propagation factor accounts for the effects of multipath and shadowing and depends on the details of the environment. In a real-world situation, pathloss effects should also be considered.