radar

In the common case where the transmitter and 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.
Note that the equation above is a simplification for vacuum without interference. In a real-world situation, pathloss effects should be considered, as well as other factors of the transmission medium.
Other mathematical developments in radar signal processing include time-frequency analysis (Weyl Heisenberg or wavelet), as well as the chirplet transform which makes use of the fact that radar returns from moving targets typically "chirp" (change their frequency as a function of time, as does the sound of a bird or bat).