Ambiguity Function - Wideband Ambiguity Function

Wideband Ambiguity Function

The wideband ambiguity function of is :

where is a time scale factor of the received signal relative to the transmitted signal given by:

for a target moving with constant radial velocity v. The reflection of the signal is represented with compression (or expansion) in time by the factor , which is equivalent to a compression by the factor in the frequency domain (with an amplitude scaling). When the wave speed in the medium is sufficiently faster than the target speed, as is common with radar, this compression in frequency is closely approximated by a shift in frequency Δf = f_c*v/c (known as the doppler shift). This approximation results in the narrowband ambiguity function given above, which can be computed efficiently by making use of the FFT algorithm.