Doppler and acceleration tolerances of high-gain, wideband linear FM correlation sonars

An analysis is presented of the decorrelation effects of target velocity and acceleration on high-gain, wideband linear FM correlation sonars that match the received signal against a family of velocity reference functions, each of which is a different time-compressed or -expanded replica of the transmitted signal. Such sonars are shown to have velocity (i.e., Doppler) and acceleration tolerances far different from that predicted by narrowband radar theory. Unlike the narrowband case, the wideband velocity tolerance may be quite small and is approximately independent of the carrier frequency and inversely proportional to the time-bandwidth product (TW). Narrowband radar-type calculations of velocity tolerance can give erroneous results far in excess of the true value. This is because the narrowband velocity tolerance is derived entirely on the basis of temporal overlap loss, whereas the actual tolerance depends primarily on the slope difference between the frequency-time sweeps of the received and reference signals. High acceleration tolerance, without separate acceleration processing channels, can be achieved by cross-correlating the acceleration return with a "best match" velocity reference function. The resultant wideband acceleration tolerance is approximately inversely proportional to WT
²
and better than the narrowband tolerance by a factor of 12 Q (Q = carrier frequency/bandwidth). This improvement arises because the wideband reference functions are able to partially compensate for the nonlinearity imparted to the transmitted frequency-time sweep by an accelerating target, whereas such compensation is not possible in narrowband systems employing carrier-shifted reference functions.