Ambiguity Diagram for Linear FM Sonar

Abstract

Ambiguity diagrams are useful in estimating the range and Doppler resolution of radar and sonar systems in which the returning echo is correlated with a stored replica of the transmitted pulse. In the conventional approach for linear FM pulses, the equations are simplified by regarding the Doppler shift as a simple frequency translation, applied equally to all frequencies within the bandwidth. This approximation, while satisfactory for most radar applications, is in general not valid for sonar pulses. In this paper, the general equations are derived for the correlation function of a linear FM pulse, taking into account the effect o the Doppler shift on both the frequency sweep rate and the carrier frequency. An ideal point target is assumed. Computations based on a close approximation to the general case have been made for four 1-sec pulses with carrier frequencies of 10 and 20 kc/sec and sweep rates of 50 and 600 cps2. The ambiguity diagrams for the low sweep rate are almost identical with those of the “radar case,” whereas the diagrams for the high sweep rate are greatly shortened. A criterion for the applicability of the radar approximation is developed.