Ambiguity Function - Square Pulse

Square Pulse

Consider a simple square pulse of duration and amplitude :

where is the Heaviside step function. The matched filter output is given by the autocorrelation of the pulse, which is a triangular pulse of height and duration (the zero-Doppler cut). However, if the measured pulse has a frequency offset due to Doppler shift, the matched filter output is distorted into a sinc function. The greater the Doppler shift, the smaller the peak of the resulting sinc, and the more difficult it is to detect the target.

In general, the square pulse is not a desirable waveform from a pulse compression standpoint, because the autocorrelation function is too short in amplitude, making it difficult to detect targets in noise, and too wide in time, making it difficult to discern multiple overlapping targets.