FORMING THE AMBIGUITY FUNCTION OF A COHERENT PULSE TRAIN USING WEIGHTING OF COMPONENT AMPLITUDES

Abstract

A uniformly spaced coherent train of pulses is commonly used in radar systems for improving Doppler resolution. The Doppler resolution is defined by the total coherent duration of the processed signal and can be very high for such sequences. But the ambiguity function of the pulse train still suffers from significant sidelobes. Transmitting the same signal periodically and then processing the returns coherently introduces large ambiguities in the matched filter delay-Doppler response, or the pulse train ambiguity function, which occur at multiples of pulse repetition interval along the delay axis and at multiples of pulse repetition frequency along Doppler. Thus, modifications are usually applied to reduce these sidelobes. Different parameters of the pulse train can be varied to optimize the ambiguity function and improve resolution properties. The most common way is by implementing interpulse amplitude weighting. In many works, exact analytical formulas for the ambiguity function of pulse sequences have been obtained, but they are quite cumbersome, so it is difficult to determine from them how exactly the sequence parameters affect the shape of the ambiguity function.

In this paper, a simple analytical expression for the cross-section of the pulse train ambiguity function along the Doppler axis is obtained. It valid for zero time offset. It allows us to simply understand and clearly determine the effect of intra- and inter-pulse weighting on the shape of the ambiguity surface along the central Doppler frequency axis. It is shown by simulation that this effect is preserved for non-zero time offsets. The Hamming window was used in this paper to process the pulses. In the case of inter-pulse weighting, it applies to all pulses in the sequence. In the case of intra-pulse weighting, the amplitude of each pulse was varied using this window.