Range and Doppler resolution of the modified narrowband ambiguity function for Costas waveforms

The narrowband ambiguity function (NAF) of the Costas waveforms is modified by generalizing the expression of the frequency in each subpulse. Compared with the original one, the modified ambiguity diagram (MAD) is extended or compressed along the Doppler shift axis, depending on the difference between the interval of the adjacent frequency channel and the inverse of each subpulse duration. The range and Doppler resolution is then derived from the modified NAF. The factors influencing the result are pointed out as well. Finally, the sections and -3dB contours of the MAD are presented to verify the validity of our proposed results.