Frequency coded waveforms for enhanced delay-Doppler resolution

In this research, we propose techniques for the construction of frequency coding sequences that give rise to frequency coded waveforms having ambiguity functions with a clear area-containing no sidelobes-in a connected region surrounding the main lobe. In this sense, the proposed sequences have excellent delay-Doppler resolution properties and achieve locally optimal ambiguity functions in the region surrounding the main lobe. These sequences are called pushing sequences. First, two important properties of pushing sequences are investigated: the group D₄ dihedral symmetry property and the frequency omission property. We also note that Costas sequences have these two properties and the implications of this are investigated. Next, we show how to construct pushing sequences having ambiguity functions with arbitrary-size clear areas. Finally, we analyze the sidelobe distribution and provide the general form of all sidelobe peak positions, and both the lower and upper bound of each sidelobe peak level.