Ambiguity and Doppler tolerance analyses of frequency-stepped, Sudoku-variant waveforms

One obtains a frequency-hopping waveform from a traditional 9 × 9 Sudoku by zeroing out all entries besides a fixed integer and using the non-zero integer positions as the frequency-hopping permutation. Using a new and general approach to describing Doppler tolerance of Setlur et al., we previously computed the narrowband ambiguity function to formally compare Doppler tolerances of Sudoku-based frequency-hopping waveforms with Doppler tolerances of waveforms made from Costas arrays and from random permutations. The analyses in this paper will expand our previous analyses to pulse trains, to Sudokus having additional constraints (Hyper Sudoku and X-Sudoku) in support of more waveform structure, and to larger Sudoku (Superdoku) in support of higher time-bandwidth products. The ambiguity analyses investigate the peak sidelobe levels found from using various permutations as well as the sidelobe levels around the central peak of the ambiguity function.