A Formal Study of the Doppler Tolerance of Costas and Sudoku Waveforms

We apply a new, formal measure of Doppler tolerance to frequency-hopping waveforms made from Costas arrays and Sudoku-based permutations. We first give a combinatorial structure theorem for Sudoku permutations that facilitates waveform analysis. We form statistical profiles of Doppler tolerance envelopes computed from thresholding narrowband ambiguity functions of these waveforms and compare against those from randomly-chosen permutations. As functions of temporal offsets, the statistical profiles indicate a wide range of Doppler tolerance, suggesting that permutation adaptivity is a worthwhile degree of freedom to exploit for moving target indication in frequency-challenged environments. We find that Sudoku-based waveforms behave much like randomly-chosen permutations with respect to Doppler tolerance.