Abstract
Sudoku puzzles, often seen in magazines and newspapers, are logic-based challenges where each entry within the puzzle is comprised of symbols adhering to row, column and box constraints. Previously, we had investigated their potential in frequency-hopped waveforms to achieve desirable radar ambiguity functions and compared them with random, as well as the more familiar Costas sequences. This paper further examines the properties of Sudoku codes in more detail through computational search and analysis. We examine the co-hit and cross-hit arrays, defined as the correlation between two sequences, to quickly and efficiently evaluate numerous Sudoku puzzles. Additionally, we investigate the use of Sudoku puzzles for antenna applications, including array interleaving, array thinning and random element spacing.
Highlights
Sudoku is a combinatorial number-placement puzzle that has its roots in the well-studied Latin squares [1]
Comparing the Sudoku co-hit arrays with Latin squares, we find that the Sudoku puzzles offer slightly better side-lobe performance with a greater percentage of Sudoku frequency codes offering “one” and “two” numbers of coincidences
We showed through our computational search that there exist Costas sequences within Sudoku puzzles and that some
Summary
Sudoku is a combinatorial number-placement puzzle that has its roots in the well-studied Latin squares [1]. Our initial work showed that Sudoku-based waveforms can achieve low ambiguities in both range and Doppler planes, giving a “thumbtack”-like response. Such a surface is not attainable in practice, several waveform sequences based on continuous. Electronics 2017, 6, 13 discrete frequency coding [8] techniques have been developed that approximate the ideal ambiguity diagram, while at the same time allowing practical system designs For such waveforms, any translation of the sequence parallel to the coordinate axes (frequency and time: velocity and range) produces a very low number of out-of-phase coincidences with improved resolution characteristics over other frequency-hopped signals, such as the linear frequency-hopping sequence [9].
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