Radar Ambiguity Functions of Binary-Coded and Frequency-Hopped Waveforms Designed Based on the Permutations of Sudoku Matrix

The combinatorial number-placement puzzle, known worldwide as Sudoku puzzle, has been utilized as an encoder for generating diverse phase-coded and frequency-coded waveforms for high-resolution radar. In this article, we develop a Sudoku-based binary encoding scheme that generates a complete set of orthogonal and quasi-orthogonal binary codewords, referred to as Sudoku code, from the unique numeric permutations of a solved Sudoku matrix. The correlation and the orthogonality properties of the Sudoku binary sequences are described and compared with the correlation properties of the pseudorandom maximal-length sequences. Binary code-diverse waveforms and a frequency-hopping waveform with a unique Sudoku permutation as its frequency-coding sequence are introduced. The radar ambiguity functions of the Sudoku binary code-diverse and the frequency-hopped waveforms are derived too. Computer plots of the ambiguity functions of Sudoku binary code-diverse waveforms of different orders, a Sudoku-based frequency-hopping waveform, and a Costas frequency-coded waveform are presented. Performance analysis and comparison of the numerical results reveal that the ambiguity function of a Sudoku binary code-diverse waveform resembles the radar thumbtack ambiguity function, and it is more attractive for the applications of high-resolution radar than that of the Sudoku-based frequency-hopping waveforms.