Sudoku Binary Codes and Signaling Schemes for the Applications of Radar and Wireless Communications

Abstract

In this paper, the popular Sudoku puzzle that is a square 9 x 9 matrix, arranged into 3 x 3 blocks, is used to generate new binary coded sequences that are attractive for the applications of radar and wireless communications. Each of the Sudoku codewords corresponds to the set of decimal integer numbers 1 to 9 placed in the Sudoku matrix in a unique pattern, referred to as permutation, such that each row, each column, diagonal, and each 3 x 3 block contains each of the nine integers exactly once. The signal model and the autocorrelation function of the Sudoku binary coded sequences are presented. Multicarrier (MC) code division multiple access (CDMA), and frequency-hopping (FH) CDMA signaling schemes, widely used in wireless communications and radar, are described based on the use of Sudoku binary codes.