Algebraic Construction of Optimal Frequency Hopping Patterns Based on Welch Costas Arrays

This paper systematically expounded the theory of optimal frequency hopping patterns based on Welch Costas arrays with 1-gap row, a theory established after studying the properties and mathematical models of the frequency hopping patterns obtained by making two-dimensional cyclic shift to Welch Costas arrays. The algebraic construction and the autocorrelation and cross-correlation properties of the Welch Costas arrays with 1-gap row were studied and certain theorems were proved. The optimal frequency hopping patterns will have ideal autocorrelation and cross-correlation when designed by means of Welch Costas arrays with 1-gap row.