Orthogonal Pattern Division Multiple Access Utilizing Optimal Frequency Hopping Patterns Constructed With Welch Costas Arrays

This paper explores the autocorrelation and cross-correlation properties of Welch Costas arrays and introduces a method for constructing optimal frequency hopping patterns with ideal autocorrelation and cross-correlation through two-dimensional cyclic shift on a Welch Costas array. Additionally, it proposes orthogonal pattern division multiple access (OPDMA) utilizing these optimal patterns. The paper examines the relationship between the design parameters of these patterns and cellular system parameters, tailoring frequency hopping patterns for cellular system users. Furthermore, it conducts computations and analyses on the autocorrelation and cross-correlation of the designed patterns, demonstrating their ideal properties. It also discusses the role of delay distance and Doppler distance in achieving ideal cross-correlation between the optimal frequency hopping patterns. OPDMA emerges as a novel two-dimensional orthogonal multiple access technology offering signal immunity, effectively overcoming interference from multipath propagation, Doppler shift, and inter-user interference. This simplifies receiver design and enhances overall system performance, presenting potential applications in future cellular mobile communications, frequency hopping communications, radar, and sonar systems.