A Construction Method for the Random Factor-Based G Function

In consideration of the prevailing methodology for constructing G functions, there are certain limitations such as fixed change rules and restricted flexibility when producing frequency-hopping sequences. This paper introduces a novel construction method for the Random Factor-based G function (RFGF). This approach incorporates random factors to dynamically divide the frequency set into equal intervals and randomly selects the frequency hopping frequency within each subset. This effectively reduces the correlation between adjacent frequency-hopping frequencies, enhancing the randomness of the sequence and the system's anti-interference performance. Furthermore, this method utilizes chaotic sequences to scramble data information, further strengthening the security of the information. The experimental results demonstrate that the frequency-hopping sequence generated by this proposed G function construction method outperforms the sequence generated by the time-varying iterative decomposition in terms of randomness, uniformity, and two-dimensional continuity. Specifically, under the same parameter conditions, the two-dimensional continuity is improved by 36.87%.