An Extended Family of No-Hit-Zone Frequency Hopping Sequences for UAVs Cluster Communication

This paper studies the optimal design and performance analysis of a novel class of no-hit-zone frequency hopping sequence (NHZ-FHS) set in large-scale UAV clusters using quasi-synchronous frequency hopping multiple access (QS-FHMA) communication. Although the NHZ-FHS set can offer interference-free FHMA performance when the arrival signal delay $(\tau)$ does not exceed the NHZ $(Z)$, i.e., $\vert \tau\vert \leq Z$, the number of users in the conventional NHZ-FHS set is strictly limited, thus limiting their application in UAV clusters. Therefore, we consider an extended family of NHZ-FHSs consists of several conventional $\mathbf{NHZ}$ -FHS subsets to form a new FHS set. Moreover, collisions are guaranteed to occur between users using different subsets of frequency hopping sequences only in the zero time delay region, and it is also essential to minimize the Hamming correlation in the zero delay region in this paper. In this paper, such FHS sets are called extended NHZ-FHS (ENHZ-FHS) sets. We derive a lower bound on the maximum Hamming correlation and then provide a construction of the optimal ENHZ-FHS set meeting our proposed lower bound with equality. The theoretical analysis and simulation results show that the ENHZ-FHS set proposed in this paper can meet the communication requirements of UAV clusters with large capacities.