New Bounds on the Partial Hamming Correlation of Wide-Gap Frequency-Hopping Sequence Sets

In frequency-hopping systems, there should be a wide frequency-hopping gap between two adjacent frequencies in case the received signals are prone to be interfered by staying at one frequency point for a long time. In this paper, a bound on the maximum partial Hamming autocorrelation of wide-gap frequency-hopping sequence (WGFHS) and two bounds on the maximum partial Hamming correlation of WGFHS sets are discussed. Moreover, the proposed bounds are tighter than the existing Eun-Jin-Hong-Song bound and Zhou-Tang-Niu-Udaya bounds in the sense that they can be achieved by the parameters of some WGFHSs and they are obtained in the literature for the first time.