New Bounds on the Partial Hamming Correlation of Wide-Gap Frequency-Hopping Sequence Sets With Low Hit Zone

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 sequences (WGFHSs), two bounds on the maximum partial Hamming correlation of WGFHS sets, two bounds on the maximum Hamming correlation of WGFHS sets with low hit zone and two bounds on the maximum partial Hamming correlation of WGFHS sets with low hit zone are derived. Moreover, the proposed bounds are tighter than the Eun-Jin-Hong-Song bound, Zhou-Tang-Niu-Udaya bounds, Peng-Fan-Lee bounds and Niu-Peng-Liu bounds in the sense that they can be achieved by the parameters of some WGFHSs. To the best of our knowledge, these bounds are obtained for the first time in the literature.