Theoretical Bounds of the Aperiodic Partial Hamming Correlation for Frequency Hopping Sequences

The data link is an important network structure of unmanned swarm, and frequency hopping technology is used between network groups to achieve anti-interference performance. The aperiodic partial Hamming correlation of the frequency hopping sequence can fully measure the anti-jamming performance of the frequency hopping sequence under different correlation window length, which is very important for the evaluation of system performance.

In this paper, a theoretical bound on the Hamming correlation of the aperiodic partial for the frequency hopping sequence set is derived. And the constraint relationship among the length and number of sequences in the frequency hopping sequence set, the size of the frequency slot set, the length of the correlation window and the maximum aperiodic partial Hamming autocorrelation and the maximum aperiodic partial Hamming cross-correlation are deduced. According to the derived theoretical bounds, the optimal aperiodic partial Hamming correlation performance can be judged for the used frequency hopping sequence set.