Abstract
In frequency hopping (FH) sequence design, the wide gap is an important performance indicator. In this paper, the average Hamming correlation of wide gap FH sequence (WG-FH sequence) sets with low hit zone, which has not yet been reported previously, is studied. A lower bound on the average Hamming auto-correlation and the average Hamming cross-correlation of low-hit-zone FH sequence sets is firstly derived. The new lower bound includes the bound for conventional FH sequence sets derived by Peng et al. as a special case. Then a construction of WG-FH sequence sets with multiple low hit zones is presented, which are optimal by the new bound for these low hit zones. Finally, another class of optimal WG-FH sequence sets with multiple low hit zones is presented, which have larger wide gap.
Highlights
In frequency hopping (FH) multiple-access (MA) spreadspectrum systems, the frequencies used are chosen pseudorandomly by a code called FH sequence
We derive a lower bound on the average Hamming auto-correlation and the average Hamming cross-correlation of low-hit-zone FH sequence sets
We give a construction of WG-FH sequence sets with multiple low hit zones, which are optimal with respect to the new bound
Summary
In frequency hopping (FH) multiple-access (MA) spreadspectrum systems, the frequencies used are chosen pseudorandomly by a code called FH sequence. The average Hamming correlation of low-hit-zone FH sequences has not yet been studied. For WG-FH sequences with low hit zone, it needs to meet the condition in Theorem 3.3 if they are optimal with respect to average Hamming correlation. We study the average Hamming correlation of WG-FH sequence sets with low hit zone. We give a construction of WG-FH sequence sets with multiple low hit zones, which are optimal with respect to the new bound.
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