Construction of optimal low-hit-zone frequency hopping sequence sets under periodic partial Hamming correlation

Abstract

In practice, when a frequency-hopping sequence (FHS) set is applied in a frequency-hopping multiple-access (FHMA) system, its periodic partial Hamming correlation (PPHC) rather than its periodic Hamming correlation (PHC) within the whole period is used to evaluate the system performance. Moreover, FHS sets with low hit zone (LHZ) can be well applied in quasisynchronous (QS) FHMA systems in which some relative time delay among different users within a zone around the origin can be allowed. Therefore, it is very urgent to conduct research on LHZ FHS sets with optimal PPHC property in depth. In this paper, we first derive a new tighter lower bound on the maximum PPHC of an LHZ FHS set. Then we present a new class of optimal one-coincidence FHS sets. Finally we have a construction of LHZ FHS sets which can be optimal with respect to our new lower bound.2010 Mathematics Subject Classification: Primary: 94A55; Secondary: 94B05.

Families of Optimal Low-Hit-Zone Frequency-Hopping Sequence Sets Under the Periodic Partial Hamming Correlation Properties

“…Similar to the proof of Theorem 2, as long as k 3 < θζ o−1 ζ o−ζ , D 3 has optimal PPHC property under all the correlation window length (13)…”

“…Lemma 5 [13]: Let S be an LHZ-FHS set with N frequency-hopping sequences of length L over F with size r, and L pz be the LHZ of S with regard to H pzm (S; G). Then for any positive integer Z , 0 ≤ Z ≤ L pz , we have…”