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 quasi-synchronous (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.
Highlights
With advantages such as anti-jamming performance, anti-fading effect, multipleaccess property, and secure property, frequency-hopping multiple-access (FHMA) spread spectrum (SS) systems have been widely applied in military radio communication systems, mobile communication systems, sonar echolocation systems etc. [1, 8, 7]
In order to introduce our construction of low hit zone (LHZ) frequency hopping sequence (FHS) sets through Cartesian product, we first obtain a new class of optimal one-coincidence FHS sets which will be chose as a part of component FHS sets
Through a little modification to an existing lower bound on the maximum periodic partial Hamming correlation (PPHC) of an LHZ FHS set, we got a new tighter lower bound
Summary
With advantages such as anti-jamming performance, anti-fading effect, multipleaccess property, and secure property, frequency-hopping multiple-access (FHMA) spread spectrum (SS) systems have been widely applied in military radio communication systems, mobile communication systems, sonar echolocation systems etc. [1, 8, 7]. The Hamming correlation properties of the employed frequency hopping sequence (FHS) sets are closely related to the degree of the mutual interference, and can be viewed as evaluation criterions for the performance of FHMA systems. For any LHZ FHS set, its maximum PHC or PPHC within the LHZ together with the sequence length, the sequence set size, the frequency set size, and the correlation window length are limited by some mathematical relationships known as theoretical bounds. Afterwards, Wang et al [17] introduced constructions of LHZ FHS sets with optimal PPHC property through Cartesian product in 2015. We obtain a new tighter lower bound on the maximum PPHC of an LHZ FHS set.
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