New sets of low-hit-zone frequency-hopping sequence with optimal maximum periodic partial Hamming correlation

Recently, Chung et al. gave a general method to construct frequency-hopping sequence set(FHS set) with low-hit-zone(LHZ FHS set) by the Cartesian product. In their paper, Theorems 5 and 8 claim that k FHS sets whose maximum periodic Hamming correlation is 0 at the origin result in an LHZ FHS set based on the Cartesian product, and Proposition 4 presented an upper bound of the maximum periodic Hamming correlation of FHSs. However, their statements are imperfect or incorrect. In this paper, we give counterexamples and make corrections to them. Furthermore, based on the Cartesian product, we construct two classes of LHZ FHS sets with optimal maximum periodic partial Hamming correlation property. It is shown that new FHS sets are optimal by the maximum periodic partial Hamming correlation bound of LHZ FHS set.

Lower bounds on the periodic Hamming correlations of frequency hopping sequences with low hit zone

In this paper, several periodic Hamming correlation lower bounds for frequency hopping sequences with low hit zone, with respect to the size p of the frequency slot set, the sequence length L, the family size M, low hit zone LH （ or no hit zone NH ）, the maximum periodic Hamming autocorrelation sidelobe Ha and the maximum periodic Hamming crosscorrelation He, are established. It is shown that the new bounds include the known LempeI-Greenberger bounds, T.S. Seay bounds and Peng-Fan bounds for the conventional frequency hopping sequences as special cases.

CONSTRUCTION OF FREQUENCY HOPPING SEQUENCES WITH NO HIT ZONE

In this paper,a property of Frequency Hopping (FH) sequence set with No Hit Zone (NHZ) is analyzed. Based on matrix transform and mapping methods,respectively,two classes of NHZ FH sequences are presented. These NHZ FH sequences have good Hamming auto-correlation and Hamming cross-correlation properties. FH Code-Division Multiple Access (FH-CDMA) communication systems employing such NHZ FH sequences will eliminate multiple-access interference if the maximum time delay is shorter than the length of the NHZ.

Cipher quasi-chaotic code for frequency hopping communications

The chaotic frequency hopping (FH) communication systems have been presented so far. The chaotic sequences possesses good randomness and sensitive dependence on initial conditions, which is quite advantageous to run the FH codes in code-division multiple access (CDMA) systems. But the finite precision of computation and the fact of the low-dimensional chaos predicted easily cause difficulty in chaotic application. In this paper, some disadvantages associated with the conventional FH codes and the chaotic code scrambled by m-sequences are reviewed briefly. In order to overcome these drawbacks to some extents, a new higher performance FH code called cipher quasi-chaotic (CQC) code is proposed, which is generated by combining the clock-controlled stream cipher technique and chaotic dynamics. Performance analysis applying in FH communication systems of this kind of code is given. The privacy of the CQC sequence is also analyzed.

Frequency hopping sequences based on d-form functions

By using d-form function, a new construction of frequency hopping sequence with optimal Hamming correlation is presented in this article, which generalizes the results presented by Ding （2007）. Furthermore, a new class of non-power function style d-form function is proposed and an upper bound of the Hamming autocorrelation of the corresponding sequence is also derived.