Daiyuan Peng

Lower bounds on the Hamming auto- and cross correlations of frequency-hopping sequences

Frequency hopping (FH) sequences have found wide applications in various modern FH spread-spectrum communications and radar systems. In FH spread-spectrum communications, the interference occurs when two distinct transmitters use the same frequency simultaneously. In order to evaluate the goodness of FH sequence design, the Hamming correlation function is used as an important measure. In this correspondence, by considering separately the maximum Hamming autocorrelation sidelobe H/sub a/, and the maximum Hamming cross correlation H/sub c/, several new lower bounds on the size p of the frequency slot set F, the sequence length L, the family size M, and correlation properties are established. The new periodic bounds include the known Lempel-Greenberger bounds as special case when M=2, and are tighter than the Seay bounds under certain conditions when M>2. Furthermore, the new bounds disclose more information on the relationship between the maximum autocorrelation sidelobe and the maximum cross correlation compared with the Lempel-Greenberger bounds and Seay bounds. Besides, the aperiodic FH bounds which have not yet been previously reported are also presented and discussed in this correspondence.

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 Hc, are established. It is shown that the new bounds include the known Lempel-Greenberger bounds, T.S. Seay bounds and Peng-Fan bounds for the conventional frequency hopping sequences as special cases.

New Constructions for Optimal Sets of Frequency-Hopping Sequences

In this paper, two generic constructions of optimal frequency-hopping sequence (FHS) sets employing d-form functions with difference-balanced property are presented. They generalize the previous constructions of optimal FHS sets using m-sequences and produce new optimal FHS sets that cannot be produced by the earlier constructions. By choosing appropriate d-form functions with difference-balanced property, both constructions lead to FHSs with large linear complexity. In addition, one of the proposed constructions gives new optimal parameters of FHS sets.

New family of hopping sequences for time/frequency-hopping CDMA systems

In this paper, a new family of hopping sequences with very large family size suitable for use in time/frequency-hopping (TH/FH) code-division multiple-access (CDMA) systems is proposed and investigated. The construction of the new hopping sequences is based upon the polynomial theory over the finite field, and the new hopping sequences are called the polynomial hopping sequences. It is shown that the new time/frequency-hopping sequences include the well-known cubic hopping sequences, quadratic hopping sequences, and linear hopping sequences as special cases, and are good candidates for the large-capacity ultrawide-bandwidth (UWB) radio systems.

New Bound on Frequency Hopping Sequence Sets and Its Optimal Constructions

In this paper, we derive a new bound on maximum nontrivial Hamming correlation of frequency hopping (FH) sequences from the Singleton bound in error correcting code literature, and we discuss the relation between the new bound and the known ones on FH sequences. Further, we construct two classes of FH sequences from punctured Reed-Solomon codes and one class of FH sequences from polynomial functions, which meet the new bound.

Average hamming correlation for the cubic polynomial hopping sequences

The average Hamming correlation is an important performance indicator of the frequency hopping sequences. In this paper, the lower bound on the average Hamming correlation for frequency hopping sequences with respect to the size q of the frequency slot set, the sequence length L, the family size M, the average Hamming autocorrelation Aa and the average Hamming crosscorrelation Ac is established. The average Hamming correlation for the cubic polynomials hopping sequences over a finite field GF(p) is also derived and discussed. It is shown that the cubic polynomials hopping sequences over a finite field GF(p) are the optimal average Hamming correlation sets.

A Class of Optimal Frequency Hopping Sequences Based upon the Theory of Power Residues

The average Hamming correlation is an important performance indicator of the frequency hopping sequences. In this paper, the theoretical bound on the average Hamming correlation for frequency hopping sequences is established. Besides, a new family of frequency hopping sequences is proposed and investigated. The construction of new frequency hopping sequences is based upon the theory of power residues, and the new frequency hopping sequences are called the power residue frequency hopping sequences. It is shown that new frequency hopping sequences are optimal with respect to both average Hamming correlation family and the optimal maximum Hamming correlation.

Frequency/time hopping sequence sets with optimal partial Hamming correlation properties

Frequency hopping/time hopping(FH/TH) sequences have found wide applications in various modern FH/TH spread spectrum communications, such as digital cellular mobile communication, short-range wireless communication, personal communication, and multi-user radar, sonar systems. In order to evaluate the goodness of FH/TH sequences design, the periodic Hamming correlation function is used as an important measure. Usually, the length of correlation window is shorter than the period of the chosen FH/TH sequence, so the study of the partial Hamming correlation of FH/TH sequence is particularly important. In this paper, a new class of FH/TH sequence sets with good partial Hamming correlation properties is proposed and investigated. The construction of new FH/TH sequence sets is based upon the generalized m-sequence and generalized Gordon-Mills-Welch sequence over a polynomial residue class ring. It is shown that new FH/TH sequence sets are optimal with respect to the partial Hamming correlation bound.

A new frequency-hopping sequence set based upon generalized cyclotomy

In this paper, a new set of frequency-hopping sequences is proposed, and the Hamming correlation distribution of the new set is investigated. The construction of new frequency hopping sequences is based upon generalized cyclotomy. It is shown that the proposed frequency-hopping sequence set is optimal with respect to the average Hamming correlation bound.

Complete weight enumerators of some linear codes from quadratic forms

Linear codes with few weights have applications in secrete sharing, authentication codes, association schemes, and strongly regular graphs. In this paper, a construction of q-ary linear codes with few weights employing general quadratic forms over the finite field Fq