The frequency hopping sequence plays a crucial role in determining the system's anti-jamming performance, in frequency hopping communication systems. If the adjacent frequency points of FHS can ensure wide-gap, it will better improve the anti-interference capability of the FH communication system. Moreover, if the period of the sequence is expanded, and each frequency point does not repeat in the same sequence, the system's ability to resist electromagnetic interference will be enhanced. And a one-coincidence frequency-hopping sequence set consists of FHSs with maximum Hamming autocorrelation 0 and cross-correlation 1. In this paper, we present two constructions of wide-gap frequency-hopping sequence sets. One construction is a new class of wide-gap one-coincidence FHS set, and the other is a WGFHS set with long period. These two WGFHS sets are optimal with respect to WG-Peng-Fan bound. And each sequence of these WGFHS sets is optimal with respect to WG-Lempel-Greenberger bound.

Low-hit-zone frequency-hopping sequences (LHZ-FHSs) are frequency-hopping sequences with low Hamming correlation in a low-hit-zone (LHZ), which have important applications in quasi-synchronous communication systems. However, the strict quasi-synchronization may be hard to maintain at all times in practical FHMA networks, it is also necessary to minimize the Hamming correlation for time-shifts outside of the LHZ. The main objective of this letter is to propose a lower bound on the maximum correlation magnitude outside the low-hit-zone for LHZ-FHS sets. It turns out that the proposed bound is tight or almost tight in the sense that it can be achieved by some LHZ-FHS sets.

Frequency-hopping sequence (FHS) sets with low-hit-zone (LZH) can be well applied in quasi-synchronous (QS) frequency-hopping multiple-access (FHMA) systems to reduce the mutual interference among different users. On the other hand, LHZ-FHS sets with wide-gap (WG) property can effectively resist the broadband blocking interference, the single frequency narrowband interference, the multipath fading and the tracking interference. In this letter, a new family of WG-LHZ-FHS sets is constructed. Besides, these new WG-LHZ-FHS sets possess optimal average periodic Hamming correlation (APHC) properties.

Notes on two constructions of zero-difference balanced (ZDB) functions are made in this letter. Then ZDB functions over Ze×∏ki=0 Fqi are obtained. And it shows that all the known ZDB functions using cyclotomic cosets over Zn are special cases of a generic construction. Moreover, applications of these ZDB functions are presented.

Frequency-hopping sequence (FHS) sets with low-hit-zone (LHZ) have Hamming correlations maintained at a low level as long as the relative time delay between different sequences are limited in a zone around the origin, and thus can be well applied in quasi-synchronous (QS) frequency-hopping multiple-access (FHMA) systems to reduce the mutual interference between different users. Moreover, the periodic partial Hamming correlation (PPHC) properties of employed LHZ-FHS sets usually act as evaluation criterions for the performances of QS-FHMA systems in practice. In this letter, a new class of LHZ-FHS sets is constructed via interleaving techniques. Furthermore, these new LHZ-FHS sets also possess optimal PPHC properties and parameters not included in the related literature.

As an optimal combinatorial object, cyclic perfect Mendelsohn difference family (CPMDF) was introduced by Fuji-Hara and Miao to construct optimal optical orthogonal codes. In this paper, we propose a direct construction of disjoint CPMDFs from the Zeng-Cai-Tang-Yang cyclotomy. Compared with a recent work of Fan, Cai, and Tang, our construction doesn't need to depend on a cyclic difference matrix. Furthermore, strictly optimal frequency-hopping sequences (FHSs) are a kind of optimal FHSs which has optimal Hamming auto-correlation for any correlation window. As an application of our disjoint CPMDFs, we present more flexible combinatorial constructions of strictly optimal FHSs, which interpret the previous construction proposed by Cai, Zhou, Yang, and Tang.

Zero-difference balanced (ZDB) functions, which have many applications in coding theory and sequence design, have received a lot of attention in recent years. In this letter, based on two known classes of ZDB functions, a new class of ZDB functions, which is defined on the group (Z2e-1×Zn,+) is presented, where e is a prime and n=p1m1p2m2…pkmk, pi is odd prime satisfying that e|(pi-1) for any 1≤i≤k . In the case of gcd(2e-1,n)=1, the new constructed ZDB functions are cyclic.

In this letter, we first investigate some new properties of a known power residue frequency-hopping sequence (FHS) set which is established as an optimal one-coincidence frequency-hopping sequence (OC-FHS) set with near-optimal set size. Next, combining the mathematical structure of power residue theory with interleaving technique, we present a new class of optimal OC-FHS set, using the Chinese Remainder Theorem (CRT). As a result, one optimal OC-FHS set with prime length is extended to another optimal OC-FHS set with composite length in which the construction preserves the maximum Hamming correlation (MHC) and the set size as well as the optimality of the Lempel-Greenberger bound.

The average Hamming correlation is an important performance indicator of frequency-hopping sequences (FHSs). In this letter, the average partial Hamming correlation (APHC) properties of FHSs are discussed. Firstly, the theoretical bound on the average partial Hamming correlation of FHSs is established. It works for any correlation window with length 1≤ω≤υ, where υ is the sequence period, and generalizes the bound developed by Peng et al which is valid only when ω=υ. A sufficient and necessary condition for a set of FHSs having optimal APHC for any correlation window is then given. Finally, sets of FHSs with optimal APHC are presented.

No nontrivial optimal sets of frequency-hopping sequences (FHSs) of period 2(2n-1) for a positive integer n ≥ 2 have been found so far, when their frequency set sizes are less than their periods. In this paper, systematic doubling methods to construct new FHS sets are presented under the constraint that the set of frequencies has size less than or equal to 2n. First, optimal FHS sets with respect to the Peng-Fan bound are constructed when frequency set size is either 2n-1 or 2n. And then, near-optimal FHS sets with frequency set size 2n-1 are designed by applying the Chinese Remainder Theorem to Sidel'nikov sequences, whose FHSs are optimal with respect to the Lempel-Greenberger bound. Finally, a general construction is given for near-optimal FHS sets whose frequency set size is less than 2n-1. Our constructions give new parameters not covered in the literature, which are summarized in Table1.

In this letter, we give a generalized construction for sets of frequency-hopping sequences (FHSs) based on power-residue sequences. Our construction encompasses a known optimal construction and can generate new optimal sets of FHSs which simultaneously achieve the Peng-Fan bound and the Lempel-Greenberger bound.

In quasi-synchronous frequency-hopping multiple access (QS-FHMA) systems, no-hit-zone frequency-hopping sequence (NHZ-FHS) sets are commonly employed to minimize multiple access interference. Several new constructions for optimal NHZ-FHS sets are presented in this paper, which are based on interleaving techniques. Two types of NHZ-FHS sets of length 2N for any integer N ≥ 3 are constructed, whose NHZ sizes are some even integers. An optimal NHZ-FHS set of length 2N with odd NHZ size for any integer N ≥ 6 is also presented. And then, optimal NHZ-FHS sets of length kN are given by generalizing one of the proposed constructions for NHZ-FHS sets of length 2N, where k and N are any positive integers such that 2 ≤ k < N. All the FHSs in the new NHZ-FHS sets are non-repeating FHSs which are optimal with respect to the Lempel-Greenberger bound. Our constructions give new parameters which are flexible in the selection of NHZ size and set size.

In frequency-hopping (FH) multiple access systems, frequency-hopping sequences (FHSs) with optimal Hamming correlation properties are needed. Based on the d-form functions with ideal autocorrelation properties, a new set of FHSs is constructed. The new FHS set is optimal with respect to the Peng-Fan bounds and each FHS in the set is optimal with respect to the Lempel-Greenberger bound.

Stability of slotted ALOHA systems with retransmission cutoff, in which a packet is discarded after the certain number of unsuccessful transmissions, is investigated on slow-frequency-hopped channels with the aid of the catastrophe theory. The result of this paper can be viewed as extension of the result derived by Kim. The balance function is first formulated. Then, the cusp point and the bifurcation sets are numerically evaluated. We visualize how retransmission cutoff effects on bistable region. Using the result, we can design parameters of slotted ALOHA systems with retransmission cutoff such that the system operates with the unique stable equilibrium point.

We propose a p-persistent protocol for slow-frequency-hopped slotted random access networks, assuming that all the users know the number of backlog users in a slot. The proposed protocol delays new packet transmission until the number of users with a packet to be retransmitted decreases to the threshold or less. Performance of the proposed protocol is evaluated with a two-dimensional Markov chain for systems with finite population in terms of throughput efficiency and the average transmission delay. Numerical results show that the proposed protocol can achieve better performance by suppressing new packet transmission, compared to the conventional frequency-hopped slotted ALOHA. The optimum value of the threshold is also numerically derived.

2.4-GHz-band mid-speed (1- to 2-Mbit/sec) wireless LAN systems are being widely used in offices and factories. Electromagnetic interference can occur between these systems because they use the same frequency range. In this paper, we investigate the characteristics of the interference between wireless LAN systems that use direct-sequence (DS) systems and frequency-hopping (FH) systems. The interference characteristics were measured for three DS systems and one FH system that meet the IEEE 802.11 and RCR standards and that use different modulation methods. Our results indicate that throughput depends on the system and the modulation method. We have also developed a model that can be used to calculate the interference characteristics between DS and FH systems by considering the bandwidth of their transmission signals, the dwell time of the FH system, and the time that the DS system needs to transmit a data frame. We used this model to calculate the bit error rate (BER) characteristics of the systems used in our experiment, and the results indicate that BER characteristics depend on the modulation method. The throughput characteristics of the systems used in our experiment were also calculated, and agreed with the experiment results within +/- 5 dB. The throughput characteristics of wireless LAN systems based on IEEE 802.11 were also calculated when the signal level was higher than the receiver noise level. The results show that FH systems require a D/U ratio about 7 or 8 dB higher than the ratio required in DS systems because the parameters in the standard differ between FH and DS systems.

A method for determination of the location, shape, and material properties of a 3D object from measurements of the scattered field, when the object is successively illuminated by a number of incident fields is presented. This work extends the method previously developed for reconstructions of 2D permittivity and conductivity from electromagnetic measurements to the more complicated full-vector 3D electromagnetic inversion. Furthermore, a frequency hopping strategy to improve the resolution of the unknown objects when the frequency is raised, is underlined. Results of numerical experiments are presented to illustrate both strengths and weaknesses of the method.