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 - , 2017, DOI: 10.6040/j.issn.1671-9352.2.2016.169 Abstract: 摘要： 基于d-型函数,提出了两类具有最优周期部分汉明相关的跳频序列的构造方法。研究表明,对于任意相关窗长,新构造的跳频序列都是最优的。Abstract: Based on the d-function, two kinds of methods for constructing FH sequences with the optimal period partially Hamming correlation are proposed. The results show that the frequency hopping sequence are optimal for any correlation window length
 Mathematics , 2011, Abstract: In frequency-hopping multiple-access (FHMA) systems, the average Hamming correlation (AHC) among frequency-hopping sequences (FHSs) as well as the maximum Hamming correlation (MHC) is an important performance measure. Therefore, it is a challenging problem to design FHS sets with good AHC and MHC properties for application. In this paper, we analyze the AHC properties of an FHS set, and present new constructions for FHS sets with optimal AHC. We first calculate the AHC of some known FHS sets with optimal MHC, and check their optimalities. We then prove that any uniformly distributed FHS set has optimal AHC. We also present two constructions of FHS sets with optimal AHC based on cyclotomy. Finally, we show that if an FHS set is obtained from another FHS set with optimal AHC by an interleaving, it has optimal AHC.
 Bin Wen ISRN Combinatorics , 2013, DOI: 10.1155/2013/479408 Abstract: Frequency hopping spread spectrum and direct sequence spread spectrum are two main spread coding technologies. Frequency hopping sequences are needed in FH-CDMA systems. In this paper, a construction of optimal sets of frequency hopping sequences is presented. The construction is based on the set-theoretic characterization of an optimal set of FH sequences. 1. Introduction Frequency hopping spread spectrum and direct sequence spread spectrum are two main spread coding technologies. Frequency hopping sequences are an integral part of spread-spectrum communication systems such as FH-CDMA systems (for a description of such systems, see [1]). In modern radar and communication systems, frequency-hopping (FH) spread-spectrum techniques have become popular (see [2], for example). Assume that is a set of available frequencies, called an alphabet. Let be the set of all sequences of length over . Any element of is called a frequency hopping sequence (FHS) of length over . Given two FH sequences, and , we define their Hamming correlation to be where if and if , and where and all operations among position indices are performed modulo . If , is the Hamming autocorrelation. If , is the Hamming cross correlation. 2. Lower Bounds on the Correlations of FHSs FH sequences for FH-CDMA systems are required to have good Hamming correlations and large linear span [3]; the linear span is defined to be the length of the shortest linear feedback shift register that can produce the sequence. FH sequences’ design normally involves six parameters: the size of the frequency library , the sequence length , the family size of the subset , the maximum out-of-phase Hamming autocorrelations , the maximum Hamming cross correlations , and the linear span. It is generally desired that the family of FH sequences has the following properties: (1)the maximum out-of-phase Hamming autocorrelations should be as small as possible,(2)the maximum Hamming cross correlations should be as small as possible,(3)the family size for given , , , and should be as large as possible,(4)the linear span should be as large as possible. In order to evaluate the theoretical performance of the FH sequences, it is important to find some theoretical bounds for these parameters. Given , , and of , Lempel and Greenberger [4] and Peng and Fan [5] derived lower bounds on and of FH sequences in . We restate their results in this section, which will be used later as the criteria to determine whether the new FH sequences constructed in this paper are optimal or not. For any single FH sequence , let be the maximum
 Mathematics , 2010, Abstract: In this paper, using the theory of polynomial residue class rings, a new construction is proposed for frequency hopping patterns having optimal Hamming autocorrelation with respect to the well-known $Lempel$-$Greenberger$ bound. Based on the proposed construction, many new $Peng$-$Fan$ optimal families of frequency hopping sequences are obtained. The parameters of these sets of frequency hopping sequences are new and flexible.
 Mathematics , 2010, Abstract: Frequency hopping (FH) sequences play a key role in frequency hopping spread spectrum communication systems. It is important to find FH sequences which have simultaneously good Hamming correlation, large family size and large period. In this paper, a new set of FH sequences with large period is proposed, and the Hamming correlation distribution of the new set is investigated. The construction of new FH sequences is based upon Whiteman's generalized cyclotomy. It is shown that the proposed FH sequence set is optimal with respect to the average Hamming correlation bound.
 Sandeep Chalasani Mathematics , 2008, Abstract: Like other pseudorandom sequences, decimal sequences may be used in designing a Code Division Multiple Access (CDMA) system. They appear to be ideally suited for this since the cross-correlation of d-sequences taken over the LCM of their periods is zero. But a practical system will not, in most likelihood, satisfy the condition that the number of chips per bit is equal to the LCM for all sequences that are assigned to different users. It is essential, therefore, to determine the partial cross-correlation properties of d-sequences. This paper has performed experiments on d-sequences and found that the partial cross-correlation is less than for PN sequences, indicating that d-sequences can be effective for use in CDMA.
 电子与信息学报 , 2009, Abstract: In this paper, the generalized orthogonal sequences and N-shift partial length D0 orthogonal sequences with partial correlations are investigated. In particular, the partial correlation properties of Loosely Synchronized (LS) sequences are analyzed in details. The results show that LS sequences have partial correlation orthogonal property at 4-shift with half length, which can be utilized to construct partial length auto-complementary sequences and even-shift partial length cross-complementary sequences. Multiple-access interference can be eliminated in synchronous Code Division Multiple Access(CDMA) systems if the N-shift partial length D0 sequences are adopted.
 电子与信息学报 , 2005, Abstract: The performance analysis of chaotic Frequency-Hopping(FH)sequences,which are generated by quantization function and reshaping operation based on chaotic map,is presented in this paper.Theory analysis and performance experimental at results show that this sequence is Bernoulli sequence and its Hamming correlation is shown to be Poisson distributed.It is comparable to other FH sequences on the properties of uniform distribution,Hamming correlation and linear complexity when they have the same number of frequency slots and the same period,but much less requirements of iterative operation.It can be concluded that more FH sequences can be generated by this method and they are suitable for FH code-division multiple-access systems.
 王喜风,王可人,郭建蓬,周少琼 重庆邮电大学学报(自然科学版) , 2011, Abstract: To generate wide-gap frequency hopping(FH) sequences in real-time, a generator based on Tent double-way coupled map lattice is presented. A quantization algorithm, combing multi-bit quantization and reshaping operation, and a modified shift replace algorithm used to widen the FH sequences are included. A wide-gap FH sequences generator is realized on FPGA after it is converted from floating pointed operation to fixed pointed operation, and the generator has several advantages, including simple structure, low complexity of algorithm, few resources and easy control. The results of performance testing show that the wide-gap FH sequences generated by the generator have wide hopping gap, good balance demands and hamming correlation property.
 Mathematics , 2010, Abstract: Optimal partitioned cyclic difference packings (PCDPs) are shown to give rise to optimal frequency-hopping sequences and optimal comma-free codes. New constructions for PCDPs, based on almost difference sets and cyclic difference matrices, are given. These produce new infinite families of optimal PCDPs (and hence optimal frequency-hopping sequences and optimal comma-free codes). The existence problem for optimal PCDPs in ${\mathbb Z}_{3m}$, with $m$ base blocks of size three, is also solved for all $m\not\equiv 8,16\pmod{24}$.
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