最优低碰撞区跳频序列集构造与性能分析

田新钰; 陈晓玉; 张继韬

doi:10.11999/JEIT260343

最优低碰撞区跳频序列集构造与性能分析

doi: 10.11999/JEIT260343 cstr: 32379.14.JEIT260343

田新钰^{1, 2},
陈晓玉^{1, 2, ,},
张继韬^{1, 2}

1.
燕山大学信息科学与工程学院秦皇岛 066004
2.
河北省信息传输与信号处理重点实验室秦皇岛 066004

基金项目: 河北省自然科学基金资助项目(No.F2025203055)，河北省高等学校科学技术研究基金资助项目(No.ZD2022026)，河北省重点实验室基金资助项目(No.202250701010046)

详细信息

通讯作者:
陈晓玉　chenxiaoyu@ysu.edu.cn

中图分类号: TN911.2
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- 文章访问数: 23
- HTML全文浏览量: 8
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- 被引次数: 0
出版历程
- 收稿日期: 2026-03-22
- 修回日期: 2026-06-29
- 录用日期: 2026-06-29
- 网络出版日期: 2026-07-11

Construction and Performance Analysis of Optimal Low-Hit-Zone Frequency Hopping Sequence Sets

TIAN Xinyu^{1, 2},
CHEN Xiaoyu^{1, 2
, ,},
ZHANG Jitao^{1, 2}

1.
School of Information Science and Engineering, Yanshan University, Qinhuangdao 066004, China
2.
Hebei Province Key Laboratory of Information Transmission and Signal Processing, Qinhuangdao 066004, China

Funds: The Natural Science Foundation of Hebei Province (No.F2025203055), The Science Research Project of Hebei Education Department (No.ZD2022026), The Key Laboratory Project of Hebei Province (No.202250701010046)

摘要

摘要: 电磁干扰(Electromagnetic interference, EMI)严重影响同步系统可靠性。现有5G方案采用全频带Zadoff-Chu(ZC)序列，在高密度接入场景下受限于正交码资源，面临明显的容量瓶颈。针对此挑战，该文提出一种跳频(Frequency hopping, FH)与ZC序列结合的方案。通过构造关于Peng-Fan-Lee界最优的多子集低碰撞区(Low-hit-zone, LHZ)跳频序列集，利用其多子集结构为车联网局部簇同步资源划分提供序列支撑。仿真结果表明，在子带选择性阻塞干扰环境下，所提FH-ZC同步方案相较于全频带ZC基准方案具有更高的同步检测概率，同时，所提多子集按簇分配方式能够更好地适配局部簇同步场景的竞争结构，并在多用户并发条件下表现出更优的同步检测鲁棒性。
- 跳频序列 /
- Peng–Fan–Lee界 /
- 汉明相关 /
- 低碰撞区 /
- 电磁干扰
Abstract: Objective Electromagnetic interference (EMI) is a critical factor restricting the reliability of synchronization systems. Furthermore, existing 5G synchronization methods extensively utilize Zadoff-Chu (ZC) sequences for user differentiation through cyclic shifts. However, constrained by finite sequence lengths and limited orthogonal resources, these methods encounter significant capacity bottlenecks in high-density access scenarios. To address these challenges, this paper investigates the problem from two perspectives. First, at the system level, an enhanced synchronization framework is developed by integrating frequency hopping (FH) technology with ZC sequences. By leveraging code-time-frequency domain encoding, this design enhances the concurrency support capability for local clusters, while the frequency-agile nature of the FH patterns significantly strengthens interference robustness against complex EMI. Second, motivated by the local cluster structure of V2X networks, this paper constructs a class of multi-subset low-hit-zone (LHZ) frequency hopping sequence (FHS) sets, which provides a sequence resource organization method for local-cluster synchronization scenarios. Methods Building upon the theoretical framework of Cai et al., this paper reconstructs the underlying mapping mechanisms and introduces disjoint cyclic perfect Mendelsohn difference families (CPMDF) sets to derive optimal FHS sets with respect to the Peng–Fan bound. By further expanding the generating units via Cartesian products and proposing a novel column-incoherent partitioning criterion, we develop a class of LHZ FHS sets characterized by an inherent multi-subset structure. It is shown that every nonempty subset of the constructed family is optimal with respect to the Peng–Fan–Lee bound Compared with Global-LHZ-FH-ZC, Clustered-LHZ-FH-ZC exhibits better synchronization-detection robustness by better matching the local-cluster competition structure. At the system implementation level, we propose a joint FH-ZC synchronization architecture that utilizes predefined hopping patterns and the frequency-domain correlation of ZC sequences for subband signal detection. A Peak-to-Sidelobe Ratio (PSLR) decision metric and an early-termination strategy are adopted to evaluate synchronization preamble detection under interference. Furthermore, a multi-user simulation model is developed to evaluate the synchronization-detection performance of the proposed sequences under collision accumulation and EMI. Results and Discussions This paper constructs a class of FHS sets that is optimal with respect to the Peng–Fan bound, as well as a class of multi-subset LHZ FHS sets. It is further shown that any nonempty subset of the latter is optimal with respect to the Peng–Fan–Lee bound. (Example 2) illustrates the construction as well as the intra-subset and inter-subset Hamming Correlation properties of the proposed multi-subset LHZ FHS sets. The comparative data in (Table. 1) demonstrates that, under the given frequency resource constraints, the total number of sequences generated by the proposed construction is larger than several existing constructions under the compared parameter settings, reflecting superior resource utilization. Moreover, (Table. 2) provides a comparative analysis between the proposed sequence sets and existing constructions in the literature. To the best of our knowledge, such optimal sequence families characterized by a multi-subset structure have not been previously reported in the literature. (Fig. 2 and Fig. 3) intuitively demonstrate the performance advantages of the proposed FH-ZC architecture. The simulation results indicate that, owing to the optimized design of the frequency hopping patterns, this method achieves enhanced synchronization stability and higher detection probability under subband-selective blocking interference caused by EMI compared to the existing 5G synchronization baseline scheme. Finally, (Fig. 4) indicates that the detection probability decreases as the number of active users increases, indicating that accumulated same-frequency collisions are a major cause of synchronization-performance degradation. Compared with Global-LHZ-FH-ZC, Clustered-LHZ-FH-ZC exhibits better synchronization-detection robustness under the local-cluster competition structure characterized by strong intra-cluster competition and weak inter-cluster coupling. Conclusions To address the demand for sequence capacity in massive access scenarios, this paper proposes a class of multi-subset LHZ FHS sets. By leveraging Cartesian products to expand the generating sequence sets and employing column-incoherent partitioning for subset division, we construct a class of multi-subset LHZ-FHS sets that simultaneously achieve large capacity and optimality within the LHZ. The proposed multi-subset structure is better matched to the competition structure of local-cluster synchronization scenarios, significantly enhancing both the scale and utilization rate of sequence resources through its unique subset structure, thereby providing a richer resource pool for high-density multi-user environments. Simulation results under the considered physical-layer model indicate that the constructed LHZ FHS subsets can reduce frequency-collision effects in multi-user synchronization detection, and that the FH-ZC scheme achieves higher synchronization preamble detection probability than the Fixed-ZC baseline under subband-selective blocking interference caused by EMI.
- Frequency hopping sequence (FHS) /
- Peng–Fan–Lee bound /
- Hamming correlation /
- Low-hit-zone (LHZ) /
- Electromagnetic interference (EMI)

HTML全文

图 1 面向大规模V2X接入的异构簇结构与多源干扰场景模型

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图 2 不同干扰子带数下的PD对比

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图 3 1帧下不同检测数量对比ZC

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图 4 活跃用户数PD的影响

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表 1 现有最优LHZ FHS集与本文相对(3)的规模占比对比

参数$ (L,\ell,N,{L}_{\text{z}},{H}_{\text{m}}({\boldsymbol{G}}_{\delta })) $	$ \eta $	循环等价	参考文献
(124，4，25，29，4)	1.45×10^–3%	是	[8]
(62，4，25，31，2)	0.79%	否	[9]
(171，10，7，28，24)	2.08×10^-17%	是	[10]
(35，15，35，6，1)	7.3%	否	[11]
(24，9，720，7，3)	76.2%	否	本文

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表 2 现有最优LHZ FHS集与本文的参数对比

参数$ (L,N,\ell,{L}_{\text{z}},{H}_{\text{m}}(\boldsymbol{S})) $	子集个数	限制	参考文献
$ \left({q}^{n}-1,{q}^{k}\left\lfloor \dfrac{{q}^{n}-1}{{L}_{z}+1}\right\rfloor ,{q}^{k},{L}_{z},{q}^{n-k}\right) $	1	$ 2\leq {L}_{z}\leq \left\lfloor \dfrac{{q}^{n}-1}{2}\right\rfloor -1 $	[8]
$ \left(\dfrac{{v}^{n}-1}{l},T,{v}^{n-1},{L}_{z},\left\lceil \dfrac{W}{N}\right\rceil \right) $	1	$ l\|v-1 $，$ n\geq 2 $，$ \gcd (l,n)=1 $，$ k=n-1 $	[9]
$ \left(\dfrac{{q}^{n}-1}{d},\left\lfloor \dfrac{{q}^{n}-1}{d({L}_{z}+1)}\right\rfloor d,{q}^{n-1},{L}_{z},\dfrac{q-1}{d}\right) $	1	$ 2\leq {L}_{z}\leq \left\lfloor \dfrac{{q}^{n}-1}{2d}\right\rfloor -1 $	[10]
$ (qL,qM,qv,1,L-1) $	1	$ q\geq 1 $	[11]
$ (p({p}^{r}-1),{p}^{r-1},{p}^{r},p({p}^{r}-1),\left\lceil \dfrac{L}{{p}^{r}-1}\right\rceil ) $	1	$ r\geq 2 $	[15]
$ (p({p}^{r}-1),{p}^{r},{p}^{r},{p}^{r}-2,p) $	$ {p}^{(k-1)r} $	$ r\geq 2 $，$ p\geq 2 $ $ k\geq 1 $，$ \ell\equiv 1 \left(\mathrm{mod}k\right) $$ \gcd (\ell,k)=1 $	本文

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