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

TIAN Xinyu; CHEN Xiaoyu; ZHANG Jitao

doi:10.11999/JEIT260343

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TIAN Xinyu, CHEN Xiaoyu, ZHANG Jitao. Construction and Performance Analysis of Optimal Low-Hit-Zone Frequency Hopping Sequence Sets[J]. Journal of Electronics & Information Technology. doi: 10.11999/JEIT260343

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TIAN Xinyu, CHEN Xiaoyu, ZHANG Jitao. Construction and Performance Analysis of Optimal Low-Hit-Zone Frequency Hopping Sequence Sets[J]. Journal of Electronics & Information Technology. doi: 10.11999/JEIT260343

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

doi: 10.11999/JEIT260343 cstr: 32379.14.JEIT260343

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)

Received Date: 2026-03-22
Accepted Date: 2026-06-29
Rev Recd Date: 2026-06-29

Available Online: 2026-07-11

Abstract

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)

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References(19)

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