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Keywords = no-hit zone

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10 pages, 1357 KB  
Article
Design of Balanced Wide Gap No-Hit Zone Sequences with Optimal Auto-Correlation
by Duehee Lee, Seho Lee and Jin-Ho Chung
Mathematics 2025, 13(15), 2454; https://doi.org/10.3390/math13152454 - 30 Jul 2025
Viewed by 943
Abstract
Frequency-hopping multiple access is widely adopted to blunt narrow-band jamming and limit spectral disclosure in cyber–physical systems, yet its practical resilience depends on three sequence-level properties. First, balancedness guarantees that every carrier is occupied equally often, removing spectral peaks that a jammer or [...] Read more.
Frequency-hopping multiple access is widely adopted to blunt narrow-band jamming and limit spectral disclosure in cyber–physical systems, yet its practical resilience depends on three sequence-level properties. First, balancedness guarantees that every carrier is occupied equally often, removing spectral peaks that a jammer or energy detector could exploit. Second, a wide gap between successive hops forces any interferer to re-tune after corrupting at most one symbol, thereby containing error bursts. Third, a no-hit zone (NHZ) window with a zero pairwise Hamming correlation eliminates user collisions and self-interference when chip-level timing offsets fall inside the window. This work introduces an algebraic construction that meets the full set of requirements in a single framework. By threading a permutation over an integer ring and partitioning the period into congruent sub-blocks tied to the desired NHZ width, we generate balanced wide gap no-hit zone frequency-hopping (WG-NHZ FH) sequence sets. Analytical proofs show that (i) each sequence achieves the Lempel–Greenberger bound for auto-correlation, (ii) the family and zone sizes satisfy the Ye–Fan bound with equality, (iii) the hop-to-hop distance satisfies a provable WG condition, and (iv) balancedness holds exactly for every carrier frequency. Full article
(This article belongs to the Special Issue Mathematical Modeling and Analysis for the Security and Privacy of Cyber–Physical Systems (CPSs))
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17 pages, 1697 KB  
Article
Block-Cipher No-Hit-Zone Sequence-Assisted Spectrum Control Scheme for Distributed Systems
by Wendong Gao, Lei Guan, Pei Hui, Hanwen Zhang and Zan Li
Electronics 2025, 14(9), 1802; https://doi.org/10.3390/electronics14091802 - 28 Apr 2025
Cited by 1 | Viewed by 832
Abstract
In distributed systems, the dense access of wireless devices introduces significant challenges, including severe quasi-synchronous multiple access interference (MAI) and transmission security threats, which limit the effectiveness of traditional orthogonality-based spectrum control schemes. To address these challenges, this paper proposes a new block-cipher [...] Read more.
In distributed systems, the dense access of wireless devices introduces significant challenges, including severe quasi-synchronous multiple access interference (MAI) and transmission security threats, which limit the effectiveness of traditional orthogonality-based spectrum control schemes. To address these challenges, this paper proposes a new block-cipher no-hit-zone (BC-NHZ) sequence-assisted spectrum control transmission scheme, aimed at enhancing privacy protection and improving overall communication capacity for distributed systems. The BC-NHZ scheme employs block cipher encryption and establishes control sequences to represent the spectrum usage scheme. Moreover, we mathematically prove that the parameters of the BC-NHZ scheme achieve optimal results with respect to the bound of the Hamming correlation. Numerical analysis and simulation results validate the practical feasibility of the BC-NHZ scheme, demonstrating its reliability to relax synchronous requirements while providing enhanced transmission privacy protection performance. Full article
(This article belongs to the Special Issue Security and Privacy in Distributed Machine Learning)
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