{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,18]],"date-time":"2026-08-18T05:08:45Z","timestamp":1787029725545,"version":"build-2736575974"},"reference-count":30,"publisher":"MDPI AG","issue":"12","license":[{"start":{"date-parts":[[2026,6,11]],"date-time":"2026-06-11T00:00:00Z","timestamp":1781136000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100012456","name":"National Social Science Foundation of China","doi-asserted-by":"crossref","award":["2025-SKJJ-D-036"],"award-info":[{"award-number":["2025-SKJJ-D-036"]}],"id":[{"id":"10.13039\/501100012456","id-type":"DOI","asserted-by":"crossref"}]},{"name":"Natural Science Foundation of Hubei Province of China","award":["2025AFB419"],"award-info":[{"award-number":["2025AFB419"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>To further enhance the covert communication capability of satellite\u2013ground-integrated sensor networks, a dual-polarization constellation joint modulation scheme based on frequency-hopping double-layer multi-parameter weighted fractional Fourier transform (FH-DL-MPWFRFT) is proposed from the perspective of physical layer security. The proposed scheme integrates the constellation confusion property of weighted fractional Fourier transform (WFRFT) with the anti-interception capability of frequency-hopping (FH) phase scrambling. Specifically, the weighted parameters of conventional 4-WFRFT are extended to construct a multi-parameter and multi-layer signal representation, and FH phase scrambling is introduced to realize dynamic constellation rotation and phase-domain encryption. Furthermore, a secure transmission model for satellite\u2013ground-integrated sensor networks is established, revealing the constellation optimization principle and the fission-fusion mechanism of dual-polarization signals. Simulation results show that, compared with the non-FH benchmark, the proposed scheme significantly improves waveform-level anti-interception performance; even when eavesdropper obtains the modulation scheme and partial transform parameters, the symbol error rate (SER) of quadrature phase shift keying (QPSK) and four-phase modulation (4PM) signals remains around 0.4 to 0.5 under parameter mismatch, indicating that effective demodulation is difficult to achieve.<\/jats:p>","DOI":"10.3390\/s26123716","type":"journal-article","created":{"date-parts":[[2026,6,11]],"date-time":"2026-06-11T12:14:58Z","timestamp":1781180098000},"page":"3716","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Research on Covert Communication in Satellite\u2013Ground-Integrated Sensor Networks Based on FH-DL-MPWFRFT"],"prefix":"10.3390","volume":"26","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-7307-2599","authenticated-orcid":false,"given":"Lei","family":"Ni","sequence":"first","affiliation":[{"name":"Early Warning Intelligence Department, Air Force Early Warning Academy, Wuhan 430019, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Yichao","family":"Cai","sequence":"additional","affiliation":[{"name":"Early Warning Intelligence Department, Air Force Early Warning Academy, Wuhan 430019, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Xiaobai","family":"Li","sequence":"additional","affiliation":[{"name":"Early Warning Intelligence Department, Air Force Early Warning Academy, Wuhan 430019, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Hang","family":"Hu","sequence":"additional","affiliation":[{"name":"College of Information and Navigation, Air Force Engineering University, Xi\u2019an 710077, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Zheng","family":"Chu","sequence":"additional","affiliation":[{"name":"Next-Generation Internet of Everything Laboratory, Department of Electrical and Electronic Engineering, University of Nottingham Ningbo China, Ningbo 315100, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0009-0004-2445-4119","authenticated-orcid":false,"given":"Yuzhi","family":"Qi","sequence":"additional","affiliation":[{"name":"Early Warning Intelligence Department, Air Force Early Warning Academy, Wuhan 430019, China"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2026,6,11]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Li, W., Li, L., and Zhu, L. 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