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Adv. Signal Process."],"abstract":"<jats:title>Abstract<\/jats:title><jats:p>Real-time Doppler estimation of sonar signals is of great significance to underwater communication and detection. The Hyperbolic-Frequency-Modulated (HFM) waveform-based speed spectrum estimation is one of the modern methods for underwater Doppler estimation, and this paper presents a detailed analyses of the derivation and the performance of this method. The analyzing results show the robustness of the method on multipath channels and multi-highlight targets and provide the main lobe width of the speed spectrum. Moreover, the paper examines the spectral properties of the HFM signal from the frequency-domain Doppler invariance property, which could provide insights for better understanding and utilization of this Doppler invariant waveform.<\/jats:p>","DOI":"10.1186\/s13634-022-00964-2","type":"journal-article","created":{"date-parts":[[2022,12,28]],"date-time":"2022-12-28T14:10:53Z","timestamp":1672236653000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Performance analysis on the speed spectrum estimation based on dual-HFM waveform"],"prefix":"10.1186","volume":"2022","author":[{"given":"Runyu","family":"Wei","sequence":"first","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0001-7223-4656","authenticated-orcid":false,"given":"Xuan","family":"Li","sequence":"additional","affiliation":[]},{"given":"Yubin","family":"Fu","sequence":"additional","affiliation":[]},{"given":"Xiaochuan","family":"Ma","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2022,12,28]]},"reference":[{"issue":"1","key":"964_CR1","doi-asserted-by":"publisher","first-page":"100","DOI":"10.1109\/48.289455","volume":"19","author":"M Stojanovic","year":"1994","unstructured":"M. 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