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This letter proposes a joint channel estimation and Schmidl & Cox synchronization for the orthogonal chirp-division multiplexing (OCDM) scheme. First, it is proven that a symbol composed of two identical halves in the Fresnel domain has two identical halves in the time domain, which is required by the considered synchronization technique. In sequel, a Fresnel-domain pilot symbol that enables joint channel estimation and synchronization is proposed, allowing overhead reduction and hence higher data rates. Finally, measurement and simulation results validate the obtained findings for both passband and baseband OCDM schemes.