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In recent years, orthogonal chirp-division multiplexing (OCDM) has been increasingly considered as an alternative multicarrier scheme, e.g., to orthogonal frequency-division multiplexing, in digital communication applications. Among reasons for thar are its demonstrated superior performance resulting from its robustness to impairments such as frequency selectivity of channels and intersymbol interference. Furthermore, the so-called unbiased channel estimation in the discrete-Fresnel domain has also been investigated for both communication and sensing systems, however without considering the effects of frequency shifts. This article investigates the suitability of the aforementioned discrete-Fresnel domain channel estimation in OCDM-based radar systems as an alternative to the correlation-based processing previously adopted, e.g., in the radar-communication (RadCom) literature, which yields high sidelobe level depending on the symbols modulated onto the orthogonal subchirps. In this context, a mathematical formulation for the aforementioned channel estimation approach is introduced. Additionally, extensions to multi-user/multiple-input multiple-output and RadCom operations are proposed. Finally, the performance of the proposed schemes is analyzed, and the presented discussion is supported by simulation and measurement results. In summary, all proposed OCDM-based schemes yield comparable radar sensing performance to their orthogonal frequency-division multiplexing counterpart, while achieving improved peak-to-average power ratio and, in the RadCom case, communication performance.