A real demand for underwater acoustic (UWA) communications exists in oceanography, ocean exploration and undersea navigation. A new Doppler resilient digital communication, based on quadratic frequency modulations (QFM) is presented. The binary information is transmitted using two orthogonal QFM chirps. This signal modulation is suitable for low-data-rate communication such as telemetry. The first motivation of this paper resides in the performance of the non-coherent detector for binary QFM signal detection. It is shown that for some spreading factors, the detection of QFM signal waveform gives better performance than a linear frequency modulation (LFM) signal waveform in terms of bit error rate. The second motivation is that the non-coherent receiver is more Doppler resilient for QFM waveforms than LFM. An analytical demonstration is given, which predicts the simulated results. Real underwater commutations were accomplished on the Atlantic Ocean on February 2015.