The communication process for high-sensitivity and synchronous demodulation signals between a transmitter (2) and a receiver (3) comprises a first synchronisation phase followed by a modulation and demodulation phase of the data. To achieve this, the transmitter transmits a pseudo-periodic chirp signal to the receiver, where a frequency conversion of the chirp signal is performed in a mixer (33) by an oscillating signal (So) at constant frequency of a local oscillator (34) to supply an intermediate signal, which is filtered and sampled for a logic unit (37). An assembly (38) of m pairs DFT blocks phase-shifted in relation to one another and operating in parallel is provided in the logic unit. A processing unit (39) receives the result of the pairs of the assembly to determine frequency and phase errors between the transmitter and the receiver on the basis of two peaks detected by one of the pairs above a threshold to synchronise the receiver.