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A new measurement method for through-the-wall detection of life signs is proposed hereinafter. The method analyzes the phase modulation that a sinusoidal signal, generated by means of a proper continuous-wave microwave transceiver, undergoes when reflected by the chest periodic displacement associated with breathing. It takes advantage of a suitable spatial smoothing decorrelation strategy applied to the traditional algorithm for MUltiple SIgnal Classification (MUSIC), mandated to single out the spectral components of the received phase signal. With respect to other measurement solutions, already available in the literature and exploiting either the traditional discrete-time Fourier transform, or matched filters, or standard singular value decomposition, the proposed method assures competitive performance in detecting the respiratory activity from the received microwave signal and effective noise/clutter rejection. The results of several tests both in simulated and actual scenarios, i.e., people behind walls in a furnished room, prove the efficacy and reliability of the method also in the presence of critical measurement conditions such as low signal-to-noise ratios and chest displacement associated with shallow breathing.