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In this work, we propose a signal processing technique for beam-steering radar architectures allowing concurrent two-dimensional (2-D) localization and vital signs monitoring of human subjects. We demonstrated it by using a single-input single-output (SISO) frequencymodulated continuous wave (FMCW) radar which integrates two frequency-scanning antennas (FSAs). This method is capable of isolating the Doppler signal generated by each single subject from the contributions of all the reflections in the monitored environment. This allows determining the number of individuals in the room and accurately measuring their vital signs parameters (respiration and heart rates) and 2-D positions (range and azimuth information). The spectral analysis, the data matrix generation and the signal processing technique are detailed and discussed. Experimental results demonstrated the feasibility of the proposed approach, showing the ability in determining the number of subjects present in the room, in accurately measuring and tracking over time their vital signs parameters, and in 2-D localization with errors within the limits of the radar range and angular resolutions. Practical applications arise for healthcare, Hospital 4.0, Internet of Medical Things (IoMT), ambient assisted living, smart buildings and through-wall sensing.