Non-contact wireless sensing approaches have emerged in recent years, in order to enable novel enhanced developments in the framework of healthcare and biomedical scenarios. One of these technologically advanced solutions is given by software-defined radar platforms, a low-cost radar implementation, where all operations are implemented and easily changed via software. In the present paper, a software-defined radar implementation with Doppler elaboration features is presented, to be applied for the non-contact monitoring of human respiration signals. A quadrature receiver I/Q (In-phase/Quadrature) architecture is adopted in order to overcome the critical issues related to the occurrences of null detection points, while the phase-locked loop components included in the software defined radio transceiver are successfully exploited to guarantee the phase correlation between I/Q signal components. The proposed approach leads to a compact, low-cost, and flexible radar solution, whose application abilities may be simply changed via software, with no need for hardware modifications. Experimental results on a human target are discussed so as to demonstrate the feasibility of the proposed approach for vital signs detection.