We report a novel and robust non-contact vital signs (NCVS) sensor system capable of accurately monitoring the breathing rates (BR) of a human subject up to 1.8 m away. The NCVS sensor system is designed using an SDR (software defined radio) technology with a commercially available NI-2901 2-Channel SDR box that can operate from 70 MHz to 6 GHz, along with low-cost log-periodic dipole antennas (LPDA) and LabVIEW programming for signal processing to extract real-time vital signs data by direct-downconversion (i.e., zero-IF receiver). Statistical analysis of a large number of NCVS datasets shows the breathing rate readings are accurate, and consistently within 1 BPM (Breath-per-Minute) vs. data obtained from contact-based respiration belt. The experimental results validate the attractiveness and feasibility of this SDR-enabled NCVS sensor system for continuous remote monitoring of human BR for potential clinical and telemedicine applications. This work, to our best knowledge, reports and demonstrates the world's first robust SDR-based zero-IF non-contact respiration monitor.