In recent years, checking sleep quality has become essential from a healthcare perspective. In this paper, we propose a respiratory rate (RR) monitoring system that can be used in the bedroom without wearing any sensor devices directly. To develop the system, passive radio-frequency identification (RFID) tags are introduced and attached to a blanket, instead of attaching them to the human body. The received signal strength indicator (RSSI) and phase values of the passive RFID tags are continuously obtained using an RFID reader through antennas located at the bedside. The RSSI and phase values change depending on the respiration of the person wearing the blanket. Thus, we can estimate the RR using these values. After providing an overview of the proposed system, the RR estimation flow is explained in detail. The processing flow includes noise elimination and irregular breathing period estimation methods. The evaluation demonstrates that the proposed system can estimate the RR and respiratory status without considering the user's body posture, body type, gender, or change in the RR.