Continuous monitoring of respiratory rate (cycle) during sleep for diseases such as sleep apnea and sudden infant death syndrome (SIDS) can be lifesaving. Wireless radio communications signals are everywhere and can be harnessed for contactless monitoring of the respiratory rates.The amplitude of the received signal strength changes periodically depending on the exhalation and inhalation of the subject. In this paper, subspace-based multiple signal classification (MUSIC) algorithm is applied to estimate the respiratory rate for better results. The proposed method and the other power spectral density (PSD) methods for respiratory estimations are compared with the real laboratory measurements. It is demonstrated that the proposed method estimates the respiratory rate with high accuracy and outperforms the other PSD-based methods which are commonly used in the literature.