In some diseases (sleep apnea, sudden infant death syndrome etc.), continuous monitoring of respiration rate of patient at home during sleep is critically important. Nowadays wireless communications signals are widely used in our homes. In this paper, we propose a contactless respiration monitoring system which uses only ambient wireless communications signals to estimate the respiration rate of a person. Laboratory experiments show that the strentgh of the received radio frequency (RF) signals changes due to inhaling/exhaling of a person between the propagation path of the transmitter and the receiver. In this study, a subspace based MUSIC algorithm is proposed to estimate the respiration rate of a person using ambient wireless signals. It is shown in various laboratory experiments, where real data is collected with software defined radios, the MUSIC algorithm can successfully estimate the respiration rate with minimum error compared to the FFT-based Maximum Likelihood Estimation (MLE) approach.