Relay selection is a simple technique that achieves spatial diversity in cooperative relay networks. Generally, relay selection algorithms require channel state information (CSI) feedback from all cooperating relays to make a selection decision. This requirement poses two important challenges, which are often neglected in the literature. Firstly, the fed back channel information is usually corrupted by additive noise. Secondly, CSI feedback generates a great deal of feedback overhead (air-time) that could result in significant performance hits. In this paper, we propose a compressive sensing (CS) based relay selection algorithm that reduces the feedback overhead of relay networks under the assumption of noisy feedback channels. The proposed algorithm exploits CS to first obtain the identity of a set of relays with favorable channel conditions. Following that, the CSI of the identified relays is estimated using least squares estimation without any additional feedback. Both single and multiple relay selection cases are considered. After deriving closed-form expressions for the asymptotic end-to-end SNR at the destination and the feedback load for different relaying protocols, we show that CS-based selection drastically reduces the feedback load and achieves a rate close to that obtained by selection algorithms with dedicated error-free feedback. © 1972-2012 IEEE.