In Cognitive Radio (CR) ad hoc networks, secondary users (SU) attempt to utilize valuable spectral resources without causing significant interference to licensed primary users (PU). While there is a large body of research on spectrum opportunity detection, exploitation, and adaptive transmission in CR, most existing approaches focus only on avoiding PU activity when making sensing decisions. Since the myopic sensing strategy results in congestion and poor throughput, several collision-avoidance sensing approaches were investigated in the literature. However, they provide limited improvement. A channel-aware myopic sensing strategy that adapts the reward to the fading channel state information (CSI) of the SU link is proposed. This CSI varies over the CR spectrum and from one SU pair to another due to multipath and shadow fading, thus randomizing sensing decisions and increasing the network throughput. The proposed joint CSI adaptation at the medium access control (MAC) and physical layers provides large throughput gain over randomized sensing strategies and/or conventional adaptive transmission methods. The performance of the proposed CSI-aided sensing strategy is validated for practical network scenarios and demonstrated to be robust to CSI mismatch, sensing errors, and spatial channel correlation.