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Cognitive Radio (CR) networks allow users to opportunistically transmit in the licensed spectrum bands, as long as the performance of the Primary Users (PUs) of the band is not degraded. Consequently, variation in spectrum availability with time and periodic spectrum sensing undertaken by the CR users have a pronounced effect on the higher layer protocol performance, such as at the transport layer. This paper investigates the limitations of classical TCP newReno in a CR ad hoc network environment, and proposes TCP CRAHN, a window-based TCP-friendly protocol. Our approach incorporates spectrum awareness by a combination of explicit feedback from the intermediate nodes and the destination. This is achieved by adapting the classical TCP rate control algorithm running at the source to closely interact with the physical layer channel information, the link layer functions of spectrum sensing and buffer management, and a predictive mobility framework that is developed at the network layer. An analysis of the expected throughput in TCP CRAHN is provided, and simulation results reveal significant improvements by using our approach. To the best of our knowledge, our approach takes the first steps toward the design of a transport layer for CR ad hoc networks.