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In this paper, we study cooperative transmissions over CR relay networks with imperfect spectrum sensing. More specifically, we formulate the CR relay selection problem as a partially observable Markov decision process. By integrating the spectrum sensing at physical layer, the spectrum access protocols at medium access control layer, as well as the concept of effective capacity at data-link layer, our proposed scheme aims at maximizing the supported arrival-rate subject to a given statistical delay QoS constraint from a cross-layer design perspective. Simulation results are presented to demonstrate the effectiveness of the proposed scheme.