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In this paper, we first explore a selective cooperation framework for secondary user transmissions in a cognitive radio network with single relay. In the selective cooperation framework, two transmission modes (i.e., relay diversity transmission and non-relay direct transmission) are considered. We study two specific selective cooperation schemes with and without an acknowledgement (ACK) from a cognitive destination as to if it succeeds in decoding or not, called ACK and non-ACK based selective cooperation, respectively. We derive closed-form outage probability expressions for the two schemes with imperfect spectrum sensing, showing that an outage probability floor occurs in high signal-to-noise ratio (SNR) regions due to mutual interference between primary and secondary users. We consider the use of the outage probability floor to generalize the traditional diversity-multiplexing tradeoff (DMT) definition, based on which a DMT analysis is conducted for the non-ACK and ACK based selective cooperation schemes. We then extend the selective cooperation framework to a multiple-relay cognitive radio network considering the best cognitive relay only to participate in assisting secondary transmissions, referred to as the selective best-relay cooperation. We also consider the non-ACK and ACK based selective best-relay cooperation schemes and develop their DMTs by using the generalized DMT definition.