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Cognitive radio is a novel paradigm that can substantially improve the efficiency of radio spectrum utilization. In this paper, we investigate the outage performance analysis of an amplify-and-forward (AF) relay cooperative network where the relays are equipped with cognitive radios. We consider a space-time-division (STD) protocol based on a distributed extended orthogonal space-time-block-coded (D-EO-STBC) scheme and provide a closed-form expression for outage probability, both with perfect and imperfect spectrum acquisition in Rayleigh fading channels. Simulations show that the new scheme provides better outage performance than the conventional schemes based on a time-division (TD) protocol. The analytical outage probability expressions are finally validated through simulations.