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In this paper, we study the optimal power allocation of wireless relay nodes which are used in the secondary user (SU) communication of a cognitive radio (CR) network. We consider the behavior of transmitting powers of SUs where those powers are limited to the tolerable interference as seen by the primary user (PU) communication. To improve the performance of the secondary communication based on minimizing the outage probability, we re-formulate the power allocation problem with a new set of constraints. These are obtained by considering the co-channel interference generated by the SU communication to the PU communication. The power allocation problem is solved for both regenerative and non regenerative relay models under Rayleigh fading conditions. SU communication with N number of relays is discussed and compared. The outage probability of SU communication is limited by the interference power threshold (IPT) constraints of PUs and is affected significantly by the IPT levels of PUs.