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We consider a cognitive relay networks with two source-destination pairs assisted by a cognitive relay such that one of the source-destination pair is a cognitive user (CU), and the other is primary user (PU). Two source-destination (S-D) pairs and cognitive relay share a single common channel instead of waiting for an idle channel which is traditional for a cognitive radio. The cognitive relay receives messages from both sources, and assists them in communicating the messages to their respective destinations. Assuming a slotted-system operating in a half-duplex mode, we propose relaying schemes using "amplify-and-forward" (AF). We examine the lower bound of achievable rate for cognitive user and primary user. For not affecting the communication of the primary user, we characterize the power allocation of cognitive user and cognitive relay by imposing constraints on the transmission power of cognitive user and cognitive relay, so that they operate below the noise floor of primary user. Rate of cognitive radio user can be enhanced by optimizing the power allocation of cognitive user and cognitive relay.