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This study investigates the performance of a cognitive amplify-and-forward (AF) relay network over composite asymmetric multipath/shadowing fading channels, whereby a new power allocation method is adopted at the secondary source and relay, assuming the mean-value interference channel. To quantify the performance of the proposed structure, closed-form outage probability and ergodic capacity expressions are derived. Moreover, asymptotic ergodic capacity analysis is performed to observe the effects of limited feedback and fading/shadowing severity in the system. The analytical results are validated with Monte-Carlo simulations, and they show that the proposed structure can be a realistic scenario for next-generation wireless systems, and a system designer can test the overall performance of the proposed system without dealing with complex prototypes.