Cognitive relay network is a spectrum dynamic paradigm that exploits the unused portions of the licensed spectrum. This is based on merging both cooperative relaying techniques and cognitive radio network to achieve spectrum efficiency and enhance the overall system performance. In this paper, the presence of mobile users at the destination node is considered. Here, the end users can navigate at relatively fast vehicular velocities causing dynamic multipath fading and high Doppler shift. which can be fairly modeled using Nakagami−𝑚 fading channel (i.e., 𝑚 < 1). In a spectrum scarcity environment, a secondary user must deploy an optimal power allocation policy to get higher transmission rates while the overall interference affecting the primary user (PU) is kept below a certain threshold value. In particular, the outage probability performance is studied over the mixed Rayleigh and Nakagami−𝑚 fading channels for different scenarios based on the statistical characteristics of signal-to-noise ratio. The first scenario is the cognitive dual hop amplify and forward relay network over independent and non-identical (i.n.i.d) distributed mixed fading channels. In the second scenario, the cognitive relay network consists of a single amplify and forward relay in addition to the direct link transmission with a selection combining at the destination over i.n.i.d distributed mixed fading channels. Numerical results are presented to evaluate the impact of the fading parameter, 𝑚, the maximum aggregated intrusion constraint, and the locations of the primary users (PUs) on different channel scenarios at high vehicular speeds.