This paper investigates the power allocation and outage performance of MIMO full-duplex relaying (MFDR), based on orthogonal space-time block codes (OSTBC), in cognitive radio systems. OSTBC transmission is used as a simple means to achieve multi-antenna diversity gain. Cognitive MFDR systems not only have the advantage of increasing spectral efficiency through spectrum sharing, but they can also extend coverage through the use of relays. In cognitive MFDR systems, the primary user experiences interference from the secondary source and relay simultaneously, owing to full duplexing. It is therefore necessary to optimize the transmission powers at the secondary source and relay. In this paper, we propose an optimal power allocation (OPA) scheme based on minimizing the outage probability in cognitive MFDR systems. We also analyse the outage probability of the secondary user in noise-limited and interference-limited environments in Nakagami-m fading channels. Simulation results show that the proposed schemes achieve performance improvements in terms of reducing outage probability.