Cognitive radio (CR) technology is a revolutionary wireless communication paradigm that targets at the efficient and flexible utilization of the limited radio spectrum resource. This paper considers a spectrum underlay CR system operating in a fading environment, where the secondary users (SUs) have specific communication quality requirements. In this system, the unlicenced SUs may coexist with the licenced primary users, as long as the average interference‐power that they cause to the primary users does not exceed a threshold value.The concept of spatial correlation (cross‐correlation) of Nakagami‐m fading channels is introduced in the quality of service‐driven CR system. Specifically, we present a power allocation scheme that aims at maximising the SU's effective capacity, and we study the effects of the spatial channel correlation on the performance of the proposed scheme. In order to investigate thoroughly the impact of fading correlation, two different scenarios are studied, depending on which links are considered correlated, the receive correlation model and the transmit correlation model. The performance of the proposed allocation scheme is evaluated through simulations. Finally, the effects of spatial channel correlation for different system requirements and scenarios are presented and discussed. Copyright © 2013 John Wiley & Sons, Ltd.