In this paper, the effective capacity, a link-layer model supporting Quality of Service (QoS) metrics such as user data rate, packet loss rate and service delay, is analyzed. We consider an underlay cognitive cooperative relay network (CCRN) subject to independent non-identically distributed aH fading. An analytical expression of the effective capacity is derived by means of Fox H-functions and Meijer G-functions along with the Mellin transform of the product of two H-functions. The network performance is analyzed against the QoS exponent and the peak interference power constraint imposed by primary users.