This article investigates the issue of radio resource allocation strategies for cognitive networks based on the underlay approach, while adhering to the interference constraint on the primary user. Joint rate and power allocation problem is considered for secondary users (SUs) with homogeneous and heterogenous traffic subject to the QoS and interference threshold constraints. Two well-known fairness approaches [max-min and proportional fairness (PF)] are compared for the proposed optimization problem. Three scenarios are considered. The first scenario corresponds to elastic traffic in which all the SUs are elastic users. In the second, it is assumed that all the SUs are streaming users. Considering the proportional and max min fairness, it is observed that for both fairness criterion the streaming users achieving higher throughput and fairness, compared with the elastic users due to the fact that for streaming users, stringent transmission rate guarantees are necessary to ensure real-time communication. Moreover, considering the requirements of future wireless networks, a cross-layer resource-allocation is proposed for heterogeneous traffic in the third scenario. A combination of streaming traffic (which requires a maximum guaranteed average delay) and elastic traffic (with flexible rate requirements) is investigated. The optimization problem allocates the available resources to the streaming users such that the delay constraints of the streaming users are satisfied. Through extensive simulations, the effect of streaming traffic, Interference threshold, minimum processing gain, imperfect channel state information and signal-to-interference-noise ratio constraint on the total throughput of elastic users are investigated. Simulation results demonstrate that in all scenarios PF outperforms max min fairness. Furthermore, it is shown that increasing the number of streaming traffic results in lower throughput of elastic users for both PF and max min fairness.