This paper studies resource allocation for a multi-carrier based cognitive radio network under the assumption of statistical channel state information (CSI). To circumvent the inherent high computational complexity investigating the joint power-rate-subcarrier of the outage-constrained sum rate maximization problem, we adopt a sub-optimal strategy by solving independently the subcarrier and power-rate problem. Firstly, we propose a heuristic subcarrier allocation paradigm by utilizing an outage-based metric. Secondly, we conservatively approximate the intractable non-convex power- rate control problem and propose a sequential-based algorithm to efficiently obtain a solution to the problem.The proposed algorithm has been shown to converge to solutions that are stationary points of the original power-rate problem. Extensive simulation results are provided to demonstrate the efficiency of our proposed algorithm