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Heterogeneous wireless networks give rise to a multi-radio access environment which becomes crucial for load balancing to avoid network congestion and providing high quality services to maximize radio resource utilization. To this end, a joint power and bandwidth allocation with QoS support algorithm is proposed using convex optimization method in this letter. The algorithm achieves the goal of the total system capacity maximization, while efficiently satisfying the minimum rate constraint of delay-constraint service traffic and proportional fairness of best-effort service traffic. The simulation results show that the proposed algorithm significantly outperforms the existing scheme in QoS guarantee.