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In recent years, cognitive radio technology (CR) has been proposed to allow unlicensed secondary users (SUs) to opportunistically access the channels unused by primary users. As a result, there is a lot of recent interests on studying cognitive radio cellular networks (CogCells) that can support both PUs and SUs. Due to the limited transmission range of SUs, in this work we consider supporting Multi-hop infrastructure-based secondary systems (SSs), where SUs can communicate with the BS over multiple hops. The use of SSs improves the reliability and coverage compared to its single-hop counterpart. In addition, SUs are allowed to access multiple channels, which helps to increase transmission reliability and coverage and relieve interference at PUs. To enable multi-hop secondary transmissions, it is also important to support efficient routing. In CogCells, efficient admission control, channel assignment and routing is crucial for the coverage optimization of SSs and to ensure the QoS requirements in CogCells. In this paper, we mathematically formulate the problem of joint admission control, channel assignment and QoS routing to maximize the coverage of SUs in a CogCell system that supports multi-hop secondary transmissions, taking into account the interference constraints and QoS requirements from the PUs and admitted SUs. To our best knowledge, this is the first study that attempts to optimize the coverage of SUs in multi-hop CogCells with the concurrent support of the above three important procedures. We show that the problem is NP-hard and propose three different algorithms to solve the coverage optimization problem and give the theoretical analyses of its performances in terms of approximation ratio to the optimum. Our solutions include a greedy heuristic approximation scheme, an algorithm that can provide exact solution, and a new approximation solution with a poly-logarithmic approximation ratio guarantee, e.g., the performance of our algorithm is within a poly-l- - ogarithmic factor of that of any optimal algorithm for the problem. Our preliminary simulation results indicate that our new approximation algorithms can effectively exploit the increased number of SUs and channels, and performs much better than the theoretical worst case bound.