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Wireless mesh network (WMN) is a promising technology for broadband Internet access due to its low cost, ease of deployment, increased coverage, and robustness. Equipping each mesh router with multiple radios can greatly improve the capacity of WMNs since the radios at each node can simultaneously transmit data on orthogonal channels. Channel assignment is an important problem in multi-radio multi-channel WMNs where the goal is to assign a channel to each radio so that the resulting network topology is connected and the network capacity is maximized. Various channel assignment schemes assume that the number of radios at each node is given, but how this number is determined is not specified. In this work, we propose a joint radio and channel assignment (JRCA) algorithm that determines the number of radios required at each node based on the traffic demand and produces the channel assignment for each radio to minimize the interference among the links operating on the same channel. Thus, our algorithm can produce a network configuration that meets the customer demand and maximize the network capacity. Simulation results show that JRCA can achieve higher throughput with fewer radios at the network nodes, compared to fixed-radio WMNs. In addition to this, we believe that our work, to our best knowledge, is the first of its kind that couples the problem of radio allocation and channel assignment in a joint manner.