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Wireless Mesh Networks (WMNs) have emerged to provide cost-effective broadband Internet accesses. Today's IEEE 802.11 PHY and MAC specifications support multi-channel and multi-rate capabilities. Designing an efficient channel assignment protocol utilizing available channels and data rates is a hot issue to leverage the network capacity. In multi-rate networks, low-rate links severely decrease the capacity of high-rate links, known as performance anomaly. In this paper, we design a Cooperative Channel Assignment (CoCA) protocol to address the performance anomaly in WMNs. For the channel assignment of family architecture, CoCA utilizes the Estimated Delivery Time (EDT) metric and the balancing algorithm. With the EDT metric, CoCA separates different rate links via multiple channels. By using the balancing algorithm, CoCA also increases throughput fairness. Our simulation results show that CoCA outperforms the existing well-known channel assignment protocols for WMNs.