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Multi-rate multi-channel multi-radio wireless mesh networks (WMNs) have emerged as the next generation wireless mesh communications due to the availability of cheap, off-the-shelf IEEE 802.11 hardware. However, in a multi-rate IEEE 802.11 network, transmission over low rate links consumes disproportionally more time and resources as compared to that of high rate links. This performance anomaly occurs as a result of interference between low and high rate links as the overall throughput is reduced by the low rate links. Multiple non-overlapping channels can be used to reduce interference by using nodes (mesh routers) to communicate over distinct channels based on their respective data rates. In this paper, a Mesh-based Data Rate-Aware Channel Assignment (MesDRCA) algorithm is introduced to improve network capacity in IEEE 802.11 based multi-rate WMNs. The main idea of MesDRCA is to assign links having identical or comparable data rates on a common channel in order to minimize usage of channel resources. This reduces interference due to multi-rate links, thus improving throughput performance. Results obtained through extensive simulations show that MesDRCA gives better performance in terms of packet delivery ratio and aggregate network throughput over an existing channel assignment scheme.