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Since the IEEE 802.11 standard supports multiple data rates at the physical layer, many rate adaptation mechanisms have been proposed to utilize this multi-rate capability by dynamically switching rates in response to different channel conditions. In IEEE 802.11b networks, the guarantee of an equal transmission opportunity for all participating nodes results in performance anomaly. Traditional solutions have some limitations when solving performance anomaly, especially when dealing with multi-hop networks. Competition in ad hoc networks usually occurs between multi-hop paths. However, competitive nodes' data rates could not reflect the whole competitive paths' rate information. In this paper, we propose a new cross-layer MAC mechanism, which allows nodes acquire the whole path's rate information by exchanging information between MAC and Routing layer. We estimate each path's competitive level, which represents the whole path's data transmission capability, and use it as the criteria for allocating the channel. When collision happens, nodes on the path with higher competitive level have a more time share of channel. We evaluate the performance of our mechanism on the network simulator NS-2. Compared with RBAR, by solving performance anomaly in multi-hop networks, the proposed protocol can increase the aggregate throughput by 5%-15% while decreasing the average end-to-end delay by 30%.