The high-frequency segment (10-66 GHz) of the IEEE 802.16 standard seems promising for the implementation of wireless backhaul networks carrying large volumes of Internet traffic. In contrast to wireline backbone networks, where channel errors seldom occur, the TCP protocol in IEEE 802.16 Worldwide Interoperability for Microwave Access networks is conditioned exclusively by wireless channel impairments rather than by congestion. This renders a cross-layer design approach between the transport and physical layers more appropriate during fading periods. In this paper, an adaptive coding and modulation (ACM) scheme for TCP throughput maximization is presented. In the current approach, Internet traffic is modulated and coded employing an adaptive scheme that is mathematically equivalent to the replicator dynamics model. The stability of the proposed ACM scheme is proven, and the dependence of the speed of convergence on various physical-layer parameters is investigated. It is also shown that convergence to the strategy that maximizes TCP throughput may be further accelerated by increasing the amount of information from the physical layer.