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In this paper, we discuss a cross-layer design for joint user scheduling and adaptive rate control for downlink wireless transmission. We take a stochastic learning-based approach to achieve this. The scheduling is performed at the medium access control (MAC) layer, whereas the rate selection takes place at the physical/link (PHY/LINK) layer. These two components residing in the two layers exchange information to ensure that user defined rate requests are satisfied by the right combination of transmission schedules and rate selections. The method is highly efficient for low mobility applications with mobile speeds in the order of a few kilometers per hour. While simple to implement, this technique requires no explicit channel estimation phase. The only feedback used are the single bit ACK/NACK signal indicating the correct reception/failure of the packet. As shown in the convergence theorems, the algorithm achieves optimal performance in "stationary" channels. With slowly varying channels, the rate selection algorithm sees a "quasi-stationary" channel and adaptively converges to an optimal solution. Simulations performed using a third-generation wireless system, namely, high-speed downlink packet access (HSDPA) validate the theoretical results.