— Throughput maximization in a packet switched wireless communication system is considered in this paper. The channel variation is accounted for by modeling the channel as a finite state Markov channel. To maximize the throughput, rate adaptation is performed based on a single bit acknowledgement feedback. In general, when the window of packets considered is large, obtaining a global optimal rate adaptation solution is computationally difficult. A successive rate adaptation is derived which we show is necessarily sub-optimal by relating it to the optimal solution. This is complemented by a particle filter that is used to estimate the a posterior distribution of the channel. Numerical results illustrate that significant throughput can be recovered for slowly varying channels.