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To combat the detrimental effects of the variability in wireless channels, we consider cross-layer rate adaptation based on limited feedback. In particular, based on limited feedback in the form of link-layer acknowledgements (ACK) and negative acknowledgements (NAK), we maximize the physical-layer transmission rate subject to an upper bound on the expected packet error rate. We take a robust approach in that we do not assume any particular prior distribution on the channel state. We first analyze the fundamental limitations of such systems and derive an upper bound on the achievable rate for signaling schemes based on uncoded QAM and random Gaussian ensembles. We show that, for channel estimation based on binary ACK/NAK feedback, it may be preferable to use a separate training sequence at high error rates, rather than to exploit low-error-rate data packets themselves. We also develop an adaptive recursive estimator, which is provably asymptotically optimal and asymptotically efficient.