A GSM communication system uses a channel estimator to generate a channel impulse response estimate from received bursts. Preferred embodiments of such a system include a first correlation unit that uses N midamble bits to evaluate received signals and produce first correlation outputs over a wide search range. A positioning unit identifies candidate first correlation outputs having the best estimation quality within a sliding observation window and uses those outputs as the initial channel impulse response (CIR) estimate. The initial CIR is provided to a second correlation unit that block correlates M (greater than N) midamble bits to the received signal samples. The second correlation unit performs correlation stage by stage with compensation based on the initial and updated CIR to improve the channel estimation.