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A data-aided feedforward algorithm has been proposed by Kuo and Fitz (see IEEE Trans. Commun., vol.45, p.1412-26, 1997) for carrier frequency estimation in M-ary phase-shift keying (PSK) transmissions over frequency-flat Rayleigh fading channels. Its accuracy is very good but the estimation range may be limited under certain operating conditions. Also, its application requires a knowledge of the Doppler bandwidth. We show that the estimation range can be greatly extended without sacrificing the estimation accuracy and a simple technique is indicated to measure the Doppler bandwidth. This allows the algorithm to operate in an adaptive manner in a time-varying environment.