In this paper we present an autocorrelation-based method for estimating the carrier frequency offset of an MPSK signal with random data modulation. Although autocorrelation-based techniques imply heavy usage of hardware resources, this technique is scalable and lends itself well to systolic VLSI implementations. The performance of the open-loop estimator presented is close to the Cramer-Rao lower bound (CRLB) for the frequency estimation from a block of random PSK symbols at low signal-to-noise (SNR) ratios. The estimator can be used in frequency acquisition of burst and continuous modems operating under low SNR and large frequency offset conditions. This paper has been submitted to 33rd Annual Conference on InformationSciences and Systems, March 17-19, 1999, John Hopkins University,Baltimore, Md.</I