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New methods for estimating the autocorrelation function (acf) of a complex Gaussian stationary process are presented. These methods are based on a general invariance property for the autocorrelation of a common class of the above processes. This property suggests estimation procedures based on magnitude hard limiting and phase quantization. The procedures are an extension of the relay estimator, currently employed for real processes. The computational cost and the general properties of the methods are discussed. In particular, some estimators especially suited for very simple implementations are considered. The performance of the complex hybrid sign estimator is evaluated and compared to that of the classical Direct estimator. The proposed methods are attractive for many applications in the field of digital signal processing.