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The performances of several signal-to noise ratio (SNR) estimation techniques reported in the literature are compared to identify the "best" estimator. The SNR estimators are investigated by the computer simulation of baseband binary phase-shift keying (PSK) signals in real additive white Gaussian noise (AWGN) and baseband 8-PSK signals in complex AWGN. The mean square error is used as a measure of performance. In addition to comparing the relative performances, the absolute levels of performance are also established; the simulated performances are compared to a published Cramer-Rao bound (CRB) for real AWGN and a CRB for complex AWGN that is derived here. Some known estimator structures are modified to perform better on the channel of interest. Estimator structures for both real and complex channels are examined.