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We consider the samples of a pure tone in additive white Gaussian noise (AWGN) for which we wish to determine the signal-to-noise ratio (SNR) defined here to be α=(A2/2σ2), where A is the tone amplitude, and σ2 is the noise variance. A and σ2 are assumed to be deterministic but unknown a priori. If the variance of an unbiased estimator of α is σαˆ2, we show that at high SNR, the normalized standard a deviation satisfies the Cramer-Rao lower bound (CRLB) according to σαˆ/α≥√(2/N), where N is the number of independent observables used to obtain the SNR estimate σˆ.
Date of Publication: Sep 2002