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Knowing accurate noise variance and signal power is crucial to most spectrum-sensing algorithms such as energy detection, matched filter detection, and cyclostationary detection. In this paper, we consider a practical scenario when these two parameters are unknown and are needed to be estimated before the spectrum sensing. This task is non-trivial without knowing the status of the primary user, and we categorize the related spectrum sensing as a blind one. We develop the estimation algorithms for unknown parameters by exploiting the signal constellation of the primary user. Three different parameter estimators that do not require any training are then proposed based on the moments of the received signals. Since the secondary user may not know the primary user's signal constellation, we develop a robust approach that approximates a finite quadrature amplitude modulation (QAM) constellation by a continuous uniform distribution. We also derive the modified Cramer-Rao bound (CRB) for noise variance estimation. Then the optimal moment pair is found from minimizing the mean squared error (MSE) of the signal-to-noise ratio (SNR). The method of choosing the spectrum sensing threshold by taking into consideration the estimation error is also discussed.