Spectrum sensing is used in cognitive radio systems to detect the availability of spectrum holes for secondary usage. The simplest and most famous spectrum sensing techniques are based either on energy detection or eigenspace analysis from Random Matrix Theory (RMT) such as using the Marchenko-Pastur law. These schemes suffer from uncertainty in estimating the noise variance which reduces their performance. In this paper we propose a new method to evaluate the noise variance that can eliminate the limitations of the aforementioned schemes. This method estimates the noise variance from a measurement set of noisy signals or noise-only signals. Extensive simulations show that the proposed method performs well in estimating the noise variance. Its performance greatly improves with increasing numbers of measurements and also with increasing numbers of samples taken per measurement.