The Radio Spectrum is used to transmit electromagnetic waves of different frequencies. With the passage of time people are getting aware of new technologies and as a result demand for different services has been increased. This results in the shortage of available spectrum. Spectrum utilization has now become a challenging task due to increase in wireless communications. Major licensed bands, such as those allocated for television broadcasting is not been fully utilized which results in spectrum wastage. This led to the idea of cognitive radio, first presented officially by Mitola and Maguire in 1999. Cognitive radio is a software-defined radio system, or SDR, a radio whose functionality is completely defined in software. Changes in SDR can be made by just changing the software. Mitola and Maguire proposed that the unused spectrum can be utilized by Secondary users (Unlicensed users) without creating harmful interference to Primary users (Licensed users). Secondary user can use the spectrum when primary user is inactive and should vacate the channel as soon as the primary user becomes active. An Efficient Signal Detection algorithm can perform this task. Detection of primary user signal is an elementary problem in cognitive radio. Energy detection, Match-filtering and Cyclostationary methods are widely used for spectrum sensing. This thesis will explore spectrum sensing methods and will analyze the performance of different techniques including methods based on the eigenvalue of the covariance matrix of received signals used as the test statistic. Different methods working with and without noise power will be simulated to demonstrate the performance of spectrum sensing techniques.