One of the most challenging issues in cognitive radio system is to sense the spectrum environment accurately and determine whether the primary user is active, or not over a specific band reliably. So, there is need of good sensing algorithm have the property have low sensing time, ability to detect primary signal at low SNR. In this paper, Singular Value Decomposition (SVD) spectrum sensing methodologies for cognitive radio are studied over different fading channels as AWGN channel, Rayleigth fading channel, Rician fading channel & Nakagami Fading Channel Energy detection method is classical method of detection but it requires knowledge of noise power for signal detection and it gives poor performance under low SNR The proposed detection method overcomes the drawback of energy detection method. SVD does not require the knowledge of signal properties, channel and uncertainty noise parameter in such a way it is suitable for blind spectrum sensing. Threshold is computed using random matrix theory (RMT) is exploited to formulate the detection method depending on sample covariance matrix of received signal. The Singular Value Decomposition (SVD) based detection algorithm is simulated by using MATLAB Software Platform. In this Paper, Simulation Result shows that SVD algorithm using Covariance matrix approach over Nakagami fading channel gives approx. 0.025 to 0.035 better performance of detection at low SNR with compare to reference AWGN & other different fading channel.