A locally optimum detector for detection of random signals under a weakly correlated noise model over fading channels

avoid interference from secondary users to primary holders with license in spectrum, it is need to have an appropriate spectrum sensing. In methods like spectrum sensing, where samples of noise are correlated, the impairments from independent noise samples do not provide optimum performances. So, in case of random signals over a weakly correlated noise model in fading channels requires a locally optimum detection method has been proposed in this paper. A low signal to noise ratio regime has derived based on the probabilities of false alarm and detection of proposed detector. The average probabilities of false alarm and detection of proposed detector are derivated for different channel gains. The simulation and numerical results helps to compare and define that the proposed method is more appropriate than the conventional energy detection method. Finally we take a scenario in which the estimated and real correlations are different. The effect of correlation mismatch on the probabilities of false alarm and detection in proposed method are estimated.