No / Eigenvalue based spectrum sensing schemes such as Maximum Minimum Eigenvalue (MME), Maximum Energy Detection (MED) and Energy with Minimum Eigenvalue (EME) have higher spectrum sensing performance without requiring any prior knowledge of Primary User (PU) signal but the decision hypothesis used in these eigenvalue based sensing schemes depends on the calculation of maximum eigenvalue from covariance matrix of measured signal. Calculation of the covariance matrix followed by eigenspace analysis of the covariance matrix is a resource intensive operation and takes overhead time during critical process of spectrum sensing. In this paper we propose a new blind spectrum sensing scheme based on the approximation of the maximum eigenvalue using state of the art results from Random Matrix Theory (RMT). The proposed sensing scheme has been evaluated through extensive simulations on wireless microphone signals and the proposed scheme shows higher probability of detection (Pd) performance. The proposed spectrum sensing also shows higher detection performance as compared to energy detection scheme and RMT based sensing schemes such as MME and EME.