The collaborative Spectrum Sensing (SS) to detect random signals contaminated by additive Gaussian noise is studied. A novel soft decision rule based on the L_p-norm of square root of the Secondary Users (SUs) energies is proposed. The proposed scheme considers the bandwidth limitation for sharing sensing information between the SUs. Whereas the existing literature on L_p-norm detectors have assumed independent observations of the SUs, they would be highly correlated when Primary User (PU) is active. Therefore, we consider the correlated observations of the distributed SUs for the both cases of equal and unequal received Signal-to-Noise Ratios (SNRs). We derive the optimal L_p-norm vector parameter based on minimization of the overall error probability while meeting the spectral efficiency and sensing performance requirements. To this end, we use modified deflection coefficient metric to simplify optimization problem. Furthermore, in order to evaluate the performance of the proposed detector, the closed form expressions for detection and false alarm probabilities are computed analytically. The provided closed-form analytical results in addition to simulation results show that the proposed detector outperforms significantly the traditional energy combining detector.