In this paper the analytical and simulation results of probability of detection and false alarm of a co-operative cognitive radio network are compared under both awgn and Rayleigh fading environment. After getting the confidence level of above 95% from the simulation, a neural network (NN) is trained with simulation data where the analytical result is given as the target of the NN. Finally the results are verified with the profile of MSE (mean square error) of three data set (train, validation and test), regression on data set, confusion matrices and error histogram. Here we use Backpropagation algorithm and Hopfield model, all the results yield error of less than 4.5%. The concept of paper is applicable at fusion center (FC) to make proper judgment of presence of primary user (PU).