A globally optimal Neyman-Pearson test for hard decisions fusion in cooperative spectrum sensing

The problem of calculating the local and global decision thresholds in hard decisions based cooperative spectrum sensing is well known for its mathematical intractability. Previous work relied on simple suboptimal counting rules for decision fusion in order to avoid the exhaustive numerical search required for obtaining the optimal thresholds. In this paper, a globally optimal decision fusion rule for Primary User signal detection based on the Neyman-Pearson (NP) criterion is derived. The algorithm is based on a novel representation for the global performance metrics in terms of the regularized incomplete beta function. Based on this mathematical representation, it is shown that the globally optimal NP hard decision fusion test can be put in the form of a conventional one dimensional convex optimization problem. The proposed optimal scheme does not require knowledge of the instantaneous channel gain and it outperforms conventional counting rules, such as the OR, AND, and MAJORITY rules. Simulation results show that the optimal fusion rule offers significant SNR gain in cognitive radio networks with large number of cooperating users.