Globally Optimal Cooperation in Dense Cognitive Radio Networks
  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. However, these simple rules are not globally optimal as they do not maximize the overall global detection probability by jointly selecting local and global thresholds. Instead, they maximize the detection probability for a specific global threshold. 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. A binary search for the global threshold can be applied yielding a complexity of O(log2(N)), where N represents the number of cooperating users. The logarithmic complexity is appreciated because we are concerned with dense networks, and thus N is expected to be large. The proposed optimal scheme outperforms conventional counting rules, such as the OR, AND, and MAJORITY rules. It is shown via simulations that, although the optimal rule tends to the simple OR rule when the number of cooperating secondary users is small, it offers significant SNR gain in dense cognitive radio networks with large number of cooperating users. 
Ahmed M. Alaa and Omar A. Nasr
cs.NI cs.IT math.IT