Optimal n-out-of- K Voting Rule for Cooperative Spectrum Sensing with Energy Detector over Erroneous Control Channel

In this paper we optimize the n-out-of-K voting rule by minimizing the global error rate for cooperative spectrum sensing with single bit reporting over erroneous control channel, when all the K users are similar. We show that the optimal choice of n i.e. n* depends on the operating SNR, probability of error over control channel, Pe, and the threshold, v, used by the K users. We then derive the expressions of Receiver operating Characteristics (RoC) curves applicable to any detector where AND, OR and majority rule is optimal. Results are verified by using energy detector. Since the RoC expressions are complex, additional insight is obtained by deriving feasible region for OR and AND rule. It is observed that 1) OR and AND rule are never optimal, for practical cases, 2) In contrast to the case with error free control channels, Majority rule is not always optimal if the effective probability of false alarm and the probability of miss detection are of the same order.