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Optimization of hard fusion spectrum sensing using the k-out-of-N rule is considered. Two different setups are used to derive the optimal k. A throughput optimization setup is defined by minimizing the probability of false alarm subject to a probability of detection constraint representing the interference of a cognitive radio with the primary user, and an interference management setup is considered by maximizing the probability of detection subject to a false alarm rate constraint. It is shown that the underlying problems can be simplified to equality constrained optimization problems and an algorithm to solve them is presented. We show the throughput optimization and interference management setups are dual. The simulation results show the majority rule is optimal or near optimal for the desirable range of false alarm and detection rates for a cognitive radio network. Furthermore, an energy efficient setup is considered …