In this paper we propose a novel approach to obtain the optimal operating point of the spectrum sensing in overlay spectrum sharing. The operating point of the spectrum sensing is specified by the receiver operating characteristic (ROC) curve which is a fundamental spectrum sensing behavior that relates its false alarm and missed detection probabilities. Our objective is to maximize the ergodic capacity of the secondary service in the presence of inaccurate spectrum sensing. We formulate an optimization problem to obtain the optimal transmission power strategy and ROC operating point of the spectrum sensing. Constraints of the considered optimization problem include the secondary service maximum transmission power as well as the maximum primary service collision probability. Two iterative sub-optimal schemes are then proposed to find the solutions of the optimization problem. Numerical results show that both proposed schemes quickly converge after a few iterations. Moreover, it is observed that the proposed schemes significantly outperform other conventional approaches.