In this paper, spectrum-sensing based resource allocation for a cognitive radio network that contains multiple secondary users (SUs) and a primary user (PU) is investigated. Each SU firstly performs the individual spectrum sensing and forwards the result to a fusion center to make the global decision. If PU is determined absent, then SUs access the primary band with their regular transmit power. Otherwise SUs still access the licensed band but with a limited transmit power to avoid harmful interference to PU. We target at designing the optimal sensing time, bandwidth allocation, power allocation, and the detection threshold to maximize the total achievable rate of SUs subject to the constraints of their peak transmit powers as well as the interference constraint to PU. The original optimization is divided into several subproblems that can be solved separately with low computational complexity. Numerical results demonstrate the superiority of the proposed one over the existing candidates.