  In this paper we propose the capacity optimization over sensing threshold for
sensing-based cognitive radio networks. The objective function of the proposed
optimization is to maximize the capacity at the secondary user subject to the
constraints on the transmit power and the sensing threshold in order to protect
the primary user. The defined optimization problem is a convex optimization
over the transmit power and the sensing threshold where the concavity on
sensing threshold is proved. The problem is solved by using Lagrange duality
decomposition method in conjunction with a subgradient iterative algorithm and
the numerical results show that the proposed optimization can lead to
significant capacity maximization for the secondary user as long as the primary
user can afford.
