This paper proposes a new underlay cooperative cognitive radio system, where a paid cooperation between the primary and the secondary systems is allowable. We consider both decoding strategy at the secondary receiver and the power efficiency optimization problem, in order to maximize the rate of the cognitive system. The secondary user has to communicate to the receiver in the presence of primary transmission, under two constraints: the total budget of power and the interference limit at the primary user. In this paper, we investigate the utility to optimally distribute the maximum allowed power with Gradient Descent method, when the Superposition Coding strategy is applied at the secondary system. The decoding strategy is a heuristic method that aims to maximize the sum rate of both the primary and the secondary users, taking into account the interweave and underlay cognitive radio constraints.