Cognitive radio technology is used to improve spectrum efficiency by having the cognitive radios act as secondary users to access primary frequency bands when they are not currently being used. In general conditions, cognitive secondary users are mobile nodes powered by battery and consuming power is one of the most important problem that facing cognitive networks; therefore, the power consumption is considered as a main constraint. In this paper, we study the performance of cognitive radio networks considering the sensing parameters as well as power constraint. The power constraint is integrated into the objective function named power efficiency which is a combination of the main system parameters of the cognitive network. We prove the existence of optimal combination of parameters such that the power efficiency is maximized. Then we reformulate the objective function to incorporate the throughput. According to different constraints or degree of significance, we may put proper weight to each term so that we could obtain more preferable combination of parameters. Computer simulations have given the optimal solution curve for different weights. We can draw the conclusion that if we put more emphasis on power efficiency, the transmit power is a more critical parameter, however if throughput is more important, the effect of sensing time is significant.