Cognitive radio networks can be designed to manage the radio spectrum more efficiently by utilizing the spectrum holes in primary user's licensed frequency bands. The currently available unlicensed spectrum is reaching its limit and various demands for applications and data rates in wireless communications requires additional spectrum which imposes limits on spectrum access. These requirements demand for efficient and intelligent use of spectrum. The system model and the problem of the optimum spectrum allocation in cognitive radios are introduced and formulated. According to the Federal Communications Commission (FCC), cognitive radios are defined as radio systems that continuously perform spectrum sensing, dynamically identify unused spectrum, and then operate in those spectrum holes where the licensed (primary) radio systems are idle. In this way, spectrum utilization efficiency is dramatically enhanced. in this paper, For our CR system, we consider to the dynamic spectrum allocation (DSA).