Increasing demand for wireless technology and inefficient use of radio resources, such as frequency spectrum and power leads to the incompetence of past policies for resource allocation. For example using fixed spectrum allocation for heterogeneous wireless technologies has proven to be inefficient and leads to spectrum shortage. Most of the time, bands are not occupied or utilized well by licensed users. On the other hand the effective use of transmitted power can minimize the interference created for other receiving nodes and obviously maximize the battery life. So, in recent years, many power control algorithms have been proposed, especially in wireless networks. In order to increase utilization of radio resources, cognitive radio (CR) has been proposed. CR detects unused spectrum frequencies and communicates over them. In fact CR makes spectrum allocation more dynamic in both spatial and temporal dimensions. But this new technology has brought about new challenges. One of the most important challenges in this case is spectrum sharing. New approaches to spectrum sharing are needed that increase frequency utilization and maintain robust performance in networks of CRs. In order to guarantee a CR network with robust performance and without interference between users, we need a powerful algorithm for users to access the spectrum. In this thesis, after a survey on different methods of spectrum sharing such as game theory, optimization method and introduction of distributed power control algorithm, a new way for spectrum sharing is proposed. The proposed way is spectrum sharing based on power control. The purposes of this algorithm are to make efficient use of system resources and to increase of system performance. This way tries to use adaptive modulation and power control to access corresponding BER at each receiver node. We will show that altering the modulation will result in improved utilization of the spectrum sharing in Cognitive Radio networks. Furthermore, changing the modulation type according to the channel state quality is an effective way to battle fading effect of the channel. This method provides minimum-interference spectrum sharing and it also helps to optimize the use of power and spectrum The simulation results are provided to show that the proposed algorithm achieve significant performance in spectrum sharing and power saving, also the simulation results are compared with results of a Cognitive Radio network without power control to show the differences. Different practical and software optimization techniques are discussed in details. In the end, there is a summary of thesis and suggestions for further studies. Keywords: Wireless Networks, Cognitive Radio, Spectrum Sharing, Power Control