During the last few years, we have witnessed that radio spectrum is becoming a valuable and scarce resource due to the increasing demand of multimedia services. However, recent research has shown that most of the available radio spectrum is not used effectively and is wasted. So, to utilize the radio spectrum effectively, a new technology has been introduced known as “Cognitive Radio”. In cognitive radio, a secondary user (SU) uses the vacant holes in licensed spectrum when it is not occupied by a primary user (PU) without causing interference to the PU transmission. Accessing vacant holes in the licensed user spectrum without causing interference to the PU is a complicated task. Therefore, alternative spectrum sharing techniques have gained popularity. Using these techniques, an SU can share the licensed spectrum with a PU at the same time without causing interference to the PU transmission. As a result, a secondary user should have an optimal power allocation policy in order to get a high transmission rate while still keeping the interference caused to the primary user below a threshold value. Under limited spectrum conditions, spectrum sharing relay networks have gained much popularity by providing reliability over direct transmission. In this thesis, we investigate an amplify-and-forward (AF) relay network performance in a spectrum sharing environment. Here, we consider the impact of the primary transmitter on the spectrum sharing system in the presence of a Nakagami-m fading channel, where the fading parameter m (m is an integer) can be used to deal with a variety of channel scenarios.