As resources are limited, radio spectrum becomes congested due to the growth of wireless applications. However, measurements address the fact that most of the licensed spectrums experience low utilization even in intensively teeming areas. In the exertion to improve the utilization of the limited spectrum resources, cognitive radio networks have emerged as a powerful technique to resolve this problem. There are two types of user in cognitive radio networks (CRNs) named as primary user (PU) and secondary user (SU). Therein, the CRN enables the SU to utilize the unused licensed frequency of the PU if it possibly finds the vacant spectrum or white space (known as opportunistic spectrum access). Alternatively, SU can transmit simultaneously with the PU provided that transmission power of SU does not cause any harmful interference to the PU (known as spectrum sharing systems). In this thesis work, we study fundamental knowledge of the CRNs and focus on the performance analysis of the single input multiple output (SIMO) system for spectrum sharing approach. We assume that a secondary transmitter (SU-Tx) has full channel state information (CSI). The SU-Tx can adjust its transmit power not to cause harmful interference to the PU and obtain an optimal transmit rate. In particular, we derive the closed-form expressions for the cumulative distribution function (CDF), outage probability and an analytical expression for symbol error probability (SEP). / As resources are limited, radio spectrum becomes congested due to the growth of wireless applications. However, measurements address the fact that most of the licensed spectrums experience low utilization even in intensively teeming areas. In the exertion to improve the utilization of the limited spectrum resources, cognitive radio networks have emerged as a powerful technique to resolve this problem. There are two types of user in cognitive radio networks (CRNs) named as primary user (PU) and secondary user (SU). Therein, the CRN enables the SU to utilize the unused licensed frequency of the PU if it possibly finds the vacant spectrum or white space (known as opportunistic spectrum access). Alternatively, SU can transmit simultaneously with the PU provided that transmission power of SU does not cause any harmful interference to the PU (known as spectrum sharing systems). In this thesis work, we study fundamental knowledge of the CRNs and focus on the performance analysis of the single input multiple output (SIMO) system for spectrum sharing approach. We assume that a secondary transmitter (SU-Tx) has full channel state information (CSI). The SU-Tx can adjust its transmit power not to cause harmful interference to the PU and obtain an optimal transmit rate. In particular, we derive the closed-form expressions for the cumulative distribution function (CDF), outage probability and an analytical expression for symbol error probability (SEP). / Iqbal Hasan Haider, cell: +46704571807 MD. Fazla Rabby, cell: +46734965477