| Empowered with advancements in wireless technologies, radio spectrum regulators are formulating a new spectrum management paradigm. Under this paradigm, it is possible for a secondary user (SU) who does not necessarily have a spectrum license to share a spectrum band with a primary user (PU) (the license holder) provided that operations of the PU are not disturbed. A more interesting scenario is when there are many SUs willing to utilize the spectrum band of the PU. The aggregate interference power received by the PU due to the transmissions of SUs is a key parameter determining the availability of spectrum sharing opportunities. One of our contributions is a cumulant-based characterization of this aggregate interference power. We introduce a comprehensive method to determine the cumulants under various system and channel conditions. These cumulants are utilized to understand the dynamics of the aggregate interference power, to approximate its distribution, and hence to investigate the spectrum sharing opportunities.;Furthermore, this thesis studies the effect of the spatial size of the secondary network on spectrum sharing opportunities. We verify that asymptotic results obtained for infinite fields are applicable for finite but relatively large fields as well. We also demonstrate that in some cases, however, asymptotic results are too pessimistic hiding some spectrum sharing opportunities.;Identifying the dominant region of the secondary network that would impact spectrum sharing opportunities is among our contributions. Results reveal that far interferers may tangibly contribute to spectrum sharing decisions when a higher approximation accuracy is required or when a wide exclusion region (within which no SUs are allowed to transmit) is considered. However, the dominant region shrinks with an increase in the path-loss exponent or in the level of the interference threshold specified by the PU or a regulator.;Another contribution is the investigation of the Gaussianity of the aggregate interference. We cast in a single mathematical framework the observations scattered across the literature about the Gaussianity of the distribution of the aggregate interference power. Moreover, we discuss the effect of different system and channel parameters on the convergence of the distribution of the aggregate interference to a Gaussian distribution. |
