Multi-antenna systems with resource allocation based on transmit and receive precoding matrices have proven to enhance the spectral efficiency of cellular systems. In this thesis, we extend these concepts to a spectrum sharing system with primary users and secondary users. The spectrum sharing area is modeled as an array of transmit and receive antennas, with the transmit power constraint defined as a function of the interference threshold of the primary user. The area covered by a database enabled spectrum access system is represented as spatial bins, which are regions of predefined sizes. Each bin is assumed to have a single secondary user base station and all the resources of that bin (i.e., available frequencies, transmit power, etc.) are consumed by this secondary user in that bin. With these assumptions, the service area of the database can be represented by a grid of secondary users. Such a grid of secondary users forms a array of transmit antennas with secondary users in each bin. Furthermore, the set of bins with its secondary users at the edge of the exclusion zone of the primary user are assumed to create an array of receive antennas. These receive antennas act as sensors that will measure the interference power at the edge of the exclusion zone of the primary users. So the overall system of secondary user base station transmit and receive antennas can be modeled as a multi-element antenna array system.

A regulatory interference threshold (I_th) is defined for protection of the primary user at the edge of exclusion zones. This interference threshold is used by the resource allocation algorithms in the spectrum access system to calculate the transmit and receive precoding matrices for the secondary user antenna array. Using multiple-input multiple-output theory, the receive antenna array will measure the interference from the transmit antenna array and a feedback mechanism will update the resource allocation to keep the power at the receive array below the interference threshold of the primary user. For each array, the transmit/receive matrix is a beamforming vector which consists of a set of weights, one for each antenna. Furthermore, a codebook-based strategy is used by the spectrum access system database to choose a transmit matrix from the codebook which minimizes the interference at the primary user.

The overall spectrum sharing system can be represented by a model based on four design parameters, namely, Δ = (I_th, P, V, B), where P is the transmit power constraint, V are the transmit and receive beamforming matrices, and B is the matrix with active secondary user base stations of the antenna array or the quality of service level of the secondary users. The Δ parameter is called the system index of the spectrum sharing system. We apply the multi-antenna model to the challenging problem of spectrum sharing where the primary users operational parameters, such as transmit power levels, waveform types, and service modes, can change with time. Moreover, there are several types of primary users in different bands. Most of these users are federal government systems and their operational parameters are not available to the spectrum access system database. Our framework is useful in sharing spectrum with federal primary users, since only the interference threshold is needed for sharing their bands. Furthermore, we quantify the uncertainty in the availability of these bands for secondary users and the variations in achievable capacity with sharing spectrum in these bands.