The Cross Ambiguity Function (CAF) is often used for passive geolocation of an emitter based on the time difference of arrival (TDOA) and frequency difference of arrival (FDOA) of the received signals. CAF performance has been thoroughly investigated in regards to traditional single-input single-output (SISO) signals. Little is known about how the CAF will respond to signals from multiple-input multiple-output (MIMO) systems which utilize multiple antennas. This thesis focuses on characterizing the CAF's magnitude distribution in order to determine the probability of correctly determining the correct TDOA/FDOA bin, and the resulting impact on geolocation. The received signals are studied in the presence of additive white Gaussian noise (AWGN) as well as multi-channel propagation effects such as phase ambiguities and offsets due to multi-antenna transmission. Two and four transmit antennas using either a form of spatial multiplexing or space-time block coding are the focus of this work because they are mostly commonly found in currently deployed communication systems. The effects of these transmit schemes are studied with respect to TDOA/FDOA error and the resulting position error. The analysis is performed using a detection theory framework as opposed to estimation theory in order to empha- size the impact of MIMO transmission on determining the correct TDOA/FDOA bin. A simple method using the CAF magnitude as a decision statistic is also presented so that TDOA/FDOA errors can be detected and filtered in an attempt to improve positioning estimates. / Master of Science