In this study, the theoretical framework of received signal strength (RSS) based direction finding with array of directional antennas with normal density distribution in magnitude are established. Directional antenna systems offer simple and effective solutions, when the antennas must be placed within a limited area, such as on a car. While some important studies exist, the theoretical framework to create such systems where the radiation patterns of directional antennas are modeled as von Mises distributions (i.e. circular version of normal distribution) in magnitude are lacking in the literature. Therefore, in this study first, Cramer Rao Lower Bound (CRLB) is explicitly calculated for joint estimation of angle of arrival and incident signal power. It is found that CRLB is not a function of angle of arrival, and it decreases with the increasing directivity of the antennas. Finally, maximum likelihood estimation (MLE) is discussed by analyzing its ability of convergence.