Increasing importance of localizing objects in indoor environments is the motivation for many research on localization algorithms. This paper focuses on the maximum achievable resolution for Angle of Arrival as a means to position objects inside rooms using equipment within the field of wireless sensor networks, thus dealing with restricted resources. A clear view on beam forming using antenna arrays is represented and is proven to be useful in Angle of Arrival measurements. The choice of the linear antenna array as most appropriate solution is motivated. A detailed overview of the algorithm, used to calculate the maximum realistic resolution, leads us to draw conclusions concerning the resolution. Depending on the number of anchor nodes and the composition of the antenna arrays, a reference value can be defined to calculate the realistic resolution for all room dimensions.