  Estimation of User Terminals' (UTs') Angle of Arrival (AoA) plays a
significant role in the next generation of wireless systems. Due to high
demands, energy efficiency concerns, and scarcity of available resources, it is
pivotal how these resources are used. Installed antennas and their
corresponding hardware at the Base Station (BS) are of these resources. In this
paper, we address the problem of antenna selection to minimize Cramer-Rao Lower
Bound (CRLB) of a planar antenna array when fewer antennas than total available
antennas have to be used for a UT. First, the optimal antenna selection
strategy to minimize the expected CRLB is proposed. Then, using this strategy
as a preliminary step, we present a two-stage greedy antenna selection method
whose goal is to minimize the instantaneous CRLB. The optimal start point of
the greedy algorithm is presented alongside some methods to reduce the
algorithm's computational complexity. Numerical results confirm the accuracy of
proposed solutions. They demonstrate that the proposed antenna selection method
only requires a small proportion of the total available antennas to accomplish
a significant amount of the total performance, enhancing hardware utilization
efficiency. Also, it is shown that the presented algorithm has a high error
tolerance.
