Multi-antenna radars exhibit positively correlated detection performance with the number of elements utilized. The feasibility of refining antenna arrays to reduce cost of operation with only marginal loss of performance has attracted significant attention as utilizing a large number of elements may be prohibitively costly in terms of computation and power. Under cognitive radar paradigm, the goal is to choose an optimal or near optimal subset of elements from an antenna array of pre-specified geometry while meeting certain performance and cost criteria. In this work, we present optimization based selection methods for certain array geometries to select the best K element sub-array in terms of Cramér-Rao lower bound (CRB) on direction-of- arrival (DoA) estimations. Our results indicate that it is possible to reduce K up to a certain point without significant reduction in DoA estimation performance. The maximum possible reduction in K depends on the operating signal-to-noise ratio (SNR) and how much performance loss is tolerated. Thus, once the operating SNR is known, it is possible to utilize fewer array elements with slight decrease in performance.