Antenna Selection for Enhanced DOA Estimation: Exploring the Symmetries

The performance of direction of arrival (DOA) estimation using antenna arrays is fundamentally determined by the array configuration through its influence on the Cramer-Rao bound (CRB). Thus, antenna selection strategies may be employed to reduce computational and hardware cost while optimizing the DOA estimation performance. This is done by choosing the optimal subarray that minimizes the CRB for a particular DOA or range of DOAs. However, the cost of solving this optimization problem is quite high. In this paper, we study the symmetries of the cost function that is used in implementing the antenna selection for enhanced DOA estimation in order to gain significant insights into the structure of the problem and consequently achieve significant reduction in complexity. In particular, we derive a group of transformations under which the cost function is invariant. This group then allows us to reduce the domain over which the optimization problem is to be solved.