Antenna array Cramér-Rao bound design by element relocation

We consider the use of an arbitrary planar array for direction-of-arrival (DOA) estimation, with the commonly used Cramér-Rao Bound (CRB) as a performance measure. By taking advantage of the cosine structure of the array Fisher information matrix (FIM), the FIM is reformulated to be completely represented by three parameters which depend on the array geometry, leading to a new FIM expression that reflects the impact of individual sensor relocations. The proposed expressions are particularly helpful for finding new sensor positions when given an objective FIM or CRB, and applies in certain more general scenarios. This usefulness is confirmed through the practical application of relocating a single sensor of an arbitrary planar array to achieve an FIM and CRB with given angular distribution.