Array Design for Angle of Arrival Estimation Using the Worst-Case Two-Target Cramér-Rao Bound

Array Design for Angle of Arrival Estimation Using the Worst-Case Two-Target Cramér-Rao Bound

Blog Article

Sparse array design is used to help reduce computational, hardware, and power requirements compared to uniform arrays while maintaining acceptable performance.Although minimizing the Cramér-Rao bound has been adopted previously for sparse sensing, it did not consider multiple targets and unknown target directions.To handle the unknown target directions when optimizing the Cramér-Rao bound, we propose to use the worst-case Cramér-Rao ventilationstejp bound of two uncorrelated equal power sources with arbitrary angles.This new worst-case two-target Cramér-Rao bound metric has some resemblance to the peak sidelobe level metric which is commonly used in unknown multi-target scenarios.We cast the sensor selection problem for 3-D arrays using the worst-case two-target Cramér-Rao bound as a convex semi-definite program and obtain the binary selection by randomized rounding.

We illustrate the proposed method through numerical examples, comparing it to solutions obtained by minimizing the single-target Cramér-Rao bound, minimizing the Cramér-Rao bound for known target angles, the concentric rectangular array and the boundary array.We show that our method selects a combination of edge and center elements, which read more contrasts with solutions obtained by minimizing the single-target Cramér-Rao bound.The proposed selections also exhibit lower peak sidelobe levels without the need for sidelobe level constraints.