Investigations on Cramér–Rao-Bound Conscious Optimization Strategies for Antenna Design Aimed at Phaseless Direction of Arrival Estimation

We present the result of a novel optimization strategy for the design of the antenna front-end for indoor positioning system based on Cramér–Rao bound (CRB) sensitivity analysis. The positioning system considered relies on the direction of arrival (DoA) estimation via space division multiple access (SDMA) which in turn is enabled by a smart antenna operating at 2.45 GHz. The antenna is designed via an optimization process driven by an invasive weed optimization algorithm. This is based on a multiobjective (MO) cost function relying on an ad hoc implementation of the Cramér–Rao analysis of the antenna beam set. The use of the Cramér–Rao analysis to drive the optimization represents the novelty of this article. To prove the effectiveness of the approach, the antenna front-end is limited to the essential components, albeit suitable to cover almost 180° degrees of observable area. The localization performance—validated with a simulated experiment—outperforms the results found with similar results in real life. In detail, the mean dilution of precision (DoP) ranges from 0.78° to 2.71°, with an average of 1.63° and a standard variation of 0.41°. The worst case of the best set exhibits a maximum error below 4.67°. The 95% coverage is equal to 2.22°, with a range spanning from 1.87° to 2.52°, corresponding to a spread of 0.6°. Anyhow, a full statistics over the whole Pareto set and the whole cloud of antenna geometries is presented, to validate the choice of the subset of best solutions chosen.