RIS Design for CRB Optimization in Source Localization with Electromagnetic Interference

Reconfigurable Intelligent Surface (RIS) plays an important role in enhancing source localization accuracy. Based on the information inequality of Fisher information analyses, the Cram\'{e}r-Rao Bound (CRB) of the localization error can be used to evaluate the localization accuracy for a given set of RIS coefficients. In this paper, we adopt the manifold optimization method to derive the optimal RIS coefficients that minimize the CRB of the localization error with the presence of electromagnetic interference (EMI), where the RIS coefficients are restricted to lie on the complex circle manifold. Simulation results are provided to validate the proposed studies under various circumstances.