Finding Defective Elements in Intelligent Reflecting Surface via Over-the-Air Measurements

Due to circuit failures, defective elements that cannot adaptively adjust the phase shifts of their impinging signals in a desired manner may exist on an intelligent reflecting surface (IRS). Traditional way to find these defective IRS elements requires a thorough diagnosis of all the circuits belonging to a huge number of IRS elements, which is practically challenging. In this paper, we will devise a novel approach under which a transmitter sends known pilot signals and a receiver localizes all the defective IRS elements just based on its over-the-air measurements reflected from the IRS. The key lies in the fact that the over-the-air measurements at the receiver side are functions of the set of defective IRS elements. Based on this observation, we propose a bisection based method to localize all the defective IRS elements. Specifically, at each time slot, we properly control the desired phase shifts of all the IRS elements such that half of the considered regime that is not useful to localize the defective elements can be found based on the received signals and removed. Via numerical results, it is shown that our proposed bisection method can exploit the over-the-air measurements to localize all the defective IRS elements quickly and accurately.