Optimal and Constrained RIS Profile Design for User Localization in OFDM Systems

Reconfigurable intelligent surface (RIS) has emerged as a highly promising technology for future wireless sensing applications, primarily due to its capability to dynamically manipulate the incoming signals through meticulous configuration of the RIS profile. This paper delves into the optimal design strategy for the RIS profile, aiming at maximizing the localization accuracy of the non-line-of-sight user within typical downlink orthogonal frequency division multiplexing (OFDM) systems. Assuming prior knowledge of the user’s location, we first derive the measurement model and corresponding position error bound (PEB) for the considered OFDM systems. Subsequently, under the total power budget constraint, we establish a closed-form solution for the optimal covariance matrix of the RIS profile by leveraging the subspace structure information of the channel states. Building upon this, the design of the optimal RIS profile is executed using the time-sharing technique. Taking into account the hardware limitations, we further formulate a more practical RIS profile design problem by incorporating the unit-modulus constraint for each RIS element, which, however, is non-convex and thus hard to tackle. To address this issue, we employ the alternating minimization technique to compute a suboptimal solution for the constrained RIS profile design problem. Simulation results demonstrate the remarkable PEB performance achieved by both the proposed optimal and constrained RIS profile design strategies. It is also illustrated that the proposed constrained RIS profile design surpasses other state-of-the-art alternatives, exhibiting a comparable performance to our devised optimal benchmark.