In the sixth-generation (6G) wireless network with a large number of devices, it is very important to achieve accurate and reliable positioning with limited power resource. This paper studies a multi-user localization system based on a reconfigurable intelligent surface (RIS) where the users derive position information through signals not only from the reflected links via the RIS but also from the cooperative links among users. Considering all users in the near field of the RIS, we first build the system model based on the uniform liner array (ULA) response of the RIS. Then, we derive the Cram´er-Rao lower bound (CRLB) of global users’ positions as the performance metric. Assuming that the system has limited power resource, we construct a joint power allocation and phase-shift design problem with the goal of minimizing the CRLB. Since the problem is non-convex, we propose an iterative searching (IS) algorithm which is realized by optimizing the power allocation among all nodes and phase shifts of the RIS alternatively. Finally, numerical results are presented to show that the importance of cooperation increases and cooperative users should be assigned with more power if the number of reflecting elements at the RIS is not very large and/or the channel conditions of the reflected links are not so good.

Reconfigurable intelligent surface;power allocation;phase-shift design;cooperative localization;Cram´er-Rao lower bound