Tensor-Based Framework for Multi-User RIS-Assisted ISAC in Cross Far- and Near-Field Communications

In this paper, we propose a tensor-based framework for multi-user reconfigurable intelligent surface (RIS)-assisted integrated sensing and communication (ISAC), designed to enable efficient data transmission and accurate localization across far- and near-field communications. The proposed scheme introduces a two-phase nested tensor-based ISAC transmission protocol, comprising the precoding phase and the joint symbol detection and target localization (JSDTL) phase. During the precoding phase, a third-order tensor is constructed to extract angle information from the far-field base station (BS)-RIS channel links, which is then utilized to design a precoding strategy that mitigates inter-user interference. In the JSDTL phase, the received signals are constructed into a fourth-order nested tensor incorporating angular, temporal, and coding dimensions. The algebraic structure of the nested tensor, combined with the second-order Fresnel approximation for the near-field channel model between the RIS and user equipment (UE), is leveraged to perform data recovery and target localization. Simulation results confirm that the proposed scheme achieves superior ISAC performance with reduced computational complexity, outperforming benchmark algorithms.