Robust resource allocation in multi-cell UE-specific RIS-assisted D2D relay networks under imperfect CSI

Abstract

Device-to-device (D2D) communication enhances spectral efficiency but remains constrained by limited transmission range, underlay interference, and the half-duplex overhead of conventional relays. User equipment-specific reconfigurable intelligent surfaces (UE-RIS) offer a promising alternative by enabling passive beamforming to strengthen D2D links without additional spectrum consumption. However, existing studies typically assume perfect channel state information (CSI) and single-cell operation, limiting their applicability to practical deployments. This paper proposes a robust multi-cell resource allocation (RMRA) framework for UE-RIS-assisted D2D relay networks under imperfect CSI. A hybrid uncertainty model is adopted, combining statistical Gauss-Markov CSI errors for intra-cell links with bounded norm-ball uncertainty for inter-cell links. The joint optimisation of resource reuse, transmit power allocation, and RIS phase configuration is formulated as a stochastic mixed-integer nonlinear program that maximises network spectral efficiency while satisfying outage and quality-of-service constraints. To efficiently solve the problem, a three-stage algorithm is proposed comprising distance-pruned Hungarian assignment, robust power control using Bernstein-type inequality and S-procedure based semidefinite programming, and soft actor-critic (SAC) based passive beamforming. Simulation results show that RMRA achieves a 94% D2D access rate at light load and over 75% at full load, improves sum spectral efficiency by 34.7% and 70.2% over AF relaying and direct D2D, respectively, attains 118.5 bits/s/Hz/W energy efficiency, and maintains 30.2 bits/s/Hz under severe CSI uncertainty.