Algorithm Unrolling-Based Distributed Optimization for RIS-Assisted Cell-Free Networks

The user-centric cell-free network has emerged as an appealing technology to improve the next-generation wireless network's capacity thanks to its ability to eliminate inter-cell interference effectively. However, the cell-free network inevitably brings in higher hardware cost and backhaul overhead as a larger number of base stations (BSs) are deployed. Additionally, severe channel fading in high-frequency bands constitutes another crucial issue that limits the practical application of the cell-free network. In order to address the above challenges, we amalgamate the cell-free system with another emerging technology, namely reconfigurable intelligent surface (RIS), which can provide high spectrum and energy efficiency with low hardware cost by reshaping the wireless propagation environment intelligently. To this end, we formulate a weighted sum-rate (WSR) maximization problem for RIS-assisted cell-free systems by jointly optimizing the BS precoding matrix and the RIS reflection coefficient vector. Subsequently, we transform the complicated WSR problem to a tractable optimization problem and propose a distributed cooperative alternating direction method of multipliers (ADMM) to fully utilize parallel computing resources. Inspired by the model-based algorithm unrolling concept, we unroll our solver to a learning-based deep distributed ADMM (D-ADMM) network framework. To improve the efficiency of the D-ADMM in distributed BSs, we develop a monodirectional information exchange strategy with a small signaling overhead. In addition to benefiting from domain knowledge, D-ADMM adaptively learns hyper-parameters and non-convex solvers of the intractable RIS design problem through data-driven end-to-end training.