  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.
