  A multi-cell cluster-free NOMA framework is proposed, where both intra-cell
and inter-cell interference are jointly mitigated via flexible cluster-free
successive interference cancellation (SIC) and coordinated beamforming design.
The joint design problem is formulated to maximize the system sum rate while
satisfying the SIC decoding requirements and users' minimum data rate
requirements. To address this highly complex and coupling non-convex mixed
integer nonlinear programming (MINLP), a novel distributed auto-learning graph
neural network (AutoGNN) architecture is proposed to alleviate the overwhelming
information exchange burdens among base stations (BSs). The proposed AutoGNN
can train the GNN model weights whilst automatically optimizing the GNN
architecture, namely the GNN network depth and message embedding sizes, to
achieve communication-efficient distributed scheduling. Based on the proposed
architecture, a bi-level AutoGNN learning algorithm is further developed to
efficiently approximate the hypergradient in model training. It is
theoretically proved that the proposed bi-level AutoGNN learning algorithm can
converge to a stationary point. Numerical results reveal that: 1) the proposed
cluster-free NOMA framework outperforms the conventional cluster-based NOMA
framework in the multi-cell scenario; and 2) the proposed AutoGNN architecture
significantly reduces the computation and communication overheads compared to
the conventional convex optimization-based methods and the conventional GNNs
with fixed architectures.
