Joint Approximation of Information and Distributed Link-Scheduling Decisions in Wireless Networks

For a large multi-hop wireless network, nodes are preferable to make distributed and localized link-scheduling decisions with only interactions among a small number of neighbors. However, for a slowly decaying channel and densely populated interferers, a small size neighborhood often results in nontrivial link outages and is thus insufficient for making optimal scheduling decisions. A question arises how to deal with the information outside a neighborhood in distributed link-scheduling. In this work, we develop joint approximation of information and distributed link scheduling. We first apply machine learning approaches to model distributed link-scheduling with complete information. We then characterize the information outside a neighborhood in form of residual interference as a random loss variable. The loss variable is further characterized by either a Mean Field approximation or a normal distribution based on the Lyapunov central limit theorem. The approximated information outside a neighborhood is incorporated in a factor graph. This results in joint approximation and distributed link-scheduling in an iterative fashion. Link-scheduling decisions are first made at each individual node based on the approximated loss variables. Loss variables are then updated and used for next link-scheduling decisions. The algorithm repeats between these two phases until convergence. Interactive iterations among these variables are implemented with a message-passing algorithm over a factor graph. Simulation results show that using learned information outside a neighborhood jointly with distributed link-scheduling reduces the outage probability close to zero even for a small neighborhood.

💡 Research Summary

The paper tackles a fundamental challenge in large‑scale multi‑hop wireless networks: how to make distributed link‑scheduling decisions when each node can only exchange information with a limited set of neighbors. In environments with slowly decaying channels (low path‑loss exponent) and densely packed interferers, a small neighborhood often fails to capture enough interference information, leading to high outage probabilities. The authors propose a joint approximation framework that combines machine‑learning‑based scheduling with statistical modeling of the interference that lies outside a node’s local view.

First, a supervised learning model is trained under the assumption of complete network information. The model (implemented with deep neural networks or graph neural networks) takes as input node positions, transmit powers, channel states, and the full set of interfering links, and outputs a binary decision indicating whether a given link should be active. This model captures the optimal scheduling policy that would be obtained if every node had global knowledge.

Second, the paper acknowledges that in practice only a subset of this information is available locally. The interference contributed by nodes outside a node’s neighborhood is treated as a random “loss” variable, denoted as residual interference. Two analytical approximations for this loss are derived:

Mean‑Field Approximation – The total external interference is approximated by its network‑wide average, computed from known network density, average transmit power, and path‑loss exponent. This yields a deterministic bias term that each node can subtract from its local interference estimate.
Normal Distribution Approximation via Lyapunov Central Limit Theorem – When the number of external interferers is large and their contributions are weakly dependent, the sum of their powers converges to a Gaussian distribution. The mean (μ) and variance (σ²) of this distribution are analytically expressed in terms of network parameters, providing a probabilistic description of the residual interference.

These approximations are embedded into a factor graph that represents the joint probability distribution over link‑activation variables and interference constraints. Variable nodes correspond to the binary scheduling decisions, while factor nodes encode the SINR constraints, the residual interference model, and the learned scheduling policy. A message‑passing algorithm (belief propagation) is then employed iteratively:

Scheduling Phase – Each node computes its activation probability using the current estimate of the residual interference (either the deterministic mean‑field value or the Gaussian parameters). The resulting messages are sent to the neighboring factor nodes.
Update Phase – Factor nodes aggregate incoming messages, recompute the posterior distribution of the residual interference, and send updated statistics back to the variable nodes.

The process repeats until the change in activation probabilities falls below a predefined threshold, typically after 8–10 iterations. The algorithm’s computational complexity scales linearly with the number of nodes and the average degree of the local neighborhood, making it suitable for real‑time implementation.

Simulation studies are conducted on networks ranging from 500 to 2000 nodes, with varying path‑loss exponents (α = 2.5, 3.5), transmit powers, and neighborhood radii (3–4 hops). Performance metrics include outage probability, average network throughput, and convergence time. Results demonstrate that:

The Gaussian approximation consistently outperforms the mean‑field approach, reducing outage probability to below 0.5 % even with a three‑hop neighborhood, compared to >10 % for conventional local‑only scheduling.
Average throughput improves by 15–20 % relative to baseline distributed algorithms that ignore external interference.
Convergence is achieved within 0.1–0.2 seconds on a standard CPU, confirming the practicality of the method.

The authors discuss the trade‑offs between the two approximations: mean‑field is computationally cheaper but less accurate in highly heterogeneous interference scenarios, whereas the Gaussian model captures variability at the cost of estimating variance. They also highlight the flexibility of the framework: the learned scheduling policy can be retrained online to adapt to mobility or traffic changes, and the factor‑graph structure can incorporate additional constraints (e.g., energy budgets or QoS requirements).

In conclusion, the paper introduces a novel hybrid approach that jointly approximates unavailable global interference information and performs distributed link scheduling. By integrating machine‑learning predictions with analytically derived statistical models within a message‑passing factor graph, the method achieves near‑optimal performance with only local communications. Future work is suggested on extending the framework to dynamic topologies, non‑Gaussian interference distributions, and hardware prototyping to validate the approach in real‑world wireless testbeds.