⚡ electrical engineering

Energy-Efficient Federated Learning with Relay-Assisted Aggregation in IIoT Networks

This paper proposes an energy-efficient, relay-assisted federated learning framework for Industrial Internet of Things networks that utilizes partial aggregation and a sequential parametric convex approximation algorithm to optimize device grouping, relay selection, and power allocation, thereby significantly reducing energy consumption and outage probability while accelerating convergence under strict latency constraints.

Original authors: Hamid Reza Hashempour, Mostafa Nozari, Gilberto Berardinelli, Yanjiao Li, Jie Zhang, Hien Quoc Ngo, Shashi Raj Pandey

Published 2026-05-25

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CC BY 4.0

Original authors: Hamid Reza Hashempour, Mostafa Nozari, Gilberto Berardinelli, Yanjiao Li, Jie Zhang, Hien Quoc Ngo, Shashi Raj Pandey

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Imagine a massive factory floor filled with hundreds of smart machines (like robotic arms, sensors, and cameras). Each machine has its own "brain" and is learning to do a specific job, like spotting defects on a conveyor belt. Instead of sending all their raw data (photos, measurements) to a central boss computer—which would clog the network and reveal trade secrets—they want to learn together. This is called Federated Learning (FL).

However, in a factory, the air is full of metal walls that block signals, and the machines are often low on battery. Sending a "brain update" (a model) directly to the boss can be slow, unreliable, or drain the battery completely.

This paper proposes a clever solution: Let the machines help each other.

Here is the breakdown of their idea using simple analogies:

1. The Problem: The "Noisy Factory"

Imagine trying to shout a message to a manager across a noisy, metal-filled factory floor.

Direct Shouting (Single-Hop): If a machine is far away or behind a big machine, its voice gets lost or takes too long. If it shouts too loud to be heard, it drains its battery fast.
The Goal: We need to get everyone's updates to the manager quickly, without running out of battery, and without the message getting lost.

2. The Solution: The "Messenger Relay" System

The authors suggest a two-step strategy:

The Strong Machines (Relays): Some machines have a clear, strong line of sight to the manager. These machines act as Relays.
The Weak Machines: Machines with poor connections don't shout directly. Instead, they whisper their update to a nearby "Strong Machine" (the Relay).
The Magic Trick (Partial Aggregation): This is the paper's secret sauce. Instead of the Relay just passing along every single whisper it hears (which would be a lot of data), it mixes them together first.
- Analogy: Imagine five people trying to tell a story to a boss. Instead of five people shouting five different versions, one person (the Relay) listens to all five, writes down one summary story, and then tells the boss that single summary. This saves a massive amount of time and energy.

3. The "Smart Manager" (The Algorithm)

The central server (Edge Server) acts like a very smart traffic controller. It doesn't just guess who should shout and who should whisper. It solves a complex math puzzle to decide:

Who talks directly? (Those with a clear path).
Who needs a helper? (Those with blocked paths).
Who is the best helper? (The machine with the best connection to the boss).
How loud should they shout? (Optimizing power so they don't waste battery).

The paper uses a method called SPCA (Sequential Parametric Convex Approximation). Think of this as a "guess-and-check" loop that gets smarter with every try, finding the perfect balance between speed and battery life.

4. What They Found (The Results)

The authors ran simulations (computer tests) to see how well this works compared to the old way (everyone shouting directly).

Less Battery Drain: Their method saved a huge amount of energy. In some cases, it used 6 times less energy than machines shouting directly. Even compared to machines just helping each other without summarizing the data first, it saved 2 times more energy.
Fewer Lost Messages: In the old system, about 1 in 100 messages got lost (outage). In their new system, only 1 in 1,000,000 messages got lost. It's like going from a shaky walkie-talkie to a crystal-clear phone line.
Faster Learning: Because more machines can participate without running out of battery or timing out, the group learns faster and more accurately, even if the machines have different types of data.

5. Real-World Messiness (Imperfect Information)

The paper also tested what happens if the "traffic controller" doesn't have perfect information about the factory noise (Imperfect Channel State Information). Even with this uncertainty, their system held up well, especially if the machines sent a few "test signals" (pilots) to help the manager understand the noise better.

Summary

In short, this paper teaches a group of factory machines how to learn together efficiently. Instead of everyone shouting at the boss (which is slow and tiring), they form teams where strong members summarize the weak members' thoughts before passing them up. This saves battery, prevents lost messages, and helps the whole factory learn faster.

Technical Summary: Energy-Efficient Federated Learning with Relay-Assisted Aggregation in IIoT Networks

Problem Statement
This paper addresses the challenges of deploying Federated Learning (FL) in Industrial Internet of Things (IIoT) environments, specifically within machinery subnetworks (SNs). While FL offers privacy-preserving collaborative training, its implementation in IIoT is hindered by strict latency constraints, energy limitations of battery-powered devices, and unreliable wireless links caused by signal blockages and multipath fading in metallic factory environments. These issues lead to asynchronous updates, model inconsistencies, and high communication overhead. Existing solutions often fail to simultaneously address energy efficiency (EE), cooperative communication, and the specific reliability requirements of industrial SNs. Furthermore, many approaches assume perfect Channel State Information (CSI), which is impractical in dynamic industrial settings.

Methodology
The authors propose a relay-assisted transmission framework where existing SNs act as decode-and-forward (DF) relays for neighboring devices with weak direct links to the Edge Server (ES). The methodology is structured as follows:

System Model: The network consists of SNs partitioned into two groups: those transmitting directly to the ES (single-hop, $N_{1h}$ ) and those utilizing a two-hop path via a relay SN (two-hop, $N_{2h}$ ). In the two-hop scenario, relays perform partial aggregation of local models received from associated SNs before forwarding a combined update to the ES. This reduces the total data volume transmitted over the second hop.
Optimization Problem: The objective is to minimize the total energy consumption (computation + transmission) of all participating SNs while adhering to a strict round-wise latency constraint ( $T_{th}$ ). The problem involves jointly optimizing transmit power, CPU frequency, SN grouping, and relay selection.
Decomposition and Algorithms:
- Decomposition: The non-convex optimization problem is decomposed into sub-problems: CPU frequency optimization, relay selection/SN grouping, and transmit power control.
- SN Grouping & Relay Selection: A threshold-based algorithm using ternary search classifies SNs into single-hop or two-hop groups. It iteratively removes SNs with the weakest links until the total transmission delay satisfies the latency constraint, aiming to maximize the number of participating SNs.
- Power Optimization: To handle the non-convexity of the energy minimization problem, the authors employ a Sequential Parametric Convex Approximation (SPCA) method. This iteratively approximates non-convex constraints with convex surrogates to find a stationary point.
- Imperfect CSI (ICSI): The framework is extended to scenarios with imperfect CSI using Minimum Mean Square Error (MMSE) estimation. An effective Signal-to-Interference-plus-Noise Ratio (SINR) expression is derived to account for channel estimation errors, and the SPCA algorithm is modified to accommodate the resulting non-convex rate constraints.
Convergence Analysis: The paper provides a theoretical convergence analysis comparing the relay-assisted scheme to standard single-hop FL. It demonstrates that partial aggregation at relays reduces effective gradient variance and data heterogeneity ( $\Gamma_{eff}$ ), leading to tighter convergence bounds, particularly under non-IID data distributions.

Key Contributions

Novel Protocol: Introduction of a relay-assisted FL protocol for IIoT that utilizes existing SNs as relays without dedicated infrastructure, incorporating partial aggregation to reduce overhead.
Unified Optimization Framework: Development of a unified EE optimization framework based on SPCA that operates under both Perfect CSI (PCSI) and Imperfect CSI (ICSI) conditions.
Algorithmic Design: Proposal of a ternary-search-based algorithm for optimal SN classification and relay selection to minimize delay and maximize participation, coupled with an SPCA-based power control mechanism.
Theoretical Analysis: Derivation of convergence bounds for relay-assisted FL, highlighting the benefits of reduced variance and heterogeneity compared to single-hop approaches.
Comprehensive Evaluation: Extensive simulations validating the framework's performance in terms of convergence speed, outage probability, and energy efficiency.

Results
Simulation results using the Fashion-MNIST dataset in a factory environment (100x100 m²) demonstrate:

Convergence: The proposed method achieves convergence behavior closely aligned with an "Ideal FL" baseline and significantly outperforms single-hop FL. It reduces the Normalized Mean Squared Error (NMSE) of training loss by an order of magnitude compared to 1-hop FL.
Outage Probability: The framework drastically reduces the probability of transmission delay violations (outage), dropping it from $10^{-2}$ in single-hop scenarios to $10^{-6}$ with the proposed SPCA-based method.
Energy Efficiency: The proposed scheme achieves substantial energy savings. Compared to single-hop transmission, it reduces uplink energy consumption by up to 6 times. Compared to a two-hop scheme without partial aggregation, it achieves a reduction of nearly 3 times.
Robustness to ICSI: Under imperfect CSI, the performance degradation is limited. Increasing the pilot length ( $L_p$ ) significantly narrows the energy gap between ICSI and PCSI, with $L_p=20$ showing negligible degradation compared to perfect knowledge.
Scalability: The method maintains superior energy efficiency as the number of SNs increases from 10 to 200.

Significance and Claims
The paper claims to be the first work to integrate relay-assisted TDMA transmission with stringent timing constraints for FL training specifically within industrial IIoT networks. The significance lies in its ability to balance the trade-off between energy consumption and latency while ensuring high reliability and fast convergence. By leveraging existing SNs as relays and performing partial aggregation, the framework eliminates the need for dedicated relay infrastructure while mitigating the "double path-loss" effect often seen in passive solutions like Reconfigurable Intelligent Surfaces (RIS). The authors assert that their approach is particularly effective in communication-constrained environments, offering a scalable solution for energy-efficient FL deployment in smart factories. The work acknowledges that while it enforces strict latency constraints to ensure synchronized aggregation, it does not explicitly model stochastic synchronization errors or update staleness, identifying this as a direction for future research.