⚡ electrical engineering

Energy-Efficient Federated Learning in Cooperative Communication within Factory Subnetworks

This paper proposes an energy-efficient transmission protocol for relay-assisted federated learning in industrial subnetworks that optimizes device grouping, access point association, and transmit power using a Sequential Parametric Convex Approximation method to significantly reduce energy consumption and outage probability while improving convergence speed compared to single-hop transmission.

Original authors: Hamid Reza Hashempour, Gilberto Berardinelli, Shashi Raj Pandey, Hien Quoc Ngo

Published 2026-03-24

📖 4 min read☕ Coffee break read

CC BY 4.0

Original authors: Hamid Reza Hashempour, Gilberto Berardinelli, Shashi Raj Pandey, Hien Quoc Ngo

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, high-tech factory floor filled with hundreds of smart robots, sensors, and machines. These devices are constantly collecting data about their performance, temperature, and efficiency. The factory manager wants to teach all these machines to work together smarter using Artificial Intelligence (AI).

However, there's a problem: sending all that raw data to a central "brain" (a server) is slow, expensive on battery life, and risky for privacy. Instead, the factory uses a clever method called Federated Learning (FL).

Here is how the paper explains a new, energy-saving way to make this happen, using simple analogies:

1. The Problem: The "Heavy Backpack"

Imagine every robot in the factory has a backpack. To learn, they need to write a short report (a "local model") about what they learned and send it to the main office (the server).

The Issue: If a robot is far away or behind a giant metal machine, the signal is weak. To get the report across, the robot has to shout very loudly (use high power), which drains its battery quickly.
The Constraint: The factory manager says, "You must get these reports to me within 5 seconds, or the whole production line stops."

2. The Old Way: The "Solo Runner"

In the traditional setup, every robot tries to run directly to the main office to drop off its report.

If the path is clear, it's fast.
If the path is blocked by metal machinery, the robot has to sprint at full speed (high energy) to get through, or it might fail to deliver the report on time (an "outage").
Result: Many robots burn out their batteries, and some reports never arrive.

3. The New Solution: The "Relay Team"

This paper proposes a smarter strategy: Cooperative Communication. Think of it like a relay race.

The Players:
- The Runners (Sensors): The robots that have the data.
- The Main Office (pAP): The primary server that collects everything.
- The Couriers (sAPs): Secondary access points (smaller towers) scattered around the factory. They act as relays.
How it Works:
1. The Scout: Before the race starts, the system checks the terrain.
2. The Decision:
  - If a robot is close to the Main Office with a clear path, it runs directly (Single-hop).
  - If a robot is blocked by metal or far away, it doesn't shout loudly. Instead, it whispers its report to a nearby Courier (sAP).
3. The Handoff: The Courier catches the whisper, decodes it, and then runs it to the Main Office.
4. The Bonus: The Main Office is smart. It listens to both the robot's original whisper and the Courier's shout, combining them to get a clearer picture.

4. The "Smart Scheduler" (The Coach)

The paper introduces a special algorithm (the "Coach") that decides who runs which way to save the most energy.

The Coach's Job: It looks at the battery levels and the distance. It asks, "Who should run alone, and who should pass the baton to a courier?"
The Optimization: It calculates the perfect speed (frequency) and volume (transmit power) for every device so they finish exactly on time without wasting a single drop of energy.

5. The Results: Saving the Battery

The researchers tested this in a simulation of a factory. Here is what they found:

Less Outages: By using the relay couriers, fewer reports got lost. The system became much more reliable.
Double the Savings: The new method used at least 50% less energy than the old "solo runner" method.
Faster Learning: Because the robots didn't have to struggle to shout over the noise, the whole factory learned the AI model faster.

The Big Picture

Think of this paper as a manual for organizing a factory relay race. Instead of forcing every worker to sprint the whole distance (which exhausts them), the system intelligently pairs up workers with helpers (relays) to carry the load. This ensures the job gets done quickly, the workers stay fresh (energy-efficient), and the factory keeps running smoothly.

In short: It's about using teamwork and smart planning to make AI training in factories faster, cheaper, and less draining on battery power.

1. Problem Statement

The paper addresses the challenge of deploying Federated Learning (FL) within Industrial Internet of Things (IIoT) factory subnetworks. In these environments, devices (sensors/robots) collaborate to train a global AI model without sharing raw data, preserving privacy. However, two critical constraints hinder efficient deployment:

Energy Constraints: Battery-powered IoT devices must balance the energy cost of local computation (training) with the energy cost of transmitting model updates to a central server.
Latency and Reliability: Factory environments suffer from signal blockages (e.g., metallic machinery) and fading, leading to transmission delays. Strict latency requirements for industrial control cycles often cause single-hop transmissions to fail (outage), especially when devices are far from the primary access point (pAP).

The core problem is to design a transmission protocol that minimizes total energy consumption (computation + transmission) while satisfying strict latency constraints and ensuring reliable model aggregation in a relay-assisted setting.

2. System Model

The authors propose a system consisting of:

$N$ Sensors: Devices performing local FL training.
$K+1$ Access Points (APs):
- 1 Primary AP (pAP): Controls actuators and aggregates global models.
- $K$ Secondary APs (sAPs): Act as relays with only radio communication capabilities.
Transmission Modes:
- Single-hop: Devices transmit directly to the pAP.
- Two-hop (Cooperative): Devices transmit to an sAP, which decodes and forwards (Decode-and-Forward, DF) the data to the pAP. The pAP combines signals from both the direct link and the relayed link to improve reliability.
Protocol: A Time Division Multiple Access (TDMA) scheme where the uplink time slot is divided into three phases:
1. Two-hop Phase 1 (Device $\to$ sAP & pAP).
2. Single-hop Phase (Device $\to$ pAP).
3. Two-hop Phase 2 (sAP $\to$ pAP).

3. Methodology

The authors formulate a non-convex optimization problem to minimize total energy consumption subject to latency and power constraints. Due to the high coupling between variables (transmit power, CPU frequency, relay selection), they propose a decomposition approach:

A. Problem Decomposition

The problem is split into two sub-problems:

Computational Energy Minimization: Optimizing the CPU frequency ( $f_n$ ) of each device.
Transmission Energy Minimization: Optimizing transmit power ( $P_n$ ), relay selection, and device grouping.

B. CPU Frequency Optimization

To minimize local computation energy ( $E_L \propto f_n^2$ ), the authors derive that devices should operate at the lowest possible frequency that still satisfies the total time constraint. This results in a closed-form solution for the optimal frequency $f^*_n$ based on the remaining time budget after transmission.

C. Relay Selection and Power Control

Once computation energy is minimized, the focus shifts to transmission energy.

Device Classification (Relay Selection):
- An algorithm classifies devices into Single-hop ( $N_{1h}$ ) or Two-hop ( $N_{2h}$ ) groups.
- The decision is based on Channel State Information (CSI). A "1 of K" strategy is used where a device selects the sAP with the strongest effective channel gain.
- If the direct link gain exceeds the effective two-hop gain, the device uses single-hop; otherwise, it uses the cooperative two-hop mode.
Power Optimization via SPCA:
- The remaining problem (minimizing power subject to time constraints) is non-convex due to the logarithmic rate functions.
- The authors employ Sequential Parametric Convex Approximation (SPCA).
- This method iteratively approximates non-convex constraints with convex surrogates (using first-order lower bounds and auxiliary variables).
- The transformed problem becomes a Convex Semidefinite Programming (SDP) problem, solvable using standard tools like CVX.

4. Key Contributions

Novel Protocol: Integration of a relay-assisted TDMA protocol with FL training in factory subnetworks, specifically addressing the trade-off between single-hop and cooperative two-hop transmissions.
Joint Optimization Framework: A low-complexity iterative algorithm that jointly optimizes device grouping, relay selection, CPU frequency, and transmit power.
SPCA Application: The application of Sequential Parametric Convex Approximation to solve the non-convex energy minimization problem under strict latency constraints, converting it into a tractable convex form.
Energy-Latency Trade-off Analysis: A rigorous mathematical formulation that balances local computation costs against wireless transmission costs.

5. Numerical Results

Simulations were conducted using a 3x3 m² factory subnetwork with 20 sensors, using the MNIST dataset for handwritten digit recognition.

Outage Probability: The cooperative schemes (especially "1 of 4," utilizing 4 sAPs) significantly reduced the system outage probability compared to single-hop transmission, particularly at lower transmit powers.
Energy Efficiency: The proposed cooperative method achieved at least a twofold reduction in total energy consumption compared to single-hop transmission. Specifically, the "1 of 4" scheme used less than half the energy of the single-hop baseline.
Convergence: The cooperative approach allowed for faster convergence of the FL model because it ensured more devices could successfully upload their models within the strict time limits, whereas single-hop transmissions often failed due to latency violations.
Scalability: As the number of devices increased (10 to 50), the energy savings of the cooperative scheme over single-hop remained consistent and significant.

6. Significance

This paper provides a critical solution for the deployment of AI-driven Industry 4.0 applications. By demonstrating that relay-assisted cooperative communication can drastically reduce energy consumption while meeting strict industrial latency requirements, the work enables:

Longer battery life for wireless industrial sensors.
More reliable FL training in harsh, interference-prone factory environments.
A scalable framework for integrating edge AI into existing wireless infrastructure without requiring massive power upgrades.

The proposed SPCA-based algorithm offers a practical, computationally efficient tool for network operators to manage resources in energy-constrained, latency-sensitive IIoT networks.