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Over-the-Air Inference over Multi-hop MIMO Networks

Chenghong Bian, Meng Hua, Deniz Gunduz

TL;DR

The paper tackles the problem of performing neural inference directly over wireless multi-hop MIMO links under transmit power constraints. It introduces PrototypeNet, an end-to-end trainable network whose per-hop precoders are learned to mimic FC layers despite channel effects and noise, with two loss formulations that balance accuracy and power. The method demonstrates that noise-aware training with a power-focused objective (L2) outperforms alternatives, and that additional hops can improve accuracy at modest SNR, while a multiple-block transmission strategy helps when antenna counts are limited. Collectively, the work provides a practical framework for over-the-air inference in multi-hop wireless networks and offers design insights for precoding and network width under real-world constraints.

Abstract

A novel over-the-air machine learning framework over multi-hop multiple-input and multiple-output (MIMO) networks is proposed. The core idea is to imitate fully connected (FC) neural network layers using multiple MIMO channels by carefully designing the precoding matrices at the transmitting nodes. A neural network dubbed PrototypeNet is employed consisting of multiple FC layers, with the number of neurons of each layer equal to the number of antennas of the corresponding terminal. To achieve satisfactory performance, we train PrototypeNet based on a customized loss function consisting of classification error and the power of latent vectors to satisfy transmit power constraints, with noise injection during training. Precoding matrices for each hop are then obtained by solving an optimization problem. We also propose a multiple-block extension when the number of antennas is limited. Numerical results verify that the proposed over-the-air transmission scheme can achieve satisfactory classification accuracy under a power constraint. The results also show that higher classification accuracy can be achieved with an increasing number of hops at a modest signal-to-noise ratio (SNR).

Over-the-Air Inference over Multi-hop MIMO Networks

TL;DR

The paper tackles the problem of performing neural inference directly over wireless multi-hop MIMO links under transmit power constraints. It introduces PrototypeNet, an end-to-end trainable network whose per-hop precoders are learned to mimic FC layers despite channel effects and noise, with two loss formulations that balance accuracy and power. The method demonstrates that noise-aware training with a power-focused objective (L2) outperforms alternatives, and that additional hops can improve accuracy at modest SNR, while a multiple-block transmission strategy helps when antenna counts are limited. Collectively, the work provides a practical framework for over-the-air inference in multi-hop wireless networks and offers design insights for precoding and network width under real-world constraints.

Abstract

A novel over-the-air machine learning framework over multi-hop multiple-input and multiple-output (MIMO) networks is proposed. The core idea is to imitate fully connected (FC) neural network layers using multiple MIMO channels by carefully designing the precoding matrices at the transmitting nodes. A neural network dubbed PrototypeNet is employed consisting of multiple FC layers, with the number of neurons of each layer equal to the number of antennas of the corresponding terminal. To achieve satisfactory performance, we train PrototypeNet based on a customized loss function consisting of classification error and the power of latent vectors to satisfy transmit power constraints, with noise injection during training. Precoding matrices for each hop are then obtained by solving an optimization problem. We also propose a multiple-block extension when the number of antennas is limited. Numerical results verify that the proposed over-the-air transmission scheme can achieve satisfactory classification accuracy under a power constraint. The results also show that higher classification accuracy can be achieved with an increasing number of hops at a modest signal-to-noise ratio (SNR).
Paper Structure (9 sections, 18 equations, 2 figures, 1 algorithm)

This paper contains 9 sections, 18 equations, 2 figures, 1 algorithm.

Table of Contents

  1. Introduction
  2. System Model
  3. Methodology
  4. PrototypeNet
  5. Calculation of $\mathbf{F}_i$
  6. Multiple-Block Transmission Strategy
  7. Numerical Experiments
  8. Performance Evaluation
  9. Conclusion

Figures (2)

  • Figure 1: The flowchart of the multi-hop MIMO network and the PrototypeNet. We consider a $N$-hop MIMO network and it is equivalent to the PrototypeNet with $(N+1)$ FC layers (including the one at the destination node). The second loss function, $\mathcal{L}_2$, defined in \ref{['eq:optim_z']} is used to train the PrototypeNet.
  • Figure 2: Classification performance of the proposed scheme in terms of the average power consumption. (a) The performance obtained by the PrototypeNet with different loss functions, number of antennas, ($M$) and number of transmissions, ($J$). (b) The performance of the PrototypeNet with different number of hops ($N$). (c) Performance of multi-hop MIMO network compared with a direct precoding baseline.