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In-Context Learning for MIMO Equalization Using Transformer-Based Sequence Models

Matteo Zecchin, Kai Yu, Osvaldo Simeone

TL;DR

The paper addresses equalization for non-linear MIMO channels using in-context learning with decoder-only transformers, where a context of pilot examples enables direct prediction of transmitted symbols without updating model parameters. By pre-training on many related tasks, the transformer exhibits a threshold behavior: with enough pre-training diversity, it approaches the MMSE equalizer with the true data-generating prior, even under quantization. The method outperforms standard meta-learning approaches for short pilot sequences and demonstrates robust adaptation to varying SNR and non-linear distortions, highlighting practical potential for AI-enabled receivers in dynamic wireless environments. The work also contrasts ICL with Bayes-derived baselines and discusses complexity trade-offs, offering insights into when ICL is advantageous in real-time communication systems.

Abstract

Large pre-trained sequence models, such as transformer-based architectures, have been recently shown to have the capacity to carry out in-context learning (ICL). In ICL, a decision on a new input is made via a direct mapping of the input and of a few examples from the given task, serving as the task's context, to the output variable. No explicit updates of the model parameters are needed to tailor the decision to a new task. Pre-training, which amounts to a form of meta-learning, is based on the observation of examples from several related tasks. Prior work has shown ICL capabilities for linear regression. In this study, we leverage ICL to address the inverse problem of multiple-input and multiple-output (MIMO) equalization based on a context given by pilot symbols. A task is defined by the unknown fading channel and by the signal-to-noise ratio (SNR) level, which may be known. To highlight the practical potential of the approach, we allow the presence of quantization of the received signals. We demonstrate via numerical results that transformer-based ICL has a threshold behavior, whereby, as the number of pre-training tasks grows, the performance switches from that of a minimum mean squared error (MMSE) equalizer with a prior determined by the pre-trained tasks to that of an MMSE equalizer with the true data-generating prior.

In-Context Learning for MIMO Equalization Using Transformer-Based Sequence Models

TL;DR

The paper addresses equalization for non-linear MIMO channels using in-context learning with decoder-only transformers, where a context of pilot examples enables direct prediction of transmitted symbols without updating model parameters. By pre-training on many related tasks, the transformer exhibits a threshold behavior: with enough pre-training diversity, it approaches the MMSE equalizer with the true data-generating prior, even under quantization. The method outperforms standard meta-learning approaches for short pilot sequences and demonstrates robust adaptation to varying SNR and non-linear distortions, highlighting practical potential for AI-enabled receivers in dynamic wireless environments. The work also contrasts ICL with Bayes-derived baselines and discusses complexity trade-offs, offering insights into when ICL is advantageous in real-time communication systems.

Abstract

Large pre-trained sequence models, such as transformer-based architectures, have been recently shown to have the capacity to carry out in-context learning (ICL). In ICL, a decision on a new input is made via a direct mapping of the input and of a few examples from the given task, serving as the task's context, to the output variable. No explicit updates of the model parameters are needed to tailor the decision to a new task. Pre-training, which amounts to a form of meta-learning, is based on the observation of examples from several related tasks. Prior work has shown ICL capabilities for linear regression. In this study, we leverage ICL to address the inverse problem of multiple-input and multiple-output (MIMO) equalization based on a context given by pilot symbols. A task is defined by the unknown fading channel and by the signal-to-noise ratio (SNR) level, which may be known. To highlight the practical potential of the approach, we allow the presence of quantization of the received signals. We demonstrate via numerical results that transformer-based ICL has a threshold behavior, whereby, as the number of pre-training tasks grows, the performance switches from that of a minimum mean squared error (MMSE) equalizer with a prior determined by the pre-trained tasks to that of an MMSE equalizer with the true data-generating prior.
Paper Structure (11 sections, 18 equations, 6 figures)

This paper contains 11 sections, 18 equations, 6 figures.

Table of Contents

  1. Introduction
  2. System Model
  3. Signal Model
  4. ICL-Based Equalization
  5. Pre-Training (Meta-Learning)
  6. Baselines
  7. MMSE Equalizer for a Known Task
  8. MMSE Equalizer with Known SNR and a Given Channel Distribution
  9. Transformer-based Sequence Model for Equalization
  10. Results
  11. Conclusion

Figures (6)

  • Figure 1: Illustration of in-context learning for MIMO equalization.
  • Figure 2: Decoder-only transformer for ICL-based MIMO equalization.
  • Figure 3: Test mean squared error of the ICL and MLP equalizers as a function of the pilot sequence length $N$.
  • Figure 4: Test mean squared error of the ICL-based and reference MMSE equalizers with different channel priors (Sec. \ref{['subsec:knowndist']}) as a function of the number of pre-training tasks $M$ ($b=4$).
  • Figure 5: Test mean squared error as a function of the SNR level for the ICL-based equalizer trained at fixed SNR levels of 0 or 30 dB, as well as for the ICL-based equalizer trained on tasks with SNR levels uniformly drawn within the range $[0,30]$ dB. Also shown is the MSE of the benchmark MMSE and LMMSE estimators with task knowledge presented in Sec. \ref{['subsec:ideal']} ($b=4$).
  • ...and 1 more figures