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Precoding-Oriented CSI Feedback Design with Mutual Information Regularized VQ-VAE

Xi Chen, Homa Esfahanizadeh, Foad Sohrabi

TL;DR

The paper tackles efficient CSI feedback for precoding in FDD massive MIMO under a fixed uplink budget. It introduces a precoding-oriented framework based on vector quantized variational autoencoders (VQ-VAE) augmented with a differentiable mutual-information lower bound to regularize the learned codebooks, promoting more uniform codeword usage. A multi-codebook design per user and an end-to-end training objective that regularizes mutual information between UE observations and feedback enable higher sum rates compared to a DL baseline and approach variable-length neural compression performance. The results show improved codeword utilization and CSI interpretability, with learned codewords correlating strongly to channel parameters such as AoD, signaling practical gains for downlink precoding in mmWave massive MIMO. Overall, the approach provides a principled, tractable path to fixed-length CSI feedback that preserves downlink performance in realistic, limited-bandwidth settings.

Abstract

Efficient channel state information (CSI) compression at the user equipment plays a key role in enabling accurate channel reconstruction and precoder design in massive multiple-input multiple-output systems. A key challenge lies in balancing the CSI feedback overhead with the achievable downlink rate, i.e., maximizing the utility of limited feedback to maintain high system performance. In this work, we propose a precoding-oriented CSI feedback framework based on a vector quantized variational autoencoder, augmented with an information-theoretic regularization. To achieve this, we introduce a differentiable mutual information lower-bound estimator as a training regularizer to promote effective utilization of the learned codebook under a fixed feedback budget. Numerical results demonstrate that the proposed method achieves rates comparable to variable-length neural compression schemes, while operating with fixed-length feedback. Furthermore, the learned codewords exhibit significantly more uniform usage and capture interpretable structures that are strongly correlated with the underlying channel state information.

Precoding-Oriented CSI Feedback Design with Mutual Information Regularized VQ-VAE

TL;DR

The paper tackles efficient CSI feedback for precoding in FDD massive MIMO under a fixed uplink budget. It introduces a precoding-oriented framework based on vector quantized variational autoencoders (VQ-VAE) augmented with a differentiable mutual-information lower bound to regularize the learned codebooks, promoting more uniform codeword usage. A multi-codebook design per user and an end-to-end training objective that regularizes mutual information between UE observations and feedback enable higher sum rates compared to a DL baseline and approach variable-length neural compression performance. The results show improved codeword utilization and CSI interpretability, with learned codewords correlating strongly to channel parameters such as AoD, signaling practical gains for downlink precoding in mmWave massive MIMO. Overall, the approach provides a principled, tractable path to fixed-length CSI feedback that preserves downlink performance in realistic, limited-bandwidth settings.

Abstract

Efficient channel state information (CSI) compression at the user equipment plays a key role in enabling accurate channel reconstruction and precoder design in massive multiple-input multiple-output systems. A key challenge lies in balancing the CSI feedback overhead with the achievable downlink rate, i.e., maximizing the utility of limited feedback to maintain high system performance. In this work, we propose a precoding-oriented CSI feedback framework based on a vector quantized variational autoencoder, augmented with an information-theoretic regularization. To achieve this, we introduce a differentiable mutual information lower-bound estimator as a training regularizer to promote effective utilization of the learned codebook under a fixed feedback budget. Numerical results demonstrate that the proposed method achieves rates comparable to variable-length neural compression schemes, while operating with fixed-length feedback. Furthermore, the learned codewords exhibit significantly more uniform usage and capture interpretable structures that are strongly correlated with the underlying channel state information.
Paper Structure (13 sections, 1 theorem, 25 equations, 4 figures, 1 table)

This paper contains 13 sections, 1 theorem, 25 equations, 4 figures, 1 table.

Table of Contents

  1. Introduction
  2. System Model
  3. Learning-based Precoding-Oriented CSI Feedback Design
  4. Precoding-oriented CSI Feedback Design with Mutual Information Regularized VQ-VAE
  5. Vector Quantized Variational Autoencoder
  6. Differentiable MI Lower Bound
  7. MI Empowered VQ-VAE for CSI Feedback Design
  8. Numerical results
  9. Channel Model
  10. Sum Achievable Rate v.s. Feedback Bits Performance
  11. Channel interpretability of learned codeword
  12. Codebook Usage with Allocated Bits
  13. Conclusion

Key Result

Theorem 4.1

Assuming $Z=T(X)$, where $T:\mathcal{X}\rightarrow\mathcal{Z}$ is a deterministic function, we have where $z$, $z'$ are two r.v.s. independently drawn from $P_Z$. Here, $\delta(\cdot)=1$ if its argument is zero, and $\delta(\cdot)=0$ otherwise.

Figures (4)

  • Figure 1: The structure of VQ-VAE with MI regularizer illustrated for a single UE precoder-oriented CSI feedback design.
  • Figure 2: Performance comparison in terms of sum achievable rate.
  • Figure 3: Channel information and its assigned codeword.
  • Figure 4: The number of feedback bits per UE is fixed to $10$. Histograms of codeword usage across different training epochs: (Top) DNN-based method in sohrabi2021deep; (Bottom) Our proposed method exhibits a more uniform distribution.

Theorems & Definitions (2)

  • Theorem 4.1
  • proof