# A Learnable Optimization and Regularization Approach to Massive MIMO CSI Feedback

arXiv: https://arxiv.org/abs/2209.15340 · HTML: https://mlsanity.com/paper/2209.15340/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 30 Sep 2022.

## Built on by (most cited first, 2 of 2)

- [An Efficient Network with Novel Quantization Designed for Massive MIMO CSI Feedback](https://mlsanity.com/paper/2405.20068/) (2024)
- [Quantization Design for Deep Learning-Based CSI Feedback](https://mlsanity.com/paper/2503.08125/) (2025)

## Abstract (arXiv)

Channel state information (CSI) plays a critical role in achieving the potential benefits of massive multiple input multiple output (MIMO) systems. In frequency division duplex (FDD) massive MIMO systems, the base station (BS) relies on sustained and accurate CSI feedback from the users. However, due to the large number of antennas and users being served in massive MIMO systems, feedback overhead can become a bottleneck. In this paper, we propose a model-driven deep learning method for CSI feedback, called learnable optimization and regularization algorithm (LORA). Instead of using l1-norm as the regularization term, a learnable regularization module is introduced in LORA to automatically adapt to the characteristics of CSI. We unfold the conventional iterative shrinkage-thresholding algorithm (ISTA) to a neural network and learn both the optimization process and regularization term by end-toend training. We show that LORA improves the CSI feedback accuracy and speed. Besides, a novel learnable quantization method and the corresponding training scheme are proposed, and it is shown that LORA can operate successfully at different bit rates, providing flexibility in terms of the CSI feedback overhead. Various realistic scenarios are considered to demonstrate the effectiveness and robustness of LORA through numerical simulations.