# Downlink MIMO Channel Estimation from Bits: Recoverability and Algorithm

arXiv: https://arxiv.org/abs/2411.16043 · HTML: https://mlsanity.com/paper/2411.16043/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 18 of its 62 references that are in the map.
- First posted on arXiv 25 Nov 2024.

## Builds on (most cited first, 18 of 18)

- [Spectrally-normalized margin bounds for neural networks](https://mlsanity.com/paper/1706.08498/) (2017)
- [Compressed Sensing using Generative Models](https://mlsanity.com/paper/1703.03208/) (2017)
- [DeepMIMO: A Generic Deep Learning Dataset for Millimeter Wave and Massive MIMO Applications](https://mlsanity.com/paper/1902.06435/) (2019)
- [Spectrum Cartography via Coupled Block-Term Tensor Decomposition](https://mlsanity.com/paper/1911.12468/) (2019)
- [Integrated Sensing and Communication with Massive MIMO: A Unified Tensor Approach for Channel and Target Parameter Estimation](https://mlsanity.com/paper/2401.01738/) (2024)
- [Deep Spectrum Cartography: Completing Radio Map Tensors Using Learned Neural Models](https://mlsanity.com/paper/2105.00177/) (2021)
- [Learning tensors from partial binary measurements](https://mlsanity.com/paper/1804.00108/) (2018)
- [Tensor denoising and completion based on ordinal observations](https://mlsanity.com/paper/2002.06524/) (2020)
- [Categorical Matrix Completion](https://mlsanity.com/paper/1507.00421/) (2015)
- [Quantized Radio Map Estimation Using Tensor and Deep Generative Models](https://mlsanity.com/paper/2303.01770/) (2023)
- [FDD Massive MIMO Channel Estimation with Arbitrary 2D-Array Geometry](https://mlsanity.com/paper/1711.06548/) (2017)
- [Tensor-Based Channel Estimation for Dual-Polarized Massive MIMO Systems](https://mlsanity.com/paper/1805.02223/) (2018)
- [On Recoverability of Randomly Compressed Tensors with Low CP Rank](https://mlsanity.com/paper/2001.02370/) (2020)
- [Sparse Channel Estimation for Massive MIMO with 1-bit Feedback per Dimension](https://mlsanity.com/paper/1610.03514/) (2016)
- [Algebraic Channel Estimation Algorithms for FDD Massive MIMO systems](https://mlsanity.com/paper/1903.08938/) (2019)
- [Pushing The Limit of Type I Codebook For FDD Massive MIMO Beamforming: A Channel Covariance Reconstruction Approach](https://mlsanity.com/paper/2010.11840/) (2020)
- [CSI Sensing from Heterogeneous User Feedbacks: A Constrained Phase Retrieval Approach](https://mlsanity.com/paper/2206.13882/) (2022)
- [Accelerated and Deep Expectation Maximization for One-Bit MIMO-OFDM Detection](https://mlsanity.com/paper/2210.03888/) (2022)

## Abstract (arXiv)

In frequency division duplex (FDD) massive MIMO systems, a major challenge lies in acquiring the downlink channel state information (CSI) at the base station (BS) from limited feedback sent by the user equipment (UE). To tackle this fundamental task, our contribution is twofold: First, a simple feedback framework is proposed, where a compression and Gaussian dithering-based quantization strategy is adopted at the UE side, and then a maximum likelihood estimator (MLE) is formulated at the BS side. Recoverability of the MIMO channel under the widely used double directional model is established. Specifically, analyses are presented for two compression schemes -- showing one being more overhead-economical and the other computationally lighter at the UE side. Second, to realize the MLE, an alternating direction method of multipliers (ADMM) algorithm is proposed. The algorithm is carefully designed to integrate a sophisticated harmonic retrieval (HR) solver as subroutine, which turns out to be the key of effectively tackling this hard MLE problem.Extensive numerical experiments are conducted to validate the efficacy of our approach.