# Downlink Channel Covariance Matrix Estimation via Representation Learning with Graph Regularization

arXiv: https://arxiv.org/abs/2407.18865 · HTML: https://mlsanity.com/paper/2407.18865/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 10 of its 48 references that are in the map.
- First posted on arXiv 26 Jul 2024.

## Builds on (most cited first, 10 of 10)

- [Image-to-Image Translation with Conditional Adversarial Networks](https://mlsanity.com/paper/1611.07004/) (2016)
- [Deep Learning for Distributed Channel Feedback and Multiuser Precoding in FDD Massive MIMO](https://mlsanity.com/paper/2007.06512/) (2020)
- [Deep Learning based Downlink Channel Prediction for FDD Massive MIMO System](https://mlsanity.com/paper/1908.03360/) (2019)
- [FDD Massive MIMO Uplink and Downlink Channel Reciprocity Properties: Full or Partial Reciprocity?](https://mlsanity.com/paper/1912.11221/) (2019)
- [Machine Learning-Based CSI Feedback With Variable Length in FDD Massive MIMO](https://mlsanity.com/paper/2204.04723/) (2022)
- [Nonlinear Supervised Dimensionality Reduction via Smooth Regular Embeddings](https://mlsanity.com/paper/1710.07120/) (2017)
- [FDD massive MIMO channel spatial covariance conversion using projection methods](https://mlsanity.com/paper/1804.04850/) (2018)
- [Downlink Channel Covariance Matrix Reconstruction for FDD Massive MIMO Systems with Limited Feedback](https://mlsanity.com/paper/2204.00779/) (2022)
- [Learning Multi-Modal Nonlinear Embeddings: Performance Bounds and an Algorithm](https://mlsanity.com/paper/2006.02330/) (2020)
- [Robust Statistical Beamforming with Multi-Cluster Tracking for Time-Varying Massive MIMO (Extended Version)](https://mlsanity.com/paper/2303.00457/) (2023)

## Built on by (most cited first, 1 of 1)

- [Mean Spatial Frequency Decoupling for Learning-Based Uplink-to-Downlink Covariance Conversion in FDD Massive MIMO](https://mlsanity.com/paper/2610.00596/) (2026)

## Abstract (arXiv)

In this paper, we propose an algorithm for downlink (DL) channel covariance matrix (CCM) estimation for frequency division duplexing (FDD) massive multiple-input multiple-output (MIMO) communication systems with base station (BS) possessing a uniform linear array (ULA) antenna structure. We consider a setting where the UL CCM is mapped to DL CCM by a mapping function. We first present a theoretical error analysis of learning a nonlinear embedding by constructing a mapping function, which points to the importance of the Lipschitz regularity of the mapping function for achieving high estimation performance. Then, based on the theoretical ground, we propose a representation learning algorithm as a solution for the estimation problem, where Gaussian RBF kernel interpolators are chosen to map UL CCMs to their DL counterparts. The proposed algorithm is based on the optimization of an objective function that fits a regression model between the DL CCM and UL CCM samples in the training dataset and preserves the local geometric structure of the data in the UL CCM space, while explicitly regulating the Lipschitz continuity of the mapping function in light of our theoretical findings. The proposed algorithm surpasses benchmark methods in terms of three error metrics as shown by simulations.