# Tensor Learning-based Precoder Codebooks for FD-MIMO Systems

arXiv: https://arxiv.org/abs/2106.11374 · HTML: https://mlsanity.com/paper/2106.11374/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 8 of its 49 references that are in the map.
- First posted on arXiv 21 Jun 2021.

## Builds on (most cited first, 8 of 8)

- [An Introduction to Deep Learning for the Physical Layer](https://mlsanity.com/paper/1702.00832/) (2017)
- [Tensor Decomposition for Signal Processing and Machine Learning](https://mlsanity.com/paper/1607.01668/) (2016)
- [Theory-guided Data Science: A New Paradigm for Scientific Discovery from Data](https://mlsanity.com/paper/1612.08544/) (2016)
- [DeepMIMO: A Generic Deep Learning Dataset for Millimeter Wave and Massive MIMO Applications](https://mlsanity.com/paper/1902.06435/) (2019)
- [Deep Learning-Based Communication Over the Air](https://mlsanity.com/paper/1707.03384/) (2017)
- [Convolutional Neural Network based Multiple-Rate Compressive Sensing for Massive MIMO CSI Feedback: Design, Simulation, and Analysis](https://mlsanity.com/paper/1906.06007/) (2019)
- [Deep Convolutional Compression for Massive MIMO CSI Feedback](https://mlsanity.com/paper/1907.02942/) (2019)
- [Learning on a Grassmann Manifold: CSI Quantization for Massive MIMO Systems](https://mlsanity.com/paper/2005.08413/) (2020)

## Abstract (arXiv)

This paper develops an efficient procedure for designing low-complexity codebooks for precoding in a full-dimension (FD) multiple-input multiple-output (MIMO) system with a uniform planar array (UPA) antenna at the transmitter (Tx) using tensor learning. In particular, instead of using statistical channel models, we utilize a model-free data-driven approach with foundations in machine learning to generate codebooks that adapt to the surrounding propagation conditions. We use a tensor representation of the FD-MIMO channel and exploit its properties to design quantized version of the channel precoders. We find the best representation of the optimal precoder as a function of Kronecker Product (KP) of two low-dimensional precoders, respectively corresponding to the horizontal and vertical dimensions of the UPA, obtained from the tensor decomposition of the channel. We then quantize this precoder to design product codebooks such that an average loss in mutual information due to quantization of channel state information (CSI) is minimized. The key technical contribution lies in exploiting the constraints on the precoders to reduce the product codebook design problem to an unsupervised clustering problem on a Cartesian Product Grassmann manifold (CPM), where the cluster centroids form a finite-sized precoder codebook. This codebook can be found efficiently by running a K-means clustering on the CPM. With a suitable induced distance metric on the CPM, we show that the construction of product codebooks is equivalent to finding the optimal set of centroids on the factor manifolds corresponding to the horizontal and vertical dimensions. Simulation results are presented to demonstrate the capability of the proposed design criterion in learning the codebooks and the attractive performance of the designed codebooks.