# Quantized Radio Map Estimation Using Tensor and Deep Generative Models

arXiv: https://arxiv.org/abs/2303.01770 · HTML: https://mlsanity.com/paper/2303.01770/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Builds on 18 of its 62 references that are in the map.
- First posted on arXiv 3 Mar 2023.

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

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Spectrally-normalized margin bounds for neural networks](https://mlsanity.com/paper/1706.08498/) (2017)
- [A Max-Norm Constrained Minimization Approach to 1-Bit Matrix Completion](https://mlsanity.com/paper/1309.6013/) (2013)
- [Spectrum Cartography via Coupled Block-Term Tensor Decomposition](https://mlsanity.com/paper/1911.12468/) (2019)
- [Tag-Aware Ordinal Sparse Factor Analysis for Learning and Content Analytics](https://mlsanity.com/paper/1412.5967/) (2014)
- [A Unified Algorithmic Framework for Block-Structured Optimization Involving Big Data](https://mlsanity.com/paper/1511.02746/) (2015)
- [Learning Power Spectrum Maps from Quantized Power Measurements](https://mlsanity.com/paper/1606.02679/) (2016)
- [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)
- [Block-Randomized Stochastic Proximal Gradient for Low-Rank Tensor Factorization](https://mlsanity.com/paper/1901.05529/) (2019)
- [Spatial Signal Strength Prediction using 3D Maps and Deep Learning](https://mlsanity.com/paper/2011.03597/) (2020)
- [Hyperspectral Super-Resolution via Interpretable Block-Term Tensor Modeling](https://mlsanity.com/paper/2006.10248/) (2020)
- [Propagation Map Reconstruction via Interpolation Assisted Matrix Completion](https://mlsanity.com/paper/2207.13473/) (2022)
- [Tensor denoising and completion based on ordinal observations](https://mlsanity.com/paper/2002.06524/) (2020)
- [Tensor Completion for Radio Map Reconstruction using Low Rank and Smoothness](https://mlsanity.com/paper/1905.13689/) (2019)
- [Categorical Matrix Completion](https://mlsanity.com/paper/1507.00421/) (2015)
- [Data-Driven Spectrum Cartography via Deep Completion Autoencoders](https://mlsanity.com/paper/1911.12810/) (2019)
- [Fast and Structured Block-Term Tensor Decomposition For Hyperspectral Unmixing](https://mlsanity.com/paper/2205.03798/) (2022)

## Built on by (most cited first, 6 of 6)

- [Radio Map Estimation via Latent Domain Plug-and-Play Denoising](https://mlsanity.com/paper/2501.13472/) (2025)
- [Blind Construction of Angular Power Maps in Massive MIMO Networks](https://mlsanity.com/paper/2510.07071/) (2025)
- [Blind Radio Mapping via Spatially Regularized Bayesian Trajectory Inference](https://mlsanity.com/paper/2512.13701/) (2025)
- [Downlink MIMO Channel Estimation from Bits: Recoverability and Algorithm](https://mlsanity.com/paper/2411.16043/) (2024)
- [ReVeal-MT: A Physics-Informed Neural Network for Multi-Transmitter Radio Environment Mapping](https://mlsanity.com/paper/2512.04100/) (2025)
- [Active Learning for Low-Altitude Radio Map Construction via Plug-and-Play Flow Matching](https://mlsanity.com/paper/2609.27486/) (2026)

## Abstract (arXiv)

Spectrum cartography (SC), also known as radio map estimation (RME), aims at crafting multi-domain (e.g., frequency and space) radio power propagation maps from limited sensor measurements. While early methods often lacked theoretical support, recent works have demonstrated that radio maps can be provably recovered using low-dimensional models -- such as the block-term tensor decomposition (BTD) model and certain deep generative models (DGMs) -- of the high-dimensional multi-domain radio signals. However, these existing provable SC approaches assume that sensors send real-valued (full-resolution) measurements to the fusion center, which is unrealistic. This work puts forth a quantized SC framework that generalizes the BTD and DGM-based SC to scenarios where heavily quantized sensor measurements are used. A maximum likelihood estimation (MLE)-based SC framework under a Gaussian quantizer is proposed. Recoverability of the radio map using the MLE criterion are characterized under realistic conditions, e.g., imperfect radio map modeling and noisy measurements. Simulations and real-data experiments are used to showcase the effectiveness of the proposed approach.