Quantized Radio Map Estimation Using Tensor and Deep Generative Models

Abstract

<italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Spectrum cartography</i> (SC), also known as <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">radio map estimation</i> (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 <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">block-term tensor decomposition</i> (BTD) model and certain <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">deep generative models</i> (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 <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">quantized</i> 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 is 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.