Constructing 4D Radio Map in LEO Satellite Networks with Limited Samples

TL;DR

This work targets fine-grained spectrum monitoring in LEO satellite networks by formulating a 4D radio map across frequency and 3D space, and tackling the practical constraints of sparse sensors and sub-Nyquist sampling. It introduces DeepRM, a two-stage, unsupervised framework that decouples neural Compressive Sensing (CS) for power-spectrum reconstruction from neural Tensor Decomposition (TD) for 3D RM completion, with loss functions $\mathcal{L}_{\text{CS}}$ and $\mathcal{L}_{\text{TD}}$ and a combined objective $\mathcal{L}_{\text{Total}} = \mathcal{L}_{\text{CS}} + \mathcal{L}_{\text{TD}}$. Empirical results show DeepRM outperforms traditional CS methods and standard tensor completion baselines under severe missing data, achieving lower MSE in spectrum reconstruction and higher PSNR/SSIM in RM reconstruction at missing rates up to $98\%$, using hardware-constrained, sub-Nyquist sampling. The approach enables accurate 4D RM construction with limited sensors, supporting spectrum sharing and interference management in SAGIN without prohibitive sensor deployments, and suggesting future paths toward resource-aware scheduling and scalable, distributed implementations.

Abstract

Recently, Low Earth Orbit (LEO) satellite networks (i.e., non-terrestrial network (NTN)), such as Starlink, have been successfully deployed to provide broader coverage than terrestrial networks (TN). Due to limited spectrum resources, TN and NTN may soon share the same spectrum. Therefore, fine-grained spectrum monitoring is crucial for spectrum sharing and interference avoidance. To this end, constructing a 4D radio map (RM) including three spatial dimensions and signal spectra is important. However, this requires the large deployment of sensors, and high-speed analog-to-digital converters for extensive spatial signal collection and wide power spectrum acquisition, respectively. To address these challenges, we propose a deep unsupervised learning framework without ground truths labeling requirement, DeepRM, comprised of neural compressive sensing (CS) and tensor decomposition (TD) algorithms. Firstly, we map the CS process into the optimization of a neural networksassociated loss function, and design a sparsity-performance balance training algorithm to reconstruct a wide power spectrum under limited sub-Nquist samples. Secondly, according to the output of neural CS algorithm, we also utilize neural networks to perform TD, and construct the 3D RM for each frequency, even under very sparse sensor deployment. Extensive evaluations show that DeepRM achieves lower error than its corresponding state-of-the-art baselines, especially with limited samples.

Figures (14)

• Figure 1: The 4D RM constructing process in LEO satellite networks, where $f_i$ denotes the $i$-th frequency of the wideband.
• Figure 2: An example of a 4D RM tensor.
• Figure 3: The ground-truth power spectrum (a) and reconstructed power spectrum using FCPSE yang2019fast (a), JB-HTP (b) and SOMP (c) song2019real, where the sampling rate is 1/4 of the Nyquist sampling rate.
• Figure 4: The shadowing effect on 3D RM (a) and reconstruction performance using Tmac xu2013parallel (a) and Tmac xu2013parallel (b) under diverse missing rates.
• Figure 5: The overview of DeepRM framework ($a$); Sub-Nyquist sampling module ($a_1$); The NN architecture of $f_{\theta}(\cdot)$ ($a_2$) and $f_{\theta_i}(\cdot)$ ($i=1, 2,..., 3$) ($a_3$).