Electromagnetic Spectrum Map Reconstruction Technology Based on Tensor CP Factor Matrix Decomposition

• Published in: IEEE International Conference on Power, Intelligent Computing and Systems (Online) pp. 1736 - 1742
• Main Authors: Jiawei, Xie, Zhiyong, Yu, Yujie, Zhang
• Format: Conference Proceeding
• Language: English
• Published: IEEE 26.07.2024
• Subjects: Accuracy; Computational modeling; density clustering; Electromagnetic spectrum; electromagnetic spectrum maps; Electromagnetics; inverse distance weighting; Load modeling; Matrix decomposition; Minimization; Monitoring; Solid modeling; spatial interpolation; Tensors; urban environment
• ISSN: 2834-8567
• DOI: 10.1109/ICPICS62053.2024.10796244

Electromagnetic spectrum mapping reveals the spatial distribution patterns of the electromagnetic environment, serving as a vital tool for complex electromagnetic environment modeling and simulation. This paper initially models the multi-domain electromagnetic spectrum environment as a three-dimensional spectral tensor. Leveraging the high correlation and low-rank structure inherent in the 3rd-order spectral tensor, as well as the sparsity of monitoring sample data, we design a low-rank tensor completion model based on CP (CANDECOMP-PARAFAC) decomposition. This approach transforms the construction of electromagnetic spectrum maps into a low-rank tensor completion problem with missing data. Subsequently, by employing tensor CP decomposition, we obtain multiple low-rank factor matrices. The missing data recovery is then formulated as a minimization of the nuclear norm based on CP factor matrices, aiming to reduce the matrix dimensions subject to singular value decomposition and thereby significantly decrease computational load and completion time. The tensor is reconstructed from the CP factor matrix decomposition to retrieve the original information values at missing locations. Finally, the Alternating Direction Method of Multipliers (ADMM) is utilized for iterative solution. By fixing all but one variable and updating one variable at a time, the optimization is performed iteratively until the error is less than a predefined precision threshold \varepsilon . Addressing the issue of limited monitoring data samples or data sparsity, this paper proposes a low-rank completion algorithm based on tensor CP factor matrix decomposition. The tensor completion algorithm enables rapid and accurate reconstruction of electromagnetic spectrum maps with minimal sacrifice in construction accuracy. Simulation results demonstrate the excellent performance of the proposed algorithm.