Spectrum Map Construction Algorithm Based on Tensor Tucker Decomposition

This paper investigates the construction of dynamic electromagnetic spectrum maps using a limited amount of monitored sample data. First, the time-varying spectrum maps of the dynamic electromagnetic environment are modeled as three-dimensional spectrum tensors. The tensor Tucker decomposition is then employed to extract low-dimensional features, including physically meaningful core tensors and factor matrices. Second, a low-rank tensor completion model based on the Tucker decomposition is designed considering the correlation between the temporal, spatial, and frequency domains of the spectrum tensorand and the sparsity of the monitored sample data. This model transforms the spectrum map construction task into an optimization problem of completing low-rank tensors with missing data. To address this problem, this paper proposes two spectrum map construction algorithms that do not rely on prior information: high-precision and fast spectrum map construction algorithms. The former employs an alternating least squares method for iteratively solving the core tensor and factor matrices, achieving high-precision spectrum map construction through a “completion-decomposition” process. Meanwhile, the latter employs a sequential truncated higher-order singular value decomposition method for averaging multiple low-rank approximate tensors, offering rapid convergence and low computational complexity. Therefore, this algorithm can quickly construct spectrum maps by sacrificing a small amount of construction accuracy. The simulation results show that the proposed algorithms can accurately construct spectrum maps and outperform comparative algorithms in terms of construction accuracy, runtime consumption, and noise robustness.