3-D radio maps provide significantly richer information than their 2-D counterparts in spectrum cartography. However, reconstruction methods for 3-D radio maps remain underexplored. Classic methods, such as spatial interpolation and matrix completion, can be adapted for 3-D scenarios, but they are often computationally intensive and require a substantial number of sampling measurements. To address these challenges, we propose a novel and efficient 3-D radio map reconstruction paradigm inspired by cross tensor approximation (CTA). During the measurement phase, only piecewise straight-line paths are required, making this method well-suited for the flying trajectories of unmanned aerial vehicles (UAVs). In the reconstruction phase, we utilize the inherent tensor structure of 3-D radio maps by employing the fiber sampling tensor decomposition (FSTD) algorithm, which ensures high-quality and computationally efficient reconstruction from the measurements. To further reduce the number of measurements, we introduce a new algorithm called interpolation-integrated FSTD (II-FSTD). This algorithm builds on the original FSTD yet exploits the smoothness of radio maps to incorporate interpolation, thereby reducing the required measurement frequency. Extensive experimental results demonstrate that the proposed paradigm can reconstruct 3-D radio maps with high quality, using fewer measurements and less computational time compared to state-of-the-art techniques. Notably, in scenarios with lower measurement frequency, II-FSTD outperforms other methods, achieving superior reconstruction performance.

A flexible mathematical framework for adaptive wireless communication waveform design is of importance for the implement of the cognitive radio-based software defined radio (CR-based SDR). As one of the popular models, the "spectrally modulated spectrally encoded" (SMSE) was proposed to tackle this problem but it cannot be trivially applied to the (massive) multiple input multiple output (MIMO) systems. In this paper, we extend the useful SMSE model into MIMO systems. Inspired by the tensor technique in signal processing and machine learning, we reformulate the desired waveforms as a higher-order tensors, of which the modes correspond to various modulation parameters such as coding chips, frequency and antennas. Beside the waveform design model, we further propose a new semi-blind receiver for the new model. Due the uniqueness of the applied tensor decomposition, we proved that the proposed receiver can jointly estimate the user symbols and channel state information without the aid of pilot sequences. Experimental results demonstrate the effectiveness of the proposed model in various communication scenes and outperforms the baseline systems. approximately 3 dB compared with the ideal receiver.

Extremely low frequency (ELF) electromagnetic (EM) waves, with frequencies below 300 Hz, exhibit superior penetration through seawater, enabling longer communication ranges and enhancing the flexibility of vehicles for ocean exploration. Despite their potential, ELF propagation in seawater is more complex due to interactions with the air-sea boundary and frequency-dependent attenuation caused by seawater. Here we present a new set of approximate formulas for the EM field components for cross-medium propagation from air-to undersea, due to a vertical electric dipole (VED). The formulas, derived through asymptotic and series expansions of Sommerfeld integrals (SIs), address the limitations of existing models by accurately characterizing EM field in the transition zone between near-field and intermediate-field regions and impose no restrictions on reception depth. Comparisons and analyses with related work and numerical results demonstrate the accuracy and effectiveness of our formulas. The formulas provide simplified calculations, clear physical interpretation, and broad applicability without distance or frequency restrictions. The results enhance the feasibility of ELF communication across air-sea interfaces.

Radio maps are crucial for wireless communication applications, but their increasing volume and dimension pose significant challenges to effective utilization. Traditional tensor network-based dimension reduction (DR) methods rely on fixed structures, which are not optimal for arbitrary radio maps. To address this limitation, we propose a new DR approach, named Alternating Enumeration-Random Sampling (AE-RS) inspired by tensor network structure search (TNSS). It can adaptively select the most compact tensor network for efficient representation of various radio maps to achieve superior DR performance. AE-RS incorporates a random sampling phase after each round trip of alternating enumeration, thereby reducing the likelihood of converging to local minima. Meanwhile, we propose a Minimized Initialization-Error Penalty (MI-EP) method within AE-RS to address the issue of unsatisfactory reconstruction accuracy caused by the inappropriate setting of the balanced parameter in the objective function. Numerical results demonstrate that our methods achieve higher DR ratios while satisfying the reconstruction error constraints, compared to other TNSS and tensor network-based DR algorithms.

Effective noise removal in 3D radio maps is critical for their application in cognitive communication systems. However, real-world radio signals are often corrupted by non-Gaussian noise, which poses significant challenges to traditional denoising methods. In this paper, we propose C-NLTR, a novel denoising model specifically designed for non-Gaussian noise removal in 3D radio maps. To address the impulsive interference and heavy-tailed distortions inherent in non-Gaussian noise, we employ a correntropy-based loss function, which adaptively suppresses extreme deviations while preserving key signal structures. Furthermore, to leverage the nonlocal self-similarity and low-rank priors present in 3D radio maps, we introduce a nonlocal low-rank tensor ring decomposition, which effectively retains structural details and captures global correlations. To solve the resulting optimization problem efficiently, we develop a computationally scalable algorithm based on half-quadratic theory and a scaled gradient descent approach. Extensive experiments on the SpectrumNet dataset demonstrate that C-NLTR outperforms state-of-the-art methods for non-Gaussian noise removal, particularly excelling in severe non-Gaussian scenarios where other approaches fail. Additionally, denoising experiments on hyperspectral image datasets, including CAVE, Washington DC Mall, and real-world Indian Pines, confirm the robustness of C-NLTR across a range of noise conditions.