Radio Map Research Articles

A Radio Environment Maps Estimation Algorithm based on the Pixel Regression Framework for Underlay Cognitive Radio Networks Using Incomplete Training Data.

In the underlay cognitive radio networks, the radio environment maps (REMs) estimation is the main challenge in sensing the idle wireless spectrum resources. Traditional deep learning-based algorithms estimate the REMs on the basis of the high-quality, large-scale complete training images. However, collecting the complete radio environment images is time-consuming and requires a numerous number of power spectrum sensing nodes. For this reason, we propose a generative adversarial networks-based pixel regression framework (PRF) for underlay cognitive radio networks. The PRF algorithm relaxes the requirement of the complete training images, and estimates the radio environment maps only on the basis of the incomplete REMs images, which are easier to be collected. First, we transform the radio environment maps estimation task into a pixel regression task through the color mapping progress. Then, to extract helpful information from the incomplete training data, we design a feature enhancing module for the PRF algorithm, which intelligently learns and emphasizes the important features from the training images. Finally, we use the trained pixel regression framework to reconstruct the radio environment maps in the target area. The proposed algorithm learns accurate radio environment characteristics from the incomplete training data rather than making direct biased or imprecise radio propagation assumptions as in the traditional methods. Thus, the PRF algorithm has a better REMs reconstruction performance than the traditional methods, as verified by simulations.

The optical luminosity function of LOFAR radio-selected quasars at 1.4 ≤z≤ 5.0 in the NDWFS-Boötes field

We present an estimate of the optical luminosity function (OLF) of LOFAR radio-selected quasars (RSQs) at 1.4 < z < 5.0 in the 9.3 deg2NOAO Deep Wide-field survey (NDWFS) of the Boötes field. The selection was based on optical and mid-infrared photometry used to train three different machine learning (ML) algorithms (Random forest, SVM, Bootstrap aggregation). Objects taken as quasars by the ML algorithms are required to be detected at ≥5σsignificance in deep radio maps to be classified as candidate quasars. The optical imaging came from the Sloan Digital Sky Survey and the Pan-STARRS1 3πsurvey; mid-infrared photometry was taken from theSpitzerDeep, Wide-Field Survey; and radio data was obtained from deep LOFAR imaging of the NDWFS-Boötes field. The requirement of a 5σLOFAR detection allowed us to reduce the stellar contamination in our sample by two orders of magnitude. The sample comprises 130 objects, including both photometrically selected candidate quasars (47) and spectroscopically confirmed quasars (83). The spectral energy distributions calculated using deep photometry available for the NDWFS-Boötes field confirm the validity of the photometrically selected quasars using the ML algorithms as robust candidate quasars. The depth of our LOFAR observations allowed us to detect the radio-emission of quasars that would be otherwise classified as radio-quiet. Around 65% of the quasars in the sample are fainter thanM1450 = −24.0, a regime where the OLF of quasars selected through their radio emission, has not been investigated in detail. It has been demonstrated that in cases where mid-infrared wedge-based AGN selection is not possible due to a lack of appropriate data, the selection of quasars using ML algorithms trained with optical and infrared photometry in combination with LOFAR data provides an excellent approach for obtaining samples of quasars. The OLF of RSQs can be described by pure luminosity evolution atz < 2.4, and a combined luminosity and density evolution atz > 2.4. The faint-end slope,α, becomes steeper with increasing redshift. This trend is consistent with previous studies of faint quasars (M1450 ≤ −22.0). We demonstrate that RSQs show an evolution that is very similar to that exhibited by faint quasars. By comparing the spatial density of RSQs with that of the total (radio-detected plus radio-undetected) faint quasar population at similar redshifts, we find that RSQs may compose up to ∼20% of the whole faint quasar population. This fraction, within uncertainties, is constant with redshift. Finally, we discuss how the compactness of the RSQs radio-morphologies and their steep spectral indices could provide valuable insights into how quasar and radio activity are triggered in these systems.

Adversarial Learning-Enabled Automatic WiFi Indoor Radio Map Construction and Adaptation With Mobile Robot

Location-based service (LBS) has become an indispensable part of our daily lives. Realizing accurate LBS in indoor environments is still a challenging task. WiFi fingerprinting-based indoor positioning system (IPS) has achieved encouraging results recently, but the time and labor overhead of constructing a dense WiFi radio map remains the key bottleneck that hinders it for real-world large-scale implementation. In this article, we propose WiGAN an automatic fine-grained indoor ratio map construction and the adaptation scheme empowered by the Gaussian process regression conditioned least-squares generative adversarial networks (GPR-GANs) with a mobile robot. First, we develop a mobile robotic platform that constructs the spatial map and radio map simultaneously in the easily accessed free space. GPR-GAN first establishes a Gaussian process regression (GPR) model using the real received signal strength (RSS) measurements collected by our robotic platform via LiDAR SLAM in the free space. Then, the outputs of the GPR are adopted as the input of GAN's generator. The learning objective of GAN is to synthesize realistic RSS data in a constrained space where it has not been covered and model the irregular RSS distributions in complex indoor environments. Real-world experiments were conducted in a real-world indoor environment, which confirms the feasibility, high accuracy, and superiority of WiGAN over existing solutions in terms of both RSS estimation accuracy and localization accuracy.

The X-Ray Cavity Around Hotspot E in Cygnus A: Tunneled by a Deflected Jet

Abstract The powerful Fanaroff–Riley class II (FR II) radio galaxy Cygnus A exhibits primary and secondary hotspots in each lobe. A 2 Ms Chandra X-ray image of Cygnus A has revealed an approximately circular hole, with a radius of 3.9 kpc, centered on the primary hotspot in the eastern radio lobe, hotspot E. We infer the distribution of X-ray emission on our line of sight from an X-ray surface brightness profile of the radio lobe adjacent to the hole and use it to argue that the hole is excavated from the radio lobe. The surface brightness profile of the hole implies a depth at least 1.7 ± 0.3 times greater than its projected width, requiring a minimum depth of 13.3 ± 2.3 kpc. A similar hole observed in the 5 GHz Very Large Array radio map reinforces the argument for a cavity lying within the lobe. We argue that the jet encounters the shock compressed intracluster medium at hotspot E, passing through one or more shocks as it is deflected back into the radio lobe. The orientation of Cygnus A allows the outflow from hotspot E to travel almost directly away from us, creating an elongated cavity, as observed. These results favor models for multiple hotspots in which an FR II jet is deflected at a primary hotspot, then travels onward to deposit the bulk of its power at a secondary hotspot, rather than the dentist drill model.

Stellar Cores in the Sh 2-305 H ii Region

Abstract Using our deep optical and near-infrared photometry along with multiwavelength archival data, we here present a detailed study of the Galactic H ii region Sh 2-305 to understand the star/star-cluster formation. On the basis of excess infrared emission, we have identified 116 young stellar objects (YSOs) within a field of view of ∼18.′5 × 18.′5 around Sh 2-305. The average age, mass, and extinction (A V ) for this sample of YSOs are 1.8 Myr, 2.9 M ⊙, and 7.1 mag, respectively. The density distribution of stellar sources along with minimal spanning tree calculations on the location of YSOs reveals at least three stellar subclusterings in Sh 2-305. One cluster is seen toward the center (i.e., Mayer 3), while the other two are distributed toward the north and south directions. Two massive O-type stars (VM2 and VM4; ages ∼5 Myr) are located at the center of the Sh 2-305 H ii region. The analysis of the infrared and radio maps traces the photon-dominant regions (PDRs) in Sh 2-305. The association of the younger generation of stars with the PDRs is also investigated in Sh 2-305. This result suggests that these two massive stars might have influenced the star formation history in Sh 2-305. This argument is also supported by the calculation of various pressures driven by massive stars, the slope of the mass function/K-band luminosity function, star formation efficiency, fraction of Class i sources, and mass of the dense gas toward the subclusterings in Sh 2-305.

Indoor WLAN Intelligent Target Intrusion Sensing Using Ray-Aided Generative Adversarial Network

An indoor target intrusion sensing technique has been used in many fields, such as smart home management, security monitoring, counter-terrorism, and disaster relief. At the same time, with the wide deployment of wireless local area network (WLAN) and general support of the IEEE 802.11 protocol by various mobile devices, the target intrusion sensing can be realized based on the existing WLAN infrastructure without requiring the target to carry any special device. However, the existing indoor WLAN target intrusion sensing approaches usually depend on the radio map construction with huge labor and time cost, which is the major barrier of current systems. In response to this compelling problem, we propose the new ray-aided generative adversarial model (RaGAM) to automatically construct the radio map, which is used for the indoor WLAN intelligent target intrusion sensing and localization. To achieve the low labor and time cost, the RaGAM uses the adaptive-depth ray tree based the quasi three-dimensional ray-tracing model to depict the difference of WLAN signals between the silence and intrusion environments with the purpose of constructing the synthetic radio map. Considering the gap between the synthetic and actual radio maps, we modify the conventional generative adversarial network by the joint synthetic and unsupervised learning (or called S+U learning) from the actual unlabeled received signal strength (RSS) data to improve the precision of the proposed ray-tracing model, and consequently obtain the refined radio map. After that, the statistical characteristics of the refined radio map are utilized to construct the training set for the probabilistic neural network (PNN), and then by using the well-trained PNN to classify the newly collected RSS data, the target intrusion sensing, and localization are achieved. The experimental results show that the proposed approach cannot only perform well in terms of computation cost and the ray-tracing accuracy, but also sense the target intrusion states accurately.

A Fast Radio Map Construction Method Merging Self-Adaptive Local Linear Embedding (LLE) and Graph-Based Label Propagation in WLAN Fingerprint Localization Systems.

Indoor WLAN fingerprint localization systems have been widely applied due to the simplicity of implementation on various mobile devices, including smartphones. However, collecting received signal strength indication (RSSI) samples for the fingerprint database, named a radio map, is significantly labor-intensive and time-consuming. To solve the problem, this paper proposes a semi-supervised self-adaptive local linear embedding algorithm to build the radio map. First, this method uses the self-adaptive local linear embedding (SLLE) algorithm based on manifold learning to reduce the dimension of the high-dimensional RSSI samples and to extract a neighbor weight matrix. Secondly, a graph-based label propagation (GLP) algorithm is employed to build the radio map by semi-supervised learning from a large number of unlabeled RSSI samples to a few labeled RSSI samples. Finally, we propose a k self-adaptive neighbor weight (kSNW) algorithm, used for radio map construction in this paper, to realize online localization. The results of the experiments conducted in a real indoor environment show that the proposed method reduces the demand for large quantities of labeled samples and achieves good positioning accuracy. With only 25% labeled RSSI samples, our system can obtain positioning accuracy of more than 88%, within 3 m of localization errors.

Indoor positioning based on improved weighted KNN for energy management in smart buildings

Offering special service to residents of smart buildings to achieve the energy efficiency entails knowledge of identity information, place of residence and also the current location of people inside the building. However, localization accuracy adversely degrades in non-line-of-sight (NLOS) environments. In this study, we design a low-cost indoor positioning system based on the Wi-Fi fingerprint embedded on the smartphones. Indoor positioning system is composed of two online and offline sections. In the offline phase, a platform for collecting the radio map information is introduced. Then, the noise covariance of the received signals is estimated by adaptive Kalman filter. In the online phase, online layer clustering and K-nearest neighbor method based on the fisher information weighting and differential coordinates are presented. Simulation results show that the proposed method improves errors of less than 2 m by 40% compared to other methods. Also, the proposed algorithm is comparable to other algorithms in terms of computational complexity.

Transfer Learning for Tilt-Dependent Radio Map Prediction

Machine learning will play a major role in handling the complexity of future mobile wireless networks by improving network management and orchestration capabilities. Due to the large number of parameters that can be monitored and configured in the network, collecting and processing high volumes of data is often unfeasible or too expensive at network runtime, which calls for taking resource management and service orchestration decisions with only a partial view of the network status. Motivated by this fact, this paper proposes a transfer learning framework for reconstructing the radio map corresponding to a target antenna tilt configuration by transferring the knowledge acquired from another tilt configuration of the same antenna, when no or very limited measurements are available from the target. The performance of the framework is validated against standard machine learning techniques on a data set collected from a 4G commercial base stations. In most of the tested scenarios, the proposed framework achieves notable prediction accuracy with respect to classical machine learning approaches, with a mean absolute percentage error below 8%.

Low-cost localisation considering LOS/NLOS impacts in challenging indoor environments

One popular indoor localisation method in wireless sensor networks (WSN) and wireless local area networks (WLAN) is fingerprinting technique. However, the training stage of fingerprinting and constructing the radio map is time-consuming and labour-intensive. Here, we propose a novel method to decrease the training cost by building a simulated radio map using an improved path-loss model in which the impacts of line of sight (LOS) and non-light-of-sight (NLOS) propagations are considered. Including LOS/NLOS effects also improves distance estimation. Furthermore, the simulated radio map helps assess and improve the fingerprinting area and network parameters prior to the actual positioning. For performance evaluation, three different radio maps are created using simulation and a test field experiment and then compared based on deterministic and probabilistic algorithms. The results indicate that the improved model outperforms the typical path-loss model and the localisation error gets closer to the actual error of the fingerprinting network.

Adaptive Density Graph-Based Manifold Alignment for Fingerprinting Indoor Localization

The received signal strength (RSS) fingerprint-based indoor localization has been considered as a promising solution, due to its relatively high localization accuracy and its ease of use in widespread Wireless Local Area Network (WLAN) infrastructure. A major bottleneck is that the offline fingerprint calibration is time consuming and labor intensive. In this study, inspired by our analysis that multi-density is inherent to the RSS distribution, we present a new radio map construction scheme, called Adaptive Density Graph-based Manifold Alignment (ADG-MA), which can reduce the number of Reference Points (RPs) in offline phase. In particular, it utilizes the density features to capture the exact neighborhood relations of RSS. Furthermore, the approach labels the RSS from user traces to construct the radio map. The extensive experiments demonstrate that the proposed method can construct an accurate radio map at a low deployment cost, as well as achieve a high localization accuracy.

A Framework for Proactive Indoor Positioning in Densely Deployed WiFi Networks

A framework that incorporates channel modeling, position estimation, and error analysis methods is developed for network-based indoor positioning with radio signal strength (RSS) measurements of WiFi access points (APs). To construct an accurate channel model with RSS measurements severely influenced by propagation attenuations, multipath reflections, and shadowing effects, a novel sparse Bayesian learning algorithm is developed to model the radio power map (RPM) in indoor space. Based on the proposed RPM model, a 2-stage positioning method is further developed. In the first stage for coarse positioning, the location is determined up to a room-scale indoor space. Then, in the second stage for fine positioning, the RPMs of the given indoor space are used for location estimation in the space with a Bayesian estimator. The mean squared positioning errors are verified with the Bayesian Cramer-Rao lower bound. Extensive experiments show that the average positioning error of the proposed RPM-based approach is 1.98 meters which achieve 22% improvements over the state-of-the-art RSS-based indoor positioning methods. More importantly, the proposed modeling and positioning method can effectively exploit the spatial relationship in the RSS samples to improve positioning accuracy.

Deciphering the radio star formation correlation on kpc scales

One of the tightest correlations in astronomy is the relation between the integrated radio continuum and the far-infrared (FIR) emission. Within nearby galaxies, variations in the radio–FIR correlation have been observed, mainly because the cosmic ray electrons migrate before they lose their energy via synchrotron emission or escape. The major cosmic-ray electron transport mechanisms within the plane of galactic disks are diffusion, and streaming. A predicted radio continuum map can be obtained by convolving the map of cosmic-ray electron sources, represented by that of the star formation, with adaptive Gaussian and exponential kernels. The ratio between the smoothing lengthscales at 6 cm and 20 cm can be used to determine, between diffusion and streaming, which is the dominant transport mechanism. The dependence of the smoothing lengthscale on the star formation rate bears information on the dependence of the magnetic field strength, or the ratio between the ordered and turbulent magnetic field strengths on star formation. Star formation maps of eight rather face-on local and Virgo cluster spiral galaxies were constructed fromSpitzerandHerschelinfrared and GALEX UV observations. These maps were convolved with adaptive Gaussian and exponential smoothing kernels to obtain model radio continuum emission maps. It was found that in asymmetric ridges of polarized radio continuum emission, the total power emission is enhanced with respect to the star formation rate. At a characteristic star formation rate of $ \dot{\Sigma}_*=8 \times 10^{-3}\,M_{\odot} $ yr−1kpc−2, the typical lengthscale for the transport of cosmic-ray electrons isl = 0.9 ± 0.3 kpc at 6 cm, andl = 1.8 ± 0.5 kpc at 20 cm. Perturbed spiral galaxies tend to have smaller lengthscales. This is a natural consequence of the enhancement of the magnetic field caused by the interaction. The discrimination between the two cosmic-ray electron transport mechanisms, diffusion, and streaming is based on (i) the convolution kernel (Gaussian or exponential); (ii) the dependence of the smoothing kernel on the local magnetic field, and thus on the local star formation rate; (iii) the ratio between the two smoothing lengthscales via the frequency dependence of the smoothing kernel, and (iv) the dependence of the smoothing kernel on the ratio between the ordered and the turbulent magnetic field. Based on our empirical results, methods (i) and (ii) cannot be used to determine the cosmic ray transport mechanism. Important asymmetric large-scale residuals and a local dependence of the smoothing length onBord/Bturbare most probably responsible for the failure of methods (i) and (ii), respectively. On the other hand, the classifications based onl6 cm/l20 cm(method iii) andBord/Bturb(method iv), are well consistent and complementary. We argue that in the six Virgo spiral galaxies, the turbulent magnetic field is globally enhanced in the disk. Therefore, the regions where the magnetic field is independent of the star formation rate are more common. In addition,Bord/Bturbdecreases, leading to a diffusion lengthscale that is smaller than the streaming lengthscale. Therefore, cosmic ray electron streaming dominates in most of the Virgo spiral galaxies.

Интерпретация радиоастрономических наблюдений H2CO и H110α в областях звездообразования W40 и Serpens South молекулярного облака Aquila

This study presents the results of radio astronomy observations of the absorption spectral lines of a formaldehyde molecule (H2CO) and the H110α recombination line towards the Aquila molecular cloud. The paper interprets the radio astronomy observations of H2CO (l10-l11) and H110α in the W40 and Serpens South of the Aquila Rift molecular complex, which were obtained by the 26 m Nan-Shan radio telescope of the Xinjiang Astronomical Observatory of the Chinese Academy of Sciences. In order to construct radio maps, we also used archival data obtained by observing 12СО(2−1) and 13CO(2−1) and 6 cm continuum molecules for the Aquila Rift region. Based on the obtained observational data, the optical depth and column density were calculated for the H2CO absorption line and 13CO emission line (J = 1-0), integrated intensity maps were constructed with the ionized hydrogen region H II and imposed contours that correspond to the absorption lines of H2CO and the recombination line H110α in the direction of the Aquila molecular cloud; maps of radiation intensity 13CO (1−0), distribution of 6 cm of the radio continuum, infrared radiation superimposed on integrated absorption contours of H2CO; dependences of linear flows and peak column densities for H2CO and 13CO are obtained. In the work it is shown that the Serpens South region, highlighted by the contours during the absorption of formaldehyde H2CO, comes from the cosmic microwave background. A correlation was found between the parameter values ​​for the H2CO absorption line and the 13CO emission line. Integrated intensity maps were constructed for various values ​​of the channel velocity of the H2CO absorption line in the direction of the Aquila molecular cloud. It was revealed that the rates of H2CO and 13CO have close values ​​to each other. An analysis of the study led to the conclusion that the absorption lines of the H2CO formaldehyde molecule and the 13CO emission lines originate from the same region in the Aquila Rift complex of the Aquila molecular cloud.

Calibration-Free Indoor Positioning Using Crowdsourced Data and Multidimensional Scaling

Indoor positioning plays an important role in various location-based services (LBSs). In conventional systems, the process of constructing radio maps for positioning usually involves labor-intensive manual calibrations, which seriously limits the system’s scalability and adaptiveness. In this paper, we propose an efficient calibration-free method by leveraging on crowdsourced WiFi signal data that are captured passively through a WiFi sensing testbed. Since the ground truths of the crowdsourced data are unavailable, the radio maps cannot be directly constructed. In the proposed method, we adopt the multidimensional scaling (MDS) technique to compute the positions of the unlabeled data thereby generating radio maps. In order to enable MDS, we estimate the pairwise distances among the unlabeled data by using an improved trilateration method and a law of cosine (LoC)-based geometrical algorithm without online pairwise measurements. Experimental results show that the accuracy of the proposed method is higher than trilateration-based method and reasonably lower than that of calibration-based method. Meanwhile, the run time of the proposed method is shorter than previous optimization-based methods. The short run time allows the radio maps to be dynamically updated against the environmental variations.

Accurate Indoor-Positioning Model Based on People Effect and Ray-Tracing Propagation.

Wireless local area networks (WLAN)-fingerprinting has been highlighted as the preferred technology for indoor positioning due to its accurate positioning and minimal infrastructure cost. However, its accuracy is highly influenced by obstacles that cause fluctuation in the signal strength. Many researchers have modeled static obstacles such as walls and ceilings, but few studies have modeled the people’s presence effect (PPE), although the human body has a great impact on signal strength. Therefore, PPE must be addressed to obtain accurate positioning results. Previous research has proposed a model to address this issue, but these studies only considered the direct path signal between the transmitter and the receiver whereas multipath effects such as reflection also have a significant influence on indoor signal propagation. This research proposes an accurate indoor-positioning model by considering people’s presence and multipath using ray-tracing, we call it (AIRY). This study proposed two solutions to construct AIRY: an automatic radio map using ray tracing and a constant of people’s effect for the received signal strength indicator (RSSI) adaptation. The proposed model was simulated using MATLAB software and tested at Level 3, Menara Razak, Universiti Teknologi Malaysia. A K-nearest-neighbor (KNN) algorithm was used to define a position. The initial accuracy was 2.04 m, which then reduced to 0.57 m after people’s presence and multipath effects were considered.

Selective Unsupervised Learning-Based Wi-Fi Fingerprint System Using Autoencoder and GAN

In this article, we propose an automatic Wi-Fi fingerprint system that combines an unsupervised dual radio mapping (UDRM) algorithm with the aim of reducing the time-cost needed to acquire Wi-Fi signals. Our proposed system is appropriate for indoor environments and utilizes a minimum description length principle (MDLP)-based radio map feedback (RMF) algorithm that simultaneously optimizes and updates the radio map. In the training phase, the proposed UDRM algorithm generates a radio map of the entire building based on the measured radio map of one reference floor. It does this by selectively applying a modified autoencoder and a generative adversarial network according to the spatial structures. Our proposed learning-based UDRM algorithm does not require labeled data, which is essential for supervised and semisupervised learning algorithms. It has a relatively low dependence on received signal strength indicator (RSSI) data sets. Our proposed RMF algorithm analyzes the distribution characteristics of the RSSIs for newly measured access points (APs) and feeds the analyzed results back to the radio map. The MDLP, which is applied to the proposed algorithm, improves the positioning performance and optimizes the size of the radio map by preventing the indefinite updating of the RSSI and by updating the newly added APs in the radio map.

Collaborative SLAM Based on WiFi Fingerprint Similarity and Motion Information

Simultaneous localization and mapping (SLAM) has been extensively researched in past years particularly with regard to range-based or visual-based sensors. Instead of deploying dedicated devices that use visual features, it is more pragmatic to exploit the radio features to achieve this task, due to their ubiquitous nature and the widespread deployment of the Wi-Fi wireless network. This article presents a novel approach for collaborative simultaneous localization and radio fingerprint mapping (C-SLAM-RF) in large unknown indoor environments. The proposed system uses received signal strengths (RSS) from Wi-Fi access points (APs) in the existing infrastructure and pedestrian dead reckoning (PDR) from a smartphone, without a prior knowledge about map or distribution of AP in the environment. We claim a loop closure based on the similarity of the two radio fingerprints. To further improve the performance, we incorporate the turning motion and assign a small uncertainty value to a loop closure if a matched turning is identified. The experiment was done in an area of 130 m by 70 m and the results show that our proposed system is capable of estimating the tracks of four users with an accuracy of 0.6 m with Tango-based PDR and 4.76 m with a step counter-based PDR.

Accelerated Electron Propagation Model for the Flare Arcade of the September 23, 2014, Event from RHESSI, SDO, and Nobeyama Radioheliograph Observations

A multi-wavelength study and simulation is conducted for the solar flare SOL2014-09-23T23:11. GOES-class M2.5. Radio (Nobeyama Radioheliograph) and X-ray (Reuven Ramaty High Energy Solar Spectroscopic Imager) maps and energy spectra are studied, including their temporal and spatial evolution, with the superposition of radiation sources on the magnetic field structure. For the first time, a simulation of accelerated electrons transport in several characteristic magnetic structures of a flare arcade simultaneously is conducted. Accelerated electron injection functions, which depend on the space along the magnetic loop, pitch angle, and energy, are fitted to reconcile observations with the simulation results such that the calculated radiation parameters are consistent with the observed brightness distributions of hard X‑rays in the range of 28–135 keV and gyrosynchrotron radiation of 17 and 35 GHz. The energy spectrum of the electron beam corresponds in this case to one- and two-power law functions with spectral indices in the ranges δ1 ≈ 4–5 and δ2 ≈ 2.0–2.4 and spectrum break energy Ebr ≈ 240–320 keV, depending on the specific magnetic structure. The pitch-angle distribution of accelerated electrons is essentially an anisotropic electron flux with an divergence angle of ~80° from the magnetic looptops towards the footpoint with a dominant hard X-ray source.

Spectrum Cartography via Coupled Block-Term Tensor Decomposition

Spectrum cartography aims at estimating power propagation patterns over a geographical region across multiple frequency bands (i.e., a radio map)---from limited samples taken sparsely over the region. Classic cartography methods are mostly concerned with recovering the aggregate radio frequency (RF) information while ignoring the constituents of the radio map---but fine-grained emitter-level RF information is of great interest. In addition, many existing cartography methods work explicitly or implicitly assume random spatial sampling schemes that may be difficult to implement, due to legal/privacy/security issues. The theoretical aspects (e.g., identifiability of the radio map) of many existing methods are also unclear. In this work, we propose a joint radio map recovery and disaggregation method that is based on coupled block-term tensor decomposition. Our method guarantees identifiability of the individual radio map of \textit{each emitter} (thereby that of the aggregate radio map as well), under realistic conditions. The identifiability result holds under a large variety of geographical sampling patterns, including a number of pragmatic systematic sampling strategies. We also propose effective optimization algorithms to carry out the formulated radio map disaggregation problems. Extensive simulations are employed to showcase the effectiveness of the proposed approach.