Spectrum Cartography Research Articles

Spectrum map construction optimisation schemes: Sampling and prediction

The proliferation of electromagnetic devices presents a significant challenge in developing effective techniques for spectrum monitoring, management, and security. The utilization of spectrum cartography has been acknowledged as a viable approach to address the aforementioned difficulties. This latter presents a variety of techniques aimed at enhancing the efficiency of the current spectrum mapping methodology. The subject matter can be categorized into two primary components, namely sampling and spectrum prediction. Sampling part includes methods to find the most valuable sampling points and methods of sampling hardware optimization. Spectrum prediction includes algorithms utilizing frequency-spatial reasoning techniques to estimate the target spectrum map by data from the nearby area, and algorithms utilizing ROSMP framework to estimate the spectrum map from past data. The introduction of techniques is divided into the 2 types, together with key algorithms and devices used in each method. Additionally, the letter lists some drawbacks of certain methods and discuss their development prospects.

Spectrum cartography based on dynamic compressed sensing by using multiple domains information

Spectrum cartography based on dynamic compressed sensing by using multiple domains information

UAV Trajectory Optimization for Spectrum Cartography: A PPO Approach

Benefiting from the flexibility and low operational cost, dispatching unmanned aerial vehicles (UAVs) to collect measurements is promising in spectrum cartography (SC). The main goal is to optimize the trajectory of an UAV to seek the most informative measurement under the environment with dynamic emitters. In this letter, we formulate a Markov Decision Process to find the optimal flight trajectory of an UAV that maximizes the accuracy of SC and minimizes energy consumption. However, due to the unavailable instantaneous feedback about the accuracy of SC, the existing methods are unable to work efficiently with sparse feedback. To tackle those issues, a Proximal Policy Optimization (PPO)-based algorithm is proposed to approach the optimal navigation policy for UAV by training with the delay interactive information at the base station. Moreover, A backtracking advantage function is further constructed to cope with sparse feedback in real-world scenario, which can avoid converging to local solutions. Extensive simulation results demonstrate that our proposed algorithm can significantly increase the accuracy of SC while reducing energy consumption.

Tensor-Based Parametric Spectrum Cartography From Irregular Off-Grid Samplings

Tensor-based spectrum cartography (SC) has received increasing interests for recovering multi-dimensional radio map (RM) from sparse measurements. However, existing tensor-based SC methods largely depends on an ideal assumption, that the sparse measurements are regularly located on grids. However, this assumption is largely unrealistic since the RM is continuous in essence, and can be measured at arbitrary positions deviating from the pre-divided grids. This work addresses the problem of parametric SC from irregular off-grid samplings. The main idea is combining interpolation with the multi-linear rank- <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$(L,L,1)$</tex-math></inline-formula> block-term tensor decomposition (LL1). The interpolation is first adopted to guarantee the uniqueness of LL1, under the guidance of the proposed sampling pattern theorem. Then, the power spectrum density (PSD) and spatial loss field (SLF) of each emitter can be smoothly estimated, and SC is completed via the aggregation model. For the whole procedure, the uncertainty derived from interpolation is grid-wisely specified, and imposed as a restriction. Simulations verified that the proposed method outperforms the baselines based on on-grid samplings in harsher environments.

Radio Map Estimation: A data-driven approach to spectrum cartography

Radio maps characterize quantities of interest in radio communication environments, such as the received signal strength and channel attenuation, at every point of a geographical region. Radio map estimation typically entails interpolative inference based on spatially distributed measurements. In this tutorial article, after presenting some representative applications of radio maps, the most prominent radio map estimation methods are discussed. Starting from simple regression, the exposition gradually delves into more sophisticated algorithms, eventually touching upon state-of-the-art techniques. To gain insight into this versatile toolkit, illustrative toy examples will also be presented.

Deep Spectrum Cartography: Completing Radio Map Tensors Using Learned Neural Models

The spectrum cartography (SC) technique constructs multi-domain (e.g., frequency, space, and time) radio frequency (RF) maps from limited measurements, which can be viewed as an ill-posed tensor completion problem. Model-based cartography techniques often rely on handcrafted priors (e.g., sparsity, smoothness and low-rank structures) for the completion task. Such priors may be inadequate to capture the essence of complex wireless environments -- especially when severe shadowing happens. To circumvent such challenges, offline-trained deep neural models of radio maps were considered for SC, as deep neural networks (DNNs) are able to "learn" intricate underlying structures from data. However, such deep learning (DL)-based SC approaches encounter serious challenges in both off-line model learning (training) and completion (generalization), possibly because the latent state space for generating the radio maps is prohibitively large. In this work, an emitter radio map disaggregation-based approach is proposed, under which only individual emitters' radio maps are modeled by DNNs. This way, the learning and generalization challenges can both be substantially alleviated. Using the learned DNNs, a fast nonnegative matrix factorization-based two-stage SC method and a performance-enhanced iterative optimization algorithm are proposed. Theoretical aspects -- such as recoverability of the radio tensor, sample complexity, and noise robustness -- under the proposed framework are characterized, and such theoretical properties have been elusive in the context of DL-based radio tensor completion. Experiments using synthetic and real-data from indoor and heavily shadowed environments are employed to showcase the effectiveness of the proposed methods.

A Constrained Block-Term Tensor Decomposition Framework for Spectrum Cartography

Joint spectrum cartography and disaggregation from sparse spatial observations has been proven to be theoretically feasible based on block-term tensor decomposition (BTD) model. However, the existing BTD framework suffers from inherent drawbacks in terms of numerical stability, complexity and noise robustness. To combat with these drawbacks, we propose a new Constrained-BTD (CBTD) framework in this letter by fully utilizing practical traits of geographical power density spectrum (PSD) and spatial loss field (SLF). The cornerstone of CBTD framework is formulating the joint PSD and SLF estimation as a constrained matrix factorization problem, instead of addressing the factors of BTD. Further, a projection gradient-based (PG) algorithm, which has sublinear convergence, is proposed to handle the restrictions of PSD and SLF by projection on manifolds. Compared with the baseline methods, simulations verify that the proposed approach obtains better performances in terms of stability, complexity and noise robustness.

Dynamic spectrum cartography via canonical polyadic tensor decomposition

Spectrum cartography aims at estimating multidimensional radio map from limited geographical observations. Recovering unobserved elements in a radio map, from sequential spectrum observations over a long period in large geographic areas, poses major challenges to real-time requirement and storage. As historical information from dynamic spectrum observations is not well utilized, traditional spectrum cartography methods, which are statically applied on single or multiple time slots, are not well suitable for time-varying scenarios. To address these challenges, we propose two novel radio map reconstruction algorithms based on tensor canonical polyadic decomposition (CPD), called dynamic window size based CPD (DW-CPD) and incremental CPD (I-CPD). The dynamic window size of DW-CPD is derived based on Kruskal condition of tensor CPD, and I-CPD is derived based on an exponentially weighted least squares criterion. We prove that the solution of I-CPD converges to a stationary point of the tensor completion problem, which validates that the proposed I-CPD is suitable for applications in estimating dynamic CP factor. Simulations results show that DW-CPD and I-CPD based algorithms have similar estimation performance for dynamic spectrum cartography, and are better than the existing methods. Due to the overall advantage of performance, running time and storage, I-CPD based algorithm is preferable for real-time applications.

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.

Location-Free Spectrum Cartography

Spectrum cartography constructs maps of metrics such as channel gain or received signal power across a geographic area of interest using spatially distributed sensor measurements. Applications of these maps include network planning, interference coordination, power control, localization, and cognitive radios to name a few. Since existing spectrum cartography techniques require accurate estimates of the sensor locations, their performance is drastically impaired by multipath affecting the positioning pilot signals, as occurs in indoor or dense urban scenarios. To overcome such a limitation, this paper introduces a novel paradigm for spectrum cartography, where estimation of spectral maps relies on features of these positioning signals rather than on location estimates. Specific learning algorithms are built upon this approach and offer a markedly improved estimation performance than existing approaches relying on localization, as demonstrated by simulation studies in indoor scenarios.

Compressive Multispectral Spectrum Sensing for Spectrum Cartography.

In the process of spectrum sensing applied to wireless communications, it is possible to build interference maps based on acquired power spectral values. This allows the characterization of spectral occupation, which is crucial to take management spectrum decisions. However, the amount of information both in the space and frequency domains that needs to be processed generates an enormous amount of data with high transmission delays and high memory requirements. Meanwhile, compressive sensing is a technique that allows the reconstruction of sparse or compressible signals using fewer samples than those required by the Nyquist criterion. This paper presents a new model that uses compressed multispectral sampling for spectrum sensing. The aim is to reduce the number of data required for the storage and the subsequent construction of power spectral maps with geo-referenced information in different frequency bands. This model is based on architectures that use compressive sensing to analyze multispectral images. The operation of a centralized manager is presented in order to select the power data of different sensors by binary patterns. These sensors are located in different geographical positions. The centralized manager reconstructs a data cube with the transmitted power and frequency of operation of all the sensors based on the samples taken and applying multispectral sensing techniques. The results show that this multispectral data cube can be built with 50% of the samples generated by the devices, and the spectrum cartography information can be stored using only 6.25% of the original data.

Kriging-Based Interference Power Constraint: Integrated Design of the Radio Environment Map and Transmission Power

This paper proposes a probabilistic interference constraint method with a radio environment map (REM) for spatial spectrum sharing. The REM stores the spatial distribution of the average received signal power. We can optimize the accuracy of the measurement-based REM using the Kriging interpolation. Although several researchers have maintained a continuous interest in improving the accuracy of the REM, sufficient study has not been done to actually explore the interference constraint considering the estimation error. The proposed method uses ordinary Kriging interpolation for the spectrum cartography. According to the predicted distribution of the estimation error, the allowable interference power to the primary user is approximately formulated. Numerical results show that the proposed method can achieve the probabilistic interference constraint asymptotically. Additionally, we compare the performance of the proposed technique with three methods: the perfect estimation, the path loss-based method, and the Kriging-based method without the error prediction. The comparison results show that the proposed method has a higher spectrum sharing opportunity than the path loss-based method, even if only a small amount of measurement data is available. It is also shown that the proposed method dramatically improves the outage probability of the interference power compared to the conventional Kriging-based method.

Cooperative Estimation of Power and Direction of Transmission for a Directive Source

Reliable spectrum cartography of directive sources depends on an accurate estimation of the direction of transmission (DoT) as well as the transmission power. Joint estimation of power and DoT of a directive source using ML estimation techniques is considered in this paper. We further analyze the parametric identifiability conditions of the problem, develop the estimation algorithm, and derive the Cramer–Rao-Bound for the two situations: 1) where the source signal is known to the sensors and 2) where the sensors are not aware of the source signal but its distribution. Particularly, we devise a specific sensor placement/selection setup for the symmetric antenna patterned sources which leads to identifiability of the problem. Finally, numerical results verifies the efficiency and accuracy of the provided estimation algorithms in this paper.

Group-Lasso on Splines for Spectrum Cartography

The unceasing demand for continuous situational awareness calls for innovative and large-scale signal processing algorithms, complemented by collaborative and adaptive sensing platforms to accomplish the objectives of layered sensing and control. Towards this goal, the present paper develops a spline-based approach to field estimation, which relies on a basis expansion model of the field of interest. The model entails known bases, weighted by generic functions estimated from the field's noisy samples. A novel field estimator is developed based on a regularized variational least-squares (LS) criterion that yields finite-dimensional (function) estimates spanned by thin-plate splines. Robustness considerations motivate well the adoption of an overcomplete set of (possibly overlapping) basis functions, while a sparsifying regularizer augmenting the LS cost endows the estimator with the ability to select a few of these bases that “better” explain the data. This parsimonious field representation becomes possible, because the sparsity-aware spline-based method of this paper induces a group-Lasso estimator for the coefficients of the thin-plate spline expansions per basis. A distributed algorithm is also developed to obtain the group-Lasso estimator using a network of wireless sensors, or, using multiple processors to balance the load of a single computational unit. The novel spline-based approach is motivated by a spectrum cartography application, in which a set of sensing cognitive radios collaborate to estimate the distribution of RF power in space and frequency. Computer simulations and tests on real data corroborate that the estimated power spectrum density atlas yields the desired RF state awareness, since the maps reveal spatial locations where idle frequency bands can be reused for transmission, even when fading and shadowing effects are pronounced.