Autonomous unmanned aerial vehicles (UAVs) can be utilized as aerial relays to serve users far from terrestrial infrastructure. Unfortunately, existing algorithms for aerial relay path planning cannot accommodate general flight constraints or channel models. This is required in practice due to connectivity constraints, the presence of obstacles (e.g. buildings), and regulations. This paper proposes a framework that overcomes these limitations by spatially discretizing the flight region. To cope with the resulting exponential growth in complexity, the framework adopts a probabilistic roadmap approach, where a shortest path is found through a graph of randomly generated states. To attain high optimality with affordable complexity, the probability distribution used to generate these states is designed based on heuristic path planners with theoretical guarantees. The algorithms derived in this framework not only overcome the main limitations of existing schemes but also entail smaller computational complexity. Extensive theoretical and numerical results corroborate the merits of the proposed approach.

Radio map estimation (RME) involves spatial interpolation of radio measurements to predict metrics such as the received signal strength at locations where no measurements were collected. The most popular estimators nowadays project the measurement locations onto a regular grid and complete the resulting measurement tensor with a convolutional deep neural network. Unfortunately, these approaches suffer from poor spatial resolution and require a very large number of parameters. The first contribution addresses these limitations by means of an attention-based estimator based on transformers, which are AI models that achieved widespread popularity since they are the technology behind chatbots such as ChatGPT. The proposed scheme, named Spatial TransfOrmer for Radio Map estimation (STORM), not only outperforms the existing estimators, but also exhibits lower computational complexity, translation equivariance, rotation equivariance, and full spatial resolution. The second contribution is an extended transformer architecture that allows STORM to perform active sensing, by which the next measurement location is selected based on the previous measurements. This is particularly useful for minimization of drive tests (MDT) in cellular networks, where operators request user equipment to collect measurements. Finally, STORM is extensively validated by experiments with one ray-tracing and two real-measurement datasets.

In a spoofing attack, a malicious actor impersonates a legitimate user to access or manipulate data without authorization. The vulnerability of cryptographic security mechanisms to compromised user credentials motivates spoofing attack detection in the physical layer, which traditionally relied on channel features, such as the received signal strength (RSS) measured by spatially distributed receivers or access points. However, existing methods cannot effectively cope with the dynamic nature of channels, which change over time as a result of user mobility and other factors. To address this limitation, this work builds upon the intuition that the temporal pattern of changes in RSS features can be used to detect the presence of concurrent transmissions from multiple (possibly changing) locations, which in turn indicates the existence of an attack. Since a localization-based approach would require costly data collection and would suffer from low spatial resolution due to multipath, the proposed algorithm employs a deep neural network to construct a graph embedding of a sequence of RSS features that reflects changes in the propagation conditions. A graph neural network then classifies these embeddings to detect spoofing attacks. The effectiveness and robustness of the proposed scheme are corroborated by experiments with real-data.

Next generation communication systems require accurate beam alignment to counteract the impairments that characterize propagation in high-frequency bands. The overhead of the pilot sequences required to select the best beam pair is prohibitive when codebooks contain a large number of beams, as is the case in practice. To remedy this issue, some schemes exploit information about the user location to predict the best beam pair. However, these schemes (i) involve no measurements whatsoever, which generally results in a highly suboptimal predicted beam, and (ii) are not robust to localization errors. To address these limitations, this paper builds upon the notion of radio map to develop two algorithms that attain a balance between the quality of the obtained beam pair and measurement overhead. The proposed algorithms predict the received power corresponding to each pair and measure just the$Q$pairs with highest prediction. While the first algorithm targets simplicity, the second one relies on a Bayesian approach to endow the prediction process with robustness to localization error. The performance of both algorithms is shown to widely outperform existing methods using ray-tracing data.

Radio map estimation (RME) aims at providing a radio frequency metric, such as the received power strength, at every location of a geographical region of interest by relying on measurements acquired at multiple positions. Although a large number of estimators have been proposed so far, their performance has been analyzed mostly on simulated data. The theoretical aspects of the RME problem as well as performance bounds remain an open problem. This paper takes a step towards filling this gap by means of a theoretical analysis of the RME problem in a free-space propagation environment. First, the complexity of the estimation problem is quantified by means of upper bounds on the spatial variability of radio maps. Second, error bounds are derived for zeroth-order and first-order interpolation estimators. The proximity coefficient, which depends proportionally on the transmitted power and inversely proportionally on the cube of the distance from the transmitters to the mapped region, is proposed to quantify the complexity of the RME problem. One of the main findings is that the error of the considered estimators is roughly proportional to this proximity coefficient. Simple numerical experiments verify the tightness of the obtained bounds.

In a spoofing attack, an attacker impersonates a legitimate user to access or modify data belonging to the latter. Typical approaches for spoofing detection in the physical layer declare an attack when a change is observed in certain channel features, such as the received signal strength (RSS) measured by spatially distributed receivers. However, since channels change over time, for example due to user movement, such approaches are impractical. To sidestep this limitation, this paper proposes a scheme that combines the decisions of a position-change detector based on a deep neural network to distinguish spoofing from movement. Building upon community detection on graphs, the sequence of received frames is partitioned into subsequences to detect concurrent transmissions from distinct locations. The scheme can be easily deployed in practice since it just involves collecting a small dataset of measurements at a few tens of locations that need not even be computed or recorded. The scheme is evaluated on real data collected for this purpose.

The deployment of aerial base stations (ABSs) on unmanned aerial vehicles (UAVs) presents a promising solution for extending cellular connectivity to areas where terrestrial infrastructure is overloaded, damaged, or absent. A pivotal challenge in this domain is to decide the locations of a set of ABSs to effectively serve ground-based users. Most existing approaches oversimplify this problem by assuming that the channel gain between two points is a function of solely distance and, sometimes, also the elevation angle. In turn, this paper leverages propagation radio maps to account for arbitrary air-to-ground channel gains. This methodology enables the identification of an approximately minimal set of locations where ABSs need to be deployed to ensure that all ground terminals achieve a target service rate, while adhering to backhaul capacity limitations and avoiding designated no-fly zones. Relying on a convex relaxation technique and the alternating direction method of multipliers (ADMM), this paper puts forth a scalable solver whose computational complexity scales linearly with the number of ground terminals. Convergence is established analytically and an extensive set of simulations corroborate the merits of the proposed scheme relative to conventional methods.

Radio maps provide radio frequency metrics, such as the received signal strength, at every location of a geographic area. These maps, which are estimated using a set of measurements collected at multiple positions, find a wide range of applications in wireless communications, including the prediction of coverage holes, network planning, resource allocation, and path planning for mobile robots. Although a vast number of estimators have been proposed, the theoretical understanding of the radio map estimation (RME) problem has not been addressed. The present work aims at filling this gap along two directions. First, the complexity of the set of radio map functions is quantified by means of lower and upper bounds on their spatial variability, which offers valuable insight into the required spatial distribution of measurements and the estimators that can be used. Second, the reconstruction error for power maps in free space is upper bounded for three conventional spatial interpolators. The proximity coefficient, which is a decreasing function of the distance from the transmitters to the mapped region, is proposed to quantify the complexity of the RME problem. Numerical experiments assess the tightness of the obtained bounds and the validity of the main takeaways in complex environments.

Unmanned aerial vehicles (UAVs) with on-board relays can be used to establish multi-hop links that deliver high-speed connectivity beyond cell limits. This is of utmost importance e.g. in remote areas and in emergency scenarios. However, jointly designing the trajectories of multiple such flying relays is a complex task since the dimensionality of the underlying configuration space is too large to allow the direct application of traditional shortest-path methods. To bypass this difficulty, this work proposes a probabilistic roadmap algorithm based on a novel heuristic path design which is guaranteed to provide feasible paths for all UAVs under general conditions. This addresses the limitations of existing algorithms, which are typically based on non-linear optimization and, therefore, entail high complexity and cannot readily accommodate the presence of obstacles such as buildings. As corroborated via numerical experiments in an urban environment, the proposed scheme can establish a high-speed link with a user by means of just two aerial relays in a short time.

Radio maps find numerous applications in wireless communications and mobile robotics tasks, including resource allocation, interference coordination, and mission planning. Although numerous existing techniques construct radio maps from spatially distributed measurements, the locations of such measurements are predetermined beforehand. In contrast, this paper proposes spectrum surveying, where a mobile robot such as an unmanned aerial vehicle (UAV) collects measurements at a set of locations that are actively selected to obtain high-quality map estimates in a short surveying time. This is performed in two steps. First, two novel algorithms, a model-based online Bayesian estimator and a data-driven deep learning algorithm, are devised for updating a map estimate and an uncertainty metric that indicates the informativeness of measurements at each possible location. These algorithms offer complementary benefits and feature constant complexity per measurement. Second, the uncertainty metric is used to plan the trajectory of the UAV to gather measurements at the most informative locations. To overcome the combinatorial complexity of this problem, a dynamic programming approach is proposed to obtain lists of waypoints through areas of large uncertainty in linear time. Numerical experiments conducted on a realistic dataset confirm that the proposed scheme constructs accurate radio maps quickly.

Mobile base stations on board unmanned aerial vehicles (UAVs) promise to deliver connectivity to those areas where the terrestrial infrastructure is overloaded, damaged, or absent. A fundamental problem in this context involves determining a minimal set of locations in 3D space where such aerial base stations (ABSs) must be deployed to provide coverage to a set of users. While nearly all existing approaches rely on average characterizations of the propagation medium, this work develops a scheme where the actual channel information is exploited by means of a radio tomographic map. A convex optimization approach is presented to minimize the number of required ABSs while ensuring that the UAVs do not enter no-fly regions. A simulation study reveals that the proposed algorithm markedly outperforms its competitors.

Radio maps provide metrics such as power spectral density for every location in a geographic area and find numerous applications such as UAV communications, interference control, spectrum management, resource allocation, and network planning to name a few. Radio maps are constructed from measurements collected by spectrum sensors distributed across space. Since radio maps are complicated functions of the spatial coordinates due to the nature of electromagnetic wave propagation, model-free approaches are strongly motivated. Nevertheless, all existing schemes for radio occupancy map estimation rely on interpolation algorithms unable to learn from experience. In contrast, this paper proposes a novel approach in which the spatial structure of propagation phenomena such as shadowing is learned beforehand from a data set with measurements in other environments. Relative to existing schemes, a significantly smaller number of measurements is therefore required to estimate a map with a prescribed accuracy. As an additional novelty, this is also the first work to estimate radio occupancy maps using deep neural networks. Specifically, a fully convolutional deep completion autoencoder architecture is developed to effectively exploit the manifold structure of this class of maps.

Decentralized signal processing performs learning tasks on data distributed over a multi-node network which can be represented by a graph. Implementing linear transformations emerges as a key task in a number of applications of decentralized signal processing. Recently, some decentralized methods have been proposed to accomplish that task by leveraging the notion of graph shift operator, which captures the local structure of the graph. However, existing approaches have some drawbacks such as considering special instances of linear transformations, or reducing the family of transformations by assuming that a shift matrix is given such that a subset of its eigenvectors spans the subspace of interest. In contrast, this paper develops a decentralized method to compute linear transformations in a small number of iterations. To this end, a set of successive graph shift operators is designed. Hence, a new optimization problem is proposed whose goal is to compute the desired transformation as fast as possible.

Spectrum maps, which provide RF spectrum metrics such as power spectral density for every location in a geographic area, find numerous applications in wireless communications such as interference control, spectrum management, resource allocation, and network planning to name a few. Spectrum cartography techniques construct these maps from a collection of measurements collected by spatially distributed sensors. Due to the nature of the propagation of electromagnetic waves, spectrum maps are complicated functions of the spatial coordinates. For this reason, model-free approaches have been preferred. However, all existing schemes rely on some interpolation algorithm unable to learn from data. This paper proposes a novel approach to spectrum cartography where propagation phenomena are learned from data. The resulting algorithms can therefore construct a spectrum map from a significantly smaller number of measurements than existing schemes since the spatial structure of shadowing and other phenomena is previously learned from maps in other environments. Besides the aforementioned new paradigm, this is also the first work to perform spectrum cartography with deep neural networks. To exploit the manifold structure of spectrum maps, a deep network architecture is proposed based on completion autoencoders.

Autonomous unmanned aerial vehicles (UAVs) with on-board base station equipment can potentially provide connectivity in areas where the terrestrial infrastructure is overloaded, damaged, or absent. Use cases comprise emergency response, wildfire suppression, surveillance, and cellular communications in crowded events to name a few. A central problem to enable this technology is to place such aerial base stations (AirBSs) in locations that approximately optimize the relevant communication metrics. To alleviate the limitations of existing algorithms, which require intensive and reliable communications among AirBSs or between the AirBSs and a central controller, this paper leverages stochastic optimization and machine learning techniques to put forth an adaptive and decentralized algorithm for AirBS placement without inter-AirBS cooperation or communication. The approach relies on a smart design of the network utility function and on a stochastic gradient ascent iteration that can be evaluated with information available in practical scenarios. To complement the theoretical convergence properties, a simulation study corroborates the effectiveness of the proposed scheme.

Since the spectral efficiency of wireless communications is already close to its fundamental bounds, a significant increase in spatial efficiency is required to meet future traffic demands. Device-to-device (D2D) communications provide such an increase by allowing nearby users to communicate directly without passing their packages through the base station. To fully exploit the benefits of this paradigm, proper channel assignment and power allocation algorithms are required. The main limitation of existing schemes, which restrict D2D transmitters to operate on a single channel at a time, is circumvented by the joint channel assignment and power allocation algorithm proposed in this paper. This algorithm relies on convex relaxation to efficiently obtain nearly-optimal solutions to the mixed-integer program arising in this context. Numerical experiments corroborate the merits of the proposed scheme relative to state-of-the art alternatives.

This work addresses the problem of determining whether two multivariate random time series have the same power spectral density (PSD), which has applications, for instance, in physical-layer security and cognitive radio. Remarkably, existing detectors for this problem do not usually provide any kind of optimality. Thus, we study here the existence under the Gaussian assumption of optimal invariant detectors for this problem, proving that the uniformly most powerful invariant test (UMPIT) does not exist. Thus, focusing on close hypotheses, we show that the locally most powerful invariant test (LMPIT) only exists for univariate time series. In the multivariate case, we prove that the LMPIT does not exist. However, this proof suggests two LMPIT-inspired detectors, one of which outperforms previously proposed approaches, as computer simulations show.

Spectrum cartography constructs maps of metrics such as channel gain or received signal power across a geographic area of interest using measurements of spatially distributed sensors. Applications of these maps include network planning, interference coordination, power control, localization, and cognitive radio to name a few. Existing spectrum cartography methods necessitate knowledge of sensor locations, but such locations cannot be accurately determined from pilot positioning signals (such as those in LTE or GPS) in indoor or dense urban scenarios due to multipath. To circumvent this limitation, this paper proposes localization-free cartography, where spectral maps are directly constructed from features of these positioning signals rather than from location estimates. The proposed algorithm capitalizes on the framework of kernel-based learning and offers improved prediction performance relative to existing alternatives, as demonstrated by a simulation study in a street canyon.

A significant number of linear inference problems in wireless sensor networks can be solved by projecting the observed signal onto a given subspace. Decentralized approaches avoid the need for performing such an operation at a central processor, thereby reducing congestion and increasing the robustness and the scalability of the network. Unfortunately, existing decentralized approaches either confine themselves to a reduced family of subspace projection tasks or need an infinite number of iterations to obtain the exact projection. To remedy these limitations, this paper develops a framework for computing a wide class of subspace projections in a decentralized fashion by relying on the notion of graph filtering. To this end, a methodology to obtain the shift matrix and the corresponding filter coefficients that provide exact subspace projection in a nearly minimal number of iterations is proposed. Numerical experiments corroborate the merits of the proposed approach.

Big data applications demand efficient solvers capable of providing accurate solutions to large-scale problems at affordable computational costs. Processing data sequentially, online algorithms offer attractive means to deal with massive data sets. However, they may incur prohibitive complexity in high-dimensional scenarios if the entire data set is processed. It is therefore necessary to confine computations to an informative subset. While existing approaches have focused on selecting a prescribed fraction of the available data vectors, the present paper capitalizes on this degree of freedom to accelerate the convergence of a generic class of online algorithms in terms of processing time/computational resources by balancing the required burden with a metric of how informative each datum is. The proposed method is illustrated in a linear regression setting, and simulations corroborate the superior convergence rate of the recursive least-squares algorithm when the novel data selection is effected.

This work proposes a spectrum cartography algorithm used for learning the power spectrum distribution over a wide frequency band across a given geographic area. Motivated by low-complexity sensing hardware and stringent communication constraints, compressed and quantized measurements are considered. Setting out from a nonparametric regression framework, it is shown that a sensible approach leads to a support vector machine formulation. The simulated tests verify that accurate spectrum maps can be constructed using a simple sensing architecture with significant savings in the feedback.

The class of complex random vectors whose covariance matrix is linearly parameterized by a basis of Hermitian Toeplitz (HT) matrices is considered, and the maximum compression ratios that preserve all second-order information are derived-the statistics of the uncompressed vector must be recoverable from a set of linearly compressed observations. This kind of vectors arises naturally when sampling wide-sense stationary random processes and features a number of applications in signal and array processing. Explicit guidelines to design optimal and nearly optimal schemes operating both in a periodic and nonperiodic fashion are provided by considering two of the most common linear compression schemes, which we classify as dense or sparse. It is seen that the maximum compression ratios depend on the structure of the HT subspace containing the covariance matrix of the uncompressed observations. Compression patterns attaining these maximum ratios are found for the case without structure as well as for the cases with circulant or banded structure. Universal samplers are also proposed to compress unknown HT subspaces.

Wideband spectrum sensing provides a means to determine the occupancy of channels spanning a broad range of frequencies. Practical limitations impose that the acquisition should be accomplished at a low rate, much below the Nyquist lower bound. Dramatic rate reductions can be obtained by the observation that only a few parameters need to be estimated in typical spectrum sensing applications. This paper discusses the joint estimation of the power of a number of channels, whose power spectral density (PSD) is known up to a scale factor, using compressive measurements. First, relying on a Gaussian assumption, an efficient approximate maximum likelihood (ML) technique is presented. Next, a least-squares estimator is applied for the general non-Gaussian case.

We consider the problem of detecting a known signal with constant magnitude immersed in noise of unknown variance, when the propagation channel is frequency-flat and randomly time-varying within the observation window. A Basis Expansion Model with random coefficients is used for the channel, and a Generalized Likelihood Ratio approach is adopted in order to cope with deterministic nuisance parameters. The resulting scheme can be seen as a generalization of the wellknown Matched Filter detector, to which it reduces for time-invariant channels. Closed-form analytical expressions are provided for the distribution of the test statistic under both hypotheses, which allow to assess the detection performance.