Asymptotics of Distances Between Sample Covariance Matrices

This work considers the asymptotic behavior of the distance between two sample covariance matrices (SCM). A general result is provided for a class of functionals that can be expressed as sums of traces of functions that are separately applied to each covariance matrix. In particular, this class includes very conventional metrics, such as the Euclidean distance or Jeffrery's divergence, as well as a number of other more sophisticated distances recently derived from Riemannian geometry considerations, such as the log-Euclidean metric. In particular, we analyze the asymptotic behavior of this class of functionals by establishing a central limit theorem that allows us to describe their asymptotic statistical law. In order to account for the fact that the sample sizes of two SCMs are of the same order of magnitude as their observation dimension, results are provided by assuming that these parameters grow to infinity while their quotients converge to fixed quantities. Numerical results illustrate how this type of result can be used in order to predict the performance of these metrics in practical machine learning algorithms, such as clustering of SCMs.

Near-Field Beamfocusing with Polarized Antennas

One of the most relevant challenges in future 6G wireless networks is how to support a massive spatial multiplexing of a large number of user terminals. Recently, extremely large antenna arrays (ELAAs), also referred to as extra-large MIMO (XL-MIMO), have emerged as an potential enabler of this type of spatially multiplexed transmission. These massive configurations substantially increase the number of available spatial degrees of freedom (transmission modes) while also enabling to spatially focus the transmitted energy into a very small region, thanks to the properties of near-field propagation and the large number of transmitters. This work explores whether multiplexing of multiple orthogonal polarizations can enhance the system performance in the near-field. We concentrate on a simple scenario consisting of a Uniform Linear Array (ULA) and a single antenna element user equipment (UE). We demonstrate that the number of spatial degrees of freedom can be as large as 3 in the near-field of a Line of Sight (LoS) channel when both transmitter and receiver employ three orthogonal linear polarizations. In the far-field, however, the maximum number of spatial degrees of freedom tends to be only 2, due to the fact that the equivalent MIMO channel becomes rank deficient. We provide an analytical approximation to the achievable rate, which allows us to derive approximations to the optimal antenna spacing and array size that maximize the achievable rate

Energy-Saving Cell-Free Massive MIMO Precoders with a Per-AP Wideband Kronecker Channel Model

We study cell-free massive multiple-input multiple-output precoders that minimize the power consumed by the power amplifiers subject to per-user per-subcarrier rate constraints. The power at each antenna is generally retrieved by solving a fixed-point equation that depends on the instantaneous channel coefficients. Using random matrix theory, we retrieve each antenna power as the solution to a fixed-point equation that depends only on the second-order statistics of the channel. Numerical simulations prove the accuracy of our asymptotic approximation and show how a subset of access points should be turned off to save power consumption, while all the antennas of the active access points are utilized with uniform power across them. This mechanism allows to save consumed power up to a factor of 9$\times$ in low-load scenarios.

Deep Unfolding for Fast Linear Massive MIMO Precoders under a PA Consumption Model

Massive multiple-input multiple-output (MIMO) precoders are typically designed by minimizing the transmit power subject to a quality-of-service (QoS) constraint. However, current sustainability goals incentivize more energy-efficient solutions and thus it is of paramount importance to minimize the consumed power directly. Minimizing the consumed power of the power amplifier (PA), one of the most consuming components, gives rise to a convex, non-differentiable optimization problem, which has been solved in the past using conventional convex solvers. Additionally, this problem can be solved using a proximal gradient descent (PGD) algorithm, which suffers from slow convergence. In this work, to overcome the slow convergence, a deep unfolded version of the algorithm is proposed, which can achieve close-to-optimal solutions in only 20 iterations compared to the 3500 plus iterations needed by the PGD algorithm. Results indicate that the deep unfolding algorithm is three orders of magnitude faster than a conventional convex solver and four orders of magnitude faster than the PGD.

Self-Supervised Learning of Linear Precoders under Non-Linear PA Distortion for Energy-Efficient Massive MIMO Systems

Massive multiple input multiple output (MIMO) systems are typically designed under the assumption of linear power amplifiers (PAs). However, PAs are typically most energy-efficient when operating close to their saturation point, where they cause non-linear distortion. Moreover, when using conventional precoders, this distortion coherently combines at the user locations, limiting performance. As such, when designing an energy-efficient massive MIMO system, this distortion has to be managed. In this work, we propose the use of a neural network (NN) to learn the mapping between the channel matrix and the precoding matrix, which maximizes the sum rate in the presence of this non-linear distortion. This is done for a third-order polynomial PA model for both the single and multi-user case. By learning this mapping a significant increase in energy efficiency is achieved as compared to conventional precoders and even as compared to perfect digital pre-distortion (DPD), in the saturation regime.

Floor Map Reconstruction Through Radio Sensing and Learning By a Large Intelligent Surface

Environmental scene reconstruction is of great interest for autonomous robotic applications, since an accurate representation of the environment is necessary to ensure safe interaction with robots. Equally important, it is also vital to ensure reliable communication between the robot and its controller. Large Intelligent Surface (LIS) is a technology that has been extensively studied due to its communication capabilities. Moreover, due to the number of antenna elements, these surfaces arise as a powerful solution to radio sensing. This paper presents a novel method to translate radio environmental maps obtained at the LIS to floor plans of the indoor environment built of scatterers spread along its area. The usage of a Least Squares (LS) based method, U-Net (UN) and conditional Generative Adversarial Networks (cGANs) were leveraged to perform this task. We show that the floor plan can be correctly reconstructed using both local and global measurements.

Beam Aware Stochastic Multihop Routing for Flying Ad-hoc Networks

Routing is a crucial component in the design of Flying Ad-Hoc Networks (FANETs). State of the art routing solutions exploit the position of Unmanned Aerial Vehicles (UAVs) and their mobility information to determine the existence of links between them, but this information is often unreliable, as the topology of FANETs can change quickly and unpredictably. In order to improve the tracking performance, the uncertainty introduced by imperfect measurements and tracking algorithms needs to be accounted for in the routing. Another important element to consider is beamforming, which can reduce interference, but requires accurate channel and position information to work. In this work, we present the Beam Aware Stochastic Multihop Routing for FANETs (BA-SMURF), a Software-Defined Networking (SDN) routing scheme that takes into account the positioning uncertainty and beamforming design to find the most reliable routes in a FANET. Our simulation results show that joint consideration of the beamforming and routing can provide a 5% throughput improvement with respect to the state of the art.

User Clustering for Rate Splitting using Machine Learning

Hierarchical Rate Splitting (HRS) schemes proposed in recent years have shown to provide significant improvements in exploiting spatial diversity in wireless networks and provide high throughput for all users while minimising interference among them. Hence, one of the major challenges for such HRS schemes is the necessity to know the optimal clustering of these users based only on their Channel State Information (CSI). This clustering problem is known to be NP hard and, to deal with the unmanageable complexity of finding an optimal solution, in this work a scalable and much lighter clustering mechanism based on Neural Network (NN) is proposed. The accuracy and performance metrics show that the NN is able to learn and cluster the users based on the noisy channel response and is able to achieve a rate comparable to other more complex clustering schemes from the literature.

Exclusive Group Lasso for Structured Variable Selection

A structured variable selection problem is considered in which the covariates, divided into predefined groups, activate according to sparse patterns with few nonzero entries per group. Capitalizing on the concept of atomic norm, a composite norm can be properly designed to promote such exclusive group sparsity patterns. The resulting norm lends itself to efficient and flexible regularized optimization algorithms for support recovery, like the proximal algorithm. Moreover, an active set algorithm is proposed that builds the solution by successively including structure atoms into the estimated support. It is also shown that such an algorithm can be tailored to match more rigid structures than plain exclusive group sparsity. Asymptotic consistency analysis (with both the number of parameters as well as the number of groups growing with the observation size) establishes the effectiveness of the proposed solution in terms of signed support recovery under conventional assumptions. Finally, a set of numerical simulations further corroborates the results.

Probability of Resolution of MUSIC and g-MUSIC: An Asymptotic Approach

In this article, the outlier production mechanism of the conventional Multiple Signal Classification (MUSIC) and the g-MUSIC Direction-of-Arrival (DoA) estimation technique is investigated using tools from Random Matrix Theory (RMT). A general Central Limit Theorem (CLT) is derived that allows to analyze the asymptotic stochastic behavior of eigenvector-based cost functions in the asymptotic regime where the number of snapshots and the number of antennas increase without bound at the same rate. Furthermore, this CLT is used to provide an accurate prediction of the resolution capabilities of the MUSIC and the g-MUSIC DoA estimation method. The finite dimensional distribution of the MUSIC and the g-MUSIC cost function is shown to be asymptotically jointly Gaussian distributed in the asymptotic regime.