One of the main events of the workshop is the poster session on the afternoon Tuesday 03/5. The poster session is an excellent opportunity for workshop attendees to get to know each other and to discuss the research topics in more detail. We hope that this will result in a relaxed atmosphere for networking, informal discussions, and the exchange of research ideas. See you all on **Tuesday 3 May 2022**!

**Jafait Junior Fodop Sokoudjou**, Tecnum School of Engineering (University of Navarra)

### Tag Design and Machine Learning Workflow for Robust Chipless RFID Classification

*In this work, we describe step by step a complete workflow to apply machine learning (ML) for chipless RFID tag identification, covering: i) the tag design criteria for circular ring resonator (CRR) arrays for ML interoperability; ii) the data collection procedure to get a sufficiently representative dataset of real measurements; iii) the ML algorithms to visualize the information in the dataset and get a high accuracy prediction; and iv) a thresholding scheme to increase the certainty of the predictions. The differences of the tags’ frequency responses are maximized by optimizing the Hamming distance between the tag identifiers and by controlling the radar cross section (RCS) level of each CRR array. We show on two scenarios, fixed and flexible range (up to 160 cm), that the proposed workflow can achieve perfect accuracy in most cases for the identification of four designed tags.*

**Darian Pérez Adán**, University of A Coruña (UDC)

### An Alternating Minimization Approach for Multiuser RIS-assisted MIMO Systems

*A reconfigurable intelligent surface (RIS) is a real-time controllable reflect-array that consists of a large number of discrete elements which introduce a phase-shift to the incoming signals. These passive surfaces are helpful to partially control the radio environment by properly configuring the phase-shift matrix and, thus, the direction of the reflected signals. This work proposes the joint design of the user precoders and the RIS phase-shift matrix in the uplink of a multiuser (MU) multiple-input multiple-output (MIMO) system. The RIS phase-shift matrix and the user precoders are designed to minimize the mean square error (MSE) of the estimated user symbols via an alternating minimization projected gradient (PG) algorithm. Numerical results show that the proposed solution leads to substantial achievable sum-rate gains with respect to baseline strategies that do not account for the inter-user interference in the precoder design and the proper RIS phase-shift matrix configuration.*

**Diego Cuevas Fernández**, University of Cantabria (UC)

### Coherence-based subspace packings for MIMO noncoherent communications

*We propose a new algorithm for designing unstructured Grassmannian constellations for noncoherent MIMO communications over Rayleigh block-fading channels. The algorithm minimizes the maximum coherence between subspaces, which is shown to be equivalent to the diversity product previously proposed in the literature. The coherence criterion is optimized by means of a gradient ascent algorithm on the Grassmann manifold. The method is generalized to optimize a weighted cost function that takes into account several neighboring codewords. Simulation results suggest that the constellations designed with the proposed algorithm achieve better SER performance than existing algorithms for unstructured Grassmannian constellation designs.*

**Jesús Pérez-Arriaga**, University of Cantabria (UC)

### Online detection and SNR estimation in cooperative spectrum sensing

*Cooperative spectrum sensing has proved to be an effective method to improve the detection performance in cognitive radio systems. This work focuses on centralized cooperative schemes based on the soft fusion of the energy measurements at the cognitive radios (CRs). In these systems, the likelihood ratio test (LRT) is the optimal detection rule, but the sufficient statistic depends on the local signal-to-noise ratio (SNR) at the CRs, which are unknown in most practical cases. Therefore, the detection problem becomes a composite hypothesis test. The generalized LRT is the most popular approach in those cases. Unfortunately, in mobile environments, its performance is well below the LRT because the local energies are measured under varying SNRs. In this work, we present a new algorithm that jointly estimates the instantaneous SNRs and detects the presence of primary signals. Due to its adaptive nature, the algorithm is well suited for mobile scenarios where the local SNRs are time-varying. Simulation results show that its detection performance is close to the LRT in realistic conditions.*

**Jordi Pérez-Guijarro**, Polytechnic University of Catalonia (UPC)

### Quantum Multiple Hypothesis Testing Based on a Sequential Discarding Scheme

*We consider the quantum multiple hypothesis testing problem, focusing on the case of hypothesis represented by pure states. A sequential adaptive algorithm is derived and analyzed first. This strategy exhibits a decay rate in the error probability with respect to the expected value of measurements greater than the optimal decay rate of the fixed-length methods. A more elaborated scheme is developed next, by serially concatenating multiple implementations of the first scheme. In this case each stage considers as a priori hypothesis probability the a posteriori probability of the previous stage. We show that, by means of a fixed number of concatenations, the expected value of measurements to be performed decreases considerably. We also analyze one strategy based on an asymptotically large concatenation of the initial scheme, demonstrating that the expected number of measurements in this case is upper bounded by a constant, even in the case of zero average error probability. A lower bound for the expected number of measurements in the zero error probability setting is also derived.*

**Carolina Nolasco Ferencikova**, Tecnum School of Engineering (University of Navarra)

### Distributed clustering algorithm for adaptive pandemic control

*The COVID-19 pandemic has had severe consequences on the global economy, mainly due to indiscriminate geographical lockdowns. Moreover, the digital tracking tools developed to survey the spread of the virus have generated serious privacy concerns. In this poster, we present an algorithm that adaptively groups individuals according to their social contacts and their risk level of severe illness from COVID-19, instead of geographical criteria. The algorithm is fully distributed and therefore, individuals do not know any information about the group they belong to. Thus, we present a distributed clustering algorithm for adaptive pandemic control.*

**Josu Etxezarreta Martínez**, Tecnum School of Engineering (University of Navarra)

### Multi-qubit time-varying quantum channels are fast

*Recent experimental studies have shown that the relaxation time (T_1) and the dephasing time (T_2) of superconducting qubits fluctuate considerably over time. Time-varying quantum channel (TVQC) models have been proposed in order to consider time-varying nature of the parameters that define qubit decoherence. Realizations of multi-qubit TCQCs have been assumed to be equal for all the qubits of an error correction block, indicating that the random variables describing the fluctuations of T_1 and T_2 are qubitwise fully correlated. However, the fluctuations of the decoherence parameters are explained by the incoherent coupling of the qubits with unstable near-resonant two-level-system (TLS), indicating that such variations are local to each of the qubits of the system. In this poster, we discuss the multi-qubit TVQC when fluctuations of the decoherence parameters are local to each qubit which we name as fast time-varying quantum channels (FTVQC). Moreover, we numerically study the performance of quantum error correction codes (QECC) when they operate over FTVQCs and we conclude that their performance. Finally, we propose the ergodic quantum capacity as the asymptotically achievable limit for QECCs over this channel.*

**Fernando de Villar Rosety**, Tecnum School of Engineering (University of Navarra)

### DFT-based Linear Coding Schemes for Transmitting Analog Sources

*In the era of the Internet of Things, there are many applications where numerous devices are deployed to acquire information and send it to analyse the data and make informed decisions. In these applications, the power consumption and price of the devices are often an issue. In this work, an analog coding is studied, so that an ADC is not needed, allowing the size and power consumption of the device to be reduced. In addition, linear and DFT-based transmission schemes are proposed, so that the complexity of the operations involved is reduced, thus reducing the requirements in terms of processing capacity. The proposed schemes are proved to be asymptotically optimal among the linear ones.*

**Antonio de Marti I Olius**, Tecnum School of Engineering (University of Navarra)

### Performance of surface codes in realistic quantum hardware

*Surface codes are generally studied based on the assumption that each of the qubits that make up the surface code lattice suffers noise that is independent and identically distributed (i.i.d.). However, real benchmarks of the individual relaxation (T_1) and dephasing (T_2) times of the constituent qubits of state-of-the-art quantum processors have recently shown that the decoherence effects suffered by each particular qubit will actually vary in intensity. In this article, we propose a decoherence model that takes this non-uniform behaviour into account, the independent non-identically distributed (i.ni.d.) noise model, and we analyze how the performance of planar codes is impacted by this new model. For this purpose we employ data from four state-of-the-art superconducting processors: ibmq_brooklyn, ibm_washington, Zuchongzhi and Rigetti Aspen-11. Our results show that the i.i.d. noise assumption overestimates the performance of surface codes, which can suffer up to 85% performance decrements in terms of the code pseudo-threshold when they are subjected to the i.ni.d. noise model. Furthermore, in this work we also consider the relationship between code performance and qubit arrangement in the surface code lattice. We show how surface code performance varies as a function of qubit placement within the lattice (because of the different decoherence parameters) and we introduce an algorithm that re-arranges the qubits of the surface code lattice in a way that optimizes code performance. The optimum qubit configuration derived with this algorithm can attain planar code pseudo-threshold values that are up to 249% higher than for the general planar code architectures.*

**Iñigo Barasoain Echepare**, Tecnum School of Engineering (University of Navarra)

### Necessary and sufficient conditions for AR vector processes to be stationary

*Traditionally, vector autoregressive processes (VAR) have been referred to as both stationary and asymptotically wide-sense stationary (AWSS). Until now it was not known what relationship, if any, there was between them. In this work, we prove that both concepts are equivalent. This could facilitate the work with stationary VAR processes, since we can know the behaviour of their correlation matrices.*

**Andrei Buciulea Vlas**, Rey Juan Carlos University (URJC)

### Network Reconstruction from Stationary and Gaussian Graph Signals

*Network-topology inference from (vertex) signal observations is a prominent problem across data-science and engineering disciplines. Classical network topology-inference schemes estimate the graph from a thresholded version of either 1) the correlation matrix or 2) the partial correlation matrix. The celebrated Graphical Lasso (GL) algorithm falls into the second class and, by assuming Gaussianity, can recover the network topology from a reduced number of observations. A more general approach, inspired by recent Graph Signal Processing (GSP) results, is to infer the network topology by assuming that the signals are stationary on the sought graph. Being a more general graph learning method, its able to unveil more parsimonious network structures, but requires a larger number of observations than GL to recover the graph. Motivated by the previous discussion, this work investigates the problem of inferring the network topology upon assuming that the signals are both Gaussian and stationary on the graph. With these assumptions in place, we develop an algorithm that achieves two objectives: 1) to be more general than GL since we assume stationarity and, 2) to require less observations than stationary methods. Since the joint consideration of Gaussianity and stationarity renders the inference problem non-convex, we propose an efficient solution that leverages convex relaxations and a blockwise iterative algorithm to estimate the topology of the graph. Numerical experiments over synthetic and real-world datasets showcase the performance of the developed method and compare it with existing alternatives*.

**Samuel Rey**, Rey Juan Carlos University (URJC)

### Joint inference of multiple graphs with hidden variables from stationary graph signals

*Learning graphs from sets of nodal observations represents a prominent problem formally known as graph topology inference. However, current approaches are limited by typically focusing on inferring single networks, and they assume that observations from all nodes are available. First, many contemporary setups involve multiple related networks, and second, it is often the case that only a subset of nodes is observed while the rest remain hidden. Motivated by these facts, we introduce a joint graph topology inference method that models the influence of the hidden variables. Under the assumptions that the observed signals are stationary on the sought graphs and the graphs are closely related, the joint estimation of multiple networks allows us to exploit such relationships to improve the quality of the learned graphs. Moreover, we confront the challenging problem of modeling the influence of the hidden nodes to minimize their detrimental effect. To obtain an amenable approach, we take advantage of the particular structure of the setup at hand and leverage the similarity between the different graphs, which affects both the observed and the hidden nodes. To test the proposed method, numerical simulations over synthetic and real-world graphs are provided.*

**Sara Perez Vieites**, Carlos III University (UC3M)

### Nested smoothing algorithms for inference and tracking of heterogeneous multi-scale state-space systems

*Multi-scale problems, where variables of interest evolve in different time-scales and live in different state-spaces, can be found in many fields of science where complex series of data have to be analyzed. Here, we introduce a new recursive methodology for Bayesian inference that aims at estimating the static parameters and tracking the dynamic variables of these kind of systems. Although the proposed approach works in rather general multi-scale systems, for clarity we analyze the case of a homogeneous multi-scale model with 3 time-scales (static parameters, slow dynamic state variables and fast dynamic state variables). The proposed scheme, based on the nested filtering methodology of [S. Pérez-Vieites, I. P. Mariño, J. Míguez. Probabilistic scheme for joint parameter estimation and state prediction in complex dynamical systems. Physical Review E, 98(6), 063305, 2017], combines three intertwined layers of filtering techniques that approximate recursively the joint posterior probability distribution of the parameters and both sets of dynamic state variables given a sequence of noisy data. We explore the use of sequential Monte Carlo schemes and Gaussian filtering techniques in the different layers of computation. Some numerical results are presented for a stochastic two-scale Lorenz 96 model with unknown parameters.*

**Victor Manuel Tenorio Gómez**, Rey Juan Carlos University (URJC)

### A Robust Alternative for Graph Convolutional Neural Networks via Graph Neighborhood Filters

*Graph convolutional neural networks (GCNNs) are popular deep learning architectures that, upon replacing regular convolutions with graph filters (GFs), generalize CNNs to irregular domains. However, classical GFs are prone to numerical errors since they consist of high-order polynomials. This problem is aggravated when several filters are applied in cascade, limiting the practical depth of GCNNs. To tackle this issue, we present the neighborhood graph filters (NGFs), a family of GFs that replaces the powers of the graph shift operator with k-hop neighborhood adjacency matrices. NGFs help to alleviate the numerical issues of traditional GFs, allow for the design of deeper GCNNs, and enhance the robustness to errors in the topology of the graph. To illustrate the advantage over traditional GFs in practical applications, we use NGFs in the design of deep neighborhood GCNNs to solve graph signal denoising and node classification problems over both synthetic and real-world data.*

**Diego José Lloria Albiñana**, Universitat de València (UV)

### Deep-learning-based direction-of-arrival estimation for analog millimeter wave MIMO systems

B5G networks, such as 6G, are expected to continue using millimeter wave (mmWave) frequencies, *extending the spectrum usage to the Terahertz frequency range. High-accuracy angle of arrival (AoA) and angle of departure (AoD) estimation in mmWave channels is critical for cell search, stable communications, and positioning. Moreover, the design of low-complexity AoA/AoD estimation algorithms is also of major importance in the deployment of practical systems to enable a fast and resource-efficient computation of beamforming weights. Parametric mmWave channel estimation allows to describe the channel matrix as a combination of direction-dependent signal paths, exploiting the sparse characteristics of mmWave channels. Previous works have shown that shifting the channel estimation problem from the angular domain to the transformed spatial domain, where estimating the AoAs/AoDs corresponds to estimating the angular frequencies of paths constituting the mmWave channel, has advantages in terms of angle accuracy and probability of detection. In this work, we propose a deep-learning-based approach to estimate the AoAs/AoDs from observation inputs in the transformed spatial domain. In particular, a previously proposed convolutional neural network for two-dimensional frequency estimation has been adapted to the problem at hand, and used to retrieve the angular frequencies. We found that the proposed deep-learning-based algorithm has a significant performance advantage with respect to other state-of-the-art approaches also based on frequency domain processing, especially at low signal-to-noise ratios*.

**Matilde Pilar Sánchez Fernández**, Universidad Carlos III de Madrid (UC3M)

### Sparse parametrical model recovery using Atomic Norm

Novel 6G wireless communication paradigms will require a multi-fold increase in overall system capacity and additional network functionalities such as extreme precise positioning, going far beyond nowadays *system capabilities. New systems will aim for multi-dimensional space awareness and ubiquitous connectivity that can only be achieved with arrays of matching dimensionality and embed antenna deployments in surfaces/volumetric spaces coexisting with additional usages of that space. A full multidimensional characterization of AoA is essential to provide user spatial orthogonality for interference control, robust angle information beamforming, low cost hybrid beamforming, or the provisioning of location-aware and tracking services. In this work, we focus on extracting multi-dimensional AoA parameters exploiting the sparse nature of signal measurements in mmWave massive MIMO systems. The approach undertaken is based on the atomic L0/L1 norms that allows grid-less resolution of the AoA in arbitrary 3D.*

**Chao Qi**, Universidad Carlos III de Madrid (UC3M)

### A High-SNR Normal Approximation for MIMO Rayleigh Block-Fading Channels

*We concern a high-SNR normal approximation of the maximum coding rate, at which a code of a given blocklength can be transmitted with a given block-error probability over a non-coherent Rayleigh block-fading channel with multiple transmit and receive antennas (MIMO). The normal approximation can be used to measure the performance of communication strategies, such as antenna placement and the optimal number of active transmit antennas analysis.*

**Rachid Boukrab**, Universidad Politécnica de Cataluña (UPC)

### GRAPH-REGULARIZED ONLINE DICTIONARY LEARNING

*Dictionary learning (DL) algorithms aim at computing an overcomplete dictionary whose atoms represent prominent features of the data. Traditional DL techniques assume that all the data vectors are available and fit into memory, and therefore, they employ batch algorithms to solve the problem. However, in some scenarios the observations are streamed or the whole dataset is too large to fit into memory. In this case, one must switch to online sample-wise algorithms to solve the problem. Moreover, conventional DL methods assume that the components of the observations are independent and identically distributed. However, it might be that the components of the data vectors are dependent. The pair-wise dependencies between components are captured by a graph that is a priori known or estimated from the data. The challenge is to include the information about the underlying topology of the data, represented by this graph, into the DL problem. In this work, we leverage graph signal processing (GSP) methods like Laplacian smoothness priors to include this information in the DL objective function. Then, we design a gradient-based online algorithm to solve to learn a dictionary whose atoms are smooth on the graph and finally test it on synthetic data.*

**Grace Silvana Villacrés** Estrada, Universidad Carlos III de Madrid (UC3M)

### Wireless Networks at high SNR

*We consider a bursty noncoherent wireless network, where the transmitters and receivers are cognizant of the statistics of the fading coefficients, but are ignorant of their realizations. We have demonstrated that, if the users do not cooperate and their codebooks are all distributed according to the same distribution, then each user’s channel capacity is bounded in the SNR, provided that the fading coefficients of the interferers (ordered according to their distance to the receiver) decay exponentially or more slowly. The question whether channel capacity can be unbounded in the SNR if the fading coefficients of the interferers decays sufficiently fast is nontrivial, since the condition that the odebooks of the users are distributed according to the same distribution prevents interference-avoiding strategies such as time-, frequency-, or code-division multiple access. In this work, we demonstrate that an unbounded information rate can be achieved nonetheless by bursty signalling.*