Exact Statistical Characterization of 2×22\times2 Gram Matrices with Arbitrary Variance Profile

This paper is concerned with the statistical properties of the Gram matrix $\mathbf{W}=\mathbf{H}\mathbf{H}^\dagger$, where $\mathbf{H}$ is a $2\times2$ complex central Gaussian matrix whose elements have arbitrary variances. With such arbitrary variance profile, this random matrix model fundamentally departs from classical Wishart models and presents a significant challenge as the classical analytical toolbox no longer directly applies. We derive new exact expressions for the distribution of $\mathbf{W}$ and that of its eigenvalues by means of an explicit parameterization of the group of unitary matrices. Our results yield remarkably simple expressions, which are further leveraged to study the outage data rate of a dual-antenna communication system under different variance profiles.Comment: 6 pages, 1 figure, 1 tabl

Power Allocation Schemes for Multicell Massive MIMO Systems

This paper investigates the sum-rate gains brought by power allocation strategies in multicell massive multipleinput multiple-output systems, assuming time-division duplex transmission. For both uplink and downlink, we derive tractable expressions for the achievable rate with zero-forcing receivers and precoders respectively. To avoid high complexity joint optimization across the network, we propose a scheduling mechanism for power allocation, where in a single time slot, only cells that do not interfere with each other adjust their transmit powers. Based on this, corresponding transmit power allocation strategies are derived, aimed at maximizing the sum rate per-cell. These schemes are shown to bring considerable gains over equal power allocation for practical antenna configurations (e.g., up to a few hundred). However, with fixed number of users (N), these gains diminish as M turns to infinity, and equal power allocation becomes optimal. A different conclusion is drawn for the case where both M and N grow large together, in which case: (i) improved rates are achieved as M grows with fixed M/N ratio, and (ii) the relative gains over the equal power allocation diminish as M/N grows. Moreover, we also provide applicable values of M/N under an acceptable power allocation gain threshold, which can be used as to determine when the proposed power allocation schemes yield appreciable gains, and when they do not. From the network point of view, the proposed scheduling approach can achieve almost the same performance as the joint power allocation after one scheduling round, with much reduced complexity

Analysis and Design of Multiple-Antenna Cognitive Radios with Multiple Primary User Signals

We consider multiple-antenna signal detection of primary user transmission signals by a secondary user receiver in cognitive radio networks. The optimal detector is analyzed for the scenario where the number of primary user signals is no less than the number of receive antennas at the secondary user. We first derive exact expressions for the moments of the generalized likelihood ratio test (GLRT) statistic, yielding approximations for the false alarm and detection probabilities. We then show that the normalized GLRT statistic converges in distribution to a Gaussian random variable when the number of antennas and observations grow large at the same rate. Further, using results from large random matrix theory, we derive expressions to compute the detection probability without explicit knowledge of the channel, and then particularize these expressions for two scenarios of practical interest: 1) a single primary user sending spatially multiplexed signals, and 2) multiple spatially distributed primary users. Our analytical results are finally used to obtain simple design rules for the signal detection threshold.Comment: Revised version (14 pages). Change in titl

Pattern of Amino Acid Substitutions in Transmembrane Domains of β-Barrel Membrane Proteins for Detecting Remote Homologs in Bacteria and Mitochondria

-barrel membrane proteins play an important role in controlling the exchange and transport of ions and organic molecules across bacterial and mitochondrial outer membranes. They are also major regulators of apoptosis and are important determinants of bacterial virulence. In contrast to -helical membrane proteins, their evolutionary pattern of residue substitutions has not been quantified, and there are no scoring matrices appropriate for their detection through sequence alignment. Using a Bayesian Monte Carlo estimator, we have calculated the instantaneous substitution rates of transmembrane domains of bacterial -barrel membrane proteins. The scoring matrices constructed from the estimated rates, called bbTM for -barrel Transmembrane Matrices, improve significantly the sensitivity in detecting homologs of -barrel membrane proteins, while avoiding erroneous selection of both soluble proteins and other membrane proteins of similar composition. The estimated evolutionary patterns are general and can detect -barrel membrane proteins very remote from those used for substitution rate estimation. Furthermore, despite the separation of 2–3 billion years since the proto-mitochondrion entered the proto-eukaryotic cell, mitochondria outer membrane proteins in eukaryotes can also be detected accurately using these scoring matrices derived from bacteria. This is consistent with the suggestion that there is no eukaryote-specific signals for translocation. With these matrices, remote homologs of -barrel membrane proteins with known structures can be reliably detected at genome scale, allowing construction of high quality structural models of their transmembrane domains, at the rate of 131 structures per template protein. The scoring matrices will be useful for identification, classification, and functional inference of membrane proteins from genome and metagenome sequencing projects. The estimated substitution pattern will also help to identify key elements important for the structural and functional integrity of -barrel membrane proteins, and will aid in the design of mutagenesis studies

Large-dimensional behavior of regularized Maronna's M-estimators of covariance matrices

Robust estimators of large covariance matrices are considered, comprising regularized (linear shrinkage) modifications of Maronna's classical M-estimators. These estimators provide robustness to outliers, while simultaneously being well-defined when the number of samples does not exceed the number of variables. By applying tools from random matrix theory, we characterize the asymptotic performance of such estimators when the numbers of samples and variables grow large together. In particular, our results show that, when outliers are absent, many estimators of the regularized-Maronna type share the same asymptotic performance, and for these estimators we present a data-driven method for choosing the asymptotically optimal regularization parameter with respect to a quadratic loss. Robustness in the presence of outliers is then studied: in the non-regularized case, a large-dimensional robustness metric is proposed, and explicitly computed for two particular types of estimators, exhibiting interesting differences depending on the underlying contamination model. The impact of outliers in regularized estimators is then studied, with interesting differences with respect to the non-regularized case, leading to new practical insights on the choice of particular estimators.Comment: 15 pages, 6 figure

Attosecond control of spin polarization in electron–ion recollision driven by intense tailored fields

Tunnel ionization of noble gas atoms driven by a strong circularly polarized laser field in combination with a counter-rotating second harmonic generates spin-polarized electrons correlated to the spin-polarized ionic core. Crucially, such two-color field can bring the spin-polarized electrons back to the parent ion, enabling the scattering of the spin-polarized electron on the spin-polarized parent ion. Here we show how one can control the degree of spin polarization as a function of electron energy and recollision time by tuning the laser parameters, such as the relative intensities of the counter-rotating fields. The attosecond precision of the control over the degree of spin polarization opens the door for attosecond control and spectroscopy of spin-resolved dynamics.Deutsche Forschungsgemeinschaft https://doi.org/10.13039/501100001659Peer Reviewe

Sensor analysis for the assessment of biomechanical parameters in endurance runners: a systematic review

Problem Statement: This systematic review focuses on the use of sensors to improve performance in endurance athletes by analyzing biomechanical parameters. Approach: The use of sensors in endurance sports has gained popularity in recent years, allowing athletes and coaches to measure and analyze different biomechanical parameters in real-time. Purpose: The main purpose of this systematic review is to answer the question of how sensors can be used and applied to improve performance in endurance runners by analyzing the biomechanical parameters they provide. Methods: Systematic review analyzing related keywords such as biomechanics, kinematics, kinetics, running, triathlon, ultra running, trail running, Stryd, SHFT, Runscribe, and performance, through scientific research articles from the database of the Electronic Library of the Isabel I University dated 02/2023 in English. A total of 192 investigations were found, of which 168 were excluded. After a detailed review, 15 relevant investigations were included. Results: Sensors can be useful to measure biomechanical parameters such as cadence, stride length, leg spring stiffness, ground contact time, and vertical oscillation, which can help to improve performance in endurance athletes. Conclusions: Sensors are a suitable tool to analyze performance improvement in endurance athletes by analyzing biomechanical parameters. However, it is important to highlight that not all sensors are similar, that it is necessary to carefully select the most suitable ones for each specific situation, and that biomechanics is also conditioned in each athlete, so universal rules cannot be established

The Road to 6G: Ten Physical Layer Challenges for Communications Engineers

While the deployment of 5G cellular systems will continue well in to the next decade, much interest is already being generated towards technologies that will underlie its successor, 6G. Undeniably, 5G will have transformative impact on the way we live and communicate, yet, it is still far away from supporting the Internet-of-Everything (IoE), where upwards of a million devices per $\textrm{km}^3$ (both terrestrial and aerial) will require ubiquitous, reliable, low-latency connectivity. This article looks at some of the fundamental problems that pertain to key physical layer enablers for 6G. This includes highlighting challenges related to intelligent reflecting surfaces, cell-free massive MIMO and THz communications. Our analysis covers theoretical modeling challenges, hardware implementation issues and scalability among others. The article concludes by delineating the critical role of signal processing in the new era for wireless communications.Comment: IEEE Communications Magazine, Accepte

Traducción, adaptación transcultural y validación de la versión española del Simple Shoulder Test (SST-Sp)

Introducción y objetivos: El Simple Shoulder Test (SST) es una herramienta de medida recientemente publicado pero ampliamente usado. El objetivo de este estudio fue desarrollar y validar una versión española del SST (SST-Sp). Material y métodos: Se realizó un estudio observacional en dos etapas. El Simple Shoulder Test (SST) fue inicialmente adaptado transculturalmente al español a través de una doble traducción y traducción inversa posteriormente validando sus características psicométricas. Los participantes (n=66) con distintos problemas de hombrocompletaron el SST-Sp, DASH, VAS y SF-12. La muestra completa se utilizó para determinar la estructura factorial, consistencia interna y la validez de criterio concurrente. La fiabilidad fue determinada en las primeras 24-48 horas con una submuestra de 21 pacientes. Resultados: El SST-Sp mostró tres factores que explicaron el 56,1 % de la varianza y se obtuvo la consistencia interna para cada factor ( a=0,738, 0,723 y 0,667) y la fiabilidad (ICC=0,687-0,944) . La estructura factorial fue tridimensional y apoyada por la validez de constructo. La validez de criterio determinada a partir de la relación entre el SST- Sp y DASH fue fuerte (r = -0,73) y justo e inversamente relacionado en VAS r = -0,537 (p < 0,001 ) . Las relaciones entre SST –Sp y la dimensión física y mental de SF- 12 fueron débiles r = -0,47 (p < 0.001) ) y r = -0,43 (p < 0,001), respectivamente. Conclusión: El SST-Sp mantiene las características de la versión inglesa original como una herramienta de medida válida para el hombro. Ha demostrado características psicométricas similares a la versión inglesa original para los criterios de validez, fiabilidad pero no en la estructura factorial.Universidad de Málaga. Campus de Excelencia Internacional Andalucía Tech

Enabling Intelligent Omni-Surfaces in the Polarization Domain: Principles, Implementation and Applications

Research in wireless communications based on reconfigurable intelligent surfaces (RIS) has surged in the communication-theoretic arena. Recently, the RIS concept has moved into the area of so-called simultaneously transmitting and reflecting intelligent omni-surfaces (STAR-IOS, or simply IOS), which extend the RIS functionality by incorporating transmission (in addition to reflection) capabilities. Development of STAR-IOS’ full and independent reconfiguration capabilities for both reflected and transmitted waves is crucial. However, such full independent reconfiguration has thus far been hampered by the intimate coupling between the transmission and reflection behavior of IOS elements. To overcome this challenge and realize the full potential of reconfigurable IOS-aided systems, in this article we advocate for the use of the polarization domain in the design and operation of STAR-IOS. Thanks to the polarization-dependent features of IOS elements, fully independent (reconfigurable) transmission and reflection modes can be delivered, thus bringing key performance improvements in, and opportunities for, new communication scenarios.This work was funded in part by Junta de Andalucía through grant EMERGIA20-00297; in part by the State Research Agency of Spain (AEI) and the European Social Fund under grant RYC2020-030536-I; in part by PID2020-112545RB-C54, PID2020-118139RB-I00, PDC2022-133900-I00, TED2021-129938B-I00, TED2021-131699B-I00 and IJC2020-043599-I funded by MCIN/AEI/10.13039/501100011033 and by the European Union NextGenerationEU/PRTR. Funding for open access charge: Universidad de Granada/CBUA