29 research outputs found
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A Flexible RFIC Architecture for High-Sensitivity Reception and Compressed-Sampling Wideband Detection
Compressed sensing (CS) is a new signal processing approach that has disrupted the Shannon-Nyquist limit based design methodology and has opened promising avenues for building energy-efficient radio frequency integrated circuits (RFICs) for detecting and estimating particular classes (i.e. sparse) of signals. Whether in application domains where naturally occurring signals are sparse or where representations of signals subject to the fidelity limits or configuration settings of the radio equipment are often found to be sparse, the emergence of CS has forced us to re-imagine the radio receiver. While realizing some of the potential benefits promised by theory, CS-RFIC architectures proposed in earlier research were not particularly suitable for mass-market applications.
This thesis demonstrates how to take a new signal processing technique all the way to the hardware level. So far, the main focus in literature has been how CS offers a significant advantage for signal processing. This work will show how CS techniques drive novel architectures down to the integrated circuit level. This requires close collaboration between communication system developers, integrated circuit designers and signal processing experts. The trans-disciplinary approach presented here has led to the unification of CS-inspired architectures for wideband signal detection with robust, legacy architectures for high-sensitivity signal reception. The result is a functionally flexible and rapidly reconfigurable CMOS RFIC compactly implemented on silicon with the potential to achieve the cost, size and power targets in mass-market applications. While the focus of this thesis is RF signal finding and reception in frequency, the CS-based RFIC design approach presented here is applicable to a wide range of other applications like direction-of-arrival and range finding.
We begin by developing a signal-model driven approach for optimizing the performance of CS RF frontends (RFFEs). We consider sparse multiband signals with supports contained within a frequency span extending from fMIN to fMAX. The resulting quadrature analog-to-information converter (QAIC) is a flexible-bandwidth, blind sub-Nyquist sampling architecture optimized for energy consumption and sensitivity performance. The QAIC addresses key drawbacks of earlier CS RFFE architectures like the modulated wideband converter (MWC) that implement frequency spans extending from 0 to fMAX. While these earlier architectures, a direct implementation of CS signal processing theory, have several beneficial properties, the true cost of their proposed analog frontend significantly diminishes the sensitivity performance and energy savings that CS methods have the potential to deliver. They use periodic pseudo-random bit sequence (PRBS) generators where the clock frequency fPRBS scales up with the maximum signal frequency fMAX. In contrast, fPRBS in the QAIC RFFE scales up with the instantaneous bandwidth IBW, where IBW = ( fMAX − fMIN ). This results in significant performance advantages in terms of energy consumption and sensitivity performance. The QAIC uncouples fPRBS from fMAX by performing wideband quadrature downconversion ahead of analog mixing with PRBSs at an intermediate frequency (IF). However, the dual heterodyne architecture of the QAIC suffers from spurious responses at IF caused by gain and phase imbalance in its wideband downconverter.
We then show how the direct RF-to-information converter (DRF2IC) compactly adds CS wideband detection to a direct conversion frequency-translational noise-cancelling (FTNC) receiver by introducing pseudo-random modulation of the local oscillator (LO) signals and by consolidating multiple CS measurements into one hardware branch. The DRF2IC inherits benefits of the FTNC receiver in signal reception mode. In CS wideband detection mode, the DRF2IC inherits key advantages from both the earlier lowpass CS architectures and the QAIC while avoiding the drawbacks of both. It uncouples fPRBS from fMAX in contrast with the MWC. In contrast with the QAIC, the DRF2IC employs a direct conversion RF chain with narrow bandwidth analog components at baseband thereby avoiding frequency-dependent gain and phase imbalance. The DRF2IC chip occupies 0.56mm2 area in 65nm CMOS. In reception mode, it consumes 46.5mW from 1.15V and delivers 40MHz RF bandwidth, 41.5dB conversion gain, 3.6dB noise figure (NF) and -2dBm blocker 1dB compression point (B1dB). In CS wideband detection mode, 66dB operational dynamic range, 40dB instantaneous dynamic range and 1.43GHz instantaneous bandwidth are demonstrated and 6 interferers each 10MHz wide scattered over a 1.27GHz span are detected in 1.2us consuming 58.5mW
Dirty RF Signal Processing for Mitigation of Receiver Front-end Non-linearity
Moderne drahtlose Kommunikationssysteme stellen hohe und teilweise
gegensätzliche Anforderungen an die Hardware der Funkmodule, wie z.B.
niedriger Energieverbrauch, große Bandbreite und hohe Linearität. Die
Gewährleistung einer ausreichenden Linearität ist, neben anderen analogen
Parametern, eine Herausforderung im praktischen Design der Funkmodule. Der
Fokus der Dissertation liegt auf breitbandigen HF-Frontends für
Software-konfigurierbare Funkmodule, die seit einigen Jahren kommerziell
verfügbar sind. Die praktischen Herausforderungen und Grenzen solcher
flexiblen Funkmodule offenbaren sich vor allem im realen Experiment. Eines
der Hauptprobleme ist die Sicherstellung einer ausreichenden analogen
Performanz über einen weiten Frequenzbereich. Aus einer Vielzahl an
analogen Störeffekten behandelt die Arbeit die Analyse und Minderung von
Nichtlinearitäten in Empfängern mit direkt-umsetzender Architektur. Im
Vordergrund stehen dabei Signalverarbeitungsstrategien zur Minderung
nichtlinear verursachter Interferenz - ein Algorithmus, der besser unter
"Dirty RF"-Techniken bekannt ist. Ein digitales Verfahren nach der
Vorwärtskopplung wird durch intensive Simulationen, Messungen und
Implementierung in realer Hardware verifiziert. Um die Lücken zwischen
Theorie und praktischer Anwendbarkeit zu schließen und das Verfahren in
reale Funkmodule zu integrieren, werden verschiedene Untersuchungen
durchgeführt. Hierzu wird ein erweitertes Verhaltensmodell entwickelt, das
die Struktur direkt-umsetzender Empfänger am besten nachbildet und damit
alle Verzerrungen im HF- und Basisband erfasst. Darüber hinaus wird die
Leistungsfähigkeit des Algorithmus unter realen Funkkanal-Bedingungen
untersucht. Zusätzlich folgt die Vorstellung einer ressourceneffizienten
Echtzeit-Implementierung des Verfahrens auf einem FPGA. Abschließend
diskutiert die Arbeit verschiedene Anwendungsfelder, darunter spektrales
Sensing, robuster GSM-Empfang und GSM-basiertes Passivradar. Es wird
gezeigt, dass nichtlineare Verzerrungen erfolgreich in der digitalen
Domäne gemindert werden können, wodurch die Bitfehlerrate gestörter
modulierter Signale sinkt und der Anteil nichtlinear verursachter
Interferenz minimiert wird. Schließlich kann durch das Verfahren die
effektive Linearität des HF-Frontends stark erhöht werden. Damit wird der
zuverlässige Betrieb eines einfachen Funkmoduls unter dem Einfluss der
Empfängernichtlinearität möglich. Aufgrund des flexiblen Designs ist der
Algorithmus für breitbandige Empfänger universal einsetzbar und ist nicht
auf Software-konfigurierbare Funkmodule beschränkt.Today's wireless communication systems place high requirements on the
radio's hardware that are largely mutually exclusive, such as low power
consumption, wide bandwidth, and high linearity. Achieving a sufficient
linearity, among other analogue characteristics, is a challenging issue in
practical transceiver design. The focus of this thesis is on wideband
receiver RF front-ends for software defined radio technology, which became
commercially available in the recent years. Practical challenges and
limitations are being revealed in real-world experiments with these radios.
One of the main problems is to ensure a sufficient RF performance of the
front-end over a wide bandwidth. The thesis covers the analysis and
mitigation of receiver non-linearity of typical direct-conversion receiver
architectures, among other RF impairments. The main focus is on DSP-based
algorithms for mitigating non-linearly induced interference, an approach
also known as "Dirty RF" signal processing techniques. The conceived
digital feedforward mitigation algorithm is verified through extensive
simulations, RF measurements, and implementation in real hardware. Various
studies are carried out that bridge the gap between theory and practical
applicability of this approach, especially with the aim of integrating that
technique into real devices. To this end, an advanced baseband behavioural
model is developed that matches to direct-conversion receiver architectures
as close as possible, and thus considers all generated distortions at RF
and baseband. In addition, the algorithm's performance is verified under
challenging fading conditions. Moreover, the thesis presents a
resource-efficient real-time implementation of the proposed solution on an
FPGA. Finally, different use cases are covered in the thesis that includes
spectrum monitoring or sensing, GSM downlink reception, and GSM-based
passive radar. It is shown that non-linear distortions can be successfully
mitigated at system level in the digital domain, thereby decreasing the bit
error rate of distorted modulated signals and reducing the amount of
non-linearly induced interference. Finally, the effective linearity of the
front-end is increased substantially. Thus, the proper operation of a
low-cost radio under presence of receiver non-linearity is possible. Due to
the flexible design, the algorithm is generally applicable for wideband
receivers and is not restricted to software defined radios
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High Performance Local Oscillator Design for Next Generation Wireless Communication
Local Oscillator (LO) is an essential building block in modern wireless radios. In modern wireless radios, LO often serves as a reference of the carrier signal to modulate or demod- ulate the outgoing or incoming data. The LO signal should be a clean and stable source, such that the frequency or timing information of the carrier reference can be well-defined. However, as radio architecture evolves, the importance of LO path design has become much more important than before. Of late, many radio architecture innovations have exploited sophisticated LO generation schemes to meet the ever-increasing demands of wireless radio performances.
The focus of this thesis is to address challenges in the LO path design for next-generation high performance wireless radios. These challenges include (1) Congested spectrum at low radio frequency (RF) below 5GHz (2) Continuing miniaturization of integrated wireless radio, and (3) Fiber-fast (>10Gb/s) mm-wave wireless communication.
The thesis begins with a brief introduction of the aforementioned challenges followed by a discussion of the opportunities projected to overcome these challenges.
To address the challenge of congested spectrum at frequency below 5GHz, novel ra- dio architectures such as cognitive radio, software-defined radio, and full-duplex radio have drawn significant research interest. Cognitive radio is a radio architecture that opportunisti- cally utilize the unused spectrum in an environment to maximize spectrum usage efficiency. Energy-efficient spectrum sensing is the key to implementing cognitive radio. To enable energy-efficient spectrum sensing, a fast-hopping frequency synthesizer is an essential build- ing block to swiftly sweep the carrier frequency of the radio across the available spectrum. Chapter 2 of this thesis further highlights the challenges and trade-offs of the current LO gen-
eration scheme for possible use in sweeping LO-based spectrum analysis. It follows by intro- duction of the proposed fast-hopping LO architecture, its implementation and measurement results of the validated prototype. Chapter 3 proposes an embedded phase-shifting LO-path design for wideband RF self-interference cancellation for full-duplex radio. It demonstrates a synergistic design between the LO path and signal to perform self-interference cancellation.
To address the challenge of continuing miniaturization of integrated wireless radio, ring oscillator-based frequency synthesizer is an attractive candidate due to its compactness. Chapter 4 discussed the difficulty associated with implementing a Phase-Locked Loop (PLL) with ultra-small form-factor. It further proposes the concept sub-sampling PLL with time- based loop filter to address these challenges. A 65nm CMOS prototype and its measurement result are presented for validation of the concept.
In shifting from RF to mm-wave frequencies, the performance of wireless communication links is boosted by significant bandwidth and data-rate expansion. However, the demand for data-rate improvement is out-pacing the innovation of radio architectures. A >10Gb/s mm-wave wireless communication at 60GHz is required by emerging applications such as virtual-reality (VR) headsets, inter-rack data transmission at data center, and Ultra-High- Definition (UHD) TV home entertainment systems. Channel-bonding is considered to be a promising technique for achieving >10Gb/s wireless communication at 60GHz. Chapter 5 discusses the fundamental radio implementation challenges associated with channel-bonding for 60GHz wireless communication and the pros and cons of prior arts that attempted to address these challenges. It is followed by a discussion of the proposed 60GHz channel- bonding receiver, which utilizes only a single PLL and enables both contiguous and non- contiguous channel-bonding schemes.
Finally, Chapter 6 presents the conclusion of this thesis
Circuit Design Techniques For Wideband Phased Arrays
University of Minnesota Ph.D. dissertation.June 2015. Major: Electrical Engineering. Advisor: Ramesh Harjani. 1 computer file (PDF); xii, 143 pages.This dissertation focuses on beam steering in wideband phased arrays and phase noise modeling in injection locked oscillators. Two different solutions, one in frequency and one in time, have been proposed to minimize beam squinting in phased arrays. Additionally, a differential current reuse frequency doubler for area and power savings has been proposed. Silicon measurement results are provided for the frequency domain solution (IBM 65nm RF CMOS), injection locked oscillator model verification (IBM 130nm RF-CMOS) and frequency doubler (IBM 65nm RF CMOS), while post extraction simulation results are provided for the time domain phased array solution (the chip is currently under fabrication, TSMC 65nm RF CMOS). In the frequency domain solution, a 4-point passive analog FFT based frequency tunable filter is used to channelize an incoming wideband signal into multiple narrowband signals, which are then processed through independent phase shifters. A two channel prototype has been developed at 8GHz RF frequency. Three discrete phase shifts (0 & +/- 90 degrees) are implemented through differential I-Q swapping with appropriate polarity. A minimum null-depth of 19dB while a maximum null-depth of 27dB is measured. In the time domain solution, a discrete time approach is undertaken with signals getting sampled in order of their arrival times. A two-channel prototype for a 2GHz instantaneous RF bandwidth (7GHz-9GHz) has been designed. A QVCO generates quadrature LO signals at 8GHz which are phase shifted through a 5-bit (2 extra bits from differential I-Q swapping with appropriate polarity) cartesian combiner. Baseband sampling clocks are generated from phase shifted LOs through a CMOS divide by 4 with independent resets. The design achieves an average time delay of 4.53ps with 31.5mW of power consumption (per channel, buffers excluded). An injection locked oscillator has been analyzed in s-domain using Paciorek's time domain transient equations. The simplified analysis leads to a phase noise model identical to that of a type-I PLL. The model is equally applicable to injection locked dividers and multipliers and has been extended to cover all injection locking scenarios. The model has been verified against a discrete 57MHz Colpitt's ILO, a 6.5GHz ILFD and a 24GHz ILFM with excellent matching between the model and measurements. Additionally, a differential current reuse frequency doubler, for frequency outputs between 7GHz to 14GHz, design has been developed to reduce passive area and dc power dissipation. A 3-bit capacitive tuning along with a tail current source is used to better conversion efficiency. The doubler shows FOM values between 191dBc/Hz to 209dBc/Hz when driven by a 0.7GHz to 5.8GHz wide tuning VCO with a phase noise that ranges from -114dBc/Hz to -112dBc/Hz over the same bandwidth
Design of Analog-to-Digital Converters with Embedded Mixing for Ultra-Low-Power Radio Receivers
In the field of radio receivers, down-conversion methods usually rely on one (or more)
explicit mixing stage(s) before the analog-to-digital converter (ADC). These stages not
only contribute to the overall power consumption but also have an impact on area and can
compromise the receiver’s performance in terms of noise and linearity. On the other hand,
most ADCs require some sort of reference signal in order to properly digitize an analog
input signal. The implementation of this reference signal usually relies on bandgap
circuits and reference buffers to generate a constant, stable, dc signal. Disregarding this
conventional approach, the work developed in this thesis aims to explore the viability
behind the usage of a variable reference signal. Moreover, it demonstrates that not only
can an input signal be properly digitized, but also shifted up and down in frequency,
effectively embedding the mixing operation in an ADC. As a result, ADCs in receiver
chains can perform double-duty as both a quantizer and a mixing stage. The lesser known
charge-sharing (CS) topology, within the successive approximation register (SAR) ADCs,
is used for a practical implementation, due to its feature of “pre-charging” the reference
signal prior to the conversion. Simulation results from an 8-bit CS-SAR ADC designed in
a 0.13 μm CMOS technology validate the proposed technique
Design of a Direct-Modulation Transmitter with Self-Optimizing Feedback and a Highly Linear, Highly Reconfigurable, Continuously-Tunable Active-RC Baseband Filter for Multiple Standards
This work consists of two main parts: i) Design and implementation of a compact current-reusing 2.4GHz direct-modulation transmitter with on-chip automatic tuning; ii) Design and implementation of a novel highly-reconfigurable, continuously tunable, power-adjustable Active-RC filter for multiple standards. The design, analysis, and experimental verification of a proposed self-calibrating, current reused 2.4GHz, direct-modulation transmitter are introduced. A stacked arrangement of the power amplifier/voltage-controlled oscillator is presented along with a novel LC-tank-tuning algorithm with a simple, low-cost, on-chip implementation. To transmit maximum power, the tuning loop ensures the PA's resonant tank is centered around the operating frequency, and the loop requires no ADC, DSP, or external signal generator. This work also details the proposed tuning-loop algorithm and examines the frequency-dependent nonlinear power-detector. The system was implemented in TSMC 0.18[mu]m CMOS, occupies 0.7 mm² (TX) + 0.1 mm² (self tuning), and was measured in a QFN48 package on FR4 PCB. Automatically adjusting the tank-tuning bits within their tuning range results in >4dB increase in output power. With the self-tuning circuit active, the transmitter delivers a measured output power of > 0dBm to a 100-[omega] differential load, and the system consumes 22.9 mA from a 2.2-V supply. A biquad design methodology and a baseband low-pass filter is presented for wireless and wireline applications with reconfigurable frequency response, selectable order (1st/3rd/5th), continuously tunable cutoff frequency (1MHz-20MHz) and adjustable power consumption (3mW-7.5mW). A discrete capacitor array coarsely tunes the low-pass filter, and a novel Continuous Impedance Multiplier (CIM) then finely tunes the filter. Resistive/capacitive networks select between the Chebyshev and Inverse Chebyshev approximation types. Also, a new stability metric for biquads, Minimum Acceptable Phase Margin (MAPM), is presented and discussed in the context of filter compensation and passband ripple considerations. Experimental results yield an IIP3 of 31.3dBm, a THD of -40dB at 447mV[subscript pk, diff] input signal amplitude, and a DR of 71.4dB. The filters tunable range covers frequencies from 1MHz to 20MHz. In Inverse Chebyshev mode, the filter achieves a passband group delay variation less than ±2:5%. The design is fabricated in 0.13[mu]m CMOS, occupies 1.53mm², and operates from a 1-V supply
RF Power Transfer, Energy Harvesting, and Power Management Strategies
Energy harvesting is the way to capture green energy. This can be thought of as a recycling process where energy is converted from one form (here, non-electrical) to another (here, electrical). This is done on the large energy scale as well as low energy scale. The former can enable sustainable operation of facilities, while the latter can have a significant impact on the problems of energy constrained portable applications. Different energy sources can be complementary to one another and combining multiple-source is of great importance. In particular, RF energy harvesting is a natural choice for the portable applications. There are many advantages, such as cordless operation and light-weight. Moreover, the needed infra-structure can possibly be incorporated with wearable and portable devices. RF energy harvesting is an enabling key player for Internet of Things technology. The RF energy harvesting systems consist of external antennas, LC matching networks, RF rectifiers for ac to dc conversion, and sometimes power management. Moreover, combining different energy harvesting sources is essential for robustness and sustainability.
Wireless power transfer has recently been applied for battery charging of portable devices. This charging process impacts the daily experience of every human who uses electronic applications. Instead of having many types of cumbersome cords and many different standards while the users are responsible to connect periodically to ac outlets, the new approach is to have the transmitters ready in the near region and can transfer power wirelessly to the devices whenever needed. Wireless power transfer consists of a dc to ac conversion transmitter, coupled inductors between transmitter and receiver, and an ac to dc conversion receiver. Alternative far field operation is still tested for health issues. So, the focus in this study is on near field.
The goals of this study are to investigate the possibilities of RF energy harvesting from various sources in the far field, dc energy combining, wireless power transfer in the near field, the underlying power management strategies, and the integration on silicon. This integration is the ultimate goal for cheap solutions to enable the technology for broader use. All systems were designed, implemented and tested to demonstrate proof-of concept prototypes
Resonant Behaviour of Pulse Generators for the Efficient Drive of Optical Radiation Sources Based on Dielectric Barrier Discharges
Dielectric barrier discharge (DBD) excimer lamps emit vacuum-UV optical radiation. This work presents novel methods for efficiently operating DBDs with short, high-voltage pulses. Transformer-less systems utilising SiC power semiconductor switches are presented. Pulse frequencies of up to 3.1 MHz and peak inverter efficiencies of 92 % were achieved. The work encloses both mathematical backgrounds of pulsed resonant circuits and practical implementation of low-inductive power stages
Ultra-Low Power Transmitter and Power Management for Internet-of-Things Devices
Two of the most critical components in an Internet-of-Things (IoT) sensing and transmitting node are the power management unit (PMU) and the wireless transmitter (Tx). The desire for longer intervals between battery replacements or a completely self-contained, battery-less operation via energy harvesting transducers and circuits in IoT nodes demands highly efficient integrated circuits. This dissertation addresses the challenge of designing and implementing power management and Tx circuits with ultra-low power consumption to enable such efficient operation.
The first part of the dissertation focuses on the study and design of power management circuits for IoT nodes. This opening portion elaborates on two different areas of the power management field: Firstly, a low-complexity, SPICE-based model for general low dropout (LDO) regulators is demonstrated. The model aims to reduce the stress and computation times in the final stages of simulation and verification of Systems-on-Chip (SoC), including IoT nodes, that employ large numbers of LDOs. Secondly, the implementation of an efficient PMU for an energy harvesting system based on a thermoelectric generator transducer is discussed. The PMU includes a first-in-its-class LDO with programmable supply noise rejection for localized improvement in the suppression.
The second part of the dissertation addresses the challenge of designing an ultra-
low power wireless FSK Tx in the 900 MHz ISM band. To reduce the power consumption and boost the Tx energy efficiency, a novel delay cell exploiting current reuse is used in a ring-oscillator employed as the local oscillator generator scheme. In combination with an edge-combiner PA, the Tx showed a measured energy efficiency of 0.2 nJ/bit and a normalized energy efficiency of 3.1 nJ/(bit∙mW) when operating at output power levels up to -10 dBm and data rates of 3 Mbps. To close this dissertation, the implementation of a supply-noise tolerant BiCMOS ring-oscillator is discussed. The combination of a passive, high-pass feedforward path from the supply to critical nodes in the selected delay cell and a low cost LDO allow the oscillator to exhibit power supply noise rejection levels better than –33 dB in experimental results
Systematic Approaches for Telemedicine and Data Coordination for COVID-19 in Baja California, Mexico
Conference proceedings info:
ICICT 2023: 2023 The 6th International Conference on Information and Computer Technologies
Raleigh, HI, United States, March 24-26, 2023
Pages 529-542We provide a model for systematic implementation of telemedicine within a large evaluation center for COVID-19 in the area of Baja California, Mexico. Our model is based on human-centric design factors and cross disciplinary collaborations for scalable data-driven enablement of smartphone, cellular, and video Teleconsul-tation technologies to link hospitals, clinics, and emergency medical services for point-of-care assessments of COVID testing, and for subsequent treatment and quar-antine decisions. A multidisciplinary team was rapidly created, in cooperation with different institutions, including: the Autonomous University of Baja California, the Ministry of Health, the Command, Communication and Computer Control Center
of the Ministry of the State of Baja California (C4), Colleges of Medicine, and the College of Psychologists. Our objective is to provide information to the public and to evaluate COVID-19 in real time and to track, regional, municipal, and state-wide data in real time that informs supply chains and resource allocation with the anticipation of a surge in COVID-19 cases. RESUMEN Proporcionamos un modelo para la implementación sistemática de la telemedicina dentro de un gran centro de evaluación de COVID-19 en el área de Baja California, México. Nuestro modelo se basa en factores de diseño centrados en el ser humano y colaboraciones interdisciplinarias para la habilitación escalable basada en datos de tecnologías de teleconsulta de teléfonos inteligentes, celulares y video para vincular hospitales, clínicas y servicios médicos de emergencia para evaluaciones de COVID en el punto de atención. pruebas, y para el tratamiento posterior y decisiones de cuarentena. Rápidamente se creó un equipo multidisciplinario, en cooperación con diferentes instituciones, entre ellas: la Universidad Autónoma de Baja California, la Secretaría de Salud, el Centro de Comando, Comunicaciones y Control Informático.
de la Secretaría del Estado de Baja California (C4), Facultades de Medicina y Colegio de Psicólogos. Nuestro objetivo es proporcionar información al público y evaluar COVID-19 en tiempo real y rastrear datos regionales, municipales y estatales en tiempo real que informan las cadenas de suministro y la asignación de recursos con la anticipación de un aumento de COVID-19. 19 casos.ICICT 2023: 2023 The 6th International Conference on Information and Computer Technologieshttps://doi.org/10.1007/978-981-99-3236-