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Open access publications by faculty, postdocs, and graduate students in the Department of Electrical and Computer Engineering

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    STATION: State Encoding-Based Attack-Resilient Sequential Obfuscation
    (IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems, 2024-04-16) Han, Zhaokun; Dixit, Aneesh; Patnaik, Satwik; Rajendran, Jeyavijayan
    The unauthorized duplication of design intellectual property (IP) and illegal overproduction of integrated circuits (ICs) are hardware security threats plaguing the security of the globalized IC supply chain. Researchers have developed various countermeasures such as logic locking, layout camouflaging, and split manufacturing to overcome the security threat of IP piracy and unauthorized overproduction. Logic locking is a holistic solution among all countermeasures since it safeguards the design IP against untrusted entities, such as untrusted foundries, test facilities, or end-users throughout the globalized IC supply chain. There are well-known logic locking techniques for combinational circuits with well-established security properties; however, their sequential counterparts remain vulnerable. Since most practical designs are inherently sequential, it is essential to develop secure obfuscation techniques to protect sequential designs. This paper proposes a sequential obfuscation technique, STATION, building on the principles of finite state machine encoding schemes. STATION is resilient against various attacks on sequential obfuscation–input-output (I/O) query attacks and structural attacks, including the ones targeting sequential obfuscation–which have broken all state-of-the-art sequential obfuscation techniques. STATION achieves good resilience and desired security against various I/O and structural attacks, which we ascertain by launching 9 different attacks on all tested circuits. Moreover, STATION ensures tolerable overheads in power, performance, and area, such as 8.75%, 1.22%, and 5.63% on the largest tested circuit, containing 102 inputs, 7 outputs, 6.1×104 gates, 7 flip flops, 100 states, and 3.0×103 transitions.
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    Wide-angle passive beam steering using 3D modified partial Maxwell fisheye lens
    (Optics Express, 2024-02-12) Fessaras, Theodore; Nicholson, Kelvin; Gong, Wiley; Mirotznik, Mark
    This study presents a broadband, 3D gradient index beam-steering lens, derived from an optimized modification of the partial Maxwell fisheye (PMFE) design, achieving a boresight gain of 23 dBi, -80° to 80° beam steering, and <10 dB gain roll-off. Utilizing fused filament fabrication (FFF) to realize its intricate geometry, the design employs a novel polar space-filling curve (PSFC) to establish a 3D varying, effective permittivity distribution. Rigorous simulations and experimental validation attest to its effectiveness, marking the first 3D implementation of a PMFE-type lens to our knowledge. This research underscores the feasibility and diverse applications of a low-cost, wide-angle passive beam-steering dielectric lens.
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    Melting-free integrated photonic memory with layered polymorphs
    (Nanophotonics, 2024-01-31) Ullah, Kaleem; Li, Qiu; Li, Tiantian; Gu, Tingyi
    Chalcogenide-based nonvolatile phase change materials (PCMs) have a long history of usage, from bulk disk memory to all-optic neuromorphic computing circuits. Being able to perform uniform phase transitions over a subwavelength scale makes PCMs particularly suitable for photonic applications. For switching between nonvolatile states, the conventional chalcogenide phase change materials are brought to a melting temperature to break the covalent bonds. The cooling rate determines the final state. Reversible polymorphic layered materials provide an alternative atomic transition mechanism for low-energy electronic (small domain size) and photonic nonvolatile memories (which require a large effective tuning area). The small energy barrier of breaking van der Waals force facilitates low energy, fast-reset, and melting-free phase transitions, which reduces the chance of element segregation-associated device failure. The search for such material families starts with polymorphic In2Se3, which has two layered structures that are topologically similar and stable at room temperature. In this perspective, we first review the history of different memory schemes, compare the thermal dynamics of phase transitions in amorphous-crystalline and In2Se3, detail the device implementations for all-optical memory, and discuss the challenges and opportunities associated with polymorphic memory.
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    Integrative data analysis to identify persistent post-concussion deficits and subsequent musculoskeletal injury risk: project structure and methods
    (BMJ Open Sport & Exercise Medicine, 2024-01-19) Anderson, Melissa; Claros, Claudio Cesar; Qian, Wei; Brockmeier, Austin; Buckley, Thomas A
    Concussions are a serious public health problem, with significant healthcare costs and risks. One of the most serious complications of concussions is an increased risk of subsequent musculoskeletal injuries (MSKI). However, there is currently no reliable way to identify which individuals are at highest risk for post-concussion MSKIs. This study proposes a novel data analysis strategy for developing a clinically feasible risk score for post-concussion MSKIs in student-athletes. The data set consists of one-time tests (eg, mental health questionnaires), relevant information on demographics, health history (including details regarding the concussion such as day of the year and time lost) and athletic participation (current sport and contact level) that were collected at a single time point as well as multiple time points (baseline and follow-up time points after the concussion) of the clinical assessments (ie, cognitive, postural stability, reaction time and vestibular and ocular motor testing). The follow-up time point measurements were treated as individual variables and as differences from the baseline. Our approach used a weight-of-evidence (WoE) transformation to handle missing data and variable heterogeneity and machine learning methods for variable selection and model fitting. We applied a training-testing sample splitting scheme and performed variable preprocessing with the WoE transformation. Then, machine learning methods were applied to predict the MSKI indicator prediction, thereby constructing a composite risk score for the training-testing sample. This methodology demonstrates the potential of using machine learning methods to improve the accuracy and interpretability of risk scores for MSKI.
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    3-D-Printed CRLH Metamaterial-Enabled Electrically Small Antenna
    (IEEE Antennas and Wireless Propagation Letters, 2023-11-29) Li, Shuping; Lazarus, Nathan; Klemash, Mary E. Galanko; Bedair, Sarah S.; Wu, Chung-Tse Michael
    This letter presents a 3-D-printed composite right/left-handed (CRLH) metamaterial-enabled electrically small antenna (ESA) in the 300 MHz band. A 3-D conical helix strip is loaded by surrounding an electrical small monopole antenna, with a length of 0.02 λ0 (free space wavelength), which is vertically placed over a finite ground plane. The proposed ESA is based on the 3-D realization of an open-ended CRLH resonator, of which the electrical size is ka = 0.11. An equivalent circuit model is provided with corresponding circuit parameters to derive the frequency response of the proposed 3-D-CRLH ESA. A prototype is fabricated using a widely available 3-D print technology, fused filament fabrication, combined with copper electro- and electroless plating. Experimental verification of the antenna demonstrates a monopole-like radiation pattern with a peak measured gain of −5 dBi, which is suitable to be integrated into compact wireless systems.
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    Roadmap on energy harvesting materials
    (Journal of Physics: Materials, 2023-08-07) Pecunia, Vincenzo; Silva, S. Ravi; Phillips, Jamie D.; Artegiani, Elisa; et al.
    Ambient energy harvesting has great potential to contribute to sustainable development and address growing environmental challenges. Converting waste energy from energy-intensive processes and systems (e.g. combustion engines and furnaces) is crucial to reducing their environmental impact and achieving net-zero emissions. Compact energy harvesters will also be key to powering the exponentially growing smart devices ecosystem that is part of the Internet of Things, thus enabling futuristic applications that can improve our quality of life (e.g. smart homes, smart cities, smart manufacturing, and smart healthcare). To achieve these goals, innovative materials are needed to efficiently convert ambient energy into electricity through various physical mechanisms, such as the photovoltaic effect, thermoelectricity, piezoelectricity, triboelectricity, and radiofrequency wireless power transfer. By bringing together the perspectives of experts in various types of energy harvesting materials, this Roadmap provides extensive insights into recent advances and present challenges in the field. Additionally, the Roadmap analyses the key performance metrics of these technologies in relation to their ultimate energy conversion limits. Building on these insights, the Roadmap outlines promising directions for future research to fully harness the potential of energy harvesting materials for green energy anytime, anywhere.
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    Joint Equalization and Self-Interference Cancellation for Underwater Acoustic In-Band Full-Duplex Communication
    (IEEE Journal of Oceanic Engineering, 2024-01-11) Towliat, Mohammad; Guo, Zheng; Cimini, Leonard J.; Xia, Xiang-Gen; Song, Aijun
    In-band full-duplex (IBFD) communication in underwater acoustic channels is challenged by strong and time-varying self-interference (SI). To detect data symbols, the receiver needs to suppress the SI and equalize the resultant signal to compensate for the intersymbol interference (ISI) caused by the remote transmission (RT) channel. In this article, we develop a new receiver that combines adaptive decision feedback equalizer and SI cancellation (ADFE-SIC) to jointly eliminate the ISI and SI. A recursive least squares algorithm adaptively estimates the filters in ADFE-SIC. By conducting simulations and experimental tests, we show that the proposed method outperforms the conventional approach in which equalization and SI cancellation tasks are performed separately and the filter configuration is based on prior estimations of the SI and the RT channels.
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    Trajectory Design and Resource Allocation for Multi-UAV Communications Under Blockage-Aware Channel Model
    (IEEE Transactions on Communications, 2023-12-05) Yi, Pengfei; Zhu, Lipeng; Xiao, Zhenyu; Zhang, Rui; Han, Zhu; Xia, Xiang-Gen
    This paper considers an unmanned aerial vehicle (UAV)-assisted communication system for data collection in urban areas, where multiple UAVs are dispatched to harvest data from multiple ground user equipments (UEs). We adopt a blockage-aware channel model to characterize the practical blockage effects for air-to-ground (A2G) links caused by buildings. Aiming to minimize the mission completion time while satisfying the data collection requirements of UEs, we formulate a problem by jointly optimizing the UAV three-dimensional (3-D) trajectory and resource allocation, including the UE scheduling and subcarrier assignment. To solve the formulated non-convex combinatorial programming problem, we propose a suboptimal algorithm that solves two subproblems iteratively. Specifically, in each iteration, the trajectory design subproblem jointly optimizes the UAVs’ waypoints and time slot length to decrease the mission completion time, which is solved by employing block successive convex approximation (BSCA). For the resource allocation subproblem, we develop a heuristic algorithm for UE scheduling and subcarrier assignment to increase the collected data volume for a given time duration. Simulation results demonstrate the superior performance of the proposed algorithm in terms of mission completion time compared to benchmark schemes.
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    Twin-Layer RIS-Aided Differential Index Modulation Dispensing With Channel Estimation
    (IEEE Transactions on Vehicular Technology, 2023-11-06) Xiao, Zhenyu; Liu, Guangyao; Mao, Tianqi; Liu, Ruiqi; Zhang, Wei; Xia, Xiang-Gen; Hanzo, Lajos
    In this correspondence, we propose a twin-layer hierarchical differential index modulation scheme for a reconfigurable intelligent surface (RIS)-aided transmitter architecture, termed as HD-RIS-IM. More specifically, the RIS array is partitioned into perfectly tiling sub-arrays. Each sub-array is mapped across multiple time slots, where each RIS element is activated only once at a particular time slot. These sub-arrays represented by sub- matrices are then used for constructing a block-based permutation matrix for data transmission. With the aid of this hierarchical structure, additional information can be conveyed by the specific order of the sub-arrays that are activated. Furthermore, extra bits are also embedded in the particular order of the RIS elements that are activated within each sub-array. By exploiting all the distinct permutations of the activated matrices, a differential modulation scheme is proposed for the RIS-aided transmitter, which maintains an M -ary phase shift keying (MPSK) and facilitates CSI-free demodulation. Furthermore, at the receiver, we propose a low-complexity distributed maximum likelihood (ML) detector, which significantly reduces the detection complexity. Our simulation results demonstrate the performance benefits of the proposed HD-RIS-IM scheme.
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    Edge Intelligence Empowered Metaverse: Architecture, Technologies, and Open Issues
    (IEEE Network, 2023-10-06) Xu, Yanan; Feng, Daquan; Zhao, Mingxiong; Sun, Yao; Xia, Xiang-Gen
    Recently, the metaverse has emerged as a focal point of widespread interest, capturing attention across various domains. However, the construction of a pluralistic, realistic, and shared digital world is still in its infancy. Due to the ultra-strict requirements in security, intelligence, and real-time, it is urgent to solve the technical challenges existed in building metaverse ecosystems, such as ensuring the provision of seamless communication and reliable computing services in the face of a dynamic and time-varying complex network environment. In terms of digital infrastructure, edge computing (EC), as a distributed computing paradigm, has the potential to guarantee computing power, bandwidth, and storage. Meanwhile, artificial intelligence (AI) is regarded as a powerful tool to provide technical support for automated and efficient decision-making for metaverse devices. In this context, this paper focuses on integrating EC and AI to facilitate the development of the metaverse, namely, the edge intelligence-empowered metaverse. Specifically, we first outline the metaverse architecture and driving technologies and discuss EC as a key component of the digital infrastructure for metaverse realization. Then, we elaborate on two mainstream classifications of edge intelligence in metaverse scenarios, including AI for edge and AI on edge. Finally, we identify some open issues.
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    Searching for scalar ultralight dark matter via refractive index changes in fibers
    (Physical Review D, 2023-10-11) Manley, J.; Stump, R.; Petery, R.; Singh, S.
    We propose using an optical fiber-based interferometer to search for scalar ultralight dark matter (UDM) with particle mass in the range 10−17−10−13  eV/c2 (10−3−10Hz). Composed of a solid core and a hollow core fiber, the proposed detector would be sensitive to relative oscillations in the fibers’ refractive indices due to scalar UDM-induced modulations in the fine-structure constant α. We predict that, implementing detector arrays or cryogenic cooling, the proposed optical fiber-based scalar UDM search has the potential to reach new regions of the parameter space. Such a search would be particularly well-suited to probe for a solar halo of dark matter with a sensitivity exceeding that of previous dark matter searches over the particle mass range 7×10−17−2×10−14  eV/c2.
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    A unified understanding of magnetorheological elastomers for rapid and extreme stiffness tuning
    (RSC Applied Polymers, 2023-10-02) Barron, Edward J.; Williams, Ella T.; Tutika, Ravi; Lazarus, Nathan; Bartlett, Michael D.
    Magnetorheological elastomers (MREs), which adapt their mechanical properties in response to a magnetic field, can enable changes in stiffness and shape for applications ranging from vibration isolators to shape morphing robots and soft adaptive grippers. Here, a unified design approach is introduced to create MRE materials for extreme stiffness tuning, up to 70×, with rapid (∼20 ms) and reversible shape change. This guides the creation of a hybrid MRE composite architecture that incorporates a combination of magnetic particles and magnetic fluids into elastomers. The role of both solid and fluid inclusions on magnetorheological response is systematically investigated and a predictive model is developed that captures the stiffness tuning response of MREs across diverse material microstructures and compositions. This general understanding enables MRE materials with programmable response and greatly enhanced stiffness tuning and rapid response times compared to many MRE, granular jamming, and phase change approaches. This insight is utilized to optimize composites for a soft adaptive gripper which grasps and releases objects of diverse geometries.
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    A Simple Family of Non-Linear Analog Codes
    (IEEE Communications Letters, 2023-09-18) Burich, Mariano Eduardo; Garcia-Frias, Javier
    We propose novel non-linear graph-based analog codes that directly encode k real-valued source samples into n real-valued samples by using (non-linear) sample-by-sample soft quantization of the input samples followed by a linear transformation on the soft-quantized values. Different from existing analog coding schemes, the proposed analog codes are able to produce additional output symbols in a rateless manner and can be decoded utilizing message passing algorithms dealing with real-valued nodes, achieving a performance close to the theoretical limits.
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    Fundamental limits of parasitoid-driven host population suppression: Implications for biological control
    (PLoS ONE, 2023-12-22) Singh, Abhyudai
    Parasitoid wasps are increasingly being used to control insect pest populations, where the pest is the host species parasitized by the wasp. Here we use the discrete-time formalism of the Nicholson-Bailey model to investigate a fundamental question—are there limits to parasitoid-driven suppression of the host population density while still ensuring a stable coexistence of both species? Our model formulation imposes an intrinsic self-limitation in the host’s growth resulting in a carrying capacity in the absence of the parasitoid. Different versions of the model are considered with parasitism occurring at a developmental stage that is before, during, or after the growth-limiting stage. For example, the host’s growth limitation may occur at its larval stage due to intraspecific competition, while the wasps attack either the host egg, larval or pupal stage. For slow-growing hosts, models with parasitism occurring at different life stages are identical in terms of their host suppression dynamics but have contrasting differences for fast-growing hosts. In the latter case, our analysis reveals that wasp parasitism occurring after host growth limitation yields the lowest pest population density conditioned on stable host-parasitoid coexistence. For ecologically relevant parameter regimes we estimate this host suppression to be roughly 10-20% of the parasitoid-free carrying capacity. We further expand the models to consider a fraction of hosts protected from parasitism (i.e., a host refuge). Our results show that for a given host reproduction rate there exists a critical value of protected host fraction beyond which, the system dynamics are stable even for high levels of parasitism that drive the host to arbitrary low population densities. In summary, our systematic analysis sheds key insights into the combined effects of density-dependence in host growth and parasitism refuge in stabilizing the host-parasitoid population dynamics with important implications for biological control.
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    Genome-wide screening reveals metabolic regulation of stop-codon readthrough by cyclic AMP
    (Nucleic Acids Research, 2023-09-06) Lyu, Zhihui; Villanueva, Patricia; O’Malley, Liam; Murphy, Parker; Augenstreich, Jacques; Briken, Volker; Singh, Abhyudai; Ling, Jiqiang
    Translational fidelity is critical for microbial fitness, survival and stress responses. Much remains unknown about the genetic and environmental control of translational fidelity and its single-cell heterogeneity. In this study, we used a high-throughput fluorescence-based assay to screen a knock-out library of Escherichia coli and identified over 20 genes critical for stop-codon readthrough. Most of these identified genes were not previously known to affect translational fidelity. Intriguingly, we show that several genes controlling metabolism, including cyaA and crp, enhance stop-codon readthrough. CyaA catalyzes the synthesis of cyclic adenosine monophosphate (cAMP). Combining RNA sequencing, metabolomics and biochemical analyses, we show that deleting cyaA impairs amino acid catabolism and production of ATP, thus repressing the transcription of rRNAs and tRNAs to decrease readthrough. Single-cell analyses further show that cAMP is a major driver of heterogeneity in stop-codon readthrough and rRNA expression. Our results highlight that carbon metabolism is tightly coupled with stop-codon readthrough. Graphical Abstract available at: https://doi.org/10.1093/nar/gkad725
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    Characterization of Voltage Stabilization Functions of Residential PV Inverters in a Power Hardware-in-the-Loop Environment
    (IEEE Access, 2022-10-26) Kaewnukultorn, Thunchanok; Sepúlveda-Mora, Sergio B.; Hegedus, Steven
    The exponential growth of Photovoltaic (PV) technology is creating concerns for electric grid operators. As PV penetration increases, overvoltage in the distribution network can occur due to a mismatch between PV generation and load demand. However, PV smart inverters can be part of the solution to stabilize grid voltage. By providing reactive power and other grid supporting functions, PV inverters in a distribution network can mitigate this problem and enable a higher integration of renewable energy. To accomplish this, characterization and testing of advanced functions must be performed at a small scale before deploying these strategies in the field. In this work, we described in detail the components and communication interfaces of a Hardware-in-the-Loop testbed that includes two 3.8 kW PV inverters from different manufacturers. We conducted efficiency tests on the inverters and characterized the grid supporting functions for grid voltage stabilization, specifically constant power factor, volt-var, and volt-watt. We identified some abnormalities in the operation of the volt-var-watt control in one of the inverters and presented a method to overcome the limitation in remote control of another inverter using Modbus communication. Identifying, understanding, and overcoming shortcomings on the operation of PV smart inverters that provide grid supporting functions is key for the quick adoption of this technology and can help regulatory agencies to determine what is the appropriate control mode that will facilitate higher PV capacity. Additionally, we discuss the economic and technical implications of operating the inverter in active or reactive power grid control.
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    Smart PV Inverter Cyberattack Detection Using Hardware-in-the-Loop Test Facility
    (IEEE Access, 2023-08-23) Kaewnukultorn, Thunchanok; Sepúlveda-Mora, Sergio B.; Broadwater, Robert; Zhu, Dan; Tsoutsos, Nektarios G.; Hegedus, Steven
    This paper evaluates residential smart photovoltaic (PV) inverters’ responses to cyberattacks and assesses the performance of an intrusion detection strategy for smart grid devices by comparing time-series power flow results from a simulation application called Faster Than Real-Time (FTRT) Simulator to measurements from a Power Hardware-in-the-Loop (P-HIL) laboratory as a testbed. Twenty different cyberattacks from three classes - Denial of Service (DoS), Intermittent attack, and Modification - were designed and tested with grid-tied smart inverters in order to study the inverters’ responses to malicious activities. The intrusion detection strategy was developed using a comparison between the predicted PV power output from FTRT and the power flows measured from P-HIL laboratory through the API interface. Real and reactive power thresholds were assigned based on a number of repeated experiments to ensure the applicability of the thresholds. The results showed that inverters from different manufacturers have their own unique responses which could be detected by the power flow measurements. Our detection method could identify over 94% of actual malicious actions and 7.4% of no-attack hours are detected as false positives. Out of 38 under-attack hours, 2 undetected hours are due to the intermittent attacks. Different attacks can be detected based on the targeted components of the complex power that attackers are aiming to cause disturbances. Our findings additionally show that DoS can be noticed immediately after the devices have been sabotaged, and they can be detected from the active power analysis. However, modification attack detection will depend more on the reactive power measurements, while intermittent attacks remain the most challenging for the proposed detection method since the objective of intermittent attacks is to create an oscillation of the complex power components which need a relatively high time resolution for the measurement.
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    Silicon electro-optic modulators based on microscopic photonic structures: from principles to advanced modulation formats
    (Journal of Physics D: Applied Physics, 2023-08-04) Yu, Fuhao; Zeng, Zhaobang; Ji, Xiang; Tang, Kaifei; Xin, Yu; Wu, Guihan; Mao, Dun; Gu, Tingyi; Huang, Qingzhong; Jiang, Wei
    This paper reviews the progress of electro-optic modulators composed of silicon-based microscopic photonic structures. The basic principles, device structures, and advanced modulation capability of different geometric types are detailed for micro-ring modulators, photonic crystal modulators, and other related modulators. We illustrate the device operation mechanism with a focus on its photonic aspect and discuss their impacts on the modulator speed, power consumption, and thermal stabilities. The cavity enhancement and slow light effect significantly reduce the device footprint and power consumption, with the trade-off of limited operation wavelength range. Other emerging microscopic photonic structure-based silicon modulators for advanced modulation formats exhibit promising performance for further optimizations. Finally, we discuss the existing challenges and further directions of microscopic photonic structure-based silicon modulators for pertinent applications.
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    Array-Beamspace Mapping for Planar Two-Dimensional Beam-Forming
    (IEEE Access, 2023-07-21) Beardell, William L.; Murakowski, Janusz; Schneider, Garrett J.; Prather, Dennis W.
    As sixth-generation (6G) communication systems manifest at carrier frequencies well into the millimeter-wave (mmW) spectrum, the ability of conventional digital beamforming techniques to handle the beam-bandwidth product is increasingly stressed. Microwave photonic beamforming has been presented as a solution to this problem by up-converting a sampled RF field distribution to an optical carrier for analog beam-space processing, but to date has relied upon fiber arrays with the same dimensionality as the RF array, i.e., a two-dimensional RF array requires a two-dimensional fiber array and a three-dimensional optical processor to perform the Fourier transform required for two-dimensional beamforming. To address this problem, we present an approach to photonic mmW beamforming wherein two-dimensional phase information is preserved through a one-dimensional Fourier transform leveraging grating lobes in the array response. This approach carries several benefits, primarily as an enabler for leveraging photonic integrated circuits for RF-photonic beamforming, carrying with it a footprint reduction of more than ten thousand times. Furthermore, beamforming efficiency is increased for sources near the limits of the RF field-of-view; improvements to throughput power in such cases are as much as double. Theory, simulations, and experimental results in the form of images and videos are presented to validate the approach for a nineteen-element hexagonally-distributed phased array.
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    Hyperspectral image reconstruction via patch attention driven network
    (Optics Express, 2023-06-01) Qiu, Yechuan; Zhao, Shengjie; Ma, Xu; Zhang, Tong; Arce, Gonzalo R.
    Coded aperture snapshot spectral imaging (CASSI) captures 3D hyperspectral images (HSIs) with 2D compressive measurements. The recovery of HSIs from these measurements is an ill-posed problem. This paper proposes a novel, to our knowledge, network architecture for this inverse problem, which consists of a multilevel residual network driven by patch-wise attention and a data pre-processing method. Specifically, we propose the patch attention module to adaptively generate heuristic clues by capturing uneven feature distribution and global correlations of different regions. By revisiting the data pre-processing stage, we present a complementary input method that effectively integrates the measurements and coded aperture. Extensive simulation experiments illustrate that the proposed network architecture outperforms state-of-the-art methods.
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