Phase Shift Solutions Research Articles

Location Information Assisted Beamforming Design for Reconfigurable Intelligent Surface Aided Communication Systems

The large overhead arising from conventional channel estimations in reconfigurable intelligent surface (RIS) aided millimeter-wave communication systems, may offset the performance gain brought by the RIS. To tackle this issue, we propose a location information assisted beamforming design without the requirement of the channel training process. First, we establish the geometrical relationship between the channel model and the user location, and mathematically derive an approximate channel state information (CSI) error bound based on the user location error region. Then, for combating the negative impact of the location error on the communication performance, we formulate a worst-case robust beamforming optimization problem to optimize the beamformer at the base station (BS) and the phase-shift matrix at the RIS. To solve this non-convex problem, we develop a novel relaxed alternating optimization process (RAOP) by utilizing various optimization tools, such as the Lagrange multiplier, the matrix inversion lemma, the semidefinite relaxation (SDR), as well as the branch-and-bound (BnB). Additionally, we prove sufficient conditions for the SDR to yield rank-one solutions, and modify the BnB to acquire the phase-shift solution under an arbitrary constraint of possible phase-shift values. Finally, we analyse the convergence and complexity of the proposed RAOP, and carry out simulations for performance evaluations. Compared to the conventional non-robust beamforming, our method performs better and shows strong robustness against the location-error-related CSI uncertainty. Compared to the robust beamforming based on the S-procedure and penalty convex-concave procedure (CCP), our method with BnB shows the advantages of being able to converge faster and handle arbitrary phase-shift argument sets.

Joint Active and Passive Beamforming Design for Reconfigurable Intelligent Surface Enabled Integrated Sensing and Communication

To exploit the potential of the reconfigurable intelligent surface (RIS) in supporting integrated sensing and communication (ISAC), this paper proposes a novel joint active and passive beamforming design for RIS-enabled ISAC system in consideration of the target size. First, the detection probability for target sensing is derived in closed-form based on the illumination power on an approximated scattering surface area of the target, and a new concept of ultimate detection resolution (UDR) is defined for the first time to measure the target detection capability. Then, an optimization problem is formulated to maximize the signal-to-noise ratio (SNR) at the user-equipment (UE) under a minimum detection probability constraint. To solve this non-convex problem, a novel alternative optimization approach is developed. In this approach, the solutions of the communication and sensing beamformers are obtained by our proposed bisection-search based method. The optimal receive combining vector is derived from an equivalent Rayleigh-quotient problem. To optimize the RIS phase shifts, the Charnes-Cooper transformation is conducted to cope with the fractional objective, and a novel convexification process is proposed to convexify the detection probability constraint with matrix operations and a real-valued first-order Taylor expansion. After the convexification, a successive convex approximation (SCA) based algorithm is designed to yield a suboptimal phase-shift solution. Finally, the overall optimization algorithm is built, followed by detailed analyses on its computational complexity, convergence behavior and problem feasibility condition. Extensive simulations are carried out to testify the analytical properties of the proposed beamforming design, and to reveal two important trade-offs, namely, communication vs. sensing trade-off and UDR vs. sensing-duration trade-off. In comparison with several existing benchmarks, our proposed approach is validated to be superior when detecting targets with practical sizes.

Reconfigurable Intelligent Surface Deployment for Blind Zone Improvement in mmWave Wireless Networks

In this letter, we investigate the blindness compensation for millimeter wave (mmWave) wireless networks by appropriately deploying the reconfigurable intelligent surface (RIS). Specifically, to maximize the average achievable rate, the precoder of base station, RISs’ coefficients and RISs’ deployment are jointly optimized, while taking into account the users’ stochastic geographical distribution. By leveraging stochastic gradient descent (SGD)-based algorithm, we investigate the optimal deployment issue for the single- and multi-RIS cases, respectively, in which the straightforward solutions for joint precoding and RIS phase shifts are established, demonstrating a beneficial performance while maintaining a favorable computational complexity. Finally, simulation results are provided to validate our proposed methodology.

UAV Placement and Resource Allocation for Intelligent Reflecting Surface Assisted UAV-Based Wireless Networks

We design an unmanned aerial vehicle (UAV) based wireless network with wireless access and backhaul links leveraging an intelligent reflecting surface (IRS). This design aims to maximize the sum rate achieved by ground users (GUs) through optimizing the UAV placement, IRS phase shifts, and sub-channel assignments considering the wireless backhaul capacity constraint. To tackle the underlying mixed integer non-linear optimization problem (MINLP), we first derive the closed-form IRS phase shift solution; we then optimize the sub-channel assignment and UAV placement by using the alternating optimization method. Specifically, we propose an iterative sub-channel assignment method to efficiently utilize the bandwidth and balance bandwidth allocation for wireless access and backhaul links while maintaining the backhaul capacity constraint. Moreover, we employ the successive convex approximation (SCA) method to solve the UAV placement optimization sub-problem. We show the effectiveness of our proposed design via extensive numerical studies.

A compound optical path difference phase-shift solution method based on Doppler asymmetric spatial heterodyne spectral velocimetry

Asymmetric spatial heterodyne spectroscopy is a new ultra-high resolution remote sensing detection technology. Based on its features of large luminous flux, small size, and high precision, it is very suitable for high-precision detection in a deep-space environment. Because of its high sensitivity, various details may interfere with the measurement results in experiment. In this paper, from the perspective of experimental condition, considering the influences of factors such as fringe center position offset, uneven illumination, and Gaussian noise, a compound optical path difference phase-shift solution method is proposed. The simulation calculation and data analysis show that the offset of the nominal point relative to the center position will significantly affect the systematic error of spectral velocity measurement. And the compound optical path difference phase-shift solution method can smooth the environmental noise and random interference to a certain extent. For the interference fringe image with 1% Gaussian noise, the velocity measurement error can be controlled within 5‰ by using the compound optical path difference phase-shift solution method, which makes the asymmetric spatial heterodyne spectroscopy technology more suitable for space optoelectronic precision measurement.

Cooperative Multi-RIS Communications for Wideband mmWave MISO-OFDM Systems

Reconfigurable intelligent surfaces (RISs) can shape the wireless environment for enhancing the communication performance. In this letter, we propose a cooperative multi-RIS assisted transmission scheme for a millimeter-wave multi-antenna orthogonal frequency division multiplexing system. We first put forward a delay matching based scheme for simultaneously estimating the multipath channels and the transmission delays of distributed RISs, which requires limited training overhead and feedback. Based on this scheme, we obtain a closed-form solution for the RIS phase shift. Then, we derive an analytical expression of the downlink rate, which is proved to increase logarithmically with the square number of RIS reflecting elements. Simulations are conducted to verify these observations.

Phase-shift determination for a 4 × 4 intelligent photonic neural network with compatible learning.

Intelligent photonic circuits (IPCs) tuned with an appropriate phase-shift vector could enable a photonic intelligent matrix possibly implemented in multiple neural layers for a task-oriented topologies. A photonic Mach-Zehnder Interferometer (MZI) is a fundamental photonic component in IPCs, whose matrix representation could be broadcasted into an arbitrary matrix that is equipped with an optimized phase-shift vector. The initialized MZIs' phases are tentatively probed between analytical elements and a digital weight matrix that is learned from samples with efficient compatible learning for complex-valued neural networks. Nonlinear least squares is utilized to formulate a phase determination system to refine the optimal phase-shift solutions. The robustness of phase determination system for photonic neural networks is discussed in detail. For a preliminary implementation, a basic 4×4 intelligent photonic neural network is utilized to verify the proof of concept on phase-shift determination in IPC through numerical experiments.

Aeromechanical Analysis of a Complete Wind Turbine Using Nonlinear Frequency Domain Solution Method

Abstract The high-fidelity computational fluid dynamics (CFD) simulations of a complete wind turbine model usually require significant computational resources. It will require much more resources if the fluid–structure interactions (FSIs) between the blade and the flow are considered, and it has been the major challenge in the industry. The aeromechanical analysis of a complete wind turbine model using a high-fidelity CFD method is discussed in this paper. The distinctiveness of this paper is the application of the nonlinear frequency domain solution method to analyze the forced response and flutter instability of the blade as well as to investigate the unsteady flow field across the wind turbine rotor and the tower. This method also enables the aeromechanical simulations of wind turbines for various interblade phase angles in a combination with a phase shift solution method. Extensive validations of the nonlinear frequency domain solution method against the conventional time domain solution method reveal that the proposed frequency domain solution method can reduce the computational cost by one to two orders of magnitude.

Reconfigurable Intelligent Surface Assisted UAV Communication: Joint Trajectory Design and Passive Beamforming

Thanks to the line-of-sight (LoS) transmission and flexibility, unmanned aerial vehicles (UAVs) effectively improve the throughput of wireless networks. Nevertheless, the LoS links are prone to severe deterioration by complex propagation environments, especially in urban areas. Reconfigurable intelligent surfaces (RISs), as a promising technique, can significantly improve the propagation environment and enhance communication quality by intelligently reflecting the received signals. Motivated by this, the joint UAV trajectory and RIS's passive beamforming design for a novel RIS-assisted UAV communication system is investigated to maximize the average achievable rate in this letter. To tackle the formulated non-convex problem, we divide it into two subproblems, namely, passive beamforming and trajectory optimization. We first derive a closed-form phase-shift solution for any given UAV trajectory to achieve the phase alignment of the received signals from different transmission paths. Then, with the optimal phase-shift solution, we obtain a suboptimal trajectory solution by using the successive convex approximation (SCA) method. Numerical results demonstrate that the proposed algorithm can considerably improve the average achievable rate of the system.

Selective Torque Harmonic Elimination for Dual Three-Phase PMSMs Based on PWM Carrier Phase Shift

Recently, dual three-phase drives have attracted an increasing attention with their high torque density, improved fault tolerance, and direct use of the off-the-shelf three-phase inverters. This article presents a carrier-based algorithm for the selective elimination of high-frequency pulsewidth modulation (PWM) torque harmonics in dual three-phase drives. The PWM control of the power converters is one of the main sources of high-frequency torque ripple in high-power electrical machines. The proposed technique selectively eliminates the torque-ripple harmonic components by applying a proper carrier phase shift between the two three-phase subsystems of the dual three-phase drive, considering the arbitrary phase displacements among the two subwindings. Two case studies of dual three-phase machines with phase displacements of 0 and π/6 are, respectively, analyzed under the most significant carrier phase-shift solutions. The torque performance improvement and the effect on the current ripple introduced by the proposed carrier phase-shifts are presented and validated by means of numerical, finite-element, and experimental results.

Aspects of the ETH model of the pion–nucleon interaction

The ETH model of the pion-nucleon ($\pi N$) interaction contains $t$-channel $\sigma$- and $\rho$-exchange graphs, as well as the $s$- and $u$-channel contributions with the well-established $s$ and $p$ baryon states with masses below $2$ GeV as virtual particles; the model amplitudes obey crossing symmetry and isospin invariance. In the present work, we give the analytical expressions for the model contributions to the $K$-matrix elements up to (and including) the $f$ waves. We also extract a new phase-shift solution after performing a partial-wave analysis of meson-factory $\pi^\pm p$ elastic-scattering data below $100$ MeV; included in our results now are also the effects of the variation of the $\sigma$-meson mass in the interval which is currently recommended by the Particle-Data Group. Finally, we revisit the subject of the $\pi N$ $\Sigma$ term and, using the model amplitudes, obtain $\Sigma = 72.4 \pm 3.1$ MeV. Our prediction agrees well with the result extracted with Olsson's method, after a few flaws in his paper [Phys. Lett. B 482 (2000) 50] were corrected.

Spin-correlation coefficients and phase-shift analysis forp+He3elastic scattering

Angular Distributions for the target spin-dependent observables A$_{0y}$, A$_{xx}$, and A$_{yy}$ have been measured using polarized proton beams at several energies between 2 and 6 MeV and a spin-exchange optical pumping polarized $^3$He target. These measurements have been included in a global phase-shift analysis following that of George and Knutson, who reported two best-fit phase-shift solutions to the previous global p+$^3$He elastic scattering database below 12 MeV. These new measurements, along with measurements of cross-section and beam-analyzing power made over a similar energy range by Fisher \textit{et al.}, allowed a single, unique solution to be obtained. The new measurements and phase-shifts are compared with theoretical calculations using realistic nucleon-nucleon potential models.

Accurate Phase Shift Extraction for Generalized Phase-Shifting Interferometry

An accurate phase shift extraction method for generalized phase-shifting interferometry is suggested. Based on the nearly random phase distribution of the diffraction field of the object, a singular formula is derived to calculate the unknown phase shift without the requirements of an iteration process or the selection of the correct value from two or more possible phase shift solutions as needed before. This method can be used in the cases of two or more frames with both smooth and diffusing object surfaces. Computer simulations and optical experiments have satisfactorily verified the efficiency and accuracy of this method.

Direct phase shift extraction and wavefront reconstruction in two-step generalized phase-shifting interferometry

A direct phase shift extraction and wavefront reconstruction method in two-step generalized phase-shifting interferometry (GPSI) with arbitrary unknown phase shift is proposed. In this method the unknown phase shift α can be extracted by a determinate formula directly without iteration or additional judgment of its correct value from two or more phase shift solutions as necessary before. By an appropriate formula of GPSI the complex object field in the recording plane can be calculated and then the object wavefront in the original object plane obtained. This method is applicable for GPSI of any frame number K≥2 and for both the amplitude and phase objects. Computer simulations have shown that the phase shift extraction errors are below 0.01 rad in a wide range of 0.4 rad<α<2.6 rad and the computation time is greatly reduced by a factor of about 20 compared with the previous method. The effectiveness and accuracy of this method are also verified by optical experiments.

Amplitude-preserving plane-wave prestack time migration for AVO analysis

To support amplitude variation with offset (AVO) analysis in complex structure areas, we introduce an amplitude-preserving plane-wave prestack time migration approach based on the double-square-root wave equation in media with little lateral velocity variation. In its implementation, a data mapping algorithm is used to obtain offset-plane-wave data sets from the common-midpoint gathers followed by a non-recursive phase-shift solution with amplitude correction to generate common-image gathers in offset-ray-parameter domain and a structural image. Theoretical model tests and a real data example show that our prestack time migration approach is helpful for AVO analysis in complex geological environments.

Determination of target thickness and luminosity from beam energy losses

The repeated passage of a coasting ion beam of a storage ring through a thin target induces a shift in the revolution frequency due to the energy loss in the target. Since the frequency shift is proportional to the beam-target overlap, its measurement offers the possibility of determining the target thickness and hence the corresponding luminosity in an experiment. This effect has been investigated with an internal proton beam of energy 2.65 GeV at the COSY-J\ulich accelerator using the ANKE spectrometer and a hydrogen cluster-jet target. Possible sources of error, especially those arising from the influence of residual gas in the ring, were carefully studied, resulting in an accuracy of better than 5%. The luminosity determined in this way was used, in conjunction with measurements in the ANKE forward detector, to determine the cross section for elastic proton-proton scattering. The result is compared to published data as well as to the predictions of a phase shift solution. The practicability and the limitations of the energy-loss method are discussed.

Excitation functions of spin correlation parametersANN,ASS, andASLin elastic→p→pscattering between 0.45 and 2.5 GeV

Excitation functions of the spin correlation coefficients A_{NN}(p_{lab},theta_{c.m.}), A_{SS}(p_{lab},theta_{c.m.}), and A_{SL}(p_{lab},theta_{c.m.}) have been measured with the polarized proton beam of the Cooler Synchrotron COSY and an internal polarized atomic beam target. Data were taken continuously during the acceleration for proton momenta p_{lab} ranging from 1000 to 3300 MeV/c (kinetic energies T_{lab} 450 - 2500 MeV) as well as for discrete momenta of 1430 MeV/c and above 2000 MeV/c covering angles theta_{c.m.} between 30 deg and 90 deg. The data are of high internal consistency. Whereas A_{SL}(p_{lab,}theta_{c.m.}) is small and without structures in the whole range, A_{NN} and even more A_{SS} show a pronounced energy dependence. The angular distributions for A_{SS} are at variance with predictions of existing phase shift analyses at energies beyond 800 MeV. The impact of our results on phase shift solutions is discussed. The direct reconstruction of the scattering amplitudes from all available pp elastic scattering data considerably reduces the ambiguities of solutions.

ELASTIC PROTON-PROTON SCATTERING AT GEV ENERGIES: ANALYZING POWERS ANAND SPIN CORRELATION PARAMETERS ANN, ASS, AND ASL

The analyzing powers ANand spin correlation parameters ANN, ASS, and ASLof the elastic proton-proton scattering have been measured with an internal polarized atomic beam target at the cooler synchrotron COSY. Excitation functions were taken continuously during the acceleration and deceleration of the internal beam for kinetic energies ranging between 0.45 and 2.5 GeV and scattering angles 30°≤Θc.m.≤90°. The analyzing power excitation functions provide a new polarization standard in the GeV region. The spin correlation data on ASSdisagree strikingly with existing phase shift solutions. The addition of the new polarization data to the world database removes some of the ambiguities in the phase shift solutions and the direct reconstruction of scattering amplitudes. The data are compared with a recent extension of a meson-exchange potential model to higher energies.

Excitation functions of the analyzing power in elastic proton-proton scattering from 0.45 to 2.5 GeV

Excitation functions A_N(p_{lab},Theta_{c.m.}) of the analyzing power in elastic proton-proton scattering have been measured in an internal target experiment at the Cooler Synchrotron COSY with an unpolarized proton beam and a polarized atomic hydrogen target. Data were taken continuously during the acceleration and deceleration for proton kinetic energies T_{lab} (momenta p_{lab}) between 0.45 and 2.5 GeV (1.0 and 3.3 GeV/c) and scattering angles 30 deg < Theta_{c.m.} < 90 deg. The results provide excitation functions and angular distributions of high precision and internal consistency. The data can be used as calibration standard between 0.45 and 2.5 GeV. They have significant impact on phase shift solutions, in particular on the spin triplet phase shifts between 1.0 and 1.8 GeV.

Measurement of spin-correlation parameters ANN, ASS, and ASL at 2.1 GeV in proton-proton elastic scattering.

At the Cooler Synchrotron COSY/Jülich spin-correlation parameters in elastic proton-proton (pp) scattering have been measured with a 2.11 GeV polarized proton beam and a polarized hydrogen atomic beam target. We report results for A(NN), A(SS), and A(SL) for c.m. scattering angles between 30 degrees and 90 degrees. Our data on A(SS)--the first measurement of this observable above 800 MeV--clearly disagrees with predictions of available pp scattering phase-shift solutions while A(NN) and A(SL) are reproduced reasonably well. We show that in the direct reconstruction of the scattering amplitudes from the body of available pp elastic scattering data at 2.1 GeV the number of possible solutions is considerably reduced.