Ideal Phase Shift Research Articles

Phase-shifting profilometry for 3D shape measurement of moving objects on production lines

It is challenging for phase-shifting profilometry to measure objects in motion on production lines due to two main issues. Firstly, the movement of the object causes a mismatch in its position across different fringe patterns. Additionally, there is a violation of the ideal phase shift between these fringe patterns. To address these problems, we propose a method that takes advantage of the known moving direction of objects on production lines. By aligning the isophase direction of fringe patterns with the known direction of the moving objects, our method essentially solves the well-known phase error problem caused by object motion. Furthermore, we have developed a projection and imaging technique to track the measured object that is covered with different fringe patterns. Both of the previously listed issues have been resolved in this manner. The proposed method is validated by comparisons with state-of-the-art methods, proving its simplicity, broader applicability, and improved measurement accuracy.

Resource allocation for practical phase shift STAR-RIS enabled MISO-NOMA wireless network with non ideal hardware

This study investigates the sum secrecy rate SRsum of a simultaneous transmission and reflection reconfigurable intelligent surface (STAR-RIS)-enabled multiple input single-output (MISO) non-orthogonal multiple access (NOMA) downlink network with non-ideal hardware defects (HWDs) at the transceivers. Earlier STAR-RIS studies assumed an ideal phase shift model, with each element reflect and transmit the signal without regard to its phase shift. The proposed practical phase shift model accounts for the phase-dependent amplitude variation in the reflection and transmission (RAT) coefficients. The goal is to maximize the SRsum through an alternating optimization (AO) iterative algorithm, leverages a classical semidefinite relaxation (SDR) for beamformer vector design (BVD), and employs an interior point method (IPM) to calculate NOMA power allocation factors αt,αr. The analysis focuses on the evaluation of the SRsum in scenarios with eavesdroppers, under the consideration of both ideal and practical phase shift cases. The study examines the impact of different non-ideal HWDs on the SRsum of the system and provides insights into vulnerabilities and limitations arising from these effects.

Sum‐rate maximization for downlink multiuser MISO URLLC system aided by IRS with discrete phase shifters

AbstractIntelligent reflecting surface (IRS) has recently been considered as a potential technology for realizing ultra‐reliable and low‐latency (URLLC) in wireless networks. This paper proposes a resource optimization scheme to maximize the sum‐rate for an IRS‐assisted downlink multiuser multi‐input single‐output (MISO) URLLC system. For the perfect CSI scenario, we jointly optimize each user's block‐length and packet‐error probability, the precoding vectors at the base station (BS), and the passive beamforming with discrete phase shifts at the IRS. Given the problem's complexity, we design a computationally efficient iterative algorithm using successive convex approximation (SCA) and semidefinite relaxation (SDR) techniques to obtain a locally optimal solution. Specifically, for the imperfect CSI scenario, we construct a robust resource optimization problem model and incorporate the S‐procedure to address the impact of channel uncertainty, proposing an iterative algorithm based on the alternating optimization (AO) method to achieve a locally optimal solution. Simulation results demonstrate that: 1) An IRS equipped with a 2‐bit quantized resolution phase shifter is sufficient to achieve a system sum‐rate comparable to that of an ideal phase shifter; 2) Compared to other Baseline schemes, Algorithm 2 exhibits better robustness and superior performance gains under imperfect CSI.

Robust Beamforming Optimization Design for RIS-Aided MIMO Systems With Practical Phase Shift Model and Imperfect CSI

The ideal phase shift model and the acquisition of channel state information (CSI) are practically difficult to realize in reconfigurable intelligent surface (RIS) assisted communication systems. Therefore, these have greatly troubled the beamforming design of multiple-input multiple-output (MIMO) systems via RIS. This paper presents a robust beamforming design framework in the RIS-enhanced MIMO communication networks in the presence of considering practical phase shifts for the RIS and imperfect CSI of the cascade channels. More specifically, we propose an alternative optimization framework and adopt the distributed alternating direction method of multipliers (ADMM) method to solve the sum-rate maximization problem by combining the true environment model (TEM) and the mismatch environment model (MEM) with beamforming. In particular, the proposed scheme is also used for the MEM scenario. It shows that the sum rate of the ADMM scheme with MEM under low SNR is about 3 bps/Hz more than the BFP method, approximately 6 bps/Hz more than the APG method. Next, when the SNR is 5dB, the above three schemes are greater than SDR method. But, the above methods are smaller than SDR method in MEM. Then, the sum rate of the SDR method with the TEM is approximately 1.6 times of the MEM, while the CPU time of both is consistent with the computational complexity. Therefore, the differences between the two models affect the performance achieved by different methods. The proposed approach sheds a light to engineers working in wireless communication on enhancing the transmission robustness of existing wireless networks.

Accurate Modeling of Intelligent Reflecting Surface for Communication Systems

In the conventional sense, a passive intelligent reflecting surface (IRS) is perceived as an ideal phase shifter to the incident signal. It is assumed that the phase of the incident signal can be altered to any desired value without affecting its magnitude. In this paper, we question the veracity of this assumption which forms the basis for the communication model that is widely used in the scientific community. Although there exist rigorous electromagnetic (EM) based models to analyze and design metasurfaces, the same cannot be said about its successor, intelligent reflecting surface. Therefore, we attempt to present an EM-based model that accurately describes intelligent scattering by any arbitrary-shaped IRS. Our objective in this paper is to bridge the gap between the fundamental EM formulation for an IRS and the communication model that accurately captures its functioning. We use Method-of-Moments (MoM), a computational electromagnetic approach to quantify the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">intelligent</i> scattering by an arbitrary-shaped IRS. The proposed theoretical model is then validated with computational EM simulation in Feko. We then adopt the general MoM-based model for a special case where each IRS element is a center-loaded wire. Closed-form expressions for pathloss and beamwidth are derived considering free space propagation. We show analytically and numerically, that the received power predicted by the conventional model vs. what is observed through computational EM simulations can differ by 6 dB. Furthermore, we demonstrate that the impact of optimizing an IRS using the conventional model, where each element is treated as an ideal passive phase shifter, can result in an additional 6 - 8 dB of power loss. As a final remark, we propose correction to the communication model that is currently used for IRS-aided networks when each IRS element is a center-loaded wire.

A direct synthesis method of multi‐port filtering power divider with arbitrary phase shift, power division and reference impedances

AbstractIn this study, a direct synthesis approach is proposed to extract the coupling matrix of multi‐port filtering power divider (FPD) with arbitrary phase shift, power division as well as reference impedances, for the first time. This method provides an attractive technique to synthesise a multi‐functional device that combines the characteristics of bandpass filter, multi‐port power divider and ideal phase shifters as well as the impedance matching network, which can effectively diminish the overall size and improve the performance of the microwave front‐end network. A newly defined coupling matrix corresponding to arbitrary multi‐port topologies that introduces ideal phase shift by virtue of constant frequency‐independent reactance at the source and load is developed in FPD synthesis process. The coupling matrix is obtained directly by optimising the presented cost‐function in this paper, avoiding complex similar transformation process of coupling matrix. Finally, several numerical examples of multi‐port FPD with equal/unequal power division ratio, arbitrary phase shift and reference impedances are synthesised to well verify the proposed synthesis method, and a practical example is given to verify the validity of arbitrary phase shift and arbitrary reference impedance.

Design of Hybrid Beamforming System Based on Practical Circuit Parameter of 6-Bit Millimeter-Wave Phase Shifters

This paper addresses the design of a hybrid beamforming system considering the circuit parameter of six-bit millimeter-wave phase shifters based on the process design kit. The phase shifter design adopts 45 nm CMOS silicon on insulator (SOI) technology at 28-GHz. Various circuit topologies are utilized, and in particular, a design is presented based on switched LC components, connected in a cascode manner. The phase shifter configuration is connected in a cascading manner to get the 6-bit phase controls. Six different phase shifters are obtained, which are 180°, 90°, 45°, 22.5°, 11.25°, and 5.6°, with a minimum number of LC components. The circuit parameters of the designed phase shifters are then incorporated in a simulation model of hybrid beamforming for a multiuser MIMO system. The number of OFDM data symbols used in the simulation is ten for eight users, 16 QAM modulation schemes, −25 dB SNR, 120 simulation runs, and around 170 h runtime. Simulation results are obtained considering four and eight users, assuming accurate technology-based models of RFIC components of the phase shifter as well as ideal phase shifter parameters. The results indicate that the performance of the multiuser MIMO system is affected by the accuracy level of the phase shifter RF component models. The outcomes also reveal the performance tradeoff based on user data streams and the number of BS antennas. By optimizing the amount of parallel data streams per user, higher data transmission rates are achieved, while maintaining acceptable error vector magnitude (EVM) values. In addition, stochastic analysis is conducted to investigate the distribution of the RMS EVM. The outcomes show that the best fitting of RMS EVM distribution of the actual and ideal phase shifters agreed with the log-logistic and logistic distributions, respectively. The obtained (mean, variance) values of the actual phase shifters based on accurate library models are (46.997, 481.36), and for ideal components the values are (36.47, 10.44).

A Near-Field Meta-Steering Antenna System With Fully Metallic Metasurfaces

In the near-field meta-steering method, the near electric-field phase distribution is dynamically altered by rotating a pair of phase-gradient metasurfaces that are typically made out of dielectric lattices or metal patterns printed on bonded dielectric substrates. As a lightweight alternate, a new class of fully metallic metasurfaces (MMs) is proposed in this article. The lack of dielectrics not only substantially reduces the cost and weight but also increases its potential in space and high-power applications. More importantly, the new MMs are designed such that they can be made by cutting narrow slots in fully planar thin metal sheets, retaining structural rigidity while reducing the complexity, cost, and weight. The same MM works for any polarization. Each cell in the new MMs has close to ideal phase shift and transmission magnitude greater than −0.9 dB. A prototype was designed and fabricated to validate this MM-based beam-steering concept in the Ku-band. The maximum measured steering range in zenith is ±42°, with a full 360° steering in the azimuth. The measured 3 dB gain bandwidth is 700–800 MHz (5.6%–6.4%), and the measured gain variation (scan loss) when steering over the whole range is 2.2–4.5 dB. The weight density and thickness of each MM are 0.88 g/cm2 and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$0.8\lambda _{0}$ </tex-math></inline-formula> , respectively. Including the feed, the total antenna height is <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$4.9\lambda _{0}$ </tex-math></inline-formula> .

Synthesis of a New Class of Extracted Pole Filters Without the Ideal Phase Shifters

This article proposes a novel approach for extracted pole (EP) filter synthesis. The pole producing elements can be extracted without introducing phase shifters. It is made possible by extracting lowpass elements in the prototype without reducing the order of filter functions. Using the proposed elements as added redundancy, the nonideal effect in the physical model is absorbed by adjacent resonators. Those novel approaches break through the conventional framework in EP filter synthesis. The synthesized results do not introduce extra spikes caused by nonideal phase shifters in the conventional EP filters. The new theory enables the application of EP filters in broadband situations. This work also reveals the equivalence between the frequency-dependent couplings and the PPEs. The validity of the demonstrated method is illustrated via an 11-pole filter with two transmission zeros. The simulated and measured results have no extra spikes caused by the nonideal phase shifters, which verified the effectivity of the proposed theory.

Optimizing RF Efficiency of a Vector-Modulator-Driven Antenna Array

The feed vector of an antenna array determines the array pattern and the active input impedance of each element. On the other hand, the output impedance of a variable-gain power amplifier, such as that used in a vector-modulator, depends on the amplification level. The resulting impedance mismatch is typically neglected when designing and controlling antenna arrays at the cost of reduced gain, bandwidth, and beam-steering range. This letter presents a simple method to find the array feed vector that maximizes the realized gain in a given direction in a case when the power amplifier output impedance depends on its amplification level. We verify the method with simulations for a test case consisting of a 4×1 patch array fed with ideal phase-shifters and realistic amplifiers. The simulation results of the case study show that the method improves transmission efficiency by $\text{3.5 dB}$ on average compared to the traditional phase shift.

Intelligent Reflecting Surface: Practical Phase Shift Model and Beamforming Optimization

Intelligent reflecting surface (IRS) that enables the control of wireless propagation environment has recently emerged as a promising cost-effective technology for boosting the spectral and energy efficiency of future wireless communication systems. Prior works on IRS are mainly based on the ideal phase shift model assuming full signal reflection by each of its elements regardless of the phase shift, which, however, is practically difficult to realize. In contrast, we propose in this paper a practical phase shift model that captures the phase-dependent amplitude variation in the element-wise reflection design. Based on the proposed model and considering an IRS-aided multiuser system with one IRS deployed to assist in the downlink communications from a multi-antenna access point (AP) to multiple single-antenna users, we formulate an optimization problem to minimize the total transmit power at the AP by jointly designing the AP transmit beamforming and the IRS reflect beamforming, subject to the users’ individual signal-to-interference-plus-noise ratio (SINR) constraints. Iterative algorithms are proposed to find suboptimal solutions to this problem efficiently by utilizing the alternating optimization (AO) as well as penalty-based optimization techniques. Moreover, to draw essential insight, we analyze the asymptotic performance loss of the IRS-aided system that employs practical phase shifters but assumes the ideal phase shift model for beamforming optimization, as the number of IRS elements goes to infinity. Simulation results unveil substantial performance gains achieved by the proposed beamforming optimization based on the practical phase shift model as compared to the conventional ideal model.

MmWave Lens-Based MIMO System for Suppressing Small-Scale Fading and Shadowing

In this paper, we propose a generalized millimeter-Wave (mmWave) reconfigurable antenna multiple-input multiple-output (RA-MIMO) architecture that takes advantage of lens antennas. The considered antennas can generate multiple independent beams simultaneously using a single RF chain. This property, together with RA-MIMO, is used to combat small-scale fading and shadowing in mmWave bands. To this end, first, we derive a channel matrix for RA-MIMO. Then, we use rate-one space-time block codes (STBCs), together with phase-shifters at the receive reconfigurable antennas, to suppress the effect of small-scale fading. We consider two kinds of phase shifters: i) ideal which is error-free and ii) digital which adds quantization error. The goal of phase-shifters is to convert a complex-valued channel matrix into real-valued. Hence, it is possible to use rate-one STBCs for any dimension of RA-MIMO. We investigate diversity gain and derive an upper bound for symbol error rate in cases of ideal and digital phase-shifters. We show that RA-MIMO achieves the full-diversity gain with ideal phase-shifters and the full-diversity gain for digital phase-shifters when the number of quantization bits is higher than one. We investigate RA-MIMO in the presence of shadowing. Our analysis demonstrates that, by increasing the dimension of RA-MIMO, the outage probability decreases which means the effect of shadowing decreases. Numerical results verify our theoretical derivations.

Achievable Spectral Efficiency of Hybrid Beamforming Massive MIMO Systems With Quantized Phase Shifters, Channel Non-Reciprocity and Estimation Errors

This paper considers a hybrid beamforming massive multiple-input multiple-output (MIMO) system operating in time-division duplex (TDD) mode. We investigate the combined impacts of quantized phase shifters (QPSs), channel non-reciprocity and channel estimation errors on the achievable spectral efficiency (SE) of the considered system. We first introduce an equivalent hybrid beamforming structure, based on which, a generic and practical channel non-reciprocity model is built for massive MIMO systems with hybrid structure. This model jointly considers the mismatch between transceiver and receiver circuits, as well as the mutual coupling between antennas. Then we derive the generic expression of achievable SE for both the ideal phase shifters (IPSs) and QPSs cases. Furthermore, the closed-form expressions of SE are derived for IPSs and QPSs cases, respectively. The asymptotic performance in large antenna regime is also analyzed based on these expressions. Simulation results demonstrate the validity and accuracy of the derived analytical expressions. In addition, results show that the phase quantization and channel non-reciprocity both contributes to the SE degradation and the detrimental effects cannot be canceled completely even in the large-antenna regime.

Compact Multi-Wideband Array for Millimeter-Wave Communications Using Squint Beams

Millimeter-wave (mmWave) cellular systems leverage the hybrid analog-digital structure to balance the costs and the capacity performance by using fewer Radio Frequency (RF) chains and the spatial sparsity of the channel. Besides, a more broadband system is the natural outgrowth of the gigantic frequency resource in mmWave band. However, it becomes precarious when the hybrid structure is extended to the wideband systems as the wideband phase shifters are used in the array. In this article, a multi-wideband planar array structure using the concept of Sierpinski carpet fractal is proposed, which exploits the beam squinting property instead of forming several independent beams through an existing hybrid structure. Moreover, multi-subarray can form a larger antenna array without additional costs of phase shifters for the wider range of values. First, we derive several properties of the steering beams from a wideband linear array. Then, we exploit the beam squinting property of the planar arrays employing wideband ideal phase shifters to form multi-beam. The functionality of the phase shifters in an array is simplified by a set of wideband cells connected in series. The maximum cell number needed in the array is derived, and during this derivation, we find a flaw of the beam squinting method. Finally, we present numerical results on the performance of the proposed arrays with the proposed algorithm, based on a cellular scenario of one base station (BS) and multi-user, where the BS has four subarrays and each user has one subarray.

Low Cost and High Efficiency Hybrid Architecture Massive MIMO Systems Based on DFT Processing

Low cost and high efficiency, defined as energy efficiency (EE) and spectral efficiency (SE), have raised more and more attention in the fifth generation (5G) communication systems due to steadily rising hardware cost, energy consumption, and mobile traffic. This paper studies the hybrid architecture of multiuser massive MIMO systems, where the digital domain utilizes the zero‐forcing (ZF) precoding scheme and the analog domain uses discrete Fourier transform (DFT) processing that significantly reduces hardware cost and energy consumption. We derive analytical expressions on the total achievable SE and EE, as well as offering insight into some engineering parameters in the system performance. Our aim is to achieve low cost and high efficiency massive MIMO system, with constraints on the overall transmit power, the number of users, and the number of radio frequency (RF) chains. Results exhibit that the total achievable SE of the hybrid architectures with DFT precessing is inferior to the full digital architectures and hybrid architectures with the ideal phase shifters, but the performance attenuation can be compensated by providing the more input SNR and higher number of RF chains. Moreover, we find that the total achievable EE of hybrid architectures with DFT precessing outperforms other massive MIMO architectures that include a full digital implementation, ideal phase shifters, and a switched network.

Spectral and Energy Efficiency of Massive MIMO for Hybrid Architectures Based on Phase Shifters

This paper investigates the downlink achievable spectral efficiency (SE) and energy efficiency (EE) of massive MIMO for hybrid architectures based on phase shifters, where the base station (BS) has perfect channel state information and baseband processing is done zero-forcing precoding. We derive an approximated upper bound on the achievable SE for hybrid architecture with ideal phase shifters. Based on the derived analytical expression, we find that the total achievable SE increases with the number of BS antennas and users and the signal-to-noise ratio (SNR). In order to acquire the required limited feedback, we propose an algorithm to generate the corresponding quantized matrix and study hybrid architectures with quantized phase shifters. Compared to full-digital architectures, results show that hybrid architectures enjoy a much higher achievable EE in massive MIMO systems, whereas its achievable SE is inferior to full-digital architectures. In addition, results also showcase that the achievable SE of hybrid architectures can be improved by increasing the bits of phase shifters, and there exists an optimal SNR and antenna number to maximize the achievable EE of the system.

Spectral Efficiency of DFT-Based Processing Hybrid Architectures in Massive MIMO

This letter investigates the achievable spectral efficiency (SE) of massive multiple-input multiple-output transmission systems with hybrid architectures based on discrete Fourier transform (DFT) processing, where the base station (BS) has perfect channel state information and baseband processing is performed by zero-forcing precoding. We derive tractable upper and lower bounds on the achievable SE. Based on these results, the effects of the number of radio frequency (RF) chains, signal-to-noise ratio (SNR), and the number of users are revealed. Compared to hybrid architectures with ideal and quantized phase shifters, simulations indicate that the achievable SE with DFT processing is inferior to the one with ideal phase shifters. In addition, the achievable SE with DFT processing is independent of the number of BS antennas and can be improved by increasing the SNR and the number of RF chains, while there exists an optimal number of users that maximizes the total achievable SE.

Generalised direct matrix synthesis approach for lossless filters

A generalised direct matrix synthesis is proposed for microwave lossless filters with arbitrary phase shift at centre frequency and complex terminal impedances. The functions of traditional lossless filters, ideal phase shifters, and ideal impedance matching networks are thus substantially combined into one entity to provide an attractive technique for the realisation of compact narrowband microwave front-ends. The synthesis starts with a group of general S-parameters that consider both amplitude and phase responses as well as complex terminations for an Nth-order filter. A transversal array network incorporating resonators as well as non-resonating nodes is then introduced to accommodate the given S-parameters. In result, a canonical (N + 2) × (N + 2) coupling matrix with newly defined source–source and load–load couplings is generated. Some examples, including a fully canonical prototype and a mixed topology diplexer, are demonstrated to show the flexibility of the methodology. Moreover, an eighth-order coaxial cavity filter, with a −120° additional phase shift for S-parameters, is designed and fabricated. The measured results are well consistent with the synthesis ones, which validates the availability of this study in physical implementations.

&lt;italic&gt;Ka&lt;/italic&gt;-Band Wideband Large Depth-of-Field Beam Generation Through a Phase Shifting Surface Antenna

A wideband phase shifting surface (PSS) antenna is presented with stable and large quasi-nondiffraction range. The operation principles and design procedures for the wideband near-held focusing antenna with large depth-of-field are introduced. Then, the difference between the depth-of-field (Z <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">max</sub> )fixed and the half-power beamwidth-fixed wideband design is demonstrated. As an example, a wideband Z <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">max</sub> -fixed PSS antenna is designed and fabricated. Phase shifts of PSS elements are synthesized by using a least mean-square error minimization method to approximate the ideal phase shift on the aperture of the antenna within the entire bandwidth. The developed prototype can be used as a Z <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">max</sub> -fixed beam launcher from 26.5 to 30.5 GHz. This type of antenna can be easily fabricated with the standard Printed Circuit Board process and fed by a horn antenna with an arbitrary polarization. The proposed structure has unique advantages: wideband applicable, large depth-of-field, and variable polarizations.

Multiuser hybrid analogue/digital beamforming for massive multiple‐input–multiple‐output

The authors propose a generalised multi-layer architecture for the phase shifter network (PSN) in hybrid analogue/digital beamforming (BF), which provides flexible trade-offs between the performance and implementation complexity. By changing the layer number, the authors can adjust the complexity of the PSN and the achievable performance. A two-stage BF algorithm is adopted, in which the analogue and digital BF matrices are designed separately. Analogue BF is adaptive to the second-order channel statistics. A simple iterative algorithm is proposed to maximise an upper bound of the average rate of the effective channel after analogue BF. Digital BF is adaptive to the effective channel for multiuser interference cancellation. Both ideal phase shifters and discrete phase shifters with limited phase and amplitude resolutions are considered in the algorithm design. Theoretical analysis and simulation are used to demonstrate the good performance and flexibility of the proposed technique. In a 64-antenna system, it can use 16 radio-frequency chains to perform very closely to full digital BF with a fully-connected PSN, or achieve 70–80% performance with a simple PSN. It is also robust against the limited phase shifter resolution. It enables us to select the proper performance and implementation complexity according to the requirement and capability of real systems.