Discrete Phase Shifters Research Articles

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.

Beamforming Design in Reconfigurable Intelligent Surface-Assisted IoT Networks Based on Discrete Phase Shifters and Imperfect CSI

Beamforming Design in Reconfigurable Intelligent Surface-Assisted IoT Networks Based on Discrete Phase Shifters and Imperfect CSI

STAR-RIS Assisted Wireless Communications With Discrete Phase Shifter

STAR-RIS Assisted Wireless Communications With Discrete Phase Shifter

Notice of Violation of IEEE Publication Principles: An Efficient Nonlinear Quantized Constant Envelope Precoding for Massive MU-MIMO Systems

Notice of Violation of IEEE Publication Principles <BR><BR>"An Efficient Nonlinear Quantized Constant Envelope Precoding for Massive MU-MIMO Systems," <BR>by R. Liang, H. Li, W. Zhang, C. Liu and Y. Guo, <BR>in IEEE Systems Journal, Early Access <BR><BR>After a careful and considered review of the content and authorship of this paper by a duly constituted expert committee, this paper has been found to be in violation of IEEE’s Publication Principles. <BR><BR>This paper contains content from the papers cited below. Credit notices were used, but due to the absence of quotation marks or offset text, the copied content is not clearly referenced or specifically identified. <BR><BR>"VLSI Design of a 3-bit Constant-Modulus Precoder for Massive MU-MIMO," <BR>by O. Castañeda, S. Jacobsson, G. Durisi, T. Goldstein and C. Studer, <BR>in the Proceedings of the IEEE International Symposium on Circuits and Systems (ISCAS), May 2018 <BR><BR>"Quantized Precoding for Massive MU-MIMO," <BR>by S. Jacobsson, G. Durisi, M. Coldrey, T. Goldstein and C. Studer, <BR>in IEEE Transactions on Communications, vol. 65, no. 11, pp. 4670-4684, November 2017 <BR><BR> <br/> Massive multiuser multiple-input&#x2013;multiple-output (MU-MIMO) systems are foreseen as the key technology in next-generation wireless communication systems. However, many radio-frequency (RF) chains will require high power consumption and lots of hardware cost. One of the practical solutions is using low-resolution discrete phase shifters (PSs) for each antenna and RF chain. This article designs a nonlinear quantized constant envelope precoding algorithm for MU-MIMO systems with low-resolution discrete PS at the base station. In this algorithm, the quantized constant envelope precoding problem is presented as a nonconvex optimization problem. The multiuser interference is minimized by solving the optimal precoded vector and the associated precoding factors. First, we consider relaxing the nonconvex constraint on the 1-bit quantized constant envelope precoding to a continuous set of convex constraints on the unit circle. Afterwards, the semidefinite relaxation method is used to tackle the equivalent 1-bit quantized precoding problem. We further extend the algorithm to provide multi-bit quantized constant envelop precoding. Finally, the simulations are carried out under various conditions and compared with the most advanced precoding methods. The results demonstrate that this algorithm achieves a comparable performance to the existing precoding methods. At the same time, the corresponding performance-complexity tradeoff is more conducive to the expansion of the proposed algorithm to the multibit case.

Performance Analysis of Full Duplex Bidirectional Machine Type Communication System Using IRS with Discrete Phase Shifter

In this paper, passive Intelligent Reflecting Surface (IRS) is used to enhance the performance of a Full Duplex (FD) bidirectional Machine Type Communication (MTC) system with two source nodes. Each node is equipped with two antennas to operate in FD mode. In reality, self-interference and discrete phase shifting are two major impairments in FD and IRS-assisted communication, respectively. The self-interference at source nodes operating in FD mode is mitigated by increasing the number of meta-surface elements at the IRS. Bit Error Rate (BER) and outage performances are analyzed with continuous phase shifting and discrete phase shifting in IRS. Closed-form analytical expressions are derived for the outage probability and BER performances of the IRS-assisted bidirectional FD-MTC system with a continuous phase shifter. The outage and BER performances of the IRS-assisted bidirectional MTC system in the FD mode have Signal-to-Noise Ratio (SNR) improvement compared with the IRS-assisted bidirectional MTC system in Half Duplex (HD) mode, as the number of reflecting elements in IRS is doubled in the FD mode. The outage and BER performances are degraded by a discrete phase shifter. Hence, performance degradation of the proposed IRS-assisted bidirectional FD-MTC is examined for 1-bit shifter (0, π), 2-bit shifter (0, π/2, π, 3π/2), and for 3-bit shifter (0, π/4, π/2, 3π/4, π, 5π/4, 3π/2, 7π/4). The performance degradation when a discrete phase shifter is employed in IRS is compared with the ideal continuous phase shifter in IRS. Further, achievable rate analysis is carried out for finding the best location of the IRS in a bidirectional FD-MTC system.

Security Enhancement for Coupled Phase-Shift STAR-RIS Networks

The secure transmission of the simultaneously transmitting and reflecting reconfigurable intelligent surface (STAR-RIS) aided communication system is investigated. Considering the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">coupled</i> phase shifts of STAR-RISs and the fair secrecy requirement of users, a new secure beamforming design is proposed for addressing the unique <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">full-space</i> mutual eavesdropping in STAR-RIS aided communications. In particular, a penalty-based secrecy beamforming algorithm is proposed to solve the resulting non-convex optimization problem, where closed-form solutions of the coupled phase-shift coefficients are obtained in each iteration. Numerical results demonstrate that 1) the proposed scheme achieves higher secrecy capacity than conventional RIS; 2) 4-bit discrete phase shifters are sufficient for secrecy guarantee.

Low-complexity IRS beamforming based on sphere decoding and tabu search

The real-time reconfiguration of intelligent reflecting surface (IRS) is one of the crucial, yet challenging tasks required to exploit the benefits of IRS. In this paper, we study an IRS-aided multiple-input single-output (MISO) wireless network, where a coarsely quantized (few resolution bits) IRS is reconfigured to help the point-to-point communication between a multi-antenna access point (AP) and a single-antenna user. Specifically, the transmit precoders at the AP and the reflecting discrete phase shifters at the IRS are jointly optimized to maximize the signal- to-noise ratio (SNR) at the user. The optimization is studied in two practical wireless propagation environments. First, we consider an environment where the direct AP-user link is in deep fade, which enables the relaxation of the optimization problem such that it can be optimally solved by the proposed sphere-decoder (SD) algorithm. Second, a normal propagation environment for all links is considered, wherein we propose the tabu search (TS) algorithm to solve the joint active and passive beamforming problem with low complexity. The proposed TS algorithm is shown to work well, even in deep-fade AP-user link scenarios. The presented numerical results confirm the validity of our analysis and demonstrate the effectiveness of the proposed schemes over the benchmark schemes on different system setups and propagation environments.

Pilot Optimization and Channel Estimation for Two-Way Relaying Network Aided by IRS With Finite Discrete Phase Shifters

In this paper, we investigate the problem of pilot optimization and channel estimation of two-way relaying network (TWRN) aided by an intelligent reflecting surface (IRS) with finite discrete phase shifters. In a TWRN, there exists a challenging problem that the two cascading channels from User1-to-IRS-to-relay and User2-to-IRS-to-relay and two direct channels from User1-to-relay and User2-to-relay interfere with each other. Via smartly designing the initial phase shifts of IRS and pilot pattern, the two cascading channels are separated over only four pilot sequences by using simple arithmetic operations like addition and subtraction. Then, the least-squares estimator is adopted to estimate the two cascading channels and two direct channels. The corresponding sum mean square errors (MSE) of channel estimators are derived. By minimizing Sum-MSE, the optimal phase shift matrix of IRS is proved. Then, two special matrices Hadamard and discrete Fourier transform (DFT) matrix are shown to be two optimal training matrices for IRS. Furthermore, the IRS with discrete finite phase shifters is taken into account. The Hadamard matrix requires only one-bit phase shifters to achieve the optimal Sum-MSE performance for specific numbers of IRS elements. Using theoretical derivation and numerical simulations, we find that 3 or 4-bit phase shifters are sufficient for IRS to achieve a negligible MSE performance loss for any number.

Secrecy Capacity of IRS-Assisted Terahertz Wireless Communications With Pointing Errors

This letter considers an intelligent reflecting surface (IRS)-assisted terahertz (THz) communication system in the presence of an arbitrary number of colluding/non-colluding eavesdroppers (Eves). Although the instantaneous channel state information (CSI) of the legitimate user (Bob) is assumed to be available, the IRS with discrete phase shifters cannot achieve optimal phase shifts, and thus Bob suffers from phase shift quantization errors. By taking into account the availability of the statistical CSI of Eves, pointing errors caused by highly-directional THz antennas, and the phase shift quantization errors, new expressions for the secrecy capacity in both cases of Eves are derived. The accuracy of the expressions is then verified by Monte-Carlo simulations. These expressions are used to investigate the impacts of pointing errors and quantization errors on the physical layer security of IRS-assisted THz systems in the presence of colluding and non-colluding Eves.

Machine Learning-Based Beamforming Design for Millimeter Wave IRS Communications With Discrete Phase Shifters

In this letter, we investigate an intelligent reflecting surface (IRS)-assisted millimeter-wave multiple-input single-output downlink wireless communication system. By jointly calculating the active beamforming at the base station and the passive beamforming at the IRS, we aim to minimize the transmit power under the constraint of each user’ signal-to-interference-plus-noise ratio. To solve this problem, we propose a low-complexity machine learning-based cross-entropy (CE) algorithm to alternately optimize the active beamforming and the passive beamforming. Specifically, in the alternative iteration process, the zero-forcing (ZF) method and CE algorithm are applied to acquire the active beamforming and the passive beamforming, respectively. The CE algorithm starts with random sampling, by the idea of distribution focusing, namely shifting the distribution towards a desired one by minimizing CE, and a near optimal reflection coefficients with adequately high probability can be obtained. In addition, we extend the original one-bit phase shift at the IRS to the common case with high-resolution phase shift to enhance the effectiveness of the algorithms. Simulation results verify that the proposed algorithm can obtain a near optimal solution with lower computational complexity.

Performance analysis of wireless network aided by discrete-phase-shifter IRS

Discrete phase shifter of intelligent reflecting surface (IRS) generates phase quantization error (QE) and degrades the receive performance at the receiver. To make an analysis of the performance loss (PL) caused by IRS with phase QE, based on the law of large numbers, the closed-form expressions of signal-to-noise ratio (SNR) PL, achievable rate (AR), and bit error rate (BER) are successively derived under line-of-sight (LoS) channels and Rayleigh channels. Moreover, based on the Taylor series expansion, the approximate simple closed form of PL of IRS with approximate QE is also given. The simulation results show that the performance losses of SNR and AR decrease as the number of quantization bits increases, while they gradually increase with the number of IRS phase shifter elements increases. Regardless of LoS channels or Rayleigh channels, when the number of quantization bits is larger than or equal to 3, the performance losses of SNR and AR are less than 0.23 dB and 0.08 bits/s/Hz, respectively, and the BER performance degradation is trivial. In particular, the performance loss difference between IRS with QE and IRS with approximate QE is negligible when the number of quantization bits is not less than 2.

BER analysis of tightly packed planar RIS system using the level of spatial correlation and discrete phase shifter

AbstractIn this article, the bit error rate (BER) performance of a tightly packed reconfigurable intelligent surface (RIS) assisted communication system is analyzed in terms of the level of spatial correlation. In conventional models, channels are assumed to be independent and identically distributed and continuous phase shifts are available for phase compensation. However, in practice, as RIS reflecting units are arranged in more compact form (less than 0.5) due to space constraints, correlation effects among the reflecting elements are to be considered. Further, discrete phase shifters are widely used to meet practical deployment limitations. These practical constraints severely affect the error performance of the system. It necessitates that the impact of spatial correlation and discrete phase shifts on the BER performance of the system is to be analyzed. The instantaneous signal to noise ratio is the square of the sum of correlated random variables. In order to analyze the BER performance accurately, the exact statistical distribution for the sum of spatially correlated random variables is to be chosen. In this work, appropriate distribution fitting is chosen based on the level of spatial correlation. Numerical BER expressions are derived with the chosen statistical distributions. The analysis on the impact of spatial correlation and discrete phase shifter on BER performance would be more beneficial for design and practicing engineers in the field of 6G wireless communications.

Adaptive Beamforming With Continuous/Discrete Phase Shifters via Convex Relaxation

Adaptive antenna array employing phase shifters only can reduce the hardware cost and power consumption, but the related optimization is well understood to be difficult to solve. In this paper, we examine the use of both continuous phase shifters (CPS) and discrete phase shifters (DPS) in antenna array for adaptive interference suppression. First, we formulate the phase-only tuning problem with CPS via quadratically constrained quadratic program (QCQP), which can be approximated through semidefinite relaxation (SDR) and solved by convex-optimization solvers efficiently. We also demonstrate that quantizing such results directly may not necessarily give acceptable performance. Then, we propose to use binary quadratic program (BQP) for the optimization of the adaptive beamformer utilizing DPS with an arbitrary number of control bits to specify the phase-shift levels. The resultant BQP can be relaxed and solved efficiently too. Moreover, due to the similarity between the CPS and DPS formulation, we can mix them in a single beamforming scheme to provide additional compromises between the output signal-to-interference and noise ratio (SINR) performance and implementation cost. Simulations show that in the considered interference-limited environment, our proposed beamformers with CPS, DPS, and hybrid phase shifters (HPS) give desirable results as expected.

Robust and Secure Sum-Rate Maximization for Multiuser MISO Downlink Systems With Self-Sustainable IRS

This paper investigates robust and secure multiuser multiple-input single-output (MISO) downlink communications assisted by a self-sustainable intelligent reflection surface (IRS), which can simultaneously reflect and harvest energy from the received signals. We study the joint design of beamformers at an access point (AP) and the phase shifts as well as the energy harvesting schedule at the IRS for maximizing the system sum-rate. The design is formulated as a non-convex optimization problem taking into account the wireless energy harvesting capability of IRS elements, secure communications, and the robustness against the impact of channel state information (CSI) imperfection. Subsequently, we propose a computationally-efficient iterative algorithm to obtain a suboptimal solution to the design problem. In each iteration, <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\mathcal {S}$ </tex-math></inline-formula> -procedure and the successive convex approximation are adopted to handle the intermediate optimization problem. Our simulation results unveil that: 1) there is a non-trivial trade-off between the system sum-rate and the self-sustainability of the IRS; 2) the performance gain achieved by the proposed scheme is saturated with a large number of energy harvesting IRS elements; 3) an IRS equipped with small bit-resolution discrete phase shifters is sufficient to achieve a considerable system sum-rate of the ideal case with continuous phase shifts.

The Low-Complexity Design and Optimal Training Overhead for IRS-Assisted MISO Systems

A low-complexity channel estimation and passive beamforming design for intelligent reflecting surface (IRS)-assisted multiple-input single-output (MISO) systems is proposed. Specifically, we present the low-complexity framework for maximizing the achievable rate of IRS-assisted MISO systems with discrete phase shifters at each IRS element. In contrast to existing solutions, the training set of IRS reflection coefficient matrix is pre-designed and the effective superposition channel estimation and transmit beamforming design are then performed for each IRS reflection coefficient matrix in the training set. Following this, the IRS reflection optimization is simplified by selecting the one that maximizes the achievable rate from the pre-designed training set. Secondly, we analyze the theoretical performance of the proposed framework and provide the optimal training overhead for maximizing the effective achievable rate given the channel coherence time. Finally, numerical simulations evaluate the rate performance of the proposed design. In particular, simulation results demonstrate that the proposed framework is a competitive option in practical communication systems with channel estimation errors.

Intelligent Reflecting Surface Enhanced Wideband MIMO-OFDM Communications: From Practical Model to Reflection Optimization

Intelligent reflecting surface (IRS) is envisioned as a revolutionary technology for future wireless communication systems since it can intelligently change radio environment and integrate it into wireless communication optimization. However, most existing works adopted an ideal IRS reflection model, which is impractical and can cause significant performance degradation in realistic wideband systems. To address this issue, we first study the dual phase- and amplitude-squint effect of reflected signals and present a simplified practical IRS reflection model for wideband signals. Then, an IRS enhanced wideband multiuser multi-input single-output orthogonal frequency division multiplexing (MU-MISO-OFDM) system is investigated. We aim to jointly design the transmit beamformer and IRS reflection for the case of using both continuous and discrete phase shifters to maximize the average sum-rate over all subcarriers. By exploiting the relationship between sum-rate maximization and mean square error (MSE) minimization, the original problem is equivalently transformed into a multi-block/variable problem, which can be efficiently solved by the block coordinate descent (BCD) method. Complexity and convergence for both cases are analyzed or illustrated. Simulation results demonstrate that the proposed algorithm can offer significant average sum-rate enhancement compared to that achieved using the ideal IRS reflection model, which confirms the importance of the use of the practical model for the design of wideband systems.

Discrete Phase Shifters-Based Hybrid Precoding for Full-Duplex mmWave Relaying Systems

This paper considers the hybrid precoding design with quantized phase shifters (PSs) for full-duplex millimeter-wave relaying systems, in which the relay node is equipped with PSs of different resolution levels. The joint optimization of relay hybrid precoding and discrete PSs is a high-dimensional non-convex problem with both higher-order polynomial and modulus constraints. To solve this challenging problem, the optimization function under the imperfect channel state information (CSI) is reformulated into a low-complexity norm-minimization form equation. Then, a relaxed algorithm based on the alternating direction method of multipliers and quantization steps is proposed to obtain the coupling approximate solutions for the above optimized equation. And the optimality of analytical solutions is guaranteed based on the imposed termination criterion and necessary conditions. Furthermore, given the requirement of arbitrary quantization, the trade-off between spectral efficiency (SE) and energy efficiency (EE) is investigated under the imperfect CSI. Numerical results verify that the hybrid precoding with low-resolution PSs can achieve excellent SE close to the full-resolution one but with a considerably lighter burden of energy consumption. Moreover, the transmission power plays a positive role in compensating quantization loss, but the excessive value will bring the reduction of EE.

Energy Efficiency and Spectral Efficiency Tradeoff in RIS-Aided Multiuser MIMO Uplink Transmission

The emergence of reconfigurable intelligent surfaces (RISs) enables us to establish programmable radio wave propagation that caters for wireless communications, via employing low-cost passive reflecting units. This work studies the non-trivial tradeoff between energy efficiency (EE) and spectral efficiency (SE) in multiuser multiple-input multiple-output (MIMO) uplink communications aided by a RIS equipped with discrete phase shifters. For reducing the required signaling overhead and energy consumption, our transmission strategy design is based on the partial channel state information (CSI), including the statistical CSI between the RIS and user terminals (UTs) and the instantaneous CSI between the RIS and the base station. To investigate the EE-SE tradeoff, we develop a framework for the joint optimization of UTs' transmit precoding and RIS reflective beamforming to maximize a performance metric called resource efficiency (RE). For the design of UT's precoding, it is simplified into the design of UTs' transmit powers with the aid of the closed-form solutions of UTs' optimal transmit directions. To avoid the high complexity in computing the nested integrals involved in the expectations, we derive an asymptotic deterministic objective expression. For the design of the RIS phases, an iterative mean-square error minimization approach is proposed via capitalizing on the homotopy, accelerated projected gradient, and majorization-minimization methods. Numerical results illustrate the effectiveness and rapid convergence rate of our proposed optimization framework.

Nonlinear magnetoelectric effects in Y-type hexaferrite microwave resonators

The nature of the nonlinear magnetoelectric effect is investigated in platelets of single-crystal Y-type hexaferrite with a collinear ferrimagnetic structure. The effect was observed at room temperature as a shift of 1.1-to-1.4 GHz in the ferromagnetic resonance frequency of Ba2Zn2Fe12O22 (Zn2Y) rectangular resonator with the application of an in-plane DC voltage. The shift amounted to 10%–12% of the central frequency which ranged from 8 to 17 GHz (X and Ku-bands). From the experimental results, we estimated the magnetoelectric modification of effective saturation magnetization and found that it scales almost linearly with the applied DC electric power. A phenomenological model for the nonlinear magnetoelectric effect, which considers the hexaferrite magnetic symmetry, is proposed and qualitatively accounts for the observed dependence of magnetic parameters on input power. It is shown that the resonator can operate as an electrically controlled discrete phase shifter with almost π/4 phase shift and &amp;lt;4 dB insertion losses. These results are of importance for the use of Y-type hexaferrites in electrically tunable planar microwave signal processing devices.

Precision L-Band Analog-Digital Phase Shifter with a 0°–360° Phase Change

In modern satellite communication systems and airborne repeaters using an APAR, the receiving and transmitting modules usually consist of discrete phase shifters such as hybrid integrated circuits or monolithic circuits. In this paper, we consider an open-frame analog-digital phase shifter module with a 0°–360° phase change that allows ensuring the accuracy of setting the discrete phase to not more than 0.5° based on the domestic control UHF MIS varicaps. An original L-range analog-digital phase shifter with a 0°–360° phase change using a Lange bridge and phase-shifting cells based on four UHF MIS varicaps is proposed. The requirements for the type of volt-farad characteristic and the capacitance overlap coefficient of the MDP-varicap capacitance are determined. Even at the limiting (critical) UHF MIS-varicap frequency not higher than 15 GHz, the proposed scheme of the analog-digital phase shifter allows ensuring the phase shifter loss that is not greater than 1.5 dB in the L-band. The analog-digital phase shifter with a 0°–360° phase change was operated by the digital control board. An 8-bit DAC was used. The division value of the discrete control of the phase shifter is 1.4° at 256 DAC states. The obtained characteristics of the precision analog-digital phase shifter allow concluding on the propects of its use for solving synchronization problems of an active radio target simulator in testing synthetic aperture radars, as well as in the receiving and transmitting modules of a low-element APAR for the L-band.