Optimal Beamforming Research Articles

Beamforming design for multi-antenna multi-tag symbiotic radio backscatter systems

In this paper, we consider a multi-tag symbiotic radio backscatter system, where a multi-antenna source node transmits its own message to a multi-antenna destination, while multiple backscatter tags transmit information to the destination by directly reflecting the incident signals from the source. We investigate the optimal beamforming design to minimize the transmit power at the source, subject to the signal-to-interference-plus-noise ratio (SINR) constraints for the signals of the source and the tags, and the harvested power constraints at the tags. The formulated min-power optimization problem is non-convex, and we propose a semi-definite programming (SDP) based alternating optimization algorithm to optimize the transmit beamforming vector at the source and the receive beamforming vector at the destination. Numerical results show that the proposed beamforming design algorithm converges fast and outperforms the counterpart scheme significantly.

Energy-efficient resource allocation and user grouping for multi-IRS aided MU-MIMO system

In this paper, we consider a multiple-intelligent reflecting surface (IRS)-aided multi-user multiple-input-multiple-output (MU-MIMO) down-link communication system, wherein a base station (BS), equipped with multiple antennas, serves massive single-antenna users. In order to mitigate high inter-user interference, we divide all the users into a single near-user (NU) group and multiple cell-edge user (CEU) groups based on their connection with BS. In particular, we assign a single IRS for each CEU group such that the BS communicates and serves the set of CEUs using their corresponding IRS. Subsequently, we formulate a problem of energy-efficient resource allocation design subject to optimal beamforming design at BS and multiple IRS under given power constraints. Due to the non-convexity of the formulated resource allocation problem, we proposed two different alternating optimization frameworks which solve the joint optimization problem based on 1) minimum mean square error (MMSE) and Riemannian conjugate gradient (RCG) and 2) fractional programming and successive convex approximation techniques for active beamforming vectors at the BS and passive beamforming vectors for IRSs, respectively. Simulation results confirm that the MMSE-RCG-based resource allocation design attains fast convergence when compared to sequential fractional programming (SFP) based solution. Moreover, the MMSE-RCG attains better energy efficiency whereas the SFP renders better spectral performance. Nevertheless, both the proposed solution achieve 70%–80% better performance than random phase-shift settings.

Achievable Rate Region for uRLLC Interference Channel With Finite Blocklength Transmission

Finite blocklength is a favorable way to meet the extremely low-latency requirement, which leads to the classic Shannon's capacity formula no longer suitable. With the achievable rate region, optimization problems on three different scenarios are considered: (i) joint design of power and blocklength allocation for two transceiver pairs with single-antenna transmitter; (ii) beamforming and blocklength design for the two transceiver pairs with multi-antenna transmitter; (iii) beamforming and blocklength design for the multiple transceiver pairs with multi-antenna transmitter. Under the finite blocklength transmission mode, the achievable rate expression is a complicated function with respected to the blocklength and power allocation coefficients or beamforming vector, which makes the optimization problems difficult to solve. In this paper, by analyzing the monotonic and concaveconvex properties of achievable rate with interference channel (IFC), we formulate the achievable rate region as the convex hull of a series of power/beamforming and blocklength rate regions for two-user systems with IFC, as well as the Pareto boundary of achievable rate region on the blocklength and beamforming vector for the two-user systems, respectively. Sequentially, the optimal blocklength and power coefficients are derived in the closed-form and optimal beamforming vectors are also obtained by transforming the non-convex problem into convex one. Numerical results provide the perspective of looking at the rate region with finite blocklength.

Joint Receive and Passive Beamforming Optimization for RIS-Assisted Uplink RSMA Systems

In this letter, we investigate the joint optimization of transmit power allocation and receive/passive beamforming in a reconfigurable intelligent surface (RIS)-assisted uplink two-user rate-splitting multiple access (RSMA) system. Aiming at maximizing the achievable rate of one user subject to another user’s quality of service (QoS) requirements, RIS is deployed to assist the uplink transmissions from both users to a multi-antenna base station (BS). We decouple the non-convex rate maximization problem into three sub-problems and propose an alternating optimization (AO) algorithm to optimize the receive/passive beamforming and transmit power allocation. A closed-form expression is derived for the sub-problem of transmit power allocation by using the optimal decoding order and the concave-convex fractional programming beamforming problems are converted to convex ones by using the Charnes-Cooper transform. Then, a penalty term approach is applied to effectively solve the rank-1 constrained beamforming subproblems. Simulation results verify that the proposed AO algorithm attains a higher achievable rate than the existing benchmark schemes.

Joint Phase Shift and Beamforming Design in a Multi-User MISO STAR-RIS Assisted Downlink NOMA Network

Simultaneous transmitting and reflecting reconfigurable intelligent surfaces (STAR-RIS) has gradually been considered as a promising technology in the wireless communication networks. Besides, non-orthogonal multiple access (NOMA) is also the key technology in the sixth-generation (6 G) wireless communication system. In this work, we study a multiple input single output (MISO) STAR-RIS assisted NOMA downlink network and investigate the energy efficiency (EE) maximization to achieve the tradeoff between the sum rate and the power consumption. The original formulated problem is non-convex due to the coupled beamforming vectors of the users and phase shifts of the STAR-RIS. To efficiently solve the problem, we split the original non-convex problem into the phase shift and beamforming optimization problems and then solve them alternatively. In the phase shift optimization, fractional programming (FP) is applied to transform the sum rate maximum problem to convex semidefinite relaxation (SDR) one with the rank-one constraint. After this, a novel sequential rank-one constraint relaxation (SROCR) is proposed to convert the rank-one constraint into a convex one, which can effectively overcome the inadequacy of Gaussian randomization, i.e., quality of the solutions and computational complexity. Similarly, FP is applied to solve the beamforming problem by transforming it to SDR problem. It turns out that the optimal solution of the SDR beamforming optimization problem can be guaranteed to be rank-one by the mathematical proof and experiments. The simulation results demonstrate the STAR-RIS NOMA system can achieve the superior performance in EE.

Joint Active and Passive Beamforming Optimization for Multi-IRS-Assisted Wireless Communication Systems: A Covariance Matrix Adaptation Evolution Strategy

Intelligent reflecting surface (IRS) is applied in 5 G and 6 G to improve communication performance by reconfiguring signal propagation environments while maintaining low computational complexity and high energy efficiency. This paper proposes a novel methodology of joint active and passive beamforming optimization for wireless communications with the aid of multiple IRSs. In the considered system, the IRSs are deployed to assist the communication link from a multi-antenna access point (AP) to single-antenna users. We maximize the received signal to noise ratio (SNR) and sum rate of the multi-IRS-assisted communication system for single user and multiple users respectively, by solving a joint optimization problem of the active beamforming at the AP and the reflection beamforming at the IRSs. Specifically, we develop a mechanism of joint beamforming optimization for multi-IRS-assisted communications based on covariance matrix adaptation evolution strategy (CMA-ES), namely the BO-CMA algorithm, to jointly consider both the AP active beamforming and IRS reflection beamforming in the dynamic signal propagation environment. Furthermore, simulation results are provided to show that the BO-CMA algorithm is capable of significantly outperforming the benchmark schemes. Consequently, the solution based on the BO-CMA algorithm can dynamically rebuild the signal propagation environment, and improve the received SNR and the sum rate respectively for multi-IRS-assisted one user and multiple users communications.

Joint optimization of trajectory, beamforming, and power allocation in UAV-enabled WPT networks using DRL combined with water-filling algorithm

In this work, we study a wireless power transfer (WPT) network supported by an unmanned aerial vehicle (UAV), in which a UAV equipped with an array of antennas supplies wireless energy to charge ground user (GU) devices. With this configuration, we aim to maximize the lowest GU energy by jointly optimizing the UAV's trajectory, beamforming pattern, and transmitting power. Because the proposed maximization of the lowest GU energy is a non-convex optimization problem that is difficult to be solved, we transform the problem into a grid world problem in discrete-time space and propose a design of a deep reinforcement learning (DRL) approach that optimizes the loss function by determining the UAV's moving direction, beamforming angle, and transmit power level. Furthermore, we combine the water-filling algorithm with DRL, which can assist DRL in determining the hovering duration. Simulation results verify that our proposed design increases the minimum energy of GUs received from the UAV compared to the successive hover-and-fly algorithm while exploring the most appropriate path with low computational complexity.

A Study on the Optimal Magnetic Beam Forming of Coil Arrays for Long Distance Wireless Power Transmission.

Multiple-input multiple-output (MIMO) wireless power transfer (WPT) technology which employs multiple transmitter (TX) coils to simultaneously couple power to the receiver (RX) coil has proved to be an effective technique to enhance power transfer efficiency (PTE). Conventional MIMO-WPT systems rely on the phase-calculation method based on the phased-array beam steering concept to constructively combine the magnetic fields induced by the multiple TX coils at the RX coil. However, increasing the number and distance of the TX coils in an attempt to enhance the PTE tends to deteriorate the received signal at the RX coil. In this paper, a phase-calculation method is presented that enhances the PTE of the MIMO-WPT system. The proposed phase-calculation method considers the coupling between the coils and applies the phase and amplitude to calculate the coil control data. From the experimental results, the transfer efficiency is enhanced as a result of the transmission coefficient improvement from a minimum of 2 dB to a maximum of 10 dB for the proposed method as compared to the conventional one. By implementing the proposed phase-control MIMO-WPT, high-efficiency wireless charging is realizable wherever electronic devices are located in a specific space.

RIS-Assisted Secure Communications: Low-Complexity Beamforming Design

Joint active and passive beamforming optimization is investigated to enhance the physical layer security of a reconfigurable intelligent surface (RIS)-assisted multiple-antenna communication system. The problems are formulated under two criteria: secrecy rate maximization and power consumption minimization. For each design problem, a novel collaborative design algorithm is proposed by capitalizing on the mathematical structure of the optimal active beamforming vector, which requires no iterative updating between the transmit beamformer and the RIS-reflecting beamformer. Numerical results demonstrate that the proposed algorithms enjoy much lower computational complexity than the state-of-the-art alternating optimization-based methods while achieving almost identical secrecy performance.

Handover-Aware Downlink Beamforming Design for LEO Multibeam Satellite Communications

Because of their capability of providing seamless connectivity, low-Earth-orbit (LEO) satellites will play a vital role in integrated satellite–terrestrial paradigms. However, high-speed satellite motion brings frequent handovers, during which redundant transmission and even loss of data easily occur. In this letter, we propose a handover-aware downlink beamforming design. To mitigate the impact of inter-satellite handover, we reduce the blocklength of coverage-edge users, aiming at completing transmission within the remaining visible time (RVT). Hence, the capacity of these users should be evaluated in the finite-block length (FBL) regime. After obtaining a surrogate of the FBL capacity function with a low-complexity method, we formulate the beamforming optimization model as a semidefinite programming (SDP) problem and solve it with CVX. The simulation results show that the proposed scheme can reach a 99.35% transmission success rate before inter-satellite handover.

Reconfigurable Intelligent Surface for FDD Systems: Design and Optimization

Reconfigurable intelligent surface (RIS) has recently emerged as a promising technology for wireless communications, which intelligently controls the phase shift of each unit cell to form desired beams. Most prior works on RIS consider time-division duplexing (TDD) systems, in which the same phase shifts can be applied to both uplink and downlink due to the channel reciprocity. However, for frequency-division duplexing (FDD) systems, using the same phase shifts will result in beam misalignment, thereby leading to performance degradation. To address this issue, in this paper, we study the practical RIS design and beamforming optimization for FDD systems. By representing the phase shifts of RIS with the equivalent circuit model which includes the resistance, inductances, and tunable capacitance, we propose a methodology to design the circuit parameters (i.e., inductances and capacitance) to meet the desired reflection requirements (i.e., phase tuning range, reflectivity, and zero phase slope) of both the uplink and downlink transmissions in FDD systems. Given the designed inductances, a practical binary RIS reflection model corresponding to two reflection states is then proposed. Furthermore, based on the proposed reflection model, a problem is formulated to jointly optimize the active and passive beamforming such that the minimum array response gain of the uplink and the downlink is maximized. An efficient iterative algorithm is proposed to obtain a suboptimal solution. Simulation results show that our proposed RIS design outperforms those benchmarks which design the circuits by only optimizing either uplink or downlink.

Joint Active and Passive Beamforming for RIS-Aided MIMO Communications With Low-Resolution Phase Shifts

Practical hardware limitations often impose a reduced number of available phase shifts at the elements of a reconfigurable intelligent surface (RIS). Most works often assume continuous phase-shits at the RIS elements for the transmit and passive beamforming optimization, which can lead to substantial performance loss. Therefore, to harvest the gains of RIS-assisted multi-stream multiple-input multiple-output (MIMO) communications under realistic phase shifts, this letter proposes a problem formulation for the maximization of the achievable rate over the transmit precoder and RIS elements, which avoids an explicit discrete constraint while still incorporating its effect. To efficiently tackle the resulting problem when considering large arrays and RIS panels, an iterative algorithm is derived which comprises a sequence of simple projections. Simulation results demonstrate that the proposed design can be very effective, especially with low-resolution phase-shifts.

Joint Active and Passive Beamforming Design for RIS-Aided IBFD IoT Communications: QoS and Power Efficiency Considerations

In a reconfigurable intelligent surface (RIS) aided communication network, a RIS equipped with multiple passive reflecting elements assists in extending the coverage of wireless networks by overcoming the effects of non-line-of-sight propagation. Accordingly, to present the case for utilizing RIS panels in future consumer internet of things (IoT) networks, in this paper, we focus on a RIS-aided IoT network operating in in-band full-duplex (IBFD) mode. Since all the IoT node pairs communicate simultaneously through individual IBFD links at the same time-frequency resources, the nodes suffer from strong self-interference (SI) and inter-node interference. Consequently, in this paper, we investigate a joint active and passive beamforming design at each IoT node and the RIS, respectively, by minimizing the total transmission power of the network, subject to a minimum rate constraint for each IoT node and a constraint that guarantees a unit modulus phase shift at the RIS. As the original joint active and passive beamforming design problem is non-convex and intractable, we decompose the problem into two sub-problems. For a given passive beamformer design, we solve the original problem to obtain the optimal beamforming vectors at each IoT node. Next, for the obtained active beamformer, we propose two algorithms based on i) gradient descent (GD) search and ii) Riemannian conjugate gradient (RCG) to obtain the optimal passive beamformer at the RIS. Through extensive numerical analysis, we verify the effectiveness of the proposed algorithms and also show the effects of using RIS and transmitting in IBFD mode on the average rate and power of the considered consumer IoT network. We investigate the impact of several system parameters such as RIS elements, node pairs, level of hardware impairments at the transmitter and receiver, etc. We also highlight the trade-off between performance improvement and complexity due to elements used at RIS.

A Low Complexity Passive Beamforming Design for Reconfigurable Intelligent Surface (RIS) in 6G Networks

Reconfigurable intelligent surface (RIS) emerged as a promising technology for programming the wireless propagation environment, ushering wireless networks into a new era of high connectivity, and better spectrum and energy efficiency. Research has gained momentum over the past few years to study the gains of RIS and the optimal configuration of its elements. This paper is concerned with the optimal configuration of RIS elements; we consider a single base station (BS) serving multiple single-antenna users and formulate the problem of minimizing the total transmit power while jointly optimizing the allocated power to users and the RIS phase shifts. In line with the existing literature, the problem is decomposed into power control and RIS phase shift sub-problems. The power control sub-problem is the conventional power problem which is solved optimally through closed-form expression. Then, we tackle the problem of RIS passive beamforming optimization and propose two solutions leveraging a linear transformation and element-wise Karush-Kuhn-Tucker (KKT), respectively. The main idea of the linear transformation approach is to reduce the number of optimization variables to the number of users associated with the RIS from the number of its elements which is, in general, very large. On the other hand, the main idea of the element-wise KKT-based approach is to obtain a closed-form expression for the RIS phase shifts for a multi-user scenario, similar to the single-user case. Simulation results show that the proposed schemes have performance in total transmitted power close to the numerical solution and have much lower computational complexity than the baseline solutions. Moreover, simulation results show that the proposed solutions have a competitive performance in terms of optimality and complexity for large-scale RIS. Hence, our approach represents a general framework for configuring RIS elements in real scenarios.

Enhanced secrecy outage probability for multiple‐input single‐output‐VLC systems through optical beamforming and improved light emitting diodes deployment

AbstractThe authors propose to arrange the light emitting diodes (LEDs) on the ceiling for an indoor visible light communication system in order to minimise the secrecy outage probability (SOP) at the location of the legitimate user (LU). More precisely, by deriving the secrecy capacity for a multiple‐input single‐output‐VLC system, we evaluate the SOP at the LU's location which is used as the appropriate metric to determine the position of the LEDs on the ceiling. To mitigate the effect of the eavesdropper, we derive the optimal beamforming coefficients which are used at the transmitter LED array with the aim of maximising the signal‐to‐noise ratio at the LU. Simulation results show that for a SOP of 10−4, the proposed SOP‐based LED arrangement with optimal beamforming offers up to 3 dB gain in transmit power compared to the classical uniform LED arrangement with sub‐optimal zero‐forcing beamforming. Moreover, they show that by using the proposed method, the SOP is kept below a desired threshold, over a wider area inside the indoor environment compared to classical methods.

Secure wireless communications for STAR‐RIS‐assisted millimetre‐wave NOMA uplink networks

AbstractThis paper explores the potential application of simultaneously transmitting and reflecting reconfigurable intelligent surface (STAR‐RIS) in improving the physical layer security (PLS) of millimetre wave (mmWave) non‐orthogonal multiple access (NOMA) uplink communications. In particular, the legitimate users on both sides of STAR‐RIS send confidential information simultaneously to the base station (BS) while keeping it secret from the eavesdroppers near the BS by exploiting the STAR‐RIS to proactively regulate the electromagnetic propagation environment. By jointly designing the transmit power, the active beamforming at the BS, and the reflecting/transmitting coefficients at the STAR‐RIS, the authors' goal is to maximize the minimum secrecy capacity subject to the successive interference cancellation decoding order constraints. Due to the non‐convexity of the formulated problem, an efficient algorithm is proposed by capitalizing on alternating optimization, a penalty‐based approach, successive convex approximation, and semi‐definite relaxation. Firstly, a two‐layer iterative algorithm based on the penalty for the joint beamforming optimization sub‐problem is proposed. Then, the non‐convex problem is transformed into a convex positive semi‐definite programming problem for the transmit power sub‐problem. Numerical simulation results reveal that the STAR‐RIS‐aided system has more tremendous advantages and effectiveness in improving the PLS of mmWave NOMA uplink communication compared with the benchmark schemes.

Joint Data Transmission and Energy Harvesting for MISO Downlink Transmission Coordination in Wireless IoT Networks.

The advent of simultaneous wireless information and power (SWIPT) has been regarded as a promising technique to provide power supplies for an energy sustainable Internet of Things (IoT), which is of paramount importance due to the proliferation of high data communication demands of low-power network devices. In such networks, a multi-antenna base station (BS) in each cell can be utilized to concurrently transmit messages and energies to its intended IoT user equipment (IoT-UE) with a single antenna under a common broadcast frequency band, resulting in a multi-cell multi-input single-output (MISO) interference channel (IC). In this work, we aim to find the trade-off between the spectrum efficiency (SE) and energy harvesting (EH) in SWIPT-enabled networks with MISO ICs. For this, we derive a multi-objective optimization (MOO) formulation to obtain the optimal beamforming pattern (BP) and power splitting ratio (PR), and we propose a fractional programming (FP) model to find the solution. To tackle the nonconvexity of FP, an evolutionary algorithm (EA)-aided quadratic transform technique is proposed, which recasts the nonconvex problem as a sequence of convex problems to be solved iteratively. To further reduce the communication overhead and computational complexity, a distributed multi-agent learning-based approach is proposed that requires only partial observations of the channel state information (CSI). In this approach, each BS is equipped with a double deep Q network (DDQN) to determine the BP and PR for its UE with lower computational complexity based on the observations through a limited information exchange process. Finally, with the simulation experiments, we verify the trade-off between SE and EH, and we demonstrate that, apart from the FP algorithm introduced to provide superior solutions, the proposed DDQN algorithm also shows its performance gain in terms of utility to be up to 1.23-, 1.87-, and 3.45-times larger than the Advantage Actor Critic (A2C), greedy, and random algorithms, respectively, in comparison in the simulated environment.

Intelligent reflecting surface‐aided Doppler compensation for Low‐Earth orbit satellite networks: Joint power allocation and passive beamforming optimisation

AbstractDue to the reduction in costs of manufacture and launch of Low‐Earth orbit (LEO) satellites, LEO satellite communication (SATCOM) has become a promising solution to provide high data rates and low latency connectivity for future communications. However, due to the fast movement of LEO satellites, it has to face a large Doppler effect, leading to high inter‐carrier interference (ICI) power and severe received symbol error rate. To tackle this problem, a novel optimisation framework is proposed that boosts the achievable rate in LEO SATCOM networks by utilising passive beamforming of intelligent reflecting surface (IRS) to compensate for the Doppler effect. First, a carrier‐to‐interference‐noise ratio (CINR) was derived for each subcarrier and a joint optimisation problem of both power allocation is formulated to each subcarrier and passive beamforming of IRS. Moreover, a simultaneous iterative‐water‐filling‐algorithm (SIWFA) and semidefinite programing (SDP) are utilised, thereby striking a balance that minimises ICI power and maximises desired signal power. Numerical results demonstrate the superior achievable rate performance of the proposed IRS‐aided Doppler compensation for LEO SATCOM networks compared to benchmark schemes.

Resource Scheduling for Intelligent Reflecting Surface-Assisted Full-Duplex Wireless-Powered Communication Networks With Phase Errors

Intelligent reflecting surface (IRS) is envisioned as a promising technique to improve the performance of full-duplex wireless powered communication networks (FD-WPCNs). This paper investigates the joint phase beamforming design and resource management for IRS-assisted FD-WPCNs, where multiple wireless devices (WDs) can harvest downlink radio-frequency energy and transmit uplink information to the hybrid access point (HAP) over the same band with the aid of IRS. We first formulate a total transmission time minimization problem subject to the minimum transmit rate and energy causality constraints of WDs. In particular, the random phase error of IRS is integrated into our optimization model. Furthermore, we develop an alternating optimization method to obtain the optimal solution of formulated non-convex problem by iteratively solving two subproblems. For the phase beamforming optimization subproblem, we first convert the random phase errors to a deterministic expression, and then utilize the successive convex approximation method to solve the phase beamforming optimization problem. For the transmit power and time-slot allocation subproblem, the optimal transmit power of WDs is derived in closed-form expressions, and the approximation method and variable substitution technique are adopted to obtain the optimal time-slot allocation and transmit power of HAP. Finally, numerical results are provided to evaluate the performance of our proposed method, and reveal the benefits introduced by the IRS technique as compared to benchmark methods.

Feature-Enhanced Beamforming for Underwater 3-D Acoustic Imaging

A planar array of sensors and beamforming algorithms are required for underwater 3-D acoustic imaging system. However, due to limited aperture and sensor numbers, conventional beamforming usually results in wide mainlobes and high sidelobes, which severely degrade the image quality. To date, using unconventional beamforming algorithms to improve the imaging quality of underwater 3-D acoustic systems have been rarely investigated. This article proposes a feature-enhanced beamforming (FEBF) algorithm, with the goal of improving the imaging quality by utilizing more appropriate prior knowledge that objects in the angular domain in underwater 3-D imaging scenes are generally sparse but locally dense. The proposed FEBF employs the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$l_{1}$</tex-math></inline-formula> -total variation (L1-TV) mixed norm regularization. The penalized beamforming optimization is reformed into convex programming with linear constraints and solved by alternating direction method of multipliers. The results of simulation and experiment demonstrate that the proposed FEBF has the ability to effectively improve the image quality when compared with the other existing beamforming methods. This study also proposes a 2-D fast Fourier transform based acceleration strategy, which effectively reduces the computational time of the FEBF algorithm by about 4.3 × 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sup> times for forming 200 × 200 beams. The accelerated version of the proposed FEBF method is considered to have potential for real-time imaging systems.