Optimal Beamforming Research Articles

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.

3D placement of UAVs with optimal beamforming for multi-user communications

This article proposes the three-dimensional (3D) deployment of multiple unmanned aerial vehicles (UAVs) as relays between internet of things (IoT) access points (APs) and terrestrial base stations (BSs). Limited by the total battery capacity of UAVs, the 3D placement of multiple UAVs is designed to minimize the number of required UAV flights to serve the IoT APs within a pre-defined time while maximizing the number of successfully served IoT Aps, which is a nonlinear and NP-hard problem. To achieve the above goals, we linearize the problem into an integer linear programming (ILP) model and propose two genetic algorithms (GAs) by adjusting the number, 3D positions, and beamwidths of UAVs. Simulation results show that the use of flexible beamwidths for UAVs can significantly improve performance. Moreover, for different signal-to-interference-noise-ratio (SINR) thresholds, the proposed consecutive GA (ConsGA) clearly outperforms other heuristics. Moreover, the SINR and UAV bandwidth significantly affect the overall performance. Furthermore, our simulations show that the proposed discrete GA (DisGA (960)) achieves the lowest number of UAV flights compared to other algorithms while successfully meeting the SINR threshold, and its performance is the closest to that of the optimization model (i.e., ILP model).

Beamforming Phased-Array-Fed Lenses With &gt;0.5λ-Spaced Elements

We propose a phased-array-fed lens (PAFL) antenna that is capable of beamforming like a phased array but with array elements spaced beyond <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$0.5\lambda $ </tex-math></inline-formula> . The PAFL produces high-quality scanned beams using only five active feeds. This architecture represents dramatic cost and power savings over conventional phased arrays while providing many of the features. We present an optimal beamforming method to achieve the maximum gain at any angle using a subset of feeds and a multiobjective optimizer using particle swarm optimization for more granular pattern control. The method is applied to several simulated state-of-the-art lens antennas with good performance confirming the generality of the method. The theory is demonstrated with a prototype PAFL comprising a 4 inch aperture gradient-index (GRIN) lens antenna, an 8-element <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$0.725\lambda $ </tex-math></inline-formula> -spaced linear patch array operating at 29 GHz, and a commercial Ka-band SATCOM beamformer integrated circuit (IC). The prototype achieves the maximum gain at all angles and improves the scan loss by 4 dB at ±50°.

DF Relay Assisted Covert Communications: Analysis and Optimization

Covert communication is crucial to preventing the warder's detection of wireless transmission. In general, small transmit power is required to satisfy the covertness requirement, which limits the system performance between the transceivers. To overcome the limitation, a multi-antenna relay is utilized and the coordinated direct and relay transmission (CDRT) is proposed in this paper. Since both the direct link and the relay link impact the system performance, an optimization problem is formulated to maximize the covert rate, where the beamforming vectors at the source and the relay are coupled. To address this problem, a semidefinite relaxation based line search method is proposed to obtain the globally optimal beamforming vectors, which balances the direct and the relay link to satisfy the covertness requirements and achieve the maximum covert rate simultaneously. Numerical results demonstrate the superiority and robustness of the proposed CDRT scheme compared with the systems without the direct or the relay link, especially when the warder-related links are highly correlated with the direct or the relay link. Besides, the CDRT scheme also outperforms the cooperative jammer assisted covert system even when the transmission power is high since the covertness requirements can be satisfied by joint beamforming in the CDRT scheme.

A Wideband Generalization of the Near-Field Region for Extremely Large Phased-Arrays

The narrowband and far-field assumption in conventional wireless system design leads to a mismatch with the optimal beamforming required for wideband and near-field systems. This discrepancy is exacerbated for larger apertures and bandwidths. To characterize the behavior of near-field and wideband systems, we derive the beamforming gain expression achieved by a frequency-flat phased array designed for plane-wave propagation. To determine the far-field to near-field boundary for a wideband system, we propose a frequency-selective distance metric. The proposed far-field threshold increases for frequencies away from the center frequency. The analysis results in a fundamental upper bound on the product of the array aperture and the system bandwidth. We present numerical results to illustrate how the gain threshold affects the maximum usable bandwidth for the n260 and n261 5G NR bands.

ISAC-Accelerated Edge Intelligence: Framework, Optimization, and Analysis

Conventionally, the sensing and communication stages for edge intelligence systems are executed sequentially, leading to an excessive time of dataset generation and uploading. To combat the weakness, this paper proposes to accelerate edge intelligence via integrated sensing and communication (ISAC), where the sensing and communication stages are merged to make the best use of the wireless signals for the dual purpose of dataset generation and uploading. For the proposed ISAC-accelerated edge intelligence system, the resource allocation and beamforming should be jointly optimized to exploit the underlying ISAC benefits. We formulate a joint resource allocation and beamforming optimization problem. Despite the non-convexity, we obtain globally optimal solutions assuming that the constant maximal transmits power, and devise an alternating optimization algorithm for the original problem without such assumption. Furthermore, we analyze the ISAC acceleration gain of the proposed system over that of the conventional edge intelligence system. Both theoretic analysis and simulation results show that ISAC accelerates the conventional edge intelligence system when the duration of generating a sample is more than that of uploading a sample. Otherwise, the ISAC acceleration gain vanishes or even is negative. In this case, we derive a sufficient condition for positive ISAC acceleration gain.

Broadband beamforming of multiplet line arrays using subband optimal beamformers eliminating port/starboard ambiguity

Development of beamforming methods for towed sonar multiplet line arrays is stimulated by their increased use in undersea surveillance. Such methods employ various forms of narrowband optimal beamforming to resolve port/starboard ambiguity present when the array is conventionally beamformed. In this paper, we depart from the purely narrowband approach and discuss methods for port/starboard ambiguity rejection (PSAR) using a broadband formulation. The proposed methodology relies on subband beamforming for which we use non-adaptive variants of beamspace Minimum Variance Distortionless Response (MVDR) and the Linear Constraint Minimum Variance (LCMV) beamformers. We provide detailed description and comparison of both subband methods and establish a connection between them. The paper provides assessment of PSAR properties of the developed broadband beamformers using outputs of signal processing of both simulated and experimental sonar data. Experimental data for this work were obtained through the participation in the Littoral Continuous Active Sonar (LCAS) trials.

Wavenumber unwrapping for the automated analysis of SASW measurements

Depending upon the surface wave methods, the measured surface wave velocities are either normal mode velocities or apparent velocities. The “apparent” surface wave velocity corresponds to the superposed mode combining the available normal modes. The spectral-analysis-of-surface-waves (SASW) method measures the apparent surface wave velocities. However, these velocities render SASW analyses complicated because of the mode jumps induced by several wave groups. To alleviate such complications, this study introduced a beamforming technique and produced information on unwrapped wavenumber, which is vital in unwrapping the phase spectrum in SASW analyses. Additionally, incoming wave directions filtered out multiple reflections and irrelevant seismic events to retain only the surface waves directly propagating from the source. The proposed wavenumber unwrapping technique was verified using field applications, dynamic finite element analysis, and synthetic waveforms. Notably, an optimal beamforming technique was established using four geophones, making the proposed method highly practical and reducing the hardware requirements. Hopefully, the proposed analysis technique provides SASW practitioners with a more comfortable and more reliable environment in utilizing the SASW technique.

Joint Reconfigurable Intelligent Surface Location and Passive Beamforming Optimization for Maximizing the Secrecy-Rate

The physical layer security (PLS) is investigated for reconfigurable intelligent surface (RIS) assisted wireless networks, where a source transmits its confidential information to a legitimate destination with the aid of a single small RIS in the presence of a malicious eavesdropper. A new joint RIS location and passive beamforming (J-LPB) optimization scheme is proposed for the sake of maximizing the secrecy rate under the RIS location constraint and the constraint that the modulus of the reflecting coefficient at each RIS's unit is not larger than 1. Specifically, we analyze the optimal location of the RIS, and conclude that the product involving the source-RIS distance and the RIS-destination distance should be minimized. Since the product minimization problem is nonconvex, we then propose a two-tier optimization algorithm for solving it. Based on the near-optimal RIS 3D location obtained, we further formulate the passive beamforming optimization problem, and then propose to apply the Charnes-Cooper transformation along with the sequential rank-one constraint relaxation (SROCR) algorithm to solve it. Our numerical results show that the secrecy rate of the proposed J-LPB optimization scheme is higher than that of the benchmarks. Explicitly, we use the following benchmarks: the near-source-based RIS location and passive beamforming (NSB-LPB) optimization scheme, the near-destination-based RIS location and passive beamforming (NDB-LPB) optimization scheme, and the random RIS location and passive beamforming (R-LPB) optimization scheme. Finally, the benefits of our J-LPB scheme are further increased with the number of RIS units.

Beamforming Optimization for Reconfigurable Intelligent Surface With Power Splitting Aided Broadcasting Networks

Reconfigurable intelligent surface (RIS) has emerged as a promising technology for the 6G networks. In this article, we study a RIS with power splitting aided broadcasting network where one access point (AP) transmits identical messages to multiple users. The RIS is capable of reflecting a part of the incident signals to assist the AP and harvesting energy from the other part to achieve power self-sustainability by controlling reflect amplitude coefficients. We aim at minimizing the AP transmit power while ensuring the quality of service at users and the self-sustainability of the RIS by optimizing the AP transmit beamforming vector and the RIS reflect beamforming matrix which involves the reflect amplitude and phase shift coefficients. To tackle the beamforming optimization problem which is non-convex, an algorithm is proposed by employing the block coordinate descent, convex approximation and alternating direction method of multipliers techniques. Simulation results demonstrate the effectiveness of the proposed algorithm.

A novel EO-based optimum random beamforming method in mmWave-NOMA systems with sparse antenna array

Millimeter-wave (mmWave) Non-Orthogonal Multiple Access (NOMA) with random beamforming is a promising technology to guarantee massive connectivity and low latency transmissions of future generations of mobile networks. In this paper, we introduce a cost-effective and energy-efficient mmWave-NOMA system that exploits sparse antenna arrays in the transmitter. Our analysis shows that utilizing low-weight and small-sized sparse antennas in the Base Station (BS) leads to better outage probability performance. We also introduce an optimum low complexity Equilibrium Optimization (EO)-based algorithm to further improve the outage probability. The simulation and analysis results show that the systems equipped with sparse antenna arrays making use of optimum beamforming vectors outperform the conventional systems with uniform linear arrays in terms of outage probability and sum rates.

Cooperative Non-Orthogonal Multiple Access Transmission Through Full-Duplex and Half-Duplex Relays

We investigate the beamforming for cooperative non-orthogonal multiple access (NOMA) transmission through a decode-and-forward relay either with full-duplex (FD) mode or with half-duplex (HD) mode. The beamforming vectors at the source and at the relay are optimized to maximize the end-to-end sum rates of the NOMA transmission. The optimal beamforming for the second-hop of the NOMA transmission is present, from which the beamforming algorithms for the two relay modes are derived. For the FD case, the removal of self interference from the feedback loop is important and a two dimensional (2-D) search algorithm based on semi definite relaxation (SDR) is provided, where the 2-D search range is narrowed down as the algorithm iterates. For the HD mode, no iteration is necessary and only one implementation of SDR is required since the SI suppression is not needed. Simulation results show the performance advantage of the proposed FD mode system over that of HD mode in various parameter settings. This justifies the cost and complex hardware circuitry of FD mode.

Information and sensing beamforming optimization for multi-user multi-target MIMO ISAC systems

Integrated sensing and communication (ISAC) has been envisioned as a key enabler in the next-generation wireless networks. In this paper, we consider the joint information and sensing beamforming design in a multi-user and multi-target multi-input multi-output ISAC system, where a transmit BS and a sensing BS collaborate to sense targets, and the transmit BS sends information streams to communication users at the same time. To optimize the sensing performance and guarantee the communication throughput, we formulate a joint beamforming design problem to minimize the trace of the weighted Cramer–Rao bound of target parameters subject to the sum-rate constraint. The problem is challenging to solve due to the intricate non-convex objective function and constraints. We firstly exploit the weighted mean square error minimization (WMMSE) and semidefinite relaxation (SDR) techniques to devise a WMMSE–SDR algorithm that can achieve a KKT point of the problem. The SDR can be shown to be tight for a subproblem in the WMMSE–SDR algorithm, which implies zero duality for the subproblem. Based on this property and fractional programming techniques, we further reformulate the beamforming problem as a min–max form with simple constraints which then can be efficiently solved by first-order min–max optimization algorithms. Finally, the proposed algorithms are evaluated extensively in simulations. Numerical results show that both proposed algorithms can achieve promising performance in sensing and communication, and the low-complexity algorithm has a significantly reduced computation time.

Statistical Beamforming for Multi-Set Space–Time Shift-Keying-Based Full-Duplex Millimeter Wave Communications

Full-duplex (FD) communication has been shown to provide an increased achievable rate, while millimeter wave (mmWave) communications benefit from a large available bandwidth that further improves the achievable rate. On the other hand, the concept of multi-set space-time shift keying (MS-STSK) has been proposed to provide a flexible design trade-off between throughput and performance. Hence, in this work, we consider the design of an FD-aided MS-STSK transceiver for millimeter wave communications. However, a major challenge is that channel reciprocity is not valid in mmWave communications due to shorter channel coherence time. Thus, the uplink (UL) pilots cannot be utilized to estimate the downlink (DL) channel. To overcome this challenge, we propose a beamforming technique based on channel statistics without assuming channel reciprocity. For this purpose, a closed-form expression for the outage probability of the system is derived by employing the characterization of the ratio of the Indefinite Quadratic Form (IQF). The derived analytical expression is then utilized to design optimum beamforming weights using the Sequential Quadratic Programming (SQP)-based heuristic method. Moreover, an Iterative Statistical Method (ISM) of joint transmit and receive beamforming algorithm is also developed by utilizing Principle Eigenvector (PE) and Generalized Rayleigh Quotient (G-RQ) optimization techniques. Finally, we verify our simulation results with the theoretical analysis.

Energy-efficient beamforming optimization for MISO communication based on reconfigurable intelligent surface

Reconfigurable intelligent surface (RIS), a planar metasurface consisting of a large number of low-cost reflecting elements, has received much attention due to its ability to improve both the spectrum and energy efficiency (EE) by reconfiguring the wireless propagation environment. In this paper, we propose a base station (BS) beamforming and RIS phase shift optimization technique that maximizes the EE of a RIS-aided multiple-input–single-output system. In particular, considering the system circuits’ energy consumption, an EE maximization problem is formulated by jointly optimizing the active beamforming at the BS and the passive beamforming at the RIS, under the constraints of each user’ rate requirement, the BS’s maximal transmit power budget and unit-modulus constraint of the RIS phase shifts. Due to the coupling of optimization variables, this problem is a complex non-convex optimization problem, and it is challenging to solve it directly. To overcome this obstacle, we divide the problem into active and passive beamforming optimization subproblems. For the first subproblem, the active beamforming is given by the maximum ratio transmission optimal strategy. For the second subproblem, the optimal phase shift matrix at the RIS is obtained by exploiting sine cosine algorithm (SCA). Moreover, for this case where each reflection element’s working state is controlled by a circuit switch, each reflection element’s switch value is optimized with the aid of particle swarm optimization algorithm. Finally, numerical results verify the effectiveness of our proposed algorithm compared to other algorithms.

A Bipartite Graph Neural Network Approach for Scalable Beamforming Optimization

Deep learning (DL) techniques have been intensively studied for the optimization of multi-user multiple-input single-output (MU-MISO) downlink systems owing to the capability of handling nonconvex formulations. However, the fixed computation structure of existing deep neural networks (DNNs) lacks flexibility with respect to the system size, i.e., the number of antennas or users. This paper develops a bipartite graph neural network (BGNN) framework, a scalable DL solution designed for multi-antenna beamforming optimization. The MU-MISO system is first characterized by a bipartite graph where two disjoint vertex sets, each of which consists of transmit antennas and users, are connected via pairwise edges. These vertex interconnection states are modeled by channel fading coefficients. Thus, a generic beamforming optimization process is interpreted as a computation task over a weighted bipartite graph. This approach partitions the beamforming optimization procedure into multiple suboperations dedicated to individual antenna vertices and user vertices. Separated vertex operations lead to scalable beamforming calculations that are invariant to the system size. The vertex operations are realized by a group of DNN modules that collectively form the BGNN architecture. Identical DNNs are reused at all antennas and users so that the resultant learning structure becomes flexible to the network size. Component DNNs of the BGNN are trained jointly over numerous MU-MISO configurations with randomly varying network sizes. As a result, the trained BGNN can be universally applied to arbitrary MU-MISO systems. Numerical results validate the advantages of the BGNN framework over conventional methods.

A Novel Model-Assisted Decentralized Multi-Agent Reinforcement Learning for Joint Optimization of Hybrid Beamforming in Massive MIMO mmWave Systems

To meet the explosive increasing demands for high data rates, hybrid beamforming has become a promising paradigm for massive MIMO millimeter wave (mmWave) systems. In this paper, we study the joint optimization of hybrid beamforming for maximizing the achievable sum rate in networked dynamic massive MIMO mmWave systems. To address this problem, we propose a novel Model-Assisted Decentralized Multi-Agent Reinforcement Learning (MAD-MARL) algorithm, which incorporates the following three designs: 1) a model-based prediction approach, which can improve the policy learning speed greatly and also predict each agent's potential future so as to alleviate the impact of delayed information sharing in a networked system, 2) an attentional prediction sharing approach, which is to effectively reduce the non-stationarity of the environment by combining the proposed model-based prediction and self-attention strategy for reaching global consensus and cooperative inter-agent coordination in a distributed manner, and 3) a decentralized model-free learning approach, which trains the agents with the assistance of model-based predictions. Extensive simulations are conducted and the numerical results demonstrate that MAD-MARL can significantly increase the learning speed and also greatly improve the overall performance compared with existing work.

Robust Joint Beamforming Optimization for RISs-Empowered Cell-Free Networks

Reconfigurable intelligent surfaces (RISs) have emerged as a promising economical solution to implement cell-free networks. In this paper, the joint active and passive beamforming optimization of access points (APs) and RISs for the RISs-empowered cell-free network in the presence of channel state information (CSI) estimation errors is investigated. By taking the CSI estimation errors into account, we start with deriving the expression of a tight lower bound on the exact sum-rate, which is taken as the optimization criteria. Then, a robust joint beamforming optimization algorithm is proposed to obtain the highest sum-rate by using the lower bound, so as to obtain the best result out of the worst-case. In addition, a counter-intuitive but interesting result can be concluded via rigorous mathematical derivations that CSI estimation errors always impact the optimization of active transmitting beamforming matrices of APs, but surprisingly have no impact on the optimization of passive reflecting beamforming matrices of RISs when the covariance matrices of CSI estimation errors seen from two sides of each channel are proportional to an identity matrix. Simulation results demonstrate that RISs can considerably improve the sum-rate of the conventional cell-free network, and confirm the resilience of the proposed algorithm against CSI uncertainty.

Joint Optimization of Transmit Beamforming and Base Station Cache Allocation in Multi-Cell C-RAN

This paper studies a downlink cloud radio access network (C-RAN) consisting of a centralized processor (CP) and multiple cells each one of which has one cache-enabled base station (BS) connected to the CP through wireless backhaul links. In such a network, we aim to determine sizes of the cache allocated to the BSs such that the long-term delivery time of the available files is minimized. Considering the two-stage nature of this problem, we formulate a beamforming optimization problem and a cache allocation problem. The purpose of the first one is to deliver un-cached portions of files to the BSs in the shortest possible time during the beamforming stage. The second problem aims to minimize long-term expectation of delivery time through optimal cache allocation during the cache allocation stage. We rigorously prove that the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">time-varying beamformers</i> can be assumed to be piece-wise constant functions of time. Based on this finding, the beamforming optimization problem does not appear to be amenable to a computationally efficient solution. Hence, we resort to the zero-forcing (ZF) beamforming approach to tackle the beamforming optimization problem. Using the results of the beamforming optimization problem, we prove that the cache allocation problem is a convex optimization problem; hence it can be solved by any convex optimization solvers. Simulation results show that the loss of optimality due to adopting ZF beamforming is negligible. Moreover, the superiority of our proposed cache allocation scheme over several other heuristic schemes including proportional cache size allocation is shown.