Beamforming Matrix Research Articles

Power Minimization for Massive MIMO Over-the-Air Computation With Two-Timescale Hybrid Beamforming

This letter studies the massive multiple-input multiple-output (MIMO) analog uncoded over-the-air computation (AirComp), which is a promising solution in Internet-of-Things (IoT) networks for fusion centers (FCs) to compute functions of data distributed in a large number of wireless devices (WDs). To avoid the heavy overhead of the perfect real-time channel state information (CSI) estimation, we develop a two-timescale hybrid beamforming (THB) scheme in AirComp. Under this setup, we aim to minimize the transmit power over time, while ensuring a minimum required computation distortion in terms of the mean-squared error (MSE). We propose a constrained stochastic successive convex approximation (CSSCA) based algorithm to solve the formulated stochastic non-convex optimization problem for the THB design. Specifically, the short-timescale receive digital beamforming matrix at the FC is optimized at each time slot based on the real-time effective low-dimensional CSI matrices by a sum-minimization-mean-squared-error (sum-MMSE) receiver, which can better deal with the signal misalignment. By contrast, the long-timescale transmit beamforming matrix at WDs and the receive analog beamforming matrix at the FC are designed based on the available channel statistics and updated in a frame-based manner, where a frame contains a fixed number of time slots. Numerical results show that the proposed THB design algorithm achieves similar transmit power performance as that achieved by the design when the perfect real-time CSI is available.

Intelligent Reflecting Surface-Aided Joint Processing Coordinated Multipoint Transmission

This article investigates intelligent reflecting surface (IRS)-aided multicell wireless networks, where an IRS is deployed to assist the joint processing coordinated multipoint (JP-CoMP) transmission from multiple base stations (BSs) to multiple cell-edge users. By taking into account the fairness among cell-edge users, we aim at maximizing the minimum achievable rate of cell-edge users by jointly optimizing the transmit beamforming at the BSs and the phase shifts at the IRS. As a compromise approach, we transform the non-convex max-min problem into an equivalent form based on the mean-square error method, which facilities the design of an efficient suboptimal iterative algorithm. In addition, we investigate two scenarios, namely the single-user system and the multiuser system. For the former scenario, the optimal transmit beamforming is obtained based on the dual subgradient method, while the phase shift matrix is optimized based on the Majorization-Minimization method. For the latter scenario, the transmit beamforming matrix and phase shift matrix are obtained by the second-order cone programming and semidefinite relaxation techniques, respectively. Numerical results demonstrate the significant performance improvement achieved by deploying an IRS. Furthermore, the proposed JP-CoMP design significantly outperforms the conventional coordinated scheduling/coordinated beamforming coordinated multipoint (CS/CB-CoMP) design in terms of max-min rate.

Min-SINR-Maximizing Wireless-Powered AF Relay for Multisource and Multidestination Networks

This study considers a wireless-powered relay assisting multisource multidestination (MSMD) communication networks. Specifically, a beamforming and power-allocation scheme for the relay node is proposed, where a multiple-input multiple-output amplify-and-forward relay node that operates with harvested energy mediates the communication between MSMD pairs. The joint optimization of the relay beamforming matrix and of the power-splitting ratio design for the purpose of maximizing the minimum signal-to-interference-plus-noise ratios (SINRs) is challenging owing to its nonconvexity. We therefore propose an efficient algorithm for finding the optimal solution. In addition, to reduce computational complexity, a zero-forcing beamforming-based suboptimal relay design method is also presented. Simulation results show the effectiveness of the proposed schemes in terms of both SINR and sum-rate performances.

Secure Hybrid A/D Beamforming for Hardware-Efficient Large-Scale Multiple-Antenna SWIPT Systems

In this work, we investigate the problem of secure communications in a downlink large-scale multi-antenna assisted simultaneous wireless information and power transfer (SWIPT) system, where a base station (BS) transmits signals to serve a number of information decoding (ID) and energy harvesting (EH) users. Considering that the EH users can potentially eavesdrop the ID users' confidential information, we study the robust joint design of the hybrid analog-digital (A/D) beamforming (BF) matrices and of the artificial redundant signal (ARS) covariance matrix at the BS, where the aim is to maximize the worst-case sum secrecy rate for the ID users under a transmit power constraint, a nonlinear EH constraint and a unit-modulus constraint on the entries of the analog BF matrix. The corresponding optimization problem is very challenging due to the nonlinear and nonconvex objective function and constraints. Using innovative optimization techniques, we first transform the original problem into an equivalent but more tractable form, and then develop a novel joint iterative algorithm based on the penalty-concave-convex procedure (CCCP) for solving the resultant problem. We show that the proposed penalty-CCCP based algorithm for ARS-aided robust joint hybrid BF design converges to a Karush-Kuhn-Tucker solution of the original problem, and also analyze its computational complexity. Our simulation results verify that the resultant robust joint hybrid BF design algorithm relying on ARS significantly outperforms the conventional hybrid BF benchmark algorithms and efficiently achieves the performance of the fully-digital BF with reduced number of radio frequency chains and energy consumption.

Large-Scale Beamforming for Massive MIMO via Randomized Sketching

Massive MIMO system yields significant improvements in spectral and energy efficiency for future wireless communication systems. The regularized zero-forcing (RZF) beamforming is able to provide good performance with the capability of achieving numerical stability and robustness to the channel uncertainty. However, in massive MIMO systems, the matrix inversion operation in RZF beamforming becomes computationally expensive. To address this computational issue, we shall propose a novel randomized sketching based RZF beamforming approach with low computational complexity. This is achieved by solving a linear system via randomized sketching based on the preconditioned Richard iteration, which guarantees high quality approximations to the optimal solution. We theoretically prove that the sequence of approximations obtained iteratively converges to the exact RZF beamforming matrix linearly fast as the number of iterations increases. Also, it turns out that the system sum-rate for such sequence of approximations converges to the exact one at a linear convergence rate. Our simulation results verify our theoretical findings.

Sum-Rate Optimization Constrained by Consumed Power for Multi- Antenna Non-Regenerative Relay Network

Background & Objective: This paper considers a multi-pair wireless network, which communicates peer-to-peer using some multi-antenna amplify-and-forward relays. Maximizing the throughput supposing that the total relay nodes’ power consumption is constrained, is the main objective of this investigation. We prove that finding the beamforming matrix is not a convex problem. Methods: Therefore, by using a semidefinite relaxation technique we find a semidefinite programming problem. Moreover, we propose a novel algorithm for maximizing the total signal to the total leakage ratio. Numerical analyses show the effectiveness of the proposed algorithm which offers higher throughput compared to the existing total leakage minimization algorithm, with much less complexity. Results and Conclusion: Furthermore, the effect of different parameters such as, the number of relays, the number of antennas in each relay, the number of transmitter/receiver pairs and uplink and downlink channel gains are investigated.

Joint Power Allocation and Relay Beamforming Optimization for Weighted Sum-Rate Maximization in NOMA AF Relay System

This letter introduces a novel joint power-allocation (PA) and relay beamforming optimization (JPBO) algorithm for non-orthogonal multiple-access (NOMA) amplify-and-forward (AF) relay systems to achieve the maximum weighted sum-rate (WSR). In our proposed new framework, the WSR maximization problem is transformed into a tractable weighted-sum minimum mean-square-error (WSMMSE) problem. Then, the PA and the relay beamforming-matrix (BM) are alternately optimized by use of successive convex approximation (SCA) and Lagrange-multiplier (LM) algorithm. Simulation results demonstrate that our proposed new algorithm can significantly improve the WSR with a faster convergence than the existing method.

Energy Efficient Hybrid Beamforming for Multi-User Millimeter Wave Communication With Low-Resolution A/D at Transceivers

Millimeter wave (mmWave) multiple-input multiple-output (MIMO) communication systems with a large number of antennas are power hungry when using conventional high-resolution analog-to-digital/digital-to-analog converters (A/Ds). To reduce the power consumption of mmWave MIMO systems, existing studies have considered hybrid structures with a reduced number of high-resolution or low-resolution A/Ds at either the transmitter or the receiver side. In this paper, we propose and investigate a multi-user hybrid architecture with low-resolution A/Ds equipped at both the transmitter and the receivers. To mitigate the impact of utilizing low-resolution A/Ds at the transceivers, we propose a novel data transmission scheme, which exploits a weighted phased-array to synthesize the beamforming matrix in the analog domain so as to mitigate inter-user interference. Under the scheme proposed, we derive the achievable rate and the energy efficiency to establish guidelines on the optimal resolution choice of A/Ds for hybrid mmWave systems. For a typical total transmit power at the BS, e.g., 30 dBm, the proposed scheme with 5~6-bit A/Ds can significantly improve the energy efficiency by as much as 100% over that of the conventional hybrid MIMO architecture with high-resolution A/Ds (10-bit A/Ds), without significant degradation in data rate performance.

Power- and time-optimized MMSE-based joint beam-forming with relay selection for future generation MIMO networks using Modified Cuckoo-Search Optimization algorithm

Multiple Input Multiple Output (MIMO) networks operating in millimeter wave frequency band bring promising solutions for the increased demand of future generation networks in terms of data rate, signal quality, power optimization and computational complexity. A joint beam-forming (JBF) system working concurrently on source–relay–destination nodes leads to faithful delivery of signals by mitigating the effect of interferences. The traditional JBF designs in MIMO networks yield power wastage due to undesirable participation of intermediate relay nodes for message forwarding. The computational delay in beam-forming (BF) matrix update is tedious in traditional systems. This paper proposes a novel design of power-optimized JBF that facilitates optimum relay selection for solving power wastage issues. The selected relays co-operate in BF with the power constraint, and all other relays are powered down and enter into sleeping mode. Modified Cuckoo-Search Optimization (MCSO) algorithm is used for relay selection and minimum mean square error algorithm is used for BF matrix calculation. The proposed JBF is able to maximize Achievable Sum Rate (ASR) for optimum value of transmission power. The maximum power efficiency is achieved for distant communication with the aid of selected relays contributing to maximizing the ASR value. The proposed work minimizes the sum of mean square error and concurrently computes optimum time slot for BF matrix update, and hence computational delay is reduced. Thus a hybrid optimization for power and time in JBF design is achieved with relay selection and it can be widely used in future generation networks for high-quality and interference-free communication.

Secure beamforming design of SWIPT relay network with multiple users and eavesdroppers

This paper studies the secure beamforming design for simultaneous wireless information and power transfer (SWIPT) in a amplify-and-forward (AF) relay networks with multiple users and eavesdroppers. Each user node adopts the power splitting (PS) scheme to decode information and harvest energy simultaneously. Our objective is to minimize the total relay transmit power under the constraints of secure transmission rate and energy harvesting requirements by jointly optimizing the beamforming matrix, artificial noise covariance matrix and PS ratios. For this non-convex problem, we propose a two-stage optimization approach to convert the original problem into two sub-problems. The first subproblem uses semidefinite relaxation (SDR) technique to transform the original problem into a convex problem, and then finds the optimal solution of the second subproblem through k-dimensional exhaustive search algorithm. Furthermore, we also propose a low complexity suboptimal solution scheme based on particle swarm optimization (PSO) algorithm. Simulation results show that the proposed scheme saves transmitting power and achieves better performance than other schemes.

Low complexity robust recursive beamforming for two‐way full duplex relay network

In this study, a two-way full-duplex amplify-and-forward relay network is considered in which two multi-antenna fullduplex user nodes manage to exchange their information via a full-duplex multi-antenna relay. The users and relay can concurrently transmit their symbols in all time slots in the same frequency band, which leads to self-interference (SI) at all nodes. The joint beamforming algorithm is used in which the relay and users beamforming matrices are updated in each time slot to suppress the SI. This algorithm needs the channel state information (CSI) of all previous time slots, so the complexity increases as time lapses. To decrease the complexity, an algorithm is proposed in which the beamforming matrix is computed recursively. Moreover, the channel estimation error is considered when the relay and users have partial CSI. Thus, a robust algorithm, i.e. an algorithm that takes the estimation error into account is proposed to decrease the effect of estimation error. The proposed algorithm has been evaluated in terms of mean square error, achievable sum rate and BER for various values of the estimation error variances and compared with the non-robust algorithm. The results show that the superiority of the recursive robust algorithm in terms of SNR and complexity.

Reconfigurable Intelligent Surface Assisted Multiuser MISO Systems Exploiting Deep Reinforcement Learning

Recently, the reconfigurable intelligent surface (RIS), benefited from the breakthrough on the fabrication of programmable meta-material, has been speculated as one of the key enabling technologies for the future six generation (6G) wireless communication systems scaled up beyond massive multiple input multiple output (Massive-MIMO) technology to achieve smart radio environments. Employed as reflecting arrays, RIS is able to assist MIMO transmissions without the need of radio frequency chains resulting in considerable reduction in power consumption. In this paper, we investigate the joint design of transmit beamforming matrix at the base station and the phase shift matrix at the RIS, by leveraging recent advances in deep reinforcement learning (DRL). We first develop a DRL based algorithm, in which the joint design is obtained through trial-and-error interactions with the environment by observing predefined rewards, in the context of continuous state and action. Unlike the most reported works utilizing the alternating optimization techniques to alternatively obtain the transmit beamforming and phase shifts, the proposed DRL based algorithm obtains the joint design simultaneously as the output of the DRL neural network. Simulation results show that the proposed algorithm is not only able to learn from the environment and gradually improve its behavior, but also obtains the comparable performance compared with two state-of-the-art benchmarks. It is also observed that, appropriate neural network parameter settings will improve significantly the performance and convergence rate of the proposed algorithm.

Joint beamforming and time switching designs for energy-constrained cognitive two-way relay networks

In this paper, we investigate a joint beamforming and time switching (TS) design for an energy-constrained cognitive two-way relay (TWR) network. In the network, the energy-constrained secondary user (SU) relay employs TS protocol to harvest energy from the signals sent by the circuit-powered primary user (PU) transmitter, and then exploits the harvested energy to perform information forwarding. Our aim is to maximize the sum rate of SUs under the constraints of the data rate of PU, the energy harvesting and the transmit power of the SU relay. To determine the beamforming matrix and TS ratio, we decouple the original non-convex problem into two subproblems which can be solved by semidefinite relaxation and successive convex optimization methods. Furthermore, we derive closed form expressions of the optimal solutions for each subproblem, which facilitates the design of a suboptimal iterative algorithm to handle the original sum rate maximization problem. Simulation results are presented to illustrate the effectiveness and superior performance of the proposed joint design against other conventional schemes in the literature.

Beam Tracking Particle Filter for Hybrid Beamforming and Precoding Systems

Because millimeter wave (mmWave) systems can span notably wide spectral bands, mmWave systems are expected to dominate fifth-generation (5G) communication systems. Due to the short wave-length of mmWave radiation, multiple-input multiple-output (MIMO) systems can use massive antennas and precoding technology to overcome signal attenuation in mmWave channels. However, the cost and power consumption of radio frequency (RF) chains would increase substantially with the number of antennas. Hence, hybrid beamforming was proposed to reduce the number of RF chains in massive MIMO systems. Hybrid beamforming involves RF beamforming matrix construction and baseband precoding matrix derivation. This study focused on the design and implementation of an algorithm for the RF beamforming matrix construction for mobile environments. Accordingly, this study presents a mixture particle filter that exploits the temporal continuity of beam clusters in a mobile mmWave channel to reduce the computational complexity of RF beamforming matrix construction. Moreover, this beam-tracking particle filter is based on parallel processing architecture to support the tracking of multiple beam clusters in the mmWave channel. Finally, the beam-tracking particle filter was implemented on a field-programmable gate array platform and was verified in a hybrid beamforming system for mmWave MIMO systems. The particle filter processor achieved a maximal throughput of 9.198k matrices/s with a clock rate of 192 MHz, which could support a speed of up to 88.5 km/h for mobile users.

Optimization of secure wireless communications for IoT networks in the presence of eavesdroppers

The problem motivates this paper is that securing the critical data of 5G based wireless IoT network is of significant importance. Wireless 5G IoT systems consist of a large number of devices (low-cost legitimate users), which are of low complexity and under strict energy constraints. Physical layer security (PLS) schemes, along with energy harvesting, have emerged as a potential candidate that provides an effective solution to address this issue. During the data collection process of IoT, PHY security techniques can exploit the characteristics of the wireless channel to ensure secure communication. This paper focuses on optimizing the secrecy rate for simultaneous wireless information and power transfer (SWIPT) IoT system, considering that the malicious eavesdroppers can intercept the data. In particular, the main aim is to optimize the secrecy rate of the system under signal to interference noise ratio (SINR), energy harvesting (EH), and total transmits power constraints. We model our design as an optimization problem that advocates the use of additional noise to ensure secure communication and guarantees efficient wireless energy transfer. The primary problem is non-convex due to complex objective functions in terms of transmit beamforming matrix and power splitting ratios. We have considered both the perfect channel state information (CSI) and the imperfect CSI scenarios. To circumvent the non-convexity of the primary problem in perfect CSI case, we proposed a solution based on the concave-convex procedure (CCCP) iterative algorithm, which results in a maximum local solution for the secrecy rate. In the imperfect CSI scenario, we facilitate the use of S-procedure and present a solution based on the iterative successive convex approximation (SCA) approach. Simulation results present the validations of the proposed algorithms. The results provide an insightful view that the proposed iterative method based on the CCCP algorithm achieves higher secrecy rates and lower computational complexity in comparison to the other algorithms.

Research on Leakage Location of Spacecraft in Orbit Based on Frequency Weighting Matrix Beamforming Algorithm by Lamb Waves

Clashes between space debris and spacecraft in orbit may cause air leakages, which pose a substantial danger to the crew and the spacecraft. Lamb wave dispersion in spacecraft structures and the randomness of leak holes are the difficulties in leak location. To solve these problems, a frequency weighting matrix beamforming algorithm is proposed in this paper. The elastic Lamb waves that are caused by leakages are acquired by an ‘L’ shaped sensor array consisting of eight acoustic emission sensors. The angle of a leak can be obtained through the superposition of different time delays, and the intersection of two angles can be used to find the location of the leak. Traditional beamforming is improved by matching the wave speeds in different frequency bands and weightings according to the energy distribution. Narrowband filtering is used to delay overlay different signal speeds with different frequency bands via a dispersion curve. The weighting method is used to compensate the frequency band response of different leak holes. The detailed location algorithm process is introduced and verified by experiments. For 1.5 and 2 mm leak holes, location direction accuracies of 1.33° and 1.93° for one sensor array were obtained, respectively.

Robust Directional Modulation Design for Secrecy Rate Maximization in Multiuser Networks

Based on directional modulation (DM), robust beamforming matrix design for sum secrecy rate maximization is investigated in this article in multiuser systems. First, in case of random estimation error of direction angles toward eavesdroppers, a Von Mises distribution-sum secrecy rate maximization (VMD-SSRM) method is proposed to maximize the sum secrecy rate. Semidefinite relaxation and first-order approximation based on Taylor expansion are employed to solve the optimization problem in VMD-SSRM. Then in order to optimize the sum secrecy rate in the case of the worst estimation errors of direction angles, a maximum angle estimation error-SSRM (MAEE-SSRM) method is proposed. The optimization problem is constructed based on the upper and lower bounds of the estimated eavesdropping channel related coefficient and then solved by the change of the variable. Simulation results show that our two proposed methods have better sum secrecy rates than the state-of-the-art methods. Furthermore, when the estimation error of direction angle toward each eavesdropper is random but within a certain range, the secrecy performance of our VMD-SSRM method is better than that of our MAEE-SSRM method. On contrary, when the direction angle estimation error reaches its maximum, our MAEE-SSRM method performs better.

Ultra‐compact 3 × 3 Nolen matrix beamforming network

A novel compact 3 × 3 Nolen matrix beamforming network is proposed in this study. Unlike the Butler matrix and Blass matrix, in this design, the proposed feeding network only requires couplers and phase shifters and removes crossovers and load terminations. To minimise the size, the authors’ proposed novel Nolen matrix is realised by lumped-element couplers. First, the design theory for 3 × 3 Nolen matrix is derived, and the associated pyramidal layout consisting of three couplers with two coupling ratios and three-phase shifters is proposed. Based on the determined topology, the S-parameters of the proposed feeding network and desired coupling ratios are derived, and it is found that the phase differences among the output ports are dependent on the characteristics of the couplers. Then, each coupler is realised by using lumped-elements (including inductors and capacitors) in the proposed topologies, where the values of the elements are obtained by analysing the ABCD-matrix of the branch lines in the couplers. To verify the proposed concept, an experimental prototype working at 1 GHz is fabricated and tested. The simulation and measurement results agree well with each other, and an ultra-compact size 0.17λ × 0.06λ is implemented to achieve more than 90% size reduction comparing with the previous designs.

Joint Beamforming with Speed Sensitive Relay Selection for Future Wireless Generation MIMO Networks

Future wireless generation networks using MIMO systems have wide demand on transmission speed, coverage range and signal quality. The traditional joint beamforming (JBF) approaches are carried out concurrently at relay and receiver nodes. The existing beamforming (BF) architectures are computationally complex and the communication system lacks an efficient relay selection scheme. The problem becomes severe for dynamic and fast moving communication nodes. This paper proposes a novel JBF architecture with relay selection to mitigate the effects of time delay in BF matrix update in a dynamic mobile environment. Relay switching is carried out based on sensing the speed of mobile nodes. Switching phase is bypassed and BF continues with the selected relay if the mobile nodes are static or mobility is negligible. For dynamic environment, it is necessary to update BF matrix after each time when new set of relays are selected. Minimum Mean Square Error algorithm is used for BF vector calculation and Hybrid Cuckoo Search Optimization algorithm is used for speed sensitive relay selection. The proposed JBF algorithm outperforms well in terms of weighted sum rate and Sum of Mean Square Error along with guaranteed time delay for beam steering. The proposed hybrid optimized solution for speed sensitive relay selection with JBF is best suitable for next generation wireless networks.

Configuration Optimization and Channel Estimation in Hybrid Beamforming mmWave Systems With Channel Support Side Information

Hybrid beamforming (HBF) is a promising technique in millimeter-wave (mmWave) systems with a limited number of radio frequency (RF) chains. Acquiring channel state information is essential for HBF design. Various compressive-sensing-based channel estimation (CE) schemes that exploit the sparse nature of mmWave channels have been proposed. The design of an analog beamforming matrix plays a key role in providing high CE quality with low pilot overhead. In this paper, a novel and flexible HBF architecture called adaptive sum product network (ASPN) is proposed, which can realize more flexible analog beamforming with less hardwares. Based on the ASPN architecture, a novel variational-Bayesian-inference-based compressive CE algorithm is proposed, which can fully exploit the channel support side information (CSSI) at the base station under a general uncertain measurement matrix induced by the off-grid parameters for power leakage elimination. To optimally configure the degrees of freedom in the ASPN according to the CSSI, a dynamic configuration optimization algorithm is proposed by formulating the CE performance metric in terms of the configuration parameters of ASPN. The importance and effectiveness of the flexibility introduced in ASPN HBF architecture, the compressive CE algorithm as well as the configuration algorithm are illustrated by the superb performance of the proposed scheme compared to the representative state-of-the-art techniques through extensive simulation results.