Beamforming Design Research Articles

Low-complexity beamforming design for full-duplex relay-assisted cooperative NOMA

Low-complexity beamforming design for full-duplex relay-assisted cooperative NOMA

Spatial Multiplexing and Hybrid Beamforming Design For 5G Wireless System

Spatial Multiplexing and Hybrid Beamforming Design For 5G Wireless System

Relative Entropy-Based Constant-Envelope Beamforming for Target Detection in Large-Scale MIMO Radar With Low-Resoultion ADCs

Hybrid digital/analog architecture and lowresolution analog-to-digital/digital-to-analog converters (ADCs /DACs) are two low-cost implementations for large-scale millimeter wave (mmWave) systems. In this paper, we investigate the problem of constant-envelope transmit beamforming for large-scale multiple-input multiple-output (MIMO) radar system, where the transmit array adopts a hybrid digital/analog architecture with a small number of RF chains and the receive array adopts a fully digital architecture with low-resolution ADCs. We derive the relative entropy between the probability density functions associated with the two test hypotheses under low-resolution ADCs. We formulate our optimization problem by maximizing the relative entropy, subject to the constant envelope and orthogonality constraints. To suboptimally solve the resultant problem, a two-stage framework is developed. In the first stage, we optimize the transmit power at the directions of the target and clutter. In the second stage, an efficient iterative algorithm based on majorization-minimization is presented to obtain the constant-envelope beamformer according to the attained transmit power. Specifically, we apply a quadratic function as the minorizer, leading to a low-complexity solution at each iteration. In addition, to further facilitate low-cost implementation of the constant-envelope beamformer, we consider the problem of one-bit beamforming design and propose an efficient iterative method based on the Nesterov-like gradient method to solve it. Numerical simulations are provided to demonstrate the effectiveness of the proposed schemes.

Beyond Diagonal Reconfigurable Intelligent Surfaces: A Multi-Sector Mode Enabling Highly Directional Full-Space Wireless Coverage

Reconfigurable intelligent surface (RIS) has gained much traction due to its potential to manipulate the propagation environment via nearly-passive reconfigurable elements. In our previous work, we have analyzed and proposed a beyond diagonal RIS (BD-RIS) model, which is not limited to traditional diagonal phase shift matrices, to unify different RIS modes/architectures. In this paper, we create a new branch of BD-RIS supporting a multi-sector mode. A multi-sector BD-RIS is modeled as multiple antennas connected to a multi-port group-connected reconfigurable impedance network. More specifically, antennas are divided into <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">L</i> ( <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">L</i> ≥ 2) sectors and arranged as a polygon prism with each sector covering 1/ <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">L</i> space. Different from the recently introduced concept of intelligent omni-surface (or simultaneously transmitting and reflecting RIS), the multi-sector BD-RIS not only achieves a full-space coverage, but also has significant performance gains thanks to the highly directional beam of each sector. We derive the constraint of the multi-sector BD-RIS and the corresponding channel model taking into account the relationship between antenna beamwidth and gain. With the proposed model, we first derive the scaling law of the received signal power for a multi-sector BD-RIS-assisted single-user system. We then propose efficient beamforming design algorithms to maximize the sum-rate of the multi-sector BD-RIS-assisted multiuser system. Simulation results verify the effectiveness of the proposed design and demonstrate the performance enhancement of the proposed multi-sector BD-RIS.

Robust Beamforming Design for RIS-Aided Cell-Free Systems With CSI Uncertainties and Capacity-Limited Backhaul

In this paper, we consider the robust beamforming design in a reconfigurable intelligent surface (RIS)-aided cell-free (CF) system considering the channel state information (CSI) uncertainties of both the direct channels and cascaded channels at the transmitter with capacity-limited backhaul. We jointly optimize the precoding at the access points (APs) and the phase shifts at multiple RISs to maximize the worst-case sum rate of the CF system subject to the constraints of maximum transmit power of APs, unit-modulus phase shifts, limited backhaul capacity, and bounded CSI errors. By applying a series of transformations, the non-smoothness and semi-infinite constraints are tackled in a low-complexity manner that facilitates the design of an alternating optimization (AO)-based iterative algorithm. The proposed algorithm divides the considered problem into two subproblems. For the RIS phase shifts optimization subproblem, we exploit the penalty convex-concave procedure (P-CCP) to obtain a stationary solution and achieve effective initialization. For precoding optimization subproblem, successive convex approximation (SCA) is adopted with a convergence guarantee to a Karush-Kuhn-Tucker (KKT) solution. Numerical results demonstrate the effectiveness of the proposed robust beamforming design, which achieves superior performance with low complexity. Moreover, the importance of RIS phase shift optimization for robustness and the advantages of distributed RISs in the CF system are further highlighted.

Integrated Sensing, Communication, and Computation Over-the-Air: MIMO Beamforming Design

To support the unprecedented growth of the Internet of Things (IoT) applications, tremendous data need to be collected by the IoT devices and delivered to the server for further computation. By utilizing the same signals for both radar sensing and data transmission, the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">integrated sensing and communication</i> (ISAC) technique enables simultaneous data collection and delivery in the physical layer. By exploiting the analog-wave addition property in a multi-access channel, <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">over-the-air computation</i> (AirComp) has been proposed as a communication approach that also enables function computation. The promising performances of ISAC and AirComp motivate the current work on developing a framework called <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">integrated sensing, communication, and computation over-the-air</i> (ISCCO). Two schemes are designed to support <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">multiple-input-multiple-output</i> (MIMO) ISCCO simultaneously, namely the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">separated and shared</i> schemes. The separated scheme splits antenna array for radar sensing and AirComp, while all the antennas transmit a joint waveform for both radar sensing and AirComp in the shared scheme. The performance of radar sensing is evaluated by the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">mean squared error</i> (MSE) of the estimated target response matrix, while the MSE of the estimated function is adopted as the metric to evaluate the performance of the coupled communication and computation in AirComp. The design challenge of MIMO ISCCO lies in the joint optimization of beamformers at both the IoT devices and the server, which results in a non-convex problem. To solve this problem, an algorithmic solution based on the technique of semidefinite relaxation is proposed. The results reveal that the beamformer at each sensor needs to account for supporting dual-functional signals in the shared scheme, while dedicated beamformers for sensing and AirComp are needed to mitigate the mutual interference between the two functionalities in the separated scheme. The application of ISCCO on target location estimation is further demonstrated via simulation.

Double RIS-Assisted MIMO Systems Over Spatially Correlated Rician Fading Channels and Finite Scatterers

This paper investigates double RIS-assisted MIMO communication systems over Rician fading channels with finite scatterers, spatial correlation, and the existence of a double-scattering link between the transceiver. First, the statistical information is driven in closed form for the aggregated channels, unveiling various influences of the system and environment on the average channel power gains. Next, we study two active and passive beamforming designs corresponding to two objectives. The first problem maximizes channel capacity by jointly optimizing the active precoding and combining matrices at the transceivers and passive beamforming at the double RISs subject to the transmitting power constraint. In order to tackle the inherently non-convex issue, we propose an efficient alternating optimization algorithm (AO) based on the alternating direction method of multipliers (ADMM). The second problem enhances communication reliability by jointly training the encoder and decoder at the transceivers and the phase shifters at the RISs. Each neural network representing a system entity in an end-to-end learning framework is proposed to minimize the symbol error rate of the detected symbols by controlling the transceiver and the RISs’ phase shifts. Numerical results verify our analysis and demonstrate the superior improvements of phase shift designs to boost system performance.

Integrated Sensing and Communication for RIS-Assisted Backscatter Systems

To facilitate the development of Internet of Things (IoT) services, future networks are expected to simultaneously provide sensing functionality and support low-power communications. In this paper, we investigate the system sum rate maximization problem in an integrated sensing and RIS backscatter communication system, where the base station (BS) simultaneously detects backscattered signals from multiple IoT devices and senses targets based on the echo signals. We formulate a joint transmit beamforming, RIS phase shifts and receive beamforming design problem under the Cramér-Rao bound (CRB) constraint for target angle estimation. To solve the non-convex problem, we then propose a fractional programming based alternating optimization algorithm. In particular, the fractional programming technique is firstly employed to transform the formulated problem into a more tractable form, and the exact penalty method and manifold optimization are then utilized to address the CRB constraint and constant-modulus constraint, respectively. Numerical results have shown that the proposed design significantly improves the system sum rate and illustrate the trade-off between the communication and sensing performance.

Beamforming Analysis and Design for Wideband THz Reconfigurable Intelligent Surface Communications

Reconfigurable intelligent surface (RIS)-aided terahertz (THz) communications have been regarded as a promising candidate for future 6G networks because of its ultra-wide bandwidth and ultra-low power consumption. However, there exists the beam split problem, especially when the base station (BS) or RIS owns the large-scale antennas, which may lead to serious array gain loss. Therefore, in this paper, we investigate the beam split and beamforming design problems in the THz RIS communications. Specifically, we first analyze the beam split effect caused by different RIS sizes, shapes and deployments. On this basis, we apply the fully connected time delayer phase shifter hybrid beamforming (FC-TD-PS-HB) architecture at the BS and deploy distributed RISs to cooperatively mitigate the beam split effect. We aim to maximize the achievable sum rate by jointly optimizing the hybrid analog/digital beamforming, time delays at the BS and reflection coefficients at the RISs. To solve the formulated problem, we first design the analog beamforming and time delays based on different RISs’ physical directions, and then it is transformed into an optimization problem by jointly optimizing the digital beamforming and reflection coefficients. Next, we propose an alternatively iterative optimization algorithm to deal with it. Specifically, for given the reflection coefficients, we propose an iterative algorithm based on the minimum mean square error technique to obtain the digital beamforming. After, we apply Lagrangian dual reformulation (LDR) and multidimensional complex quadratic transform (MCQT) methods to transform the original problem to a quadratically constrained quadratic program, which can be solved by alternating direction method of multipliers (ADMM) technique to obtain the reflection coefficients. Finally, the digital beamforming and reflection coefficients are obtained via repeating the above processes until convergence. Simulation results verify that the proposed scheme can effectively alleviate the beam split effect and improve the system capacity.

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.

Wideband Active RISs: Architecture, Modeling, and Beamforming Design

Reconfigurable intelligent surfaces (RISs) have become a candidate for future 6G networks. The concept of active RISs has been recently proposed to overcome the multiplicative fading of RIS aided reflected links. However, due to the frequency-selective channels, the narrowband active RISs suffer from a large performance loss in wideband scenarios. To address this issue, in this letter, we propose wideband active RISs, including their architecture, modeling, and beamforming design. Specifically, the key idea of wideband active RISs is to divide all subcarriers into several groups and the subcarriers in each group are configured by a single amplifying and phase-shift circuit. Based on this architecture, we derive the frequency-domain channel model and noise model of a wideband active RIS aided communication system. Then, we formulate a beamforming design problem for sum-rate maximization, and a joint transmit precoding and reflect beamforming algorithm is proposed to solve the problem. Simulation results verify the significant performance improvement of the proposed wideband RISs in wideband scenarios.

Exploiting Constructive Interference for Backscatter Communication Systems

Backscatter communication (BackCom), one of the core technologies to realize zero-power communication, is expected to be a pivotal paradigm for the next generation of the Internet of Things (IoT). However, the "strong" direct link (DL) interference (DLI) is traditionally assumed to be harmful, and generally drowns out the "weak" backscattered signals accordingly, thus deteriorating the performance of BackCom. In contrast to the previous efforts to eliminate the DLI, in this paper, we exploit the constructive interference (CI), in which the DLI contributes to the backscattered signal. To be specific, our objective is to maximize the received signal power by jointly optimizing the receive beamforming vectors and tag selection factors, which is, however, non-convex and difficult to solve due to constraints on the Kullback-Leibler (KL) divergence. In order to solve this problem, we first decompose the original problem, and then propose two algorithms to solve the sub-problem with beamforming design via a change of variables and semi-definite programming (SDP) and a greedy algorithm to solve the sub-problem with tag selection. In order to gain insight into the CI, we consider a special case with the single-antenna reader to reveal the channel angle between the backscattering link (BL) and the DL, in which the DLI will become constructive. Simulation results show that significant performance gain can always be achieved in the proposed algorithms compared with the traditional algorithms without the DL in terms of the strength of the received signal. The derived constructive channel angle for the BackCom system with the single-antenna reader is also confirmed by simulation results.

Turbo-HB: A Sub-Millisecond Hybrid Beamforming Design for 5G mmWave Systems

Hybrid beamforming (HB) architecture has been widely considered for 5G mmWave systems. It reduces hardware complexity by allowing the number of RF chains to be far fewer than the number of antennas. A major practical challenge for HB is to obtain a beamforming solution in real-time. In 5G NR, new frame structures with short TTIs are employed to support mmWave communications. Under such frame structures, it is necessary to obtain a beamforming solution with a time resolution varying from 1 ms to 125 us -- an extremely stringent time requirement considering the complexity involved in HB. In this paper, we present the design and implementation of Turbo-HB -- a novel beamforming design under the HB architecture that is capable of offering the beamforming matrices in less than 500 us. The key ideas of Turbo-HB include: (i) reducing the complexity of computation-intensive SVD operations by exploiting channel sparsity at mmWave frequencies, and (ii) achieving large-scale parallel computation with minimal memory access. We implement Turbo-HB on an off-the-shelf Nvidia GPU and conduct extensive experiments. Our experimental results demonstrate that Turbo-HB can obtain a beamforming solution in 500 us for up to 100 RBs and 10 MU-MIMO users on each RB while offering competitive throughput performance compared to state-of-the-art (non-real-time) algorithms.

Outage analysis of cognitive inspired NOMA networks in the presence of imperfect SIC, CCI, and non-ID fading channels

This paper analyzes the outage performance of cognitive-inspired non-orthogonal multiple access (NOMA) network under imperfect successive interference cancellation (SIC), co-channel interference (CCI), and non-identical distributed fading channels. Firstly, we aim to derive the cumulative distribution function (CDF) for the optimum channel with beamforming design, the selected channel maximization, and the selected channel minimization and the probability density function (PDF) for channel interference in order to facilitate the outage performance analysis. Secondly, we obtain the closed-form expressions of outage probability for the primary and secondary destinations according to two strategies: (1) the primary destination is near secondary transmitter and (2) the primary destination is far from secondary transmitter. Thirdly, to provide some useful insights into system designs, we carry out the asymptotic analysis for the three power setting scenarios. Finally, we validate the derived theoretical analyses using Monte-Carlo method.

Outage-Minimization Coordinated Multi-Point for Millimeter-Wave OFDM With Random Blockages

We consider millimeter-wave (mmWave) orthogonal frequency division multiplexing (OFDM) systems subjected to random propagation path blockages and propose a new Coordinated multi-point (CoMP) transmission scheme that minimizes the outage probability of users with respect to given target data rates. To this end, a stochastic sum-outage-probability minimization problem is formulated for joint beamforming design, data rate allocation, and power allocation over subcarriers. In order to solve this problem efficiently, a block statistic learning approach is introduced using training data generated from <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">a priori</i> knowledge of path blockage probabilities. To initialize the stochastic learning solver, the novel initial beamforming is also proposed based on the upper bound of the original objective function, which improves convergence without tuning hyper-parameters. Numerical results confirm the effectiveness of the proposed block stochastic learning approach in terms of both convergence behavior and outage probability. Furthermore, these results confirm that the proposed approach with only blockage probabilities is comparable to the outage performance of a CoMP sum rate maximization (SRM) transmission scheme with perfect channel state information (CSI) and perfect knowledge of blockages.

Sum Rate Maximization for Active RIS-Aided Uplink Multi-Antenna NOMA Systems

Both reconfigurable intelligent surface (RIS) and non-orthogonal multiple access (NOMA) are treated as promising technologies for future wireless communications. However, the performance gain achieved by the traditional passive RIS-aided NOMA system is limited due to the double-fading effect for the base station (BS)-RIS-user channel. In this letter, a sum rate maximization problem for active RIS-aided uplink multi-antenna NOMA system is studied, in which the reflecting elements (REs) of active RIS can manipulate the phase shifts and amplify the amplitudes of incident signals. To tackle the formulated sum rate maximization problem, the original optimization problem is decomposed into three subproblems, i.e., the equalizer optimization, the power allocation, and the active RIS beamforming design. Simulation results show that the proposed active RIS-aided NOMA system can effectively improve sum rate compared with several benchmark schemes.

Low-Resolution Hybrid Beamforming in Millimeter-Wave Multi-User Systems

A new hybrid amalgam of analog and baseband digital beamforming is conceived for millimeter-wave (mmWave) multi-user networks. The base station is equipped with a large-scale antenna-array, which however relies on a limited number of radio frequency chains for mitigating the severe path-loss of mmWave band transmission. Each user is also equipped with a multi-antenna array. The analog beamformer's weight-resolution is set low for the sake of power efficient implementation. The hybrid beamformer design relies on the novel optimization criterion of directly maximizing the geometric means of users' rates, which is shown to result in fair rate-distributions for the users without imposing a minimum user-rate constraint. Furthermore, new computationally efficient algorithms are developed, which are purely based on closed-form low-complexity expressions. Hence these low-complexity solutions are eminently suitable for large-scale mmWave arrays. Numerical examples are provided for demonstrating their efficiency.

Eigenbeam-space transformation based steerable differential beamforming for linear arrays

Since linear differential arrays with small apertures can obtain high directivity and frequency-independent spatial response, much attention has been paid to the design of differential beamformers steered to the endfire direction. Although some works focus on the design of steerable differential beamformers with linear arrays, the synthesis of steerable frequency-invariant beampatterns by linear arrays still needs to be investigated. In this paper, an eigenbeam-space transformation based steerable differential beamforming is proposed for linear arrays. The major contributions are as follows. (1) For the beamformer steered away from the endfire direction, an interference suppression constraint might be imposed to ensure a valid beampattern in the situation where the interference from the endfire direction is very strong, which is not considered in the state-of-the-art approaches of the literature. (2) The synthesis of steerable differential beamformers is formulated as an optimization problem in the eigenbeam-space domain and the optimization problem is solved in a closed form. By experimentally determining the best pair of integers mt and N′, the proposed hybrid least-squares-error solution obtained in the eigenbeam-space domain has shown some advantages over the null constrained method and the weighted least-squares method implemented in the element-space domain.

Low complexity but near optimal hybrid beamforming design in tera‐hertz communication systems: principles and opportunities

AbstractNext generation communication systems go to tetra‐hertz (THz) frequency bands. In this article, low‐complexity but near‐optimal hybrid beamforming design is investigated in THz by considering its unique channel characteristics and discuss potential research opportunities. Specifically, the THz channel characteristics are explored from its propagation feature, angular orthogonality and bandwidth. The authors clarify the differences between the THz multiple‐input‐multiple‐output (MIMO) and its low‐frequency counterparts (e.g. mmWave MIMO). Low complexity but near‐optimal hybrid beamforming design in THz are summarised in the following typical scenarios, namely the single‐user and multi‐user downlink system, integrated data and energy transfer system and the intelligent reflecting surface aided system. Simulation results demonstrate the near‐optimality of our hybrid beamforming design. Some critical open issues in the THz communication system are discussed for future research interest.