Unit Modulus Constraints Research Articles

Unsupervised Learning-Based Joint Active and Passive Beamforming Design for Reconfigurable Intelligent Surfaces Aided Wireless Networks

This letter consider a reconfigurable intelligent surface (RIS) aided multi-user multiple-input single-output (MISO) downlink system, where transmit beamforming and phase shifts of RIS reflecting elements are jointly designed to maximize system sum rate. However, the unit modulus constraint of RIS phase shifts and coupling between active and passive beamforming make the optimal design a challenging task. Most of prior works adopt iterative optimization algorithms to get suboptimal solutions, which suffer from high computational complexity, hence are not applicable to practical scenarios. Responding to this, this letter proposes a deep learning based approach for joint active and passive beamforming design. Specifically, a two-stage neural network is trained offline in an unsupervised manner, which is then deployed online for real-time prediction. Simulation results indicate that the proposed approach is able to reduce computational complexity significantly with satisfactory performance compared to conventional iterative optimization algorithms.

Hybrid Analog-Digital Precoder Design for Securing Cognitive Millimeter Wave Networks

Millimeter wave (mmWave) communications and cognitive radio technologies constitute key technologies of improving the spectral efficiency of communications. Hence, we conceive a hybrid secure precoder for enhancing the physical layer security of a cognitive mmWave wiretap channel, where a secondary transmitter broadcasts confidential information signals to multiple secondary users under the interference temperature constraint of the primary user (PU). The optimization problem is formulated as jointly optimizing the analog and digital precoder for maximizing the minimum secrecy rate of all the secondary users under practical constraints. In particular, our design satisfies the constraint on the maximum interference power received by multiple PUs, as well as the secondary users’ minimum quality-of-service (Qos), and the unit-modulus constraint on the analog precoder. Due to the non-convexity of the resultant objective function and owing to the coupling between the analog and digital precoder, the optimization problem formulated is nonconvex and nonlinear, hence it is very challenging to solve directly. Hence, we first transform it into a tractable form, and develop a penalty dual decomposition (PDD) based iterative algorithm to locate its Karush-Kuhn-Tucker (KKT) solution. Finally, we generalize the proposed PDD algorithm to a secure hybrid precoder design relying on practical finite-resolution phase shifters and show that the proposed PDD algorithm can be straightforwardly adapted to handle the scenario, where each PU is equipped with multiple antennas and the CSI of multiple eavesdroppers (Eves) is imperfectly known. Our simulation results validate the efficiency of the proposed iterative algorithm.

Energy Efficiency Maximization via Joint Active and Passive Beamforming Design for Multiuser MISO IRS-Aided SWIPT

This letter studies a multiuser multiple-input single-output (MISO) intelligent reflecting surface (IRS)-aided simultaneous wireless information and power transfer (SWIPT) system. Specifically, a multi-antenna base station (BS) transmits data along with energy to a set of users to decode data and harvest energy by adopting the power splitting (PS) simultaneously. The energy efficiency indicator (EEI) is introduced to trade off between data rate and harvested energy, which is maximized by jointly optimizing beamforming vectors at the BS, PS ratio at each user, and phase shifts at the IRS. To solve this non-convex optimization problem, we first adopt the majorization-minimization (MM) approach to construct a concave-convex fractional function which can be handled via the Dinkelbach algorithm and then propose an efficient algorithm for solving two subproblems based on the alternating optimization (AO). For the first subproblem, semi-definite relaxation (SDR), MM approach, and Dinkelbach algorithm are adopted, while for the second sub-problem, a new manifold approach is proposed to handle the unit-modulus constraints due to IRS passive reflection. Simulation results demonstrate the superior performance of our proposed algorithm compared to other baseline schemes.

Intelligent Reflecting Surface Aided MIMO Cognitive Radio Systems

In cognitive radio (CR) systems, the spectrum efficiency (SE) of the secondary users (SUs) is always limited by the interference temperature constraint imposed on the primary users (PUs). Intelligent reflecting surface (IRS) has been recently proposed as a revolutionary technique which can help to enhance the SE of wireless communications. In this paper, we propose to employ an IRS to assist the SUs’ data transmission in the multiple-input multiple-output (MIMO) CR system. By jointly optimizing the transmit precoding (TPC) of the SU transmitter (ST) and the phase shifts of the IRS, we aim to maximize the achievable weighted sum rate (WSR) of SUs subject to the ST's total power, the PU's interference temperature and unit modulus constraints. To solve this complicated optimization problem in which the variables are coupled, the block coordinate descent (BCD) algorithm is introduced to alternately solve the subproblems. For each subproblem, the Lagrange dual or inner approximation method is adopted with a low complexity. Simulation results confirm the benefits of employing IRS in a MIMO CR system. The performance comparisons of the proposed algorithm with several other benchmarks are carried out by evaluating the impacts of various parameters on the WSR.

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.

Joint Design of Reconfigurable Intelligent Surfaces and Transmit Beamforming Under Proper and Improper Gaussian Signaling

This paper considers a network consisting of a multiple antenna array access point serving multiple single antenna downlink users with the assistance of a reconfigurable intelligent surface (RIS). The reflecting coefficients of the RIS can be programmed to ensure that the signals reflected from the RIS elements add coherently at the users. The joint design of these programmable reflecting coefficients and transmit beamforming to maximize the users' worst rate is addressed. Under either proper Gaussian signaling (PGS) or improper Gaussian signaling (IGS), the design poses a very computationally challenging nonconvex problem. Based on their exactly penalized optimization reformulation, which incorporates the computationally intractable unit-modulus constraints on the reflecting coefficients into the optimization objectives, new iterative algorithms of low computational complexity, which converge at least to a locally optimal solution, are developed. The provided simulations show not only the benefit of using the RIS, but also the advantage of IGS over PGS in delivering higher rates to users.

Constant Envelope MIMO-OFDM Precoding for Low Complexity Large-Scale Antenna Array Systems

Herein, we consider constant envelope precoding in a multiple-input multiple-output orthogonal frequency division multiplexing system (CE MIMO-OFDM) for frequency selective channels. In CE precoding the signals for each transmit antenna are designed to have constant amplitude regardless of the channel realization and the information symbols that must be conveyed to the users. This facilitates the use of power-efficient components, such as phase shifters (PS) and nonlinear power amplifiers, which are key for the feasibility of large-scale antenna array systems because of their low cost and power consumption. The CE precoding problem is firstly formulated as a least-squares problem with a unit modulus constraint and solved using an algorithm based on coordinate descent. The large number of optimization variables in the case of the MIMO-OFDM system motivates the search for a more computationally efficient solution. To tackle this, we reformulate the CE precoding design into an unconstrained nonlinear least-squares problem, which is solved efficiently using the Gauss-Newton algorithm. Simulation results underline the efficiency of the proposed solutions and show that they outperform state of the art techniques.

Hybrid Transceiver Optimization for Multi-Hop Communications

Multi-hop communication with the aid of large-scale antenna arrays will play a vital role in future emergence communication systems. In this paper, we investigate amplify-and-forward based and multiple-input multiple-output assisted multi-hop communication, in which all nodes employ hybrid transceivers. Moreover, channel errors are taken into account in our hybrid transceiver design. Based on the matrix-monotonic optimization framework, the optimal structures of the robust hybrid transceivers are derived. By utilizing these optimal structures, the optimizations of analog transceivers and digital transceivers can be separated without loss of optimality. This fact greatly simplifies the joint optimization of analog and digital transceivers. Since the optimization of analog transceivers under unit-modulus constraints is non-convex, a projection type algorithm is proposed for analog transceiver optimization to overcome this difficulty. Based on the derived analog transceivers, the optimal digital transceivers can then be derived using matrix-monotonic optimization. Numeral results obtained demonstrate the performance advantages of the proposed hybrid transceiver designs over other existing solutions.

Robust and Secure Beamforming for Intelligent Reflecting Surface Aided mmWave MISO Systems

In this letter, we investigate the robust and secure beamforming (RSBF) in an intelligent reflecting surface (IRS) aided millimeter wave (mmWave) multiple input single output (MISO) system, where multiple single antenna eavesdroppers (Eves) are arbitrarily distributed nearby the legitimate receiver (Bob). Considering the channel state information (CSI) of cascaded wiretap channels is imperfectly known at the legitimate transmitter (Alice), the RSBF design problems to maximize the worst case of achievable secrecy rate (ASR) are formulated under the total transmission power and unit-modulus constraints. Since the problems are difficult to solve optimally due to their non-convexity and coupled variables, we substitute the wiretap channels by a weighted combination of discrete samples and propose a RSBF scheme based on alternating optimization and semidefinite relaxation (SDR) techniques, for both colluding and noncolluding eavesdropping scenarios. Simulation results show that the proposed RSBF scheme can effectively improve the ASR and also outperforms other benchmark schemes.

Secure Beamforming for Multiple Intelligent Reflecting Surfaces Aided mmWave Systems

In this letter, secure beamforming in a multiple intelligent reflecting surfaces (IRSs)-aided millimeter-wave (mmWave) system is investigated. In this system, the secrecy rate is maximized by controlling the on-off status of each IRS as well as optimizing the phase shift matrix of the IRSs. This problem is posed as a joint optimization problem of transmit beamforming and IRS control, whose goal is to maximize the secrecy rate under the total transmission power and unit-modulus constraints. The problem is difficult to solve optimally due to the nonconvexity of constraint conditions and coupled variables. To deal with this problem, we propose an alternating optimization (AO)-based algorithm based on successive convex approximation (SCA) and manifold optimization (MO) technologies. Numerical simulations show that the proposed AO-based algorithm can effectively improve the secrecy rate and outperforms traditional single IRS-aided scheme.

Analog–Digital Hybrid Transceiver Optimization for Data Aggregation in IoT Networks

Data aggregation is a promising technology in the Internet-of-Things (IoT) network for a wide range of applications, e.g., environmental monitoring, traffic control, and real-time surveillance. In order to meet the high requirement of transmission rate for data aggregation, we investigate the transceiver optimization to improve the spectral efficiency. As a tradeoff between the system complexity and performance, hybrid transceivers are adopted for data aggregation in the IoT network. We first present the optimal structures of digital precoders and unconstrained analog transceivers to maximize the spectral efficiency. Then, we propose two different kinds of iterative algorithms to optimize the analog transceivers under nonconvex unit-modulus constraints. The first algorithm is based on the framework of the alternating direction method of multipliers (ADMM). The second one is the steepest descent (SD) algorithm based on the Riemannian geometry, which has lower computational complexity than the first one. For both algorithms, closed-form solutions are derived in each iteration. Finally, numerical results demonstrate that the performance of the proposed algorithms in the hybrid transceiver design is very close to the fully digital solution but with less hardware complexity and power consumption.

Multicell MIMO Communications Relying on Intelligent Reflecting Surfaces

Intelligent reflecting surfaces (IRSs) constitute a disruptive wireless communication technique capable of creating a controllable propagation environment. In this paper, we propose to invoke an IRS at the cell boundary of multiple cells to assist the downlink transmission to cell-edge users, whilst mitigating the inter-cell interference, which is a crucial issue in multicell communication systems. We aim for maximizing the weighted sum rate (WSR) of all users through jointly optimizing the active precoding matrices at the base stations (BSs) and the phase shifts at the IRS subject to each BS’s power constraint and unit modulus constraint. Both the BSs and the users are equipped with multiple antennas, which enhances the spectral efficiency by exploiting the spatial multiplexing gain. Due to the non-convexity of the problem, we first reformulate it into an equivalent one, which is solved by using the block coordinate descent (BCD) algorithm, where the precoding matrices and phase shifts are alternately optimized. The optimal precoding matrices can be obtained in closed form, when fixing the phase shifts. A pair of efficient algorithms are proposed for solving the phase shift optimization problem, namely the Majorization-Minimization (MM) Algorithm and the Complex Circle Manifold (CCM) Method. Both algorithms are guaranteed to converge to at least locally optimal solutions. We also extend the proposed algorithms to the more general multiple-IRS and network MIMO scenarios. Finally, our simulation results confirm the advantages of introducing IRSs in enhancing the cell-edge user performance.

Robust Joint Hybrid Analog-Digital Transceiver Design for Full-Duplex mmWave Multicell Systems

In this work, we investigate a full-duplex (FD) millimeter wave (mmWave) multicell system, where the BS of each cell receives signals from uplink (UL) users and transmits signals to downlink (DL) users at the same time, over the same frequency band. We maximize the sum rate lower bound of the FD multicell system by jointly optimizing the digital and analog beamforming matrices at the base station (BS) and the transmit power levels of the UL users under total transmit power constraints and unit-modulus constraints (due to the analog beamforming matrices), in the presence of imperfect channel state information (CSI). The problem under study is very challenging due to the highly non-convexity of the objective function and constraints. We transform this problem into an equivalent but more tractable form and propose a novel iterative algorithm based on the penalty dual decomposition (PDD) to solve it. The proposed algorithm is guaranteed to converge to the set of Karush-Kuhn-Tucker (KKT) solutions of the original problem. Moreover, we also extend our proposed algorithm to the structure of subarray. Simulation results validate the effectiveness of the proposed algorithm as compared with conventional nonrobust and half-duplex (HD) algorithms.

Unsupervised Learning for Passive Beamforming

Reconfigurable intelligent surface (RIS) has recently emerged as a promising candidate to improve the energy and spectral efficiency of wireless communication systems. However, the unit modulus constraint on the phase shift of reflecting elements makes the design of optimal passive beamforming solution a challenging issue. The conventional approach is to find a suboptimal solution using the semi-definite relaxation (SDR) technique, yet the resultant suboptimal iterative algorithm usually incurs high complexity, hence is not amenable for real-time implementation. Motivated by this, we propose a deep learning approach for passive beamforming design in RIS-assisted systems. In particular, a customized deep neural network is trained offline using the unsupervised learning mechanism, which is able to make real-time prediction when deployed online. Simulation results show that the proposed approach maintains most of the performance while significantly reduces computation complexity when compared with SDR-based approach.

Intelligent Reflect Surface Aided Secure Transmission in MIMO Channel With SWIPT

This paper considers a multiple-input multiple-output (MIMO) secure simultaneous wireless information and power transfer (SWIPT) system aided by the intelligent reflecting surface (IRS), where the transmitter (T), the information receiver (IR) and energy receiver (ER) are all equipped with multiple antennas. Assuming that the ER may be potential eavesdropper (Eve), we aim to maximize the secrecy rate via jointly designing the precoding matrix, the artificial noise (AN) covariance, and the phase shift matrix, subject to the harvested energy and unit modulus reflect coefficient (RC) constraints. The formulated secrecy rate maximization (SRM) problem is non-convex with multiple coupled variables. To tackle it, an inexact block coordinate descent (IBCD) method is proposed, where the unit modulus constraint is handled by the penalty majorization-minimization (MM) and the complex circle manifold (CCM) methods. Finally, simulation results validate the effectiveness of IRS in enhancing the security.

Secure Wireless Transmission for Intelligent Reflecting Surface-Aided Millimeter-Wave Systems

Due to the broadcast nature of millimeter wave (mmWave) communications, physical layer security has always been a fundamental but challenging concern. Fortunately, the recent advance of intelligent reflecting surface (IRS) introduces another dimension for mmWave secure communications by reconfiguring the transmission environments. In this article, we investigate the physical layer security issue for IRS-aided mmWave communications. Specifically, two scenarios are considered, i.e., with and without the knowledge of the eavesdropper’s channel. When the eavesdropper’s channel is known, under the unit modulus constraints at the IRS and the transmit power constraint at the access point (AP), the secrecy rate is maximized by jointly designing the beamforming vector of the AP and the phase shifts of the IRS. We propose an alternating optimization algorithm for improving the secrecy rate to solve the non-convex optimization problem. In particular, the phase shift matrix of the IRS is firstly optimized based on the manifold optimization algorithm. Under the given phase shift matrix of the IRS, the original problem is transformed into a difference of convex (DC) programming problem. To solve this problem, we use the successive convex approximation (SCA)-based method to transform the original problem into a convex approximation problem, and the transmit beamforming vector is obtained by solving the convex approximation problem. In addition, when the eavesdropper’s channel is unknown, under the transmit power constraint and the minimum user rate constraint, an artificial-noise (AN)-aided scheme is proposed to jam the eavesdropper by maximizing the AN power. Numerical results evaluate that the performance of our proposed schemes is better than that of the conventional scheme in terms of secrecy rate. Moreover, simulations also demonstrate that the secrecy behaviors of the IRS-aided mmWave communication system are superior to the mmWave communications without IRS.

Intelligent Reflecting Surface Aided Multigroup Multicast MISO Communication Systems

Intelligent reflecting surface (IRS) has recently been envisioned to offer unprecedented massive multiple-input multiple-output (MIMO)-like gains by deploying large-scale and low-cost passive reflection elements. By adjusting the reflection coefficients, the IRS can change the phase shifts on the impinging electromagnetic waves so that it can smartly reconfigure the signal propagation environment and enhance the power of the desired received signal or suppress the interference signal. In this paper, we consider downlink multigroup multicast communication systems assisted by an IRS. We aim for maximizing the sum rate of all the multicasting groups by the joint optimization of the precoding matrix at the base station (BS) and the reflection coefficients at the IRS under both the power and unit-modulus constraint. To tackle this non-convex problem, we propose two efficient algorithms under the majorization--minimization (MM) algorithm framework. Specifically, a concave lower bound surrogate objective function of each user's rate has been derived firstly, based on which two sets of variables can be updated alternately by solving two corresponding second-order cone programming (SOCP) problems. Then, in order to reduce the computational complexity, we derive another concave lower bound function of each group's rate for each set of variables at every iteration, and obtain the closed-form solutions under these loose surrogate objective functions. Finally, the simulation results demonstrate the benefits in terms of the spectral and energy efficiency of the introduced IRS and the effectiveness in terms of the convergence and complexity of our proposed algorithms.

Partially-Connected Hybrid Beamforming for Multi-User Massive MIMO Systems

Due to the high power consumption and hardware cost of radio frequency (RF) chains, the conventional fully-digital beamforming will be impractical for large-scale antenna systems (LSAS). To address this issue, hybrid beamforming has been proposed to reduce the number of RF chains. However, the fully-connected structure assumed in most hybrid beamforming schemes is still cost-intensive. Recently, the partially-connected structure employing notably fewer phase shifters has received considerable attention in both academia and industry. But the design of partially-connected hybrid beamforming has not been fully understood, especially in multi-user systems. In this article, we directly address the challenging non-convex non-smooth partially-connected hybrid beamforming design problem with individual signal-to-interference-plus-noise ratio (SINR) constraints and unit-modulus constraints in a multi-user massive multiple-input multiple-output (MIMO) system. An iterative alternating algorithm based on a penalty method is proposed to obtain a stationary point, which inevitably has relatively high computational complexity. Thus, two low-complexity algorithms are then proposed by utilizing matrix approximation. Numerical results demonstrate significant performance gains of the proposed algorithms over existing hybrid beamforming algorithms. Moreover, the proposed low-complexity algorithms can achieve near-optimal performance with dramatically reduced computational complexity.

Majorization-Minimization Aided Hybrid Transceivers for MIMO Interference Channels

The potential of deploying large-scale antenna arrays in future wireless systems has stimulated extensive research on hybrid transceiver designs aiming to approximate the optimal fully-digital schemes with much reduced hardware cost, and signal processing complexity. Generally, this hybrid transceiver structure requires a joint design of analog, and digital processing to enable both beamsteering, and spatial multiplexing gains. In this paper, we develop various weighted mean-square-error minimization (WMMSE) based hybrid transceiver designs for ${K}$ -user multiple-input multiple-output (MIMO) interference systems, which are applicable to both millimeter wave (mmWave) channels, and Rayleigh fading channels. Firstly, a heuristic joint design of hybrid precoder, and combiner using alternating optimization is proposed, in which the majorization-minimization (MM) method is utilized to design the analog precoder, and combiner under unit-modulus constraints. It is demonstrated that this scheme achieves comparable performance to the fully-digital WMMSE solution. To further reduce the computational complexity, a phase projection based two-stage scheme is proposed to decouple the designs of the analog, and digital precoder/combiner. Secondly, inspired by the fully-digital solutions based on the block-diagonalization zero-forcing (BD-ZF), and signal-to-leakage-plus-noise ratio (SLNR) criteria, the low-complexity MM-based BD-ZF, and SLNR hybrid designs are proposed, respectively, for approximating the corresponding fully-digital solutions. Thirdly, the partially-connected hybrid structure conceived for reducing system hardware cost, and power consumption is considered, for which the MM-based alternating optimization algorithm still works. Our numerical results characterize the sum rate performance of all proposed hybrid designs in comparison to the existing benchmarks.

Generalized Framework for Hybrid Analog/Digital Signal Processing in Massive and Ultra-Massive-MIMO Systems

The conventional fully-digital implementation of massive-MIMO systems is not efficient due to the large required number of radio-frequency (RF) chains. To address this issue, hybrid analog/digital (A/D) beamforming was proposed and to date remains a topic of ongoing research. In this paper, we explore the hybrid A/D structure as a general framework for signal processing in massive and ultra-massive-MIMO systems. To exploit the full potential of the analog domain, we first focus on the analog signal processing (ASP) network. We investigate a mathematical representation suitable for any arbitrarily connected feed-forward ASP network comprised of the common RF hardware elements in the context of hybrid A/D systems, i.e., phase-shifter and power-divider/combiner. A novel ASP structure is then proposed which is not bound to the unit modulus constraint, thereby facilitating the hybrid A/D systems design. We then study MIMO transmitter and receiver designs to exploit the full potential of digital processing as well. It is shown that replacing the linear transformation in the digital domain with a generic mapping can improve the system performance. In some cases, the performance of optimal fully-digital MIMO systems can be achieved without extra calculations compared to sub-optimal hybrid A/D techniques. An optimization model based on the proposed structure is presented that can be used for hybrid A/D system design. Specifically, precoding and combining designs under different conditions are discussed as examples. Finally, simulation results are presented which illustrate the superiority of the proposed architecture to the conventional hybrid designs for massive-MIMO systems.