Unit Modulus Constraints Research Articles

Beamforming optimization of meta-learning algorithm based on gradient descent in RIS-assisted ISAC system

In this paper, we study an integrated sensing and communication (ISAC) system assisted by reconfigurable intelligent surface (RIS). Our goal is to minimize the transmit power of the BS by jointly optimizing the active beamforming and the passive beamforming under the constraints of the signal-to-interference-plus-noise ratio (SINR) of users, the Cramer–Rao bound (CRB) of sensing and the unit-modulus of RIS reflection elements. The optimization problem is difficult to solve because the objective function is non-convex and the variables are coupled. In addition, a large number of base station (BS) antennas lead to high-dimensional transmit beamforming vectors. We first prove that the optimization variables in the optimization problem are low-dimensional coefficient matrices and passive beamforming, rather than active and passive beamforming, which reduces the complexity compared with the original problem. In addition, when the sensing channel space belongs to the communication channel space, the dedicated sensing signal is not needed. Inspired by the meta-learning technology that can solve non-convex problems, we propose a meta-learning algorithm based on gradient descent (MLAGD) to design beamforming, which tends to learn dynamic optimization strategies and iteratively update optimization variables. Specifically, we first introduce Lagrangian multipliers to transform the constrained optimization problem into the Lagrangian dual domain, and the manifold-based optimization is employed to handle the unit-modulus constraint. The meta-learning neural networks are constructed to update optimization variables through local loss function, and then network parameters are updated through global loss function. The numerical results show the effectiveness of the algorithm.

Reconfigurable Intelligent Surface Assisted Wireless Network Rate Optimization Design

To enhance the communication rate, we deploy one active reconfigurable intelligent surface (RIS) and one passive RIS to cooperatively assist the downlink communication, while meeting the constraints of base station transmission power, total Active RIS power, and RIS unit modulus constraint. Due to the nonlinear coupling of multiple variables in the objective function, non-convexity is caused. Therefore, an alternating optimization algorithm (AO) is proposed, which uses semi-definite programming (SDP) based algorithm to optimize the transmit beamforming vector, ARIS reflection matrix, and PRIS diagonal phase shift matrix. The simulation results have verified the effectiveness of the proposed algorithm, which indicates that optimizing the coefficients can significantly improve the spectrum efficiency of wireless networks.

Efficient symbol level precoding design for full-duplex integrated sensing and communication systems

Full-duplex (FD) integrated sensing and communication (ISAC) system attracts much attention because adopting the FD mode can enhance the transmission efficiency and reduce the transmission time of the ISAC system. However, the inevitable self-interference (SI) in FD mode would result in severe performance degradation. This paper considers the FD ISAC system and investigates a symbol-level precoding (SLP) design, which minimizes the Cramér-Rao Bound of target angle estimation while considering the constant-envelope power restraint, SI suppression and the quality of service requirement. Due to the non-convex fractional problem and the unit-modulus constraint, the optimization problem is reformulated by implementing the Schur complement, where the optimal waveform is obtained via the semidefinite programming algorithm. The SLP design that optimizes each symbol vector for all users may suffer high computational complexity of matrix multiplication with high numbers of users. A grouped SLP strategy in which the communication users are divided into several groups on the basis of channel correlation is proposed to reduce the complexity. The proposed grouped SLP design only suppresses group-to-group interference and converts the intra-group interference into a constructive interference, which can reduce the dimension of each precoded signal significantly, resulting in a low computational complexity. Simulation results illustrate that the proposed SLP design can effectively mitigate SI, which can improve the accuracy of target detection. Moreover, the proposed grouped-SLP design can further reduce computational complexity without dramatic performance degradation.

Cooperative Beamforming for RIS-Aided Cell-Free Massive MIMO Networks

The combination of cell-free massive multiple-input multiple-output (CF-mMIMO) and reconfigurable intelligent surface (RIS) is envisioned as a promising paradigm to improve network capacity and enhance coverage capability. However, to reap full benefits of RIS-aided CF-mMIMO, the main challenge is to efficiently design cooperative beamforming (CBF) at base stations (BSs), RISs, and users. Firstly, we investigate the fractional programing to convert the weighted sum-rate (WSR) maximization problem into a tractable optimization problem. Then, the alternating optimization framework is employed to decompose the transformed problem into a sequence of subproblems, i.e., hybrid BF (HBF) at BSs, passive BF at RISs, and combining at users. In particular, the alternating direction method of multipliers algorithm is utilized to solve the HBF subproblem at BSs. Concretely, the analog BF design with unit-modulus constraints is solved by the manifold optimization (MO) while we obtain a closed-form solution to the digital BF design that is essentially a convex least-square problem. Additionally, the passive BF at RISs and the analog combining at users are designed by primal-dual subgradient and MO methods. Moreover, considering heavy communication costs in conventional CF-mMIMO systems, we propose a partially-connected CF-mMIMO (P-CF-mMIMO) framework to decrease the number of connections among BSs and users. To better compromise WSR performance and network costs, we formulate the BS selection problem in the P-CF-mMIMO system as a binary integer quadratic programming (BIQP) problem, and develop a relaxed linear approximation algorithm to handle this BIQP problem. Finally, numerical results demonstrate superiorities of our proposed algorithms over baseline counterparts.

Robust Transmission Design for RIS-Assisted Secure Multiuser Communication Systems in the Presence of Hardware Impairments

This paper investigates reconfigurable intelligent surface (RIS)-assisted secure multiuser communication systems in the presence of hardware impairments (HIs) at the RIS and the transceivers. We jointly optimize the beamforming vectors at the base station (BS) and the phase shifts of the reflecting elements at the RIS so as to maximize the weighted minimum approximate ergodic secrecy rate (WMAESR), subject to the transmission power constraints at the BS and unit-modulus constraints at the RIS. To solve the formulated optimization problem, we first decouple it into two tractable subproblems and then use the block coordinate descent (BCD) method to alternately optimize the subproblems. Two different methods are proposed to solve the two obtained subproblems. The first method transforms each subproblem into a second order cone programming (SOCP) problem by invoking the penalty convexconcave procedure (CCP) method and the closed-form fractional programming (FP) criterion, and then directly solves them by using CVX. The second method leverages the minorization-maximization (MM) algorithm. Specifically, we first derive a concave approximation function, which is a lower bound of the original objective function, and then the two subproblems are transformed into two simple surrogate problems that admit closed-form solutions. Simulation results verify the performance gains of the proposed robust transmission methods over existing non-robust designs. In addition, the MM algorithm is shown to have much lower complexity than the SOCP-based algorithm.

RIS-Aided Multiuser MIMO-OFDM With Linear Precoding and Iterative Detection: Analysis and Optimization

In this paper, we consider a reconfigurable intelligent surface (RIS) aided uplink multiuser multi-input multi-output (MIMO) orthogonal frequency division multiplexing (OFDM) system, where the receiver is assumed to conduct low-complexity iterative detection. We aim to minimize the total transmit power by jointly designing the precoder of the transmitter and the passive beamforming of the RIS. This problem can be tackled from the perspective of information theory. But this information-theoretic approach may involve prohibitively high complexity since the number of rate constraints that specify the capacity region of the uplink multiuser channel is exponential in the number of users. To avoid this difficulty, we formulate the design problem of the iterative receiver under the constraints of a maximal iteration number and target bit error rates of users. To tackle this challenging problem, we propose a groupwise successive interference cancellation (SIC) optimization approach, where the signals of users are decoded and canceled in a group-by-group manner. We present a heuristic user grouping strategy, and resort to the alternating optimization technique to iteratively solve the precoding and passive beamforming sub-problems. Specifically, for the precoding sub-problem, we employ fractional programming to convert it to a convex problem; for the passive beamforming sub-problem, we adopt successive convex approximation to deal with the unit-modulus constraints of the RIS. We show that the proposed groupwise SIC approach has significant advantages in both performance and computational complexity, as compared with the counterpart approaches.

RIS-Aided MIMO Systems With Hardware Impairments: Robust Beamforming Design and Analysis

Reconfigurable intelligent surface (RIS) has been anticipated to be a novel cost-effective technology to improve the performance of future wireless systems. In this paper, we investigate a practical RIS-aided multiple-input-multiple-output (MIMO) system in the presence of transceiver hardware impairments, RIS phase noise and imperfect channel state information (CSI). Joint design of the MIMO transceiver and RIS reflection matrix to minimize the total average mean-square-error (MSE) of all data streams is particularly considered. This joint design problem is non-convex and challenging to solve due to the newly considered practical imperfections. To tackle the issue, we first analyze the total average MSE by incorporating the impacts of the above system imperfections. Then, in order to handle the tightly coupled optimization variables and non-convex NP-hard constraints, an efficient iterative algorithm based on alternating optimization (AO) framework is proposed with guaranteed convergence, where each subproblem admits a closed-form optimal solution by leveraging the majorization-minimization (MM) technique. Moreover, via exploiting the special structure of the unit-modulus constraints, we propose a modified Riemannian gradient ascent (RGA) algorithm for the discrete RIS phase shift optimization. Furthermore, the optimality of the proposed algorithm is validated under line-of-sight (LoS) channel conditions, and the irreducible MSE floor effect induced by imperfections of both hardware and CSI is also revealed in the high signal-to-noise ratio (SNR) regime. Numerical results show the superior MSE performance of our proposed algorithm over the adopted benchmark schemes, and demonstrate that increasing the number of RIS elements is not always beneficial under the above system imperfections.

IRS-Based Energy Efficiency and Admission Control Maximization for IoT Users With Short Packet Lengths

In this paper, we study a multiuser multiple-input single-output (MISO) machine type communication (MTC)-enabled intelligent reflecting surface (IRS) system, where a multi-antenna access point (AP) transmits information symbols to a set of Internet of Things (IoT) users with short packet transmission. In particular, the total energy efficiency (EE) and the number of IoT users that could be served fairly are maximized by jointly optimizing active and passive beamformers. An efficient algorithm based on alternating optimization (AO) is proposed to solve the main optimization problem iteratively. To this end, we adopt the difference of convex functions (DC) and successive convex approximation (SCA) to make a concave-convex function. Then, we employ the fractional programming based on the quadratic form to obtain a sub-optimal solution for the active beamformers at the AP and the number of admitted users. In the passive beamforming case, a penalty-based approach is utilized together with the SCA technique to handle the unit-modulus constraints at the IRS. Simulation results unveil an interesting tradeoff between EE and user admissibility performance. Besides, the results show the effectiveness of the IRS deployment in improving EE and successfully admitted users.

Passive Beamforming Design of IRS-Assisted MIMO Systems Based on Deep Learning.

In the intelligent reflecting surface (IRS)-assisted MIMO systems, optimizing the passive beamforming of the IRS to maximize spectral efficiency is crucial. However, due to the unit-modulus constraint of the IRS, the design of an optimal passive beamforming solution becomes a challenging task. The feature input of existing schemes often neglects to exploit channel state information (CSI), and all input data are treated equally in the network, which cannot effectively pay attention to the key information and features in the input. Also, these schemes usually have high complexity and computational cost. To address these issues, an effective three-channel data input structure is utilized, and an attention mechanism-assisted unsupervised learning scheme is proposed on this basis, which can better exploit CSI. It can also better exploit CSI by increasing the weight of key information in the input data to enhance the expression and generalization ability of the network. The simulation results show that compared with the existing schemes, the proposed scheme can effectively improve the spectrum efficiency, reduce the computational complexity, and converge quickly.

Sum-Rate Maximization for RIS-Assisted Integrated Sensing and Communication Systems With Manifold Optimization

Integrated sensing and communication (ISAC) is a key enabler for next-generation wireless communication systems to improve spectral efficiency. However, the coexistence of sensing and communication functionalities can cause harmful interference. In this paper, we propose to use a reconfigurable intelligent surface (RIS) in conjunction with ISAC to address this issue. The RIS is composed of a large number of low-cost elements that can adjust the amplitude and phase shift of impinging signals, thus providing a relatively high beamforming gain. To maximize the sum-rate of the communication system, we jointly optimize the beamformer at the base station (BS) and the phase shifts at the RIS, subject to a threshold on the interference power, the unit-norm constraint of the transmit power, and the unit modulus constraint of the RIS phase shifts. To efficiently tackle this NP-hard problem, we first reformulate the problem into a more tractable form using the fractional programming (FP) technique. Then, we exploit the geometrical properties of the constraints and adopt an alternating manifold-based optimization to compute the optimal active beamformer and the RIS phase shifts, respectively. Simulation results demonstrate that the proposed RIS-assisted design significantly reduces the mutual interference and improves the system sum-rate for the communication system.

Joint Beamforming and Phase Shift Design for Hybrid IRS and UAV-Aided Directional Modulation Networks

Recently, intelligent reflecting surfaces (IRSs) and unmanned aerial vehicles (UAVs) have been integrated into wireless communication systems to enhance the performance of air–ground transmission. To balance performance, cost, and power consumption well, a hybrid IRS and UAV-assisted directional modulation (DM) network is investigated in this paper in which the hybrid IRS consisted of passive and active reflecting elements. We aimed to maximize the achievable rate by jointly designing the beamforming and phase shift matrix (PSM) of the hybrid IRS subject to the power and unit-modulus constraints of passive IRS phase shifts. To solve the non-convex optimization problem, a high-performance scheme based on successive convex approximation and fractional programming (FP) called the maximal signal-to-noise ratio (SNR)-FP (Max-SNR-FP) is proposed. Given its high complexity, we propose a low-complexity maximal SNR-equal amplitude reflecting (EAR) (Max-SNR-EAR) scheme based on the maximal signal-to-leakage-noise ratio method, and the criteria of phase alignment and EAR. Given that the active and passive IRS phase shift matrices of both schemes are optimized separately, to investigate the effect of jointly optimizing them to improve the achievable rate, a maximal SNR majorization-minimization (MM) (Max-SNR-MM) scheme using the MM criterion to design the IRS PSM is proposed. Simulation results show that the rates harvested by the three proposed methods were slightly lower than those of the active IRS with higher power consumption, which were 35% higher than those of no IRS and random phase IRS, while passive IRS achieved only about a 17% rate gain over the latter. Moreover, compared with the Max-SNR-FP, the proposed Max-SNR-EAR and Max-SNR-MM methods caused obvious complexity degradation at the price of slight performance loss.

Robust Beamforming Design for IRS-Assisted Downlink Multi-User MISO-URLLC in an IIoT Scenario

Intelligent reflecting surfaces (IRS) have recently been regarded as having potential for supporting multi-user (MU) multiple-input single-output (MISO) ultra-reliable and low-latency communication (URLLC) by creating favorable wireless communication links in the industrial IoT (IIoT) scenario. Hence, we studied the joint robust design of a beamformer at a central controller (CC) and phase shifters at the IRS for minimizing the transmit power consumption based on perfect channel state information (CSI) and imperfect CSI, respectively. The design was formulated as a non-convex optimization problem, also taking into account the quality-of-service (QoS) demands of the actuator, unit-modulus constraints of the IRS, and the robustness against the impact of CSI imperfection. Subsequently, we proposed a computationally efficient iterative algorithm to obtain a suboptimal solution by exploiting the penalty method and the successive convex approximation (SCA) for perfect CSI, while the penalty method, S-procedure, and SCA were adopted for imperfect CSI. Finally, our simulation results revealed that (1) the required transmit power consumption for URLLC was significantly reduced by employing the proposed IRS instead of conventional wireless communication without IRS; and (2) the proposed algorithm was robust and effective for the beamforming design.

Deep Unfolding-Based Joint Beamforming and Detection Design for Ambient Backscatter Communications With IRS

In this letter, we investigate a novel ambient backscatter communication (AmBC) system in which an intelligent reflecting surface (IRS) acts as a passive transmitter to communicate with a reader. We are interested in the joint design of the IRS reflecting beamforming and symbol detection to minimize the bit error rate (BER). However, the problem is challenging to be solved optimally, since the BER is related to the clustering-based detector without a concrete close-form expression and the IRS reflecting unit modulus constraint is non-convex. To solve this issue, we propose a novel deep unfolding neural network (DUNN) combining data-driven and model-driven for passive reflecting beamforming design and symbol detection, which is learned to approximate the BER model from the training samples and the unit modulus constraint is satisfied by treating the optimization variables as network parameters. Numerical results demonstrate that the proposed scheme has superior performance of detection.

Intelligent Reflecting Surface-Aided Integrated Terrestrial-Satellite Networks

Intelligent reflecting surface (IRS) is a novel technology to manipulate wireless propagation channels via smart and controllable signal reflection. In this paper, we investigate an IRS-aided integrated terrestrial-satellite network (ITSN) system, where the IRS is deployed to assist the co-existing transmissions of the terrestrial small base stations (SBSs) and the satellite. Because of the spectrum sharing in the ITSN, the interference between the two systems should be carefully mitigated. Our objective is to maximize the weighted sum rate (WSR) of all users by jointly optimizing the frame-based coordinated transmit beamforming vectors at the SBSs, the phase shift matrix at the IRS, and the frame user scheduling, subject to SBSs’ individual power constraints and unit modulus constraints of phase shifters. To this end, we first adopt the agglomerative hierarchical clustering (AHC) method to schedule the satellite users to different frames. Then the block coordinate descent (BCD) algorithm is proposed, which alternately optimizes the transmit beamforming vectors and the reflective phase shift matrix. In particular, the optimal transmit beamforming vectors are obtained via the fractional programming (FP) technique. Meanwhile, two efficient algorithms, i.e., the Riemannian manifold (RM) and the successive convex approximation (SCA), are proposed for the phase shift optimization. Finally, simulation results are provided to demonstrate the performance gain of our schemes over other benchmark schemes.

IRS-Assisted Physical Layer Security in MIMO-NOMA Networks

In this letter, we propose deploying the intelligent reflecting surface (IRS) to enhance the physical layer security in non-orthogonal multiple access (NOMA). The secrecy sum-rate of IRS-assisted multiple-input multiple-output (MIMO) NOMA is maximized in the presence of an eavesdropper. Because of the discrete unit-modulus constraint and the nonconvex property, the secrecy sum-rate maximization problem is hard to solve. We reformulate the original problem into an equivalent parameterized optimization using rotation matrices and apply the particle swarm algorithm for global optimization. Simulation results verify that the performance of the proposed algorithm is close to the secrecy capacity of the channel, realized by exhaustive search, and outperforms other methods like alternating optimization and zero-forcing in terms of complexity and achievable rates.

Robust Transmission Design for RIS-Aided Wireless Communication With Both Imperfect CSI and Transceiver Hardware Impairments

Reconfigurable intelligent surface (RIS) has recently been regarded as a potential technique to enhance the performance of wireless communication systems by creating additional communication links. However, it is almost impossible to get the perfect channel state information (CSI) from the base station (BS) to the Internet of Things Devices (IoTDs) and the RIS-related channels. Furthermore, residual transceiver hardware impairments inevitably affect the performance of wireless communication systems. Hence, we study the robust design for an RIS-aided wireless communication system based on the imperfect CSI and hardware impairments. Minimizing the power consumption of BS is formulated by ensuring the minimum signal-to-interference-plus-noise ratio (SINR) demands of the IoTDs and the unit-modulus constraints of the RIS. Specifically, after approximating the nonconvex constraints by using the S-procedure and the successive convex approximation (SCA) methods, we adopt the block coordinate descent (BCD) technique to iteratively optimize one set of variables while keeping the other variables fixed in various channel uncertainty scenarios. Simulation results demonstrate that the influence of transceiver hardware impairments can be effectively decreased by deploying RIS even with channel uncertainty, which is more advantageous than increasing the number of BS’s antennas.

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.

Training Beam Sequence Design for mmWave Tracking Systems With and Without Environmental Knowledge

In this paper, we consider a millimeter wave multiple-input single-output tracking system, where the time-varying angle of departure (AoD) is assumed to change following a discrete state Markov process. Depending on whether the associated AoD transition function is available or not, we propose two different training beam sequence design approaches. Specifically, in the case when the AoD transition function is available, we leverage the maximum a posteriori criterion to estimate the updated AoD in each beam tracking period. Since it is infeasible to derive an explicit expression for the resultant estimation error rate, we turn to its upper bound, which possesses a closed-form expression and is therefore used as the objective function to optimize the training beam sequence. Considering the complicated objective function and the unit modulus constraints imposed by the analog phase shifters, we resort to a particle swarm algorithm to solve the formulated optimization problem. In the case when the AoD transition function is unavailable, we turn to the maximum likelihood criterion for AoD estimation. To cope with the unknown AoD transition function, we reformulate the beam tracking problem as a partially observable Markov decision process problem and develop an actor-critic reinforcement learning framework to obtain an efficient training beam sequence design. Numerical results demonstrate superiorities of the proposed training beam sequence design approaches for both two cases.

Partially Distributed Beamforming Design for RIS-Aided Cell-Free Networks

Cell-free networks are regarded as a promising technology to meet higher rate requirements for beyond fifth-generation (5G) communications. Most works on cell-free networks focus on either fully centralized beamforming to maximally enhance system performance, or fully distributed beamforming to avoid extensive channel state information (CSI) exchange among access points (APs). In order to achieve both network capacity improvement and CSI exchange reduction, we propose a partially distributed beamforming design algorithm for reconfigurable intelligent surface (RIS)-aided cell-free networks. We aim at maximizing the weighted sum-rate of all users by designing active and passive beamforming subject to transmit power constraints of APs and unit-modulus constraints of RIS elements. The weighted sum-rate maximization problem is first transformed into an equivalent weighted sum-mean-square-error (sum-MSE) minimization problem, and then alternating optimization (AO) approach is adopted to iteratively design active and passive beamformer. Specifically, active beamforming vectors are obtained by local APs and passive beamforming vector is optimized by central processing unit (CPU). Numerical results not only illustrate the proposed partially distributed algorithm achieves the remarkable performance improvement compared with conventional local beamforming methods, but also further show the considerable potential of deploying RIS in cell-free networks.

Hybrid Analog-Digital Transceiver Design for RIS-Assisted mmWave MIMO Communications

Reconfigurable intelligent surface (RIS) is a cost-effective solution to support millimeter wave (mmWave) communications suffering from severe blockage. In this letter, we aim to maximize the spectral efficiency (SE) of the RIS-assisted mmWave multiple-input multiple-output (MIMO) system by jointly optimizing the hybrid transceiver and passive RIS under the nonconvex unit-modulus constraints. It is revealed that the considered system is equivalent to a conventional mmWave system with a Kronecker-structured hybrid transmit antenna array. Using this fact, we firstly propose to jointly design the RIS and hybrid transceiver based on the idea of unitary matching. Motivated by the asymptotic orthogonality of array steering vectors for very large systems, a low-complexity two-stage scheme is also developed by simply choosing the transmit/receive array steering vectors associated with the first several largest path gains as the analog precoder/combiner. Numerical results further demonstrate the superior performance of the proposed schemes in terms of the achievable SEs and average run time.