Multiple-input Single-output Downlink Research Articles

On the Trade-Off between Energy Efficiency and Spectral Efficiency in RIS-Aided Multi-User MISO Downlink

As reconfigurable intelligent surfaces (RISs) have been gradually brought to reality, a large amount of research has been conducted to investigate the immense benefits of RISs. That is because RISs enable us to artificially direct the radio wave propagating through the environment at a relatively low cost. This paper investigates the trade-off between spectral efficiency (SE) and energy efficiency (EE) in the RIS-aided multi-user multiple-input single-output downlink. We develop an optimization framework for designing the transmitting precoding at the base station and the phase shift values at the RIS to balance the EE-SE trade-off. The proposed iterative optimization framework for the design includes quadratic transform, alternating optimization, and weighted minimization mean-square error conversion. Simulation results illustrate our optimization framework algorithm exhibits effectiveness and a fast convergence rate.

Power Efficient IRS-Assisted NOMA

In this paper, we propose a downlink multiple-input single-output (MISO) transmission scheme, which is assisted by an intelligent reflecting surface (IRS) consisting of a large number of passive reflecting elements. In the literature, it has been proved that nonorthogonal multiple access (NOMA) can achieve the same performance as computationally complex dirty paper coding, where the quasi-degradation condition is satisfied, conditioned on the users' channels fall in the quasi-degradation region. However, in a conventional communication scenario, it is difficult to guarantee the quasi-degradation, because the channels are determined by the propagation environments and cannot be reconfigured. To overcome this difficulty, we focus on an IRS-assisted MISO NOMA system, where the wireless channels can be effectively tuned. We optimize the beamforming vectors and the IRS phase shift matrix for minimizing transmission power. Furthermore, we propose an improved quasi-degradation condition by using IRS, which can ensure that NOMA achieves the capacity region with high possibility. For a comparison, we study zero-forcing beamforming (ZFBF) as well, where the beamforming vectors and the IRS phase shift matrix are also jointly optimized. Comparing NOMA with ZFBF, it is shown that, with the same IRS phase shift matrix and the improved quasi-degradation condition, NOMA always outperforms ZFBF. At the same time, we identify the condition under which ZFBF outperforms NOMA, which motivates the proposed hybrid NOMA transmission. Simulation results show that the proposed IRS-assisted MISO system outperforms the MISO case without IRS, and the hybrid NOMA transmission scheme always achieves better performance than orthogonal multiple access.

Analysis of Hierarchical Rate Splitting for Intelligent Reflecting Surfaces-Aided Downlink Multiuser MISO Communications

An intelligent reflecting surface (IRS) is an emerging technology in the next-generation (B5G and 6G) wireless communications with the aim of improving the spectral/energy efficiency of the wireless networks. In this paper, we focus on multiple IRS-aided multiuser multiple-input single-output (MISO) downlink network, where each IRS is deployed near to the cell boundary of the cellular network in order to help the downlink transmission to the cell-edge users. To achieve the significant performance benefits provided by the rate-splitting (RS) transmission in multiuser scenario, two-layer hierarchical rate splitting (2L-HRS) technique is deployed at the base station (BS) to serve all the users. Furthermore, we propose an On-Off scheme for controlling the IRSs with practical phase shifts. In order to analyze the performance of the users, we derive the closed-form expressions of outage probability for both cell-edge users and near users. By extensive Monte Carlo simulations, we demonstrate that the proposed design framework outperforms the corresponding one-layer RS (1L-RS), the multiuser linear precoding (MU-LP) and 2L-HRS without IRS. In addition, we reveal the advantages of introducing RS-based IRS in improving the cell-users’ performance. The impact of channel estimation errors due to imperfect channel state information, and the various network’s parameters, such as the number of reflecting elements and the number of cell-users, on the network performance is demonstrated.

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.

Robust Downlink Transmit Optimization Under Quantized Channel Feedback via the Strong Duality for QCQP

Consider a robust multiple-input single-output downlink beamforming optimization problem in a frequency division duplexing system. The base station (BS) sends training signals to the users, and every user estimates the channel coefficients, quantizes the gain and the direction of the estimated channel and sends them back to the BS. Suppose that the channel state information at the transmitter is imperfectly known mainly due to the channel direction quantization errors, channel estimation errors and outdated channel effects. The actual channel is modeled as in an uncertainty set composed of two inequality homogeneous and one equality inhomogeneous quadratic constraints, in order to account for the aforementioned errors and effects. Then the transmit power minimization problem is formulated subject to robust signal-to-noise-plus-interference ratio constraints. Each robust constraint is transformed equivalently into a quadratic matrix inequality (QMI) constraint with respect to the beamforming vectors. The transformation is accomplished by an equivalent phase rotation process and the strong duality result for a quadratically constrained quadratic program. The minimization problem is accordingly turned into a QMI problem, and the problem is solved by a restricted linear matrix inequality relaxation with additional valid convex constraints. Simulation results are presented to demonstrate the performance of the proposed method, and show the efficiency of the restricted relaxation.

Transfer Learning and Meta Learning-Based Fast Downlink Beamforming Adaptation

This article studies fast adaptive beamforming optimization for the signal-to-interference-plus-noise ratio balancing problem in a multiuser multiple-input single-output downlink system. Existing deep learning based approaches to predict beamforming rely on the assumption that the training and testing channels follow the same distribution which may not hold in practice. As a result, a trained model may lead to performance deterioration when the testing network environment changes. To deal with this task mismatch issue, we propose two offline adaptive algorithms based on deep transfer learning and meta-learning, which are able to achieve fast adaptation with the limited new labelled data when the testing wireless environment changes. Furthermore, we propose an online algorithm to enhance the adaptation capability of the offline meta algorithm in realistic non-stationary environments. Simulation results demonstrate that the proposed adaptive algorithms achieve much better performance than the direct deep learning algorithm without adaptation in new environments. The meta-learning algorithm outperforms the deep transfer learning algorithm and achieves near optimal performance. In addition, compared to the offline meta-learning algorithm, the proposed online meta-learning algorithm shows superior adaption performance in changing environments.

Intelligent Reflecting Surface-Assisted Cognitive Radio System

Cognitive radio (CR) is an effective solution to improve the spectral efficiency (SE) of wireless communications by allowing the secondary users (SUs) to share spectrum with primary users (PUs). Meanwhile, intelligent reflecting surface (IRS), also known as reconfigurable intelligent surface (RIS), has been recently proposed as a promising approach to enhance energy efficiency (EE) of wireless communication systems through intelligently reconfiguring the channel environment. To improve both SE and EE, in this paper, we introduce multiple IRSs to a downlink multiple-input single-output (MISO) CR system, in which a single SU coexists with a primary network with multiple PU receivers (PU-RXs). Our design objective is to maximize the achievable rate of SU subject to a total transmit power constraint on the SU transmitter (SU-TX) and interference temperature constraints on the PU-RXs, by jointly optimizing the beamforming at SU-TX and the reflecting coefficients at each IRS. Both perfect and imperfect channel state information (CSI) cases are considered in the optimization. Numerical results demonstrate that IRS can significantly improve the achievable rate of SU under both perfect and imperfect CSI cases.

Exploiting Intelligent Reflecting Surfaces in NOMA Networks: Joint Beamforming Optimization

This paper investigates a downlink multiple-input single-output intelligent reflecting surface (IRS) aided non-orthogonal multiple access (NOMA) system, where a base station (BS) serves multiple users with the aid of IRSs. Our goal is to maximize the sum rate of all users by jointly optimizing the active beamforming at the BS and the passive beamforming at the IRS, subject to successive interference cancellation decoding rate conditions and IRS reflecting elements constraints. In term of the characteristics of reflection amplitudes and phase shifts, we consider ideal and non-ideal IRS assumptions. To tackle the formulated non-convex problems, we propose efficient algorithms by invoking alternating optimization, which design the active beamforming and passive beamforming alternately. For the ideal IRS scenario, the two subproblems are solved by invoking the successive convex approximation technique. For the non-ideal IRS scenario, constant modulus IRS elements are further divided into continuous phase shifts and discrete phase shifts. To tackle the passive beamforming problem with continuous phase shifts, a novel algorithm is developed by utilizing the sequential rank-one constraint relaxation approach, which is guaranteed to find a locally optimal rank-one solution. Then, a quantization-based scheme is proposed for discrete phase shifts. Finally, numerical results illustrate that: i) the system sum rate can be significantly improved by deploying the IRS with the proposed algorithms; ii) 3-bit phase shifters are capable of achieving almost the same performance as the ideal IRS; iii) the proposed IRS-aided NOMA systems achieve higher system sum rate than the IRS-aided orthogonal multiple access system.

Resource Allocation for Multi-User Downlink MISO OFDMA-URLLC Systems

This article considers the resource allocation algorithm design for downlink multiple-input single-output (MISO) orthogonal frequency division multiple access (OFDMA) ultra-reliable low latency communication (URLLC) systems. To meet the stringent delay requirements of URLLC, short packet transmission is adopted and taken into account for resource allocation algorithm design. The resource allocation is optimized for maximization of the weighted system sum throughput subject to quality-of-service (QoS) constraints regarding the URLLC users’ number of transmitted bits, packet error probability, and delay. Despite the non-convexity of the resulting optimization problem, the optimal solution is found via monotonic optimization. The corresponding optimal resource allocation policy can serve as a performance upper bound for sub-optimal low-complexity solutions. We develop such a low-complexity sub-optimal resource allocation algorithm based on successive convex approximation and difference of convex programming. Our simulation results reveal the importance of using multiple antennas for reducing the latency and improving the reliability of URLLC systems. Moreover, the proposed sub-optimal algorithm is shown to closely approach the performance of the proposed optimal algorithm and outperforms two baseline schemes by a considerable margin, especially when the users have heterogeneous delay requirements. Finally, conventional resource allocation designs based on Shannon’s capacity formula are shown to be not applicable in MISO OFDMA-URLLC systems as they are not able to guarantee the users’ delay constraints.

Spectral and Energy Efficiency of IRS-Assisted MISO Communication With Hardware Impairments

In this letter, we analyze the spectral and energy efficiency of an intelligent reflecting surface (IRS)-assisted multiple-input single-output (MISO) downlink system with hardware impairments. An extended error vector magnitude (EEVM) model is utilized to characterize the impact of radio-frequency (RF) impairments at the access point (AP) and phase noise is considered for the imperfect IRS. We show that the spectral efficiency is limited due to the hardware impairments even when the numbers of AP antennas and IRS elements grow infinitely large, which is in contrast with the conventional case with ideal hardware. Moreover, the performance degradation at high SNR is shown to be mainly affected by the AP hardware impairments rather than the phase noise of IRS. We further obtain the optimal transmit power in closed form for energy efficiency maximization. Simulation results are provided to verify these results.

Multiuser MISO UAV Communications in Uncertain Environments With No-Fly Zones: Robust Trajectory and Resource Allocation Design

In this paper, we investigate robust resource allocation algorithm design for multiuser downlink multiple-input single-output (MISO) unmanned aerial vehicle (UAV) communication systems, where we account for the various uncertainties that are unavoidable in such systems and, if left unattended, may severely degrade system performance. We jointly optimize the two-dimensional (2-D) trajectory and the transmit beamforming vector of the UAV for minimization of the total power consumption. The algorithm design is formulated as a non-convex optimization problem taking into account the imperfect knowledge of the angle of departure (AoD) caused by UAV jittering, user location uncertainty, wind speed uncertainty, and polygonal no-fly zones (NFZs). Despite the non-convexity of the optimization problem, we solve it optimally by employing monotonic optimization theory and semidefinite programming relaxation which yields the optimal 2-D trajectory and beamforming policy. Since the developed optimal resource allocation algorithm entails a high computational complexity, we also propose a suboptimal iterative low-complexity scheme based on successive convex approximation to strike a balance between optimality and computational complexity. Our simulation results reveal not only the significant power savings enabled by the proposed algorithms compared to two baseline schemes, but also confirm their robustness with respect to UAV jittering, wind speed uncertainty, and user location uncertainty. Moreover, our results unveil that the joint presence of wind speed uncertainty and NFZs has a considerable impact on the UAV trajectory. Nevertheless, by counteracting the wind speed uncertainty with the proposed robust design, we can simultaneously minimize the total UAV power consumption and ensure a secure trajectory that does not trespass any NFZ.

On Optimal Beamforming Design for Downlink MISO NOMA Systems

This work focuses on the beamforming design for downlink multiple-input single-output (MISO) nonorthogonal multiple access (NOMA) systems. The beamforming vectors are designed by solving a total transmission power minimization (TPM) problem with quality-of-service (QoS) constraints. In order to solve the proposed nonconvex optimization problem, we provide an efficient method using semidefinite relaxation. Moreover, for the first time, we characterize the optimal beamforming in a closed form with quasi-degradation condition, which is proven to achieve the same performance as dirty-paper coding (DPC). For the special case with two users, we further show that the original nonconvex TPM problem can be equivalently transferred into a convex optimization problem and easily solved via standard optimization tools. In addition, the optimal beamforming is also characterized in a closed form and we show that it achieves the same performance as the DPC. In the simulation, we show that our proposed optimal NOMA beamforming outperforms OMA schemes and can even achieve the same performance as DPC. Our solutions dramatically simplifies the problem of beamforming design in the downlink MISO NOMA systems and improve the system performance.

Joint Power and Subcarrier Allocation Optimization for Multigroup Multicast Systems With Rate Splitting

In this article, we investigate a resource allocation problem for multicarrier multiuser MISO (multiple-input-Single-output) downlink systems, where multiple co-channel multicast groups are served simultaneously. We consider a rate-splitting transmission scheme to address the inevitable inter-group interference under an overloaded multigroup multicast scenario, where the insufficient number of transmit antennas prevents the conventional schemes from neutralizing the interference. We first formulate an optimization problem for maximizing the minimum multicast group rate among all groups on all available subcarriers. This problem involves a joint power and subcarrier allocation optimization, and is non-convex. We apply an iterative scheme based on successive convex approximation (SCA) to find the locally optimal solution. Simulation results demonstrate the performance gain of the proposed scheme compared to the state-of-the-art transmission schemes.

Co-Design for Overlaid MIMO Radar and Downlink MISO Communication Systems via Cramér–Rao Bound Minimization

This paper considers the problem of co-existence of collocated multiple-input multiple-output (MIMO) radar and downlink multiple-input single-output (MISO) communication systems, which share the same frequency band. As the interference caused by the communication systems would degrade the accuracy of radar target localization, we formulate the co-design of radar waveform and communication transmit weights by minimizing the Cramér-Rao Bound (CRB) of direction-of-arrival (DOA) estimation, subject to a set of constraints accounting for the worst-case signal-to-noise-plus-interference ratio (SINR), similarity and energy. However, the objective is nonconvex and all variables are coupled together in the SINR constraints, the formulated problem is thus NP-hard. Towards that end, a decentralized block successive upper-bound minimization (D-BSUM) method based on the decomposition theory is developed. More specifically, at each iteration of this algorithm, the radar waveform is obtained with the aid of the alternating direction method of multipliers (ADMM) algorithm, and communication weights are obtained by exploiting the semidefinite programs (SDP). It is also proved that the proposed SDP-based method gives a rank-one solution. Numerical simulations are conducted to evaluate the effectiveness of the proposed algorithm.

Interference Exploitation Precoding for Multi-Level Modulations: Closed-Form Solutions

We study closed-form interference-exploitation precoding for multi-level modulations in the downlink of multi-user multiple-input single-output (MU-MISO) systems. We consider two distinct cases: first, when the number of served users is not larger than the number of transmit antennas at the base station (BS), we mathematically derive the optimal precoding structure based on the Karush-Kuhn-Tucker (KKT) conditions. By formulating the dual problem, the precoding problem is transformed into a pre-scaling operation using quadratic programming (QP) optimization. We further consider the case where the number of served users is larger than the number of transmit antennas at the BS. By employing the pseudo inverse, we show that the optimal solution of the pre-scaling vector is equivalent to a linear combination of the right singular vectors corresponding to zero singular values, and derive the equivalent QP formulation. We also present the condition under which multiplexing more streams than the number of transmit antennas is achievable. For both considered scenarios, we propose a modified iterative algorithm to obtain the optimal precoding matrix, as well as a sub-optimal closed-form precoder. Numerical results validate our derivations on the optimal precoding structures for multi-level modulations, and demonstrate the superiority of interference-exploitation precoding for both scenarios.

Secure Transmission via Joint Precoding Optimization for Downlink MISO NOMA

Non-orthogonal multiple access (NOMA) is a prospective technology for radio resource constrained future mobile networks. However, NOMA users far from a base station (BS) tend to be more susceptible to eavesdropping because they are allocated more transmit power. In this paper, we aim to jointly optimize the precoding vectors at the BS to ensure the legitimate security in a downlink multiple-input single-output (MISO) NOMA network. When the eavesdropping channel state information (CSI) is available at the BS, we can maximize the sum secrecy rate by joint precoding optimization. Owing to its non-convexity, the problem is converted into a convex one, which is solved by a second-order-cone-programming-based iterative algorithm. When the CSI of the eavesdropping channel is not available, we first consider the case that the secure user is not the farthest from the BS, and the transmit power of the farther users is maximized via joint precoding optimization to guarantee its security. Then, we consider the case when the farthest user from the BS requires secure transmission, and the modified successive interference cancellation order and joint precoding optimization can be adopted to ensure its security. A similar method can be exploited to solve the two non-convex problems when the CSI is unknown. Simulation results demonstrate that the proposed schemes can improve the security performance for MISO NOMA systems effectively, with and without eavesdropping CSI.

Robust Secrecy Beamforming and Power-Splitting Design for Multiuser MISO Downlink With SWIPT

In this paper, we investigate the physical layer security design in multiuser multiple-input single-output downlink with simultaneous wireless information and power transfer. Specifically, by considering that legitimate receivers use power splitting to extract information and harvest energy simultaneously, we investigate the robust weighted sum secrecy rate maximization design, subject to multiple signal-to-interference-and-noise ratio and harvested energy constraints. To solve the formulated highly nonconvex problem and avoid high-rank solution obtained by the common semidefinite relaxation method, we utilize the constrained concave convex procedure and second-order cone programming to formulate a tractable problem and propose an iterative algorithm to obtain the solution. In addition, we discuss the feasibility condition and computational complexity of our algorithm. Furthermore, our algorithm can be extended to other optimization designs. Simulation results show the superiority of our proposed design.

Intelligent Reflecting Surface: A Programmable Wireless Environment for Physical Layer Security

In this paper, we introduce an intelligent reflecting surface (IRS) to provide a programmable wireless environment for physical layer security. By adjusting the reflecting coefficients, the IRS can change the attenuation and scattering of the incident electromagnetic wave so that it can propagate in a desired way toward the intended receiver. Specifically, we consider a downlink multiple-input single-output (MISO) broadcast system where the base station (BS) transmits independent data streams to multiple legitimate receivers and keeps them secret from multiple eavesdroppers. By jointly optimizing the beamformers at the BS and reflecting coefficients at the IRS, we formulate a minimum-secrecy-rate maximization problem under various practical constraints on the reflecting coefficients. The constraints capture the scenarios of both continuous and discrete reflecting coefficients of the reflecting elements. Due to the non-convexity of the formulated problem, we propose an efficient algorithm based on the alternating optimization and the path-following algorithm to solve it in an iterative manner. Besides, we show that the proposed algorithm can converge to a local (global) optimum. Furthermore, we develop two suboptimal algorithms with some forms of closed-form solutions to reduce the computational complexity. Finally, the simulation results validate the advantages of the introduced IRS and the effectiveness of the proposed algorithms

Joint Antenna Selection and Analog Precoder Design With Low-Resolution Phase Shifters

Analog precoder was introduced recently to millimeter wave (mmWave) systems with large-scale antenna arrays as a promising hardware-efficient transceiver architecture. In practice, low-resolution phase shifters (PSs) are generally adopted to achieve low hardware cost and low power consumption, which, however, makes fine beam tuning challenging. Recent achievements in antenna selection technology motivate us to exploit the augmented antenna diversity of a large-scale antenna array to compensate the accuracy loss caused by this low-resolution PS implementation. In this correspondence, we consider a narrow-band multiple-input single-output downlink mmWave system. Our goal is to jointly select a set of transmit antennas and design the analog precoder with constant amplitude and discrete phase constraints to maximize the spectral efficiency. In particular, we propose a novel joint antenna selection and analog beamformer design algorithm, which can provide satisfactory performance with low complexity. Simulation results demonstrate the advances of the proposed algorithm compared with the low-resolution analog precoding schemes without antenna selection.

Offset-Based Beamforming: A New Approach to Robust Downlink Transmission

The design of beamformers for the multi-user multiple-input single-output downlink that provide prespecified levels of quality-of-service can be quite challenging when the channel state information is not perfectly known at the base station. The constraint of having the signal-to-interference-and-noise ratio (SINR) satisfy a given threshold with high probability is intractable in general, which results in problems that are fundamentally hard to solve. We develop a high-quality approximation of the SINR outage constraint that, along with a semidefinite relaxation, enables us to formulate the robust beamformer design problem for Gaussian channel estimation errors as a convex optimization problem that can be efficiently solved. For systems with small uncertainties, further approximations yield design algorithms based on iterative evaluations of closed-form expressions that have substantially lower computational cost. Since finding the beamforming directions incurs most of that cost, analogous power loading algorithms for predefined beamforming directions are developed and their performance is shown to be close to optimal. When the system contains a large number of antennas, the proposed power loading can be obtained at a computational cost that grows only linearly in the number of antennas. The proposed power loading algorithm provides an explicit relationship between the outage probability required and the power consumed, which allows us to precisely control the power consumption, and automatically identifies users who are consuming most of the power resources. The flexibility of the proposed approach is illustrated by developing a power loading technique that minimizes an average notion of outage.