Multiuser Multiple-input Single-output Downlink Research Articles

Joint hybrid-precoding design for MU-MISO systems with a subconnected architecture

In this study, we propose a joint hybrid-precoding algorithm for multiuser multiple-input single-output downlink systems. Specifically, we consider that the base station employs an energy-efficient hybrid-precoding subconnected (SC) architecture with fixed equal subarrays (FESA) (SC-FESA). Optimizing the analog precoding matrix in an SC-FESA architecture is challenging due to its unique constraint structure. In this study, to maximize system sum rate, we propose an efficient method to transform the system’s sum-rate optimization problem into a continuous and differentiable objective function wherein only the nonzero elements of the analog precoding matrix are optimized. For the formulated problem, we develop an alternating optimization (AO) approach to jointly optimize the digital and analog precoders in succession by maximizing the system’s sum rate. Specifically, in the proposed AO method, when the digital precoder is fixed, we employ the Riemannian conjugate gradient algorithm to generate the analog precoder. Furthermore, when the analog precoder is fixed, we use the minimum mean squared error method to obtain the digital precoder. Numerical simulation results show that the proposed AO algorithm improves the sum rate and energy efficiency of the SC-FESA architecture compared to existing algorithms.

Dynamic-Controlled RIS Assisted Multi-User MISO Downlink System: Joint Beamforming Design

This paper investigates a multi-user multiple-input single-output (MISO) downlink communication system, which is assisted by a dynamic-controlled Reconfigurable Intelligent Surface (RIS). Firstly, we formulate a problem to optimize the active -and passive beamforming matrices with the goal of maximizing the sum rate (SR) of all users under the constraints of Quality of Service (QoS) requirements. A state selection matrix is creatively introduced to control the number of RIS elements used for reflection. And quantized phases are considered in order to be more practical, which is often neglected in existing works. Then, an algorithm based on block coordinate descent (BCD) is proposed to obtain the stationary solution. The algorithm can guarantee the optimal SR regardless of any proportion of closed RIS elements. Finally, we perform simulation verification and analysis the results of the proposed scheme and six baseline schemes. Simulation results show that the proposed scheme is much better than the existing schemes in terms of SR, and realizes good energy efficiency (EE) performance simultaneously. Moreover, the proposed scheme can achieve more significant EE gain by sacrificing less SR.

Embedding Model-Based Fast Meta Learning for Downlink Beamforming Adaptation

This paper studies the fast adaptive beamforming for the multiuser multiple-input single-output downlink. Existing deep learning-based approaches assume that training and testing channels follow the same distribution which causes task mismatch, when the testing environment changes. Although meta learning can deal with the task mismatch, it relies on labelled data and incurs high complexity in the pre-training and fine tuning stages. We propose a simple yet effective adaptive framework to solve the mismatch issue, which trains an embedding model as a transferable feature extractor, followed by fitting the support vector regression. Compared to the existing meta learning algorithm, our method does not necessarily need labelled data in the pre-training and does not need fine-tuning of the pre-trained model in the adaptation. The effectiveness of the proposed method is verified through two well-known applications, i.e., the signal to interference plus noise ratio balancing problem and the sum rate maximization problem. Furthermore, we extend our proposed method to online scenarios in non-stationary environments. Simulation results demonstrate the advantages of the proposed algorithm in terms of both performance and complexity. The proposed framework can also be applied to general radio resource management problems.

Robust and Secure Sum-Rate Maximization for Multiuser MISO Downlink Systems With Self-Sustainable IRS

This paper investigates robust and secure multiuser multiple-input single-output (MISO) downlink communications assisted by a self-sustainable intelligent reflection surface (IRS), which can simultaneously reflect and harvest energy from the received signals. We study the joint design of beamformers at an access point (AP) and the phase shifts as well as the energy harvesting schedule at the IRS for maximizing the system sum-rate. The design is formulated as a non-convex optimization problem taking into account the wireless energy harvesting capability of IRS elements, secure communications, and the robustness against the impact of channel state information (CSI) imperfection. Subsequently, we propose a computationally-efficient iterative algorithm to obtain a suboptimal solution to the design problem. In each iteration, <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\mathcal {S}$ </tex-math></inline-formula> -procedure and the successive convex approximation are adopted to handle the intermediate optimization problem. Our simulation results unveil that: 1) there is a non-trivial trade-off between the system sum-rate and the self-sustainability of the IRS; 2) the performance gain achieved by the proposed scheme is saturated with a large number of energy harvesting IRS elements; 3) an IRS equipped with small bit-resolution discrete phase shifters is sufficient to achieve a considerable system sum-rate of the ideal case with continuous phase shifts.

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.

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.

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.

A Deep Learning Framework for Optimization of MISO Downlink Beamforming

Beamforming is an effective means to improve the quality of the received signals in multiuser multiple-input-single-output (MISO) systems. Traditionally, finding the optimal beamforming solution relies on iterative algorithms, which introduces high computational delay and is thus not suitable for real-time implementation. In this paper, we propose a deep learning framework for the optimization of downlink beamforming. In particular, the solution is obtained based on convolutional neural networks and exploitation of expert knowledge, such as the uplink-downlink duality and the known structure of optimal solutions. Using this framework, we construct three beamforming neural networks (BNNs) for three typical optimization problems, i.e., the signal-to-interference-plus-noise ratio (SINR) balancing problem, the power minimization problem, and the sum rate maximization problem. For the former two problems the BNNs adopt the supervised learning approach, while for the sum rate maximization problem a hybrid method of supervised and unsupervised learning is employed. Simulation results show that the BNNs can achieve near-optimal solutions to the SINR balancing and power minimization problems, and a performance close to that of the weighted minimum mean squared error algorithm for the sum rate maximization problem, while in all cases enjoy significantly reduced computational complexity. In summary, this work paves the way for fast realization of optimal beamforming in multiuser MISO systems.

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.

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.

Interference Exploitation Precoding Made Practical: Optimal Closed-Form Solutions for PSK Modulations

In this paper, we propose closed-form precoding schemes with optimal performance for constructive interference (CI) exploitation in the multiuser multiple-input single-output downlink, where the cases of both strict and non-strict phase rotation are considered. For optimization with strict phase rotation, we mathematically derive the optimal precoding structure with Lagrangian and Karush–Kuhn–Tucker conditions. By formulating its dual problem, the optimization problem is further shown to be equivalent to a quadratic programming over a simplex, which can be solved more efficiently. We then extend our analysis to the case of non-strict phase rotation, where it is mathematically shown that a $K$ -dimensional optimization for non-strict phase rotation is equivalent to a $2K$ -dimensional optimization for strict phase rotation in terms of the problem formulation. The connection with the conventional zero-forcing precoding is also discussed. Based on the above-mentioned analysis, we further propose an iterative closed-form scheme to obtain the optimal precoding matrix, where within each iteration a closed-form solution can be obtained. Numerical results validate our analysis and the optimality of the proposed iterative closed-form algorithm, and further show that the proposed iterative closed-form scheme offers a flexible performance-complexity tradeoff by limiting the maximum number of iterations, which motivates the use of CI precoding in practical wireless systems.

Analog–Digital Beamforming in the MU-MISO Downlink by Use of Tunable Antenna Loads

We investigate the performance of multiuser multiple-input-single-output (MU-MISO) downlink in the presence of the mutual coupling effect at the transmitter. Contrary to traditional approaches that aim at eliminating this effect, in this paper we propose a joint analog–digital (AD) beamforming scheme that exploits this effect to further improve the system performance. A jointly optimal AD beamformer is first obtained by iteratively maximizing the minimum received signal-to-interference-plus-noise ratio in the digital domain, followed by an optimization on the load impedance of each antenna element in the analog domain. We further introduce a decoupled low-complexity approach, with which existing closed-form beamforming schemes can also be efficiently applied. For the consideration of hardware imperfections in practice, we study the case where the analog load values are quantized, and propose a sequential search scheme based on greedy algorithm to efficiently obtain the desired quantized load values. Moreover, we also investigate the imperfect channel state information (CSI) scenarios, where we prove the optimality for closed-form beamformers, and further propose the robust schemes for two typical CSI error models. Simulation results show that with the proposed schemes the mutual coupling effect can be exploited to further improve the performance for both perfect CSI and imperfect CSI.

Distributed Solutions for Energy Efficiency Fairness in Multicell MISO Downlink

This paper aims at guaranteeing the achievable energy efficiency (EE) fairness in a multicell multiuser multiple-input single-output downlink system. The design objective is to maximize the minimum EE among all base stations (BSs) subject to per-BS power constraints. This results in a max-min fractional program and as such is difficult to solve in general. Our goal is to develop decentralized algorithms for the max-min EE problem based on combining the successive convex approximation (SCA) framework and the alternating direction method of multipliers (ADMMs). Specifically, leveraging the SCA principle, we iteratively approximate the nonconvex design problem by a sequence of convex programs for which two decentralized algorithms are then proposed. In the first approach, the convex program obtained at each step of the SCA procedure is solved optimally by allowing the BSs to exchange the required information until the ADMM converges. The convergence of the first method is analytically guaranteed but the amount of backhaul signaling can be noticeable in some realistic settings. To reduce the backhaul overhead, the second method performs an abstract version of the ADMM where only one variables update is carried out. Numerical results are provided to demonstrate the effectiveness of the two proposed decentralized algorithms.

On the Performance of Random Beamforming in Sparse Millimeter Wave Channels

The performance of random beamforming (RBF) with partial channel state information (CSI) feedback is investigated here for millimeter wave (mmWave) multiuser multiple-input single-output (MU-MISO) downlink systems using the uniform random multipath (UR-MP) channel model. In particular, the required number of users in the cell for RBF to yield linear sum rate scaling with respect to the number of transmit antennas is identified under the UR-MP channel model for different levels of channel sparsity. Then, the problem of user scheduling in MU-MISO downlink is considered when the number of users in the cell is not sufficiently large (sparse user regime) for the system to operate in the identified sufficient user regime. By exploiting the sparsity of mmWave radio channels, several user scheduling algorithms based on beam aggregation with reasonable amount of feedback are proposed for the sparse user regime. Our numerical results show that the proposed algorithms yield very good sum-rate performance in sparse mmWave channels.

Robust beamforming designs for multiuser MISO downlink with per-antenna power constraints

This paper studies the robust beamforming designs for a multiuser multiple-input single-output (MISO) downlink system. Different from the conventional sum-power constraint across all transmit antennas, we consider individual power constraints per antenna at the base station. Assuming that the channel uncertainty is bounded by a spherical region, we develop the optimal robust designs to maximize the minimum worst-case signal-to-interference-plus-noise ratio (SINR) among all users. Specifically, we show that the optimal max-min SINR beamformers can be obtained by solving a sequence of “dual” min-max power problems. Relying on the S-procedure and the linear matrix inequality representation for the cone of Lorentz-positive maps (LPMs), respectively, two designs, which are referred to as Robust-SP and Robust-LPM, are proposed to efficiently solve such min-max power problems. Building on either Robust-SP or Robust LPM, a bisection search algorithm is then developed to find the robust max-min SINR beamformers with guaranteed global optimality and geometrically fast convergence speed. Using the max-min SINR solutions as a cornerstone, we further put forth the optimal robust design for the worst-case weighted sum-rate (WSR) maximization. By formulating the worst-case WSR maximization problem into a monotonic program (MP), we develop a polyblock outer approximation algorithm to obtain the globally optimal solution. Numerical results are presented to demonstrate the merits of the proposed robust beamforming designs.

Achieving Energy Efficiency Fairness in Multicell MISO Downlink

We investigate the fairness of achievable energy efficiency in a multicell multiuser multiple-input single-output (MISO) downlink system, where a beamforming scheme is designed to maximize the minimum energy efficiency among all base stations. The resulting optimization problem is a nonconvex max-min fractional program, which is generally difficult to solve optimally. We propose an iterative beamformer design based on an inner approximation algorithm which aims at locating a Karush-Kuhn-Tucker solution to the nonconvex program. By novel transformations, we arrive at a convex problem at each iteration of the proposed algorithm, which is amendable for being approximated by a second order cone program. The numerical results demonstrate that the proposed algorithm outperforms the existing schemes in terms of the convergence rate and processing time.

Exploiting Known Interference as Green Signal Power for Downlink Beamforming Optimization

We propose a data-aided transmit beamforming scheme for the multi-user multiple-input-single-output (MISO) downlink channel. While conventional beamforming schemes aim at the minimization of the transmit power subject to suppressing interference to guarantee quality of service (QoS) constraints, here we use the knowledge of both data and channel state information (CSI) at the transmitter to exploit, rather than suppress, constructive interference. More specifically, we design a new precoding scheme for the MISO downlink that minimizes the transmit power for generic phase shift keying (PSK) modulated signals. The proposed precoder reduces the transmit power compared to conventional schemes, by adapting the QoS constraints to accommodate constructive interference as a source of useful signal power. By exploiting the power of constructively interfering symbols, the proposed scheme achieves the required QoS at lower transmit power. We extend this concept to the signal to interference plus noise ratio (SINR) balancing problem, where higher SINR values compared to the conventional SINR balancing optimization are achieved for given transmit power budgets. In addition, we derive equivalent virtual multicast formulations for both optimizations, both of which provide insights of the optimal solution and facilitate the design of a more efficient solver. Finally, we propose a robust beamforming technique to deal with imperfect CSI, that also reduces the transmit power over conventional techniques, while guaranteeing the required QoS. Our simulation and analysis show significant power savings for small scale MISO downlink channels with the proposed data-aided optimization compared to conventional beamforming optimization.

Maximizing Energy Efficiency in the Vector Precoded MU-MISO Downlink by Selective Perturbation

We propose an energy-efficient vector perturbation (VP) technique for the downlink of multiuser multiple-input-single-output (MU-MISO) systems. In contrast to conventional VP where the search for perturbation vectors involves all users' symbols, here, the perturbation is applied to a subset of the transmitted symbols. This, therefore, introduces a performance-complexity tradeoff, where the complexity is greatly reduced compared to VP by limiting the dimensions of the sphere search, at the expense of a performance penalty compared to VP. By changing the size of the subset of perturbed users, the aforementioned tradeoff can be controlled to maximize energy efficiency. We further propose three distinct criteria for selecting which users' symbols to perturb, each of which yields a different performance-complexity tradeoff. The presented analytical and simulation results show that partially perturbing the data provides a favorable tradeoff, particularly at low-power transmission where the power consumption associated with the signal processing becomes dominant. In fact, it is shown that diversity close to the one for conventional VP can be achieved at energy efficiency levels improved by up to 300% compared to VP.

MMSE precoding for multiuser MISO downlink transmission with non-homogeneous user SNR conditions

This paper is concerned with linear precoding designs for multiuser downlink transmissions. We consider a multiple-input single-output (MISO) system with multiple single-antenna user equipment (UE) experiencing non-homogeneous average signal-to-noise ratio (SNR) conditions. The first part of this work examines different precoding schemes with perfect channel state information (CSI) and average SNR at the base-station (eNB). We then propose a weighted minimum mean squared error (WMMSE) precoder, which takes advantage of the non-homogeneous SNR conditions. Given in a closed-form solution, the proposed WMMSE precoder outperforms other well-known linear precoders, such as zero-forcing (ZF), regularized ZF (RZF), while achieving a close performance to the locally optimal iterative WMMSE (IWMMSE) precoder, in terms of the achievable network sum-rate. In the second part of this work, we consider the non-homogeneous multiuser system with limited and quantized channel quality indicator (CQI) and channel direction indicator (CDI) feedbacks. Based on the CQI and CDI feedback models proposed for the Long-Term Evolution Advanced standard, we then propose a robust WMMSE precoder in a closed-form solution which takes into account the quantization errors. Simulation shows a significant improvement in the achievable network sum-rate by the proposed robust WMMSE precoder, compared to non-robust linear precoder designs.

Power allocation scheme based on sum capacity maximization for signal-to-leakage-and-noise ratio precoded multiuser multiple-input single-output downlink

This paper proposes a power allocation scheme to maximize the sum capacity of all users for signal-to-leakage-and-noise ratio SLNR precoded multiuser multiple-input single-output downlink. The designed scheme tries to explore the effect of the power allocation for the SLNR precoded multiuser multiple-input single-output system on sum capacity performance. This power allocation problem can be formulated as an optimization problem. With high signal-to-interference-plus-noise ratio assumption, it can be converted into a convex optimization problem through the geometric programming and hence can be solved efficiently. Because the assumption of high signal-to-interference-plus-noise ratio cannot be always satisfied in practice, we design a globally optimal solution algorithm based on a combination of branch and bound framework and convex relaxation techniques. Theoretically, the proposed scheme can provide optimal power allocation in sum capacity maximization. Then, we further propose a judgement-decision algorithm to achieve a trade-off between the optimality and computational complexity. The simulation results also show that, with the proposed scheme, the sum capacity of all the users can be improved compared with three existing power allocation schemes. Meanwhile, some meaningful conclusions about the effect of the further power allocation based on the SLNR precoding have been also acquired. The performance improvement of the maximum sum capacity power allocation scheme relates to the transmit antenna number and embodies different variation trends in allusion to the different equipped transmit antenna number as the signal-to-noise ratio SNR changes.Copyright © 2013 John Wiley & Sons, Ltd.