Multiuser Multiple-input Single-output Systems Research Articles

Multi-IRS-Aided Millimeter-Wave Multi-User MISO Systems for Power Minimization Using Generalized Benders Decomposition

Difficulties in controlling IRSs to form the optimized passive beamforming have rarely been considered in intelligent reflecting surface (IRS)-aided systems, which are summarized as follows: 1) sending the optimized passive precoding vectors to the IRS controller incurs significant control overheads; 2) implementing the optimized passive precoding needs to set massive modes in the IRS control circuit. To address these issues, we investigate codebook-based passive beamforming for multi-IRS-aided millimeter-wave (mmWave) multi-user multiple-input single-output (MU-MISO) systems, where the control overheads are reduced to several scalars and the number of modes set in the IRS control circuit is reduced to that of codewords. Moreover, we formulate a joint passive and active precoding problem in the multi-IRS-aided mmWave MU-MISO system as a mixed-integer nonlinear programming (MINLP) problem, and then develop a generalized Benders decomposition (GBD)-based joint passive and active precoding algorithm. The proposed algorithm offers near-optimal performance (≥ 99.9%) with significantly-reduced computational complexity. Simulation results show that the proposed algorithm achieves energy savings of up to 50% and 95%, compared to the benchmark by the maximum ratio transmission and that without IRSs, respectively. In addition, the energy savings increase with the number of reflecting elements packed on each IRS as well as that of codewords.

Sum throughput optimization of wireless powered IRS-assisted multi-user MISO system

Intelligent reflecting surface (IRS) is a promising technology for beyond-5G wireless communication systems. However, the energy demand of IRS is often overlooked in existing works, leading to performance issues in practical scenarios. To address this issue, this paper proposes an operating model based on time switching (TS) protocol for an IRS-assisted multi-user multiple-input single-output (MISO) system, which can provide energy for IRS through wireless power transfer (WPT) technology. The system throughput maximization problem is addressed to improve performance. Specifically, a two-stage algorithm combined with alternating optimization, denoted as TAO, is proposed. To further improve the optimization process in large-size IRS scenarios, an improved deep deterministic policy gradient (DDPG) method combined with TAO, denoted as TAO-DDPG, is also proposed. Numerical results demonstrate that the proposed TAO-DDPG algorithm achieves similar performance to TAO while greatly reducing the optimization time.

A Bipartite Graph Neural Network Approach for Scalable Beamforming Optimization

Deep learning (DL) techniques have been intensively studied for the optimization of multi-user multiple-input single-output (MU-MISO) downlink systems owing to the capability of handling nonconvex formulations. However, the fixed computation structure of existing deep neural networks (DNNs) lacks flexibility with respect to the system size, i.e., the number of antennas or users. This paper develops a bipartite graph neural network (BGNN) framework, a scalable DL solution designed for multi-antenna beamforming optimization. The MU-MISO system is first characterized by a bipartite graph where two disjoint vertex sets, each of which consists of transmit antennas and users, are connected via pairwise edges. These vertex interconnection states are modeled by channel fading coefficients. Thus, a generic beamforming optimization process is interpreted as a computation task over a weighted bipartite graph. This approach partitions the beamforming optimization procedure into multiple suboperations dedicated to individual antenna vertices and user vertices. Separated vertex operations lead to scalable beamforming calculations that are invariant to the system size. The vertex operations are realized by a group of DNN modules that collectively form the BGNN architecture. Identical DNNs are reused at all antennas and users so that the resultant learning structure becomes flexible to the network size. Component DNNs of the BGNN are trained jointly over numerous MU-MISO configurations with randomly varying network sizes. As a result, the trained BGNN can be universally applied to arbitrary MU-MISO systems. Numerical results validate the advantages of the BGNN framework over conventional methods.

Fitness landscape analysis and niching genetic approach for hybrid beamforming in RIS-aided communications

Reconfigurable intelligent surface (RIS) is a revolutionizing technology to achieve cost-effective communications. The active beamforming at the base station (BS) and the discrete phase shifts at RIS should be jointly designed to customize the propagation environment. However, current phase-shift setting methods ignore the non-separable property of phase shifts, degrading the performance, especially in cases with a large-sized RIS. To understand the problem characteristics related to the phase shifts and further tailor an eligible method with such characteristics, this paper, for the first time, analyzes the fitness landscape of the sum-rate maximization problem (maximizing the sum rate of users in a downlink multi-user multiple-input single-output system assisted by a RIS). Results show that the problem has a severe unstructured and rugged landscape, especially in cases with a large-sized RIS. This observation answers why current methods are ineligible and provides insightful guidance for designing a more intelligent method. With the landscape findings in mind, this paper introduces a niching genetic algorithm to solve the problem. In particular, the niching idea is employed to locate multiple local optima. These local optima act as stepping stones to facilitate approaching the global optima. Simulation results demonstrate that the proposed niching genetic algorithm obtains significant capacity gains over current methods in cases with large-sized RIS.

Precoding Design for Multi-User MISO Systems With Delay-Constrained and -Tolerant Users

In both academia and industry, multi-user multiple-input single-output (MU-MISO) techniques have shown enormous gains in spectral efficiency by exploiting spatial degrees of freedom. So far, an underlying assumption in most of the existing MU-MISO design has been that all the users use infinite blocklength, so that they can achieve the Shannon capacity. This setup, however, is not suitable considering delay-constrained users whose blocklength tends to be finite. In this paper, we consider a heterogeneous setting in MU-MISO systems where delay-constrained users and delay-tolerant users coexist, called a DCTU-MISO network. To maximize the sum spectral efficiency in this system, we present the spectral efficiency for delay-tolerant users and provide a lower bound of the spectral efficiency for delay-constrained users. We consider an optimization problem that maximizes the sum spectral efficiency of delay-tolerant users while satisfying the latency constraint of delay-constrained users, and propose a generalized power iteration (GPI) precoding algorithm that finds a principal precoding vector. Furthermore, we extend a DCTU-MISO network to the multiple time slots scenario and propose a recursive GPI precoding algorithm. In simulation results, we validate proposed methods outperform baseline schemes and present the effect of network parameters on the average sum spectral efficiency.

Average Rate Approximation and Maximization for RIS-Assisted Multi-User MISO System

In this letter, we investigate a reconfigurable intelligent surface (RIS) assisted downlink multi-user multiple-input single-output (MISO) system. We derive the approximations of average rate of user equipments (UEs) under proper assumptions, and reveal the relations between average rates and system parameters. Furthermore, a RIS configuration algorithm is proposed to improve the average sum rate with low complexity by exploiting the approximation of average rate and statistical channel state information (CSI). The rationality of the assumptions, the tightness of the approximations and the effectiveness of the proposed algorithm are validated by numerical results.

Sum-Rate Analysis of a Multi-Cell Multi-User MISO System Under Double Scattering Channels

This paper aims to derive expressions of the downlink ergodic user rates in a multi-cell large-scale multi-user multiple-input single-output (MISO) system under the assumption that each base station (BS) employs maximum ratio transmission (MRT) precoding and that single-antenna users in each cell are divided into groups, where channels of users in the same group share common covariance matrices and follow the double scattering channel model. Moreover, both channel estimation errors and pilot contamination effects caused by re-use of pilot sequences in neighboring cells are taken into consideration in this work. The analysis is carried out using statistical tools under the exact and asymptotic regimes in which the number of antennas at BS N, the number of users in each cell K, and the number of scatterers S grow large at the same pace. Furthermore, the obtained exact expressions and deterministic approximations of the ergodic rates are expressed in simplified closed-forms under the special case of multi-keyhole channels to yield useful insights. They reveal that signal-to-noise plus interference ratio (SINR) without user grouping in a multi-keyhole channel is similar to that under standard Rayleigh channel in the asymptotic regime. However, under user grouping, we show that the massive multiple-input multiple-output (MIMO) gains promised by deploying large-scale antenna arrays in multi-cell settings are limited by the number of scatterers even if the number of antennas grows large. Simulation results illustrate the close match provided by the asymptotic analysis for moderate system dimensions and confirm the insights drawn from the theoretical findings.

Rank-1 Matrix Approximation-Based Channel Estimation for Intelligent Reflecting Surface-Aided Multi-User MISO Communications

The acquisition of channel state information is an essential step in enabling intelligent reflecting surfaces (IRSs) for wireless communications. In this letter, we introduce a novel procedure to estimate the cascaded channel between the base station (BS), IRS, and users in a multi-user multiple-input single-output system. The common BS-IRS channel, over which all users transmit, is leveraged to decompose the cascaded channel into a series of rank-1 matrices. Low-rank matrix recovery methods are utilized to improve upon the linear minimum mean-squared error estimate of the cascaded channel. A theoretical upper bound for the mean-square error (MSE) of the proposed estimator is derived. Numerical results reveal that the proposed techniques outperform the existing counterparts in terms of the MSE and scale with the number of BS antennas.

Error Probability Analysis and Power Allocation for Interference Exploitation Over Rayleigh Fading Channels

This paper considers the performance analysis of constructive interference (CI) precoding technique in multi-user multiple-input single-output (MU-MISO) systems with a finite constellation phase-shift keying (PSK) input alphabet. Firstly, analytical expressions for the moment generating function (MGF) and the average of the received signal-to-noise-ratio (SNR) are derived. Then, based on the derived MGF expression the average symbol error probability (SEP) for the CI precoder with PSK signaling is calculated. In this regard, new exact and very accurate asymptotic approximation for the average SEP are provided. Building on the new performance analysis, different power allocation schemes are considered to enhance the achieved SEP. In the first scheme, power allocation based on minimizing the sum symbol error probabilities (Min-Sum) is studied, while in the second scheme the power allocation based on minimizing the maximum SEP (Min-Max) is investigated. Furthermore, new analytical expressions of the throughput and power efficiency of the CI precoding in MU-MISO systems are also derived. The numerical results in this work demonstrate that, the CI precoding outperforms the conventional interference suppression precoding techniques with an up to 20 dB gain in the transmit SNR in terms of SEP, and up to 15 dB gain in the transmit SNR in terms of the throughput. In addition, the SEP-based power allocation schemes provide additional up to 13 dB gains in the transmit SNR compared to the conventional equal power allocation scheme.

Joint Symbol-Level Precoding and Reflecting Designs for IRS-Enhanced MU-MISO Systems

Intelligent reflecting surfaces (IRSs) have emerged as a revolutionary solution to enhance wireless communications by changing propagation environment in a cost-effective and hardware-efficient fashion. In addition, symbol-level precoding (SLP) has attracted considerable attention recently due to its advantages in converting multiuser interference (MUI) into useful signal energy. Therefore, it is of interest to investigate the employment of IRS in symbol-level precoding systems to exploit MUI in a more effective way by manipulating the multiuser channels. In this paper, we focus on joint symbol-level precoding and reflecting designs in IRS-enhanced multiuser multiple-input single-output (MU-MISO) systems. Both power minimization and quality-of-service (QoS) balancing problems are considered. In order to solve the joint optimization problems, we develop an efficient iterative algorithm to decompose them into separate symbol-level precoding and block-level reflecting design problems. An efficient gradient-projection-based algorithm is utilized to design the symbol-level precoding and a Riemannian conjugate gradient (RCG)-based algorithm is employed to solve the reflecting design problem. Simulation results demonstrate the significant performance improvement introduced by the IRS and illustrate the effectiveness of our proposed algorithms.

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.

Semi-Blind Interference Aligned NOMA for Downlink MU-MISO Systems

The application of non-orthogonal multiple access (NOMA) to downlink multi-user multiple-input single-output systems involves the design of a beamforming strategy in which the spatial dimension provided by each beam is shared among several users performing NOMA. This approach requires the management of both inter-cluster and intra-cluster interference. Moreover, the beamforming design is subject to instantaneous knowledge of the channel state information at the transmitter (CSIT). We propose a novel transmission scheme that combines blind interference alignment and NOMA. The proposed scheme fully cancels the inter-cluster interference for all users without the need for instantaneous CSIT, which is limited to the knowledge of the large scale effects of the channel in order to implement NOMA within each cluster. Considering user pairing, i.e., each cluster is composed of two users, we derive a method for determining the NOMA power coefficients that maximize the sum-rate, the user fairness or satisfy first the rate of a specific user by simply solving a polynomial function. Furthermore, we propose an alternative methodology based on some approximations in order to provide sub-optimal closed-form expressions of these NOMA power coefficients. Simulation results show that the proposed scheme outperforms conventional MISO-NOMA taking into consideration the costs of providing CSIT.

Construction of 1-Bit Transmit-Signal Vectors for Downlink MU-MISO Systems With PSK Signaling

We consider a downlink multi-user multiple-input single-output system where the base station has a large number of antennas with cost-effective 1-b digital-to-analog converters. For this system, we first identify that assigning the zero-power to some transmit signals (in short, zero-power allocation) can yield a non-trivial symbol-error-rate performance gain by alleviating an error-floor problem. Likewise the related works on 1-b precoding, finding an optimal transmit-signal vector (encompassing precoding and zero-power allocation) requires an exhaustive search due to its combinatorial nature. Motivated by this, we propose a low-complexity two-stage algorithm to construct such transmit-signal vector directly. In the first stage, we derive a feasible transmit-signal vector via iterative-soft-thresholding algorithm whose output ensures that each user's noiseless observation belong to a desired region (called decision region). In the second stage, a bit-flipping algorithm is performed to refine the feasible vector so that each user's received signal is more robust to additive Gaussian noises. Simulation results demonstrate that the proposed method can yield a more elegant performance-complexity tradeoff than the existing 1-b precoding methods.

Joint Antenna Array Mode Selection and User Assignment for Full-Duplex MU-MISO Systems

This paper considers a full-duplex (FD) multiuser multiple-input single-output system where a base station simultaneously serves both uplink (UL) and downlink (DL) users on the same time-frequency resource. The crucial barriers in implementing FD systems reside in the residual self-interference and co-channel interference. To accelerate the use of FD radio in future wireless networks, we aim at managing the network interference more effectively by jointly designing the selection of half-array antenna modes (in the transmit or receive mode) at the base station with time phases and user assignments. The first problem of interest is to maximize the overall sum rate subject to quality-of-service requirements, which is formulated as a highly non-concave utility function followed by non-convex constraints. To address the design problem, we propose an iterative low-complexity algorithm by developing new inner approximations, and its convergence to a stationary point is guaranteed. To provide more insights into the solution of the proposed design, a general max–min rate optimization is further considered to maximize the minimum per-user rate while satisfying a given ratio between UL and DL rates. Furthermore, a robust algorithm is devised to verify that the proposed scheme works well under channel uncertainty. The simulation results demonstrate that the proposed algorithms exhibit fast convergence and substantially outperform existing schemes.

Constructive Interference Optimization for Data-Aided Precoding in Multi-User MISO Systems

Unlike the general concept of eliminating or avoiding inter-user interference in the downlink multi-user multiple-input single-output (MISO) system, the data-aided precoding scheme attempts to exploit the constructive interference at symbol level. Positive interference can be constructed to enhance the received signal gain by predicting the phase and magnitude of the inter-user interference. In this paper, we formulate a constructive interference optimization problem that minimizes a sum of minimum mean square error (MMSE) for all users, while ensuring the minimum required constructive interference gain with a fixed total power constraint. As opposed to the existing scheme, such as constructive zero-forcing precoding or minimum power precoding subject to strict phase conservation for phase-shift keying (PSK), our proposed scheme exploits a full range of relaxation for the constructive interference region, while ensuring the link performance by minimizing the sum of mean-square error (MSE) for all users. In fact, the relaxed requirements lead to more degrees of freedom for improving the cumulative constructive interference gain (CCIG) under the varying channel conditions. Furthermore, our MMSE-based optimization approach allows for a semi-closed-form optimal solution to the data-aided precoding scheme, providing a more CCIG without incurring unacceptable complexity than other state-of-the-art schemes.

SINR Balancing via Base Station Association, Beamforming, and Power Control in Downlink Multicell MISO Systems

This paper considers the downlink channel of multicell multiuser multiple-input single-output systems with arbitrary architecture. We aim to maximize the minimum weighted signal-to-interference-plus-noise ratio (SINR) through user-base station (BS) association, coordinated beamforming among BSs, and power control subject to per BS power constraints. The problem is known to be NP-hard. In the high-SNR regime, where the performance is interference-limited, we globally optimize the upper bound, which is achieved asymptotically, of the balanced SINR. In the low-SNR regime, where the performance is restricted by the tightest per BS power constraint, we balance the transmit power using relaxed integer programming and group sparse optimization techniques. The two goals can be integrated to achieve a universally better performance. From the perspective of optimization methods, the corresponding algorithms are based on Lagrangian relaxation and are guaranteed to converge. Simulation results show that the proposed algorithms outperform the existing algorithms designed for the downlink single-input single-output systems.

Multi-Antenna Constant Envelope Wireless Power Transfer

In this paper, we study wireless power transfer in a multiuser multiple-input single-output system, where a base station equipped with multiple antennas wirelessly transfers power to distributed single-antenna users. To reduce the implementation cost, we propose a constant-envelope analog beamforming scheme to simultaneously transfer power to multiple users. The proposed scheme requires only a single radio frequency (RF) chain at the multi-antenna transmitter. We consider the beamforming design to maximize the sum-power transferred. We show that the proposed constant-envelope beamforming design only incurs about 1-dB power loss under homogeneous and independent Rayleigh fading, as compared with the optimal variable-envelope digital beamforming design (that however requires one RF chain for each transmit antenna). We further consider user fairness and study the beamforming design to maximize the minimum received power of all users. We also address the problem of maximizing the sum-power transferred under the quality-of-service constraint for each user. Moreover, we extend our beamforming design to the case with only partial channel state information at the transmitter. Numerical results show that constant-envelope analog beamforming is a promising cost-effective technique for multiuser multi-antenna wireless power transfer.

Energy-Efficient Beam Coordination Strategies With Rate-Dependent Processing Power

This paper proposes energy-efficient coordinated beamforming strategies for multi-cell multi-user multiple-input single-output system. We consider a practical power consumption model, where part of the consumed power depends on the base station or user specific data rates due to coding, decoding and backhaul. This is different from the existing approaches where the base station power consumption has been assumed to be a convex or linear function of the transmit powers. Two optimization criteria are considered, namely network energy efficiency maximization and weighted sum energy efficiency maximization. We develop successive convex approximation based algorithms to tackle these difficult nonconvex problems. We further propose decentralized implementations for the considered problems, in which base stations perform parallel and distributed computation based on local channel state information and limited backhaul information exchange. The decentralized approaches admit closed-form solutions and can be implemented without invoking a generic external convex solver. We also show an example of the pilot contamination effect on the energy efficiency using a heuristic pilot allocation strategy. The numerical results are provided to demonstrate that the rate dependent power consumption has a large impact on the system energy efficiency, and, thus, has to be taken into account when devising energy-efficient transmission strategies. The significant gains of the proposed algorithms over the conventional low-complexity beamforming algorithms are also illustrated.

A Low Complexity User Selection Algorithm for Full-Duplex MU-MISO Systems

In this paper, we propose a new user selection algorithm for full-duplex (FD) multiuser multiple-input single-output (MU-MISO) systems, where an FD base station (BS) communicates with multiple half-duplex users in both downlink and uplink channels simultaneously. Due to self-interference at the BS and co-channel interference among users, a joint downlink and uplink user selection to maximize system performance incurs high search complexity. To reduce the complexity, we introduce a two-step user selection algorithm, which successively chooses downlink users followed by uplink users based on the decomposed sum rate of the FD systems. In addition, we analyze the average sum rate performance of our proposed user selection algorithm for FD MU-MISO systems and derive a tight approximation of the performance. From the numerical results, we confirm that our analysis matches well with simulation results, and the proposed user selection algorithm for the FD MU-MISO systems exhibits a small performance loss compared with the optimal user selection algorithm with much reduced complexity.

Robust secure transmission for multiuser MISO systems with probabilistic QoS constraints

This paper considers a unicast multiuser multiple-input single-output (MISO) downlink system overheard by multiple single-antenna eavesdroppers. The objective is to jointly design the beamforming vectors and the artificial noise (AN) covariance matrix with imperfect channel state information (CSI) at the transmitter, such that the total transmit power is minimized while satisfying probabilistic quality of service (QoS) constraints at legitimate users and the eavesdroppers. Using Bernstein-type inequalities and the S-procedure, we recast the non-convex power minimization problem as two different convex semidefinite programs (SDPs) which can be solved using interior-point methods. Simulation results show that the proposed methods outperform a nonrobust method and the ones using the isotropic AN.