Weighted Sum Rate Maximization Research Articles

Joint Beamforming Design for IRS Aided Multiuser MIMO With Imperfect CSI

This paper investigates the joint beamforming design for the intelligent reflecting surface (IRS) aided multi-antenna multiuser (MU) multiple-input multiple-output (MIMO) downlink transmissions under imperfect channel state information (CSI), where the IRS can only take discrete PSs (PSs) at each element and the weighted sum rate (WSR) is adopted as the performance metric. By deriving the covariance matrix of the interference and noise at the users under the statistical channel estimation errors (CEEs) model, the joint WSR maximization problem is reformulated as an equivalent weighted minimum mean square error minimization problem and decoupled into two subproblems which are solved alternatively. In particular, two algorithms based on the majorization-minimization and gradient descent methods are proposed to obtain the optimal beamforming matrix at the IRS. Simulation results validate the accuracy of the proposed robust design and reveal that in case of imperfect CSI, the IRS can still achieve a significant improvement in WSR even with 2-bits PSs at the IRS. Moreover, it is also found that increasing the number of reflecting elements may not always be beneficial and that the optimal location of the IRS may be closer to the base station in the presence of CEEs.

Weighted Sum Rate Maximization for Two-Way Wireless Powered Interference Channels

Interference is a detrimental factor for information decoding, but it can be a helpful resource for energy harvesting in a wireless powered network. Considering a two-way wireless powered interference channel, in this study, we present a simultaneous wireless information and power transfer (SWIPT)-then-wireless information transfer (WIT) protocol. In this protocol, transmitters perform SWIPT, and receivers receive both information and energy simultaneously in the forward link (FL). Then, the receivers perform WIT using the harvested energy in the backward link (BL). To maximize the weighted sum rate of the FL and BL, we jointly optimize the transmit power and energy harvesting (EH) ratio according to time switching and power splitting policies. To solve this non-convex optimization problem, we propose an iterative power control and energy harvesting algorithm based on dual methods that reduce computational complexity. The results show that the proposed algorithm finds the optimal transmit power and EH ratio suitably and thus maximizes the weighted sum rate. Consequently, the proposed SWIPT-then-WIT protocol expands the achievable rate region significantly compared with conventional schemes that do not adaptively control the transmit power and EH ratio.

Weighted Sum Rate Maximization of the mmWave Cell-Free MIMO Downlink Relying on Hybrid Precoding

The cell-free MIMO concept relying on hybrid precoding constitutes an innovative technique capable of dramatically increasing the network capacity of millimeter-wave (mmWave) communication systems. It dispenses with the cell boundary of conventional multi-cell MIMO systems, while drastically reducing the power consumption by limiting the number of radio frequency (RF) chains at the access points (APs). In this paper, we aim for maximizing the weighted sum rate (WSR) of mmWave cell-free MIMO systems by conceiving a low-complexity hybrid precoding algorithm. We formulate the WSR optimization problem subject to the transmit power constraint for each AP and the constant-modulus constraint for the phase shifters of the analog precoders. A block coordinate descent (BCD) algorithm is proposed for iteratively solving the problem. In each iteration, the classic Lagrangian multiplier method and the penalty dual decomposition (PDD) method are combined for obtaining near-optimal hybrid analog/digital precoding matrices. Furthermore, we extend our proposed algorithm for deriving closed-form expressions for the precoders of fully digital cell-free MIMO systems. Moreover, we present the convergency analysis and complexity analysis of our proposed method. Finally, our simulation results demonstrate the superiority of the algorithms proposed for both fully digital and hybrid precoding matrices.

User scheduling and power allocation for downlink multi-cell multi-carrier NOMA systems

In Non-Orthogonal Multiple Access (NOMA), the best way to fully exploit the benefits of the system is the efficient resource allocation. For the NOMA power domain, the allocation of power and spectrum require solving the mixed-integer nonlinear programming NP-hard problem. In this paper, we investigate user scheduling and power allocation in Multi-Cell Multi-Carrier NOMA (MCMC-NOMA) networks. To achieve that, we consider Weighted Sum Rate Maximization (WSRM) and Weighted Sum Energy Efficiency Maximization (WSEEM) problems. First, we tackle the problem of user scheduling for fixed power using Fractional Programming (FP), the Lagrange dual method, and the decomposition method. Then, we consider Successive Pseudo-Convex Approximation (SPCA) to deal with the WSRM problem. Finally, for the WSEEM problem, SPCA is utilized to convert the problem into separable scalar problems, which can be parallelly solved. Thus, the Dinkelbach algorithm and constraints relaxation are used to characterize the closed-form solution for power allocation. Extensive simulations have been implemented to show the efficiency of the proposed framework and its superiority over other existing schemes.

Downlink Resource Allocation in Multiuser Cell-Free MIMO Networks With User-Centric Clustering

In this paper, we optimize user scheduling, power allocation and beamforming in distributed multiple-input multiple-output (MIMO) networks implementing user-centric clustering. We study both the coherent and non-coherent transmission modes, formulating a weighted sum rate maximization problem for each; finding the optimal solution to these problems is known to be NP-hard. We use tools from fractional programming, block coordinate descent, and compressive sensing to construct an algorithm that optimizes the beamforming weights and user scheduling and converges in a smooth non-decreasing pattern. Channel state information (CSI) being crucial for optimization, we highlight the importance of employing a low-overhead pilot assignment policy for scheduling problems. In this regard, we use a variant of hierarchical agglomerative clustering, which provides a suboptimal, but feasible, pilot assignment scheme; for our cell-free case, we formulate an <i>area-based</i> pilot reuse factor. Our results show that our scheme provides large gains in the long-term network sum spectral efficiency compared to benchmark schemes such as zero-forcing and conjugate beamforming (with round-robin scheduling) respectively. Furthermore, the results show the superiority of coherent transmission compared to the non-coherent mode under ideal and imperfect CSI for the area-based pilot-reuse factors we consider.

Double Intelligent Reflecting Surface-Assisted Multi-User MIMO Mmwave Systems With Hybrid Precoding

This work investigates the effect of double intelligent reflecting surface (IRS) in improving the spectrum efficient of multi-user multiple-input multiple-output (MIMO) network operating in the millimeter wave (mmWave) band. Specifically, we aim to solve a weighted sum rate maximization problem by jointly optimizing the digital precoding at the transmitter and the analog phase shifters at the IRS, subject to the minimum achievable rate constraint. To facilitate the design of an efficient solution, we first reformulate the original problem into a tractable one by exploiting the majorization-minimization (MM) method. Then, a block coordinate descent (BCD) method is proposed to obtain a suboptimal solution, where the precoding matrices and the phase shifters are alternately optimized. Specifically, the digital precoding matrix design problem is solved by the quadratically constrained quadratic programming (QCQP), while the analog phase shift optimization is solved by the Riemannian manifold optimization (RMO). The convergence and computational complexity are analyzed. Finally, simulation results are provided to verify the performance of the proposed design, as well as the effectiveness of double-IRS in improving the spectral efficiency.

Signaling Design for MIMO-NOMA With Different Security Requirements

Signaling design for secure transmission in two-user multiple-input multiple-output (MIMO) non-orthogonal multiple access (NOMA) networks is investigated in this paper. The base station broadcasts multicast data to all users and also integrates additional services, unicast data targeted to certain users, and confidential data protected against eavesdroppers. We categorize the above MIMO-NOMA with different security requirements into several communication scenarios. The associated problem in each scenario is nonconvex. We propose a unified approach, called the power splitting scheme, for optimizing the rate equations corresponding to the scenarios. The proposed method decomposes the optimization of the secure MIMO-NOMA channel into a set of simpler problems, including multicast, point-to-point, and wiretap MIMO problems, corresponding to the three basic messages: multicast, private/unicast, and confidential messages. We then leverage existing solutions to design signaling for the above problems such that the messages are transmitted with high security and reliability. Numerical results illustrate the efficacy of the proposed covariance matrix design in secure MIMO-NOMA transmission. The proposed method also outperforms existing solutions, when applicable. In the case of no multicast messages, we also reformulate the nonconvex problem into weighted sum rate (WSR) maximization problems by applying the block successive maximization method and generalizing the zero duality gap. The two methods have their advantages and limitations. Power splitting is a general tool that can be applied to the MIMO-NOMA with any combination of the three messages (multicast, private, and confidential) whereas WSR maximization shows greater potential for secure MIMO-NOMA communication without multicasting. In such cases, WSR maximization provides a slightly better rate than the power splitting method.

SLINR-Based Downlink Optimization in MU-MIMO Networks

Optimizing the downlink of multi-cell multiuser multiple input multiple output (MU-MIMO) networks has received substantial attention; however, the schemes in the literature consider centralized solutions requiring significant overhead in information exchange (e.g., global channel state information or CSI) and computation load (the need to solve a single large problem). This paper presents a <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">decentralized</i> weighted sum-rate (WSR) maximization algorithm for the multiuser downlink, accounting for beamforming, scheduling, and power allocation. We show that the signal-to-leakage-plus-noise ratio (SLNR) used in previous work suffers from significant drawbacks that limit its potential use in WSR maximization. We address this by proposing a new performance measure, the signal-to-leakage-plus-interference-plus-noise ratio (SLINR), which incorporates <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">intra-cell interference</i> and <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">inter-cell leakage</i> . The SLINR exploits the benefits of the SLNR approach, but by explicitly including interference, avoids many of its flaws. We derive an iterative and decentralized resource allocation approach under imperfect CSI, and our simulation results show that, despite BSs using only <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">local information</i> , the proposed algorithm comes within 3.8% of the throughput achieved by centralized schemes.

A Matrix-Inverse-Free Implementation of the MU-MIMO WMMSE Beamforming Algorithm

The WMMSE beamforming algorithm is a popular approach to address the NP-hard weighted sum rate (WSR) maximization beamforming problem. Although it efficiently finds a local optimum, it requires matrix inverses, eigendecompositions, and bisection searches, operations that are problematic for real-time implementation. In our previous work, we considered the MU-MISO case with single-antenna receivers and effectively replaced such operations by resorting to a first-order method. Here, we consider the more general and challenging MU-MIMO case with multiple-antenna receivers. Our earlier approach does not generalize to this scenario and cannot be applied to replace all the hard-to-parallelize operations that appear in the MU-MIMO case. Thus, we propose to leverage a reformulation of the auxiliary WMMSE function given by Hu et al. By applying gradient descent and Schulz iterations, we formulate the first variant of the WMMSE algorithm applicable to the MU-MIMO case that is free from matrix inverses and other serial operations and hence amenable to both real-time implementation and deep unfolding. From a theoretical viewpoint, we establish its convergence to a stationary point of the WSR maximization problem. From a practical viewpoint, we show that in a deep-unfolding-based implementation, the matrix-inverse-free WMMSE algorithm attains, within a fixed number of iterations, a WSR comparable to the original WMMSE algorithm truncated to the same number of iterations, yet with significant implementation advantages in terms of parallelizability and real-time execution.

Matrix-Inverse-Free Deep Unfolding of the Weighted MMSE Beamforming Algorithm

Downlink beamforming is a key technology for cellular networks. However, computing beamformers that maximize the weighted sum rate (WSR) subject to a power constraint is an NP-hard problem. The popular weighted minimum mean square error (WMMSE) algorithm converges to a local optimum but still exhibits considerable complexity. In order to address this trade-off between complexity and performance, we propose to apply deep unfolding to the WMMSE algorithm for a MU-MISO downlink channel. The main idea consists of mapping a fixed number of iterations of the WMMSE into trainable neural network layers. However, the formulation of the WMMSE algorithm, as provided in Shi <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">et al.</i> , involves matrix inversions, eigendecompositions, and bisection searches. These operations are hard to implement as standard network layers. Therefore, we present a variant of the WMMSE algorithm i) that circumvents these operations by applying a projected gradient descent and ii) that, as a result, involves only operations that can be efficiently computed in parallel on hardware platforms designed for deep learning. We demonstrate that our variant of the WMMSE algorithm convergences to a stationary point of the WSR maximization problem and we accelerate its convergence by incorporating Nesterov acceleration and a generalization thereof as learnable structures. By means of simulations, we show that the proposed network architecture i) performs on par with the WMMSE algorithm truncated to the same number of iterations, yet at a lower complexity, and ii) generalizes well to changes in the channel distribution.

Beamforming Design for Multiuser uRLLC With Finite Blocklength Transmission

Driven by the explosive growth of Internet of Things (IoT) devices with stringent requirements on latency and reliability, ultra-reliability and low latency communication (uRLLC) has become one of the three key communication scenarios for the 5th generation (5G) and 6G communication systems. In this paper, we focus on the beamforming design problem for the downlink multiuser uRLLC system. Since the strict demand on the reliability and latency, in general, short packet transmission is a favorable way for uRLLC systems, which indicates the classical Shannon&#x2019;s capacity formula is no longer applicable. With the finite blocklength transmission, the achievable rate is greatly influenced by the reliability and finite blocklength. Using the developed achievable rate formula for finite blocklength transmission, we respectively formulate the problems of interest as the weighted sum rate maximization, energy efficiency maximization, and user fairness optimization by considering the maximum allowable transmission power and minimum rate requirement. These problems considered are non-convex and are hard to obtain the global optimal solution, even for the local optimal solution. To overcome these difficulties, some important insights have been discovered by analyzing the function of achievable rate. For example, an analytical solution of the minimum rate requirement is provided with respective to the signal-to-interference-plus-noise ratio. Based on the discovered results, we provide algorithms to optimize the beamforming vectors and power allocation, which are guaranteed to converge to a local optimum solution to the formulated problems with low computational complexity. Our simulation results reveal that our proposed beamforming algorithms outperform the zero-forcing beamforming algorithm with equal power or water filling allocation widely used in the existing literatures.

Efficient Beam Scheduling for Half-Duplex mmWave Relay Networks

Millimeter wave (mmWave) communication is expected to play a central role in next generation mobile systems (5G) and beyond, by providing multi-Gbps data rates. However, the severe pathloss and sensitivity to blockages at mmWave frequencies significantly challenge practical implementations. One effective way to mitigate these effects and to increase the communication range is beamforming in combination with relaying. In this paper, we study the beam scheduling problem for mmWave half-duplex (HD) relay networks, where the relay topology can be arbitrary. Based on theoretically optimal scheduling results, we first implement a network simplification procedure to reduce the network topology complexity, and then propose two practically relevant beam scheduling schemes: the deterministic edge coloring (EC) scheduler and the adaptive backpressure (BP) scheduler. The former consists of a very simple one-time computation of the sequence of scheduling states, which is then repeated periodically. The one-time computation depends on the underlying network topology, and therefore it must be repeated when such topology changes. As such, this approach is more suited to quasi-static scenarios. The latter is an “online” approach which updates scheduling weights and solves at each time slots a weighted sum rate maximization. Hence, it's computational complexity may be significantly higher than that of EC, but it is better suited to dynamic time-varying scenarios. With the aid of computer simulations, we show that both the proposed schedulers guarantee network stability within the network capacity. Particularly, in comparison with two baseline schemes, the proposed schedulers achieve much smaller queuing backlogs, much smaller backlog fluctuations, and much lower packet end-to-end delays.

Joint Deployment and Multiple Access Design for Intelligent Reflecting Surface Assisted Networks

The fundamental intelligent reflecting surface (IRS) deployment problem is investigated for IRS-assisted networks, where one IRS is arranged to be deployed in a specific region for assisting the communication between an access point (AP) and multiple users. Specifically, three multiple access schemes are considered, namely non-orthogonal multiple access (NOMA), frequency division multiple access (FDMA), and time division multiple access (TDMA). The weighted sum rate maximization problem for joint optimization of the deployment location and the reflection coefficients of the IRS as well as the power allocation at the AP is formulated. The non-convex optimization problems obtained for NOMA and FDMA are solved by employing monotonic optimization and semidefinite relaxation to find a performance upper bound. The problem obtained for TDMA is optimally solved by leveraging the time-selective nature of the IRS. Furthermore, for all three multiple access schemes, low-complexity suboptimal algorithms are developed by exploiting alternating optimization and successive convex approximation techniques, where a local region optimization method is applied for optimizing the IRS deployment location. Numerical results are provided to show that: 1) near-optimal performance can be achieved by the proposed suboptimal algorithms; 2) asymmetric and symmetric IRS deployment strategies are preferable for NOMA and FDMA/TDMA, respectively; 3) the performance gain achieved with IRS can be significantly improved by optimizing the deployment location.

Weighted Sum-Rate Maximization for Multi-IRS-Assisted Full-Duplex Systems With Hardware Impairments

Smart and reconfigurable wireless communication environments can be established by exploiting well-designed intelligent reflecting surfaces (IRSs) to shape the communication channels. In this paper, we investigate how multiple IRSs affect the performance of multi-user full-duplex communication systems under hardware impairment at each node, wherein the base station (BS) and the uplink users are subject to maximum transmission power constraints. Firstly, the uplink-downlink system weighted sum-rate (SWSR) is derived as a system performance metric. Then, we formulate the resource allocation design to maximize the SWSR as an optimization problem which jointly optimizes the beamforming and the combining vectors at the BS, the transmit powers of the uplink users, and the phase shifts of multiple IRSs. Since the SWSR optimization problem is non-convex, an efficient iterative alternating approach is proposed to obtain a suboptimal solution for the design problem. In particular, we first reformulate the main problem into an equivalent weighted minimum mean-square-error form and then transform it into several convex sub-problems which can be analytically solved for given phase shifts. Then, the IRSs phases are optimized via a gradient ascent-based algorithm. Finally, numerical results are presented to clarify how multiple IRSs enhance the performance metric under hardware impairment.

Blockage-Aware Reliable mmWave Access via Coordinated Multi-Point Connectivity

The fundamental challenge of the millimeter-wave (mmWave) frequency band is the sensitivity of the radio channel to blockages, which gives rise to unstable connectivity and impacts the reliability of a system. To this end, multi-point connectivity is a promising approach for ensuring the desired rate and reliability requirements. A robust beamformer design is proposed to improve the communication reliability by exploiting the spatial macro-diversity and a pessimistic estimate of rates over potential link blockage combinations. Specifically, we provide a blockage-aware algorithm for the weighted sum-rate maximization (WSRM) problem with parallel beamformer processing across distributed remote radio units (RRUs). Combinations of non-convex and coupled constraints are handled via successive convex approximation (SCA) framework, which admits a closed-form solution for each SCA step, by solving a system of Karush-Kuhn-Tucker (KKT) optimality conditions. Unlike the conventional coordinated multi-point (CoMP) schemes, the proposed blockage-aware beamformer design has, per-iteration, computational complexity in the order of RRU antennas instead of system-wide joint transmit antennas. This leads to a practical and computationally efficient implementation that is scalable to any arbitrary multi-point configuration. In the presence of random blockages, the proposed schemes are shown to significantly outperform baseline scenarios and result in reliable mmWave communication.

Energy-Efficient Resource Allocation in C-RANs with Capacity-Limited Fronthaul

Cloud Radio Access Network (C-RAN) is a key architecture for 5G cellular wireless network that aims at improving spectral and energy efficiency of the network by uniting traditional RAN with cloud computing. In this paper, a novel resource allocation scheme that optimizes the network energy efficiency of a C-RAN is designed. First, an energy consumption model that characterizes the computation energy of the BaseBand Unit (BBU) is introduced based on empirical results collected from a programmable C-RAN testbed. Then, an optimization problem is formulated to maximize the energy efficiency of the network, subject to practical constraints including Quality of Service (QoS) requirement, radio remote head transmit power, and fronthaul capacity limits. The formulated Network Energy Efficiency Maximization (NEEM) problem jointly considers the tradeoff among the network accumulated data rate, BBU power consumption, fronthaul cost, and beamforming design. To deal with the non-convexity and mixed-integer nature of the problem, we utilize successive convex approximation methods to transform the original problem into the equivalent Weighted Sum-Rate (WSR) maximization problem. We then propose a provably-convergent iterative method to solve the resulting WSR problem. Extensive simulation results coupled with real-time experiments on a small-scale C-RAN testbed show the effectiveness of our proposed resource allocation scheme and its advantages over existing approaches.

Joint Power Allocation and Relay Beamforming Optimization for Weighted Sum-Rate Maximization in NOMA AF Relay System

This letter introduces a novel joint power-allocation (PA) and relay beamforming optimization (JPBO) algorithm for non-orthogonal multiple-access (NOMA) amplify-and-forward (AF) relay systems to achieve the maximum weighted sum-rate (WSR). In our proposed new framework, the WSR maximization problem is transformed into a tractable weighted-sum minimum mean-square-error (WSMMSE) problem. Then, the PA and the relay beamforming-matrix (BM) are alternately optimized by use of successive convex approximation (SCA) and Lagrange-multiplier (LM) algorithm. Simulation results demonstrate that our proposed new algorithm can significantly improve the WSR with a faster convergence than the existing method.

Fast Adaptive Minorization-Maximization Procedure for Beamforming Design of Downlink NOMA Systems

We develop a novel technique to accelerate minorization-maximization (MM) procedure for the non-orthogonal multiple access (NOMA) weighted sum rate maximization problem. Specifically, we exploit the Lipschitz continuity of the gradient of the objective function to adaptively update the MM algorithm. With fewer additional analysis variables and low complexity second-order cone program (SOCP) to solve in each iteration of the MM algorithm, the proposed approach converges quickly at a small computational cost. By numerical simulation results, our algorithm is shown to greatly outperform known solutions in terms of achieved sum rates and computational complexity.

An Optimization Scheme with Weighted Sum-Rate Maximization for Multi-User Wireless Powered Communication Networks

An Optimization Scheme with Weighted Sum-Rate Maximization for Multi-User Wireless Powered Communication Networks

Weighted Sum-Rate Maximization for Multi-IRS Aided Cooperative Transmission

This paper investigates multiple intelligent reflecting surfaces (IRSs) aided wireless network, where the IRSs are deployed to cooperatively assist communications between a multi-antenna base station (BS) and multiple single-antenna cell-edge users. We aim at maximizing the weighted sum rate of all the cell-edge users by jointly optimizing the BS's transmit beamforming and IRS's phase shifts. Especially, the beamforming is optimally solved by the Lagrangian method, and the phase shifts are obtained based on the Riemannian manifold conjugate gradient (RMCG) method. Numerical results show that a significant throughput is improved with aid of multiple IRSs.