Max-min Fair Problem Research Articles

Intelligent Reflecting Surface Backscatter Enabled Downlink Multi-Cell MIMO Networks

This paper proposes to leverage intelligent reflecting surface (IRS) backscatter to implement downlink communications for a multi-cell multiple-input multiple-output (MIMO) network, which represents a brand-new communication framework. In such a network, one active macro cell base station (MBS) is deployed for radiating energy signal, while each IRS acts as a small cell base station to realize its own information transmission by modulating and reflecting the signal from the MBS. Under this paradigm, we investigate two optimization problems, namely weighted sum rate maximization problem and max-min fairness problem, aiming at satisfying different communication requirements. To seek their optimal solutions, Lagrangian dual transform and alternate methods are employed to optimize the active beamforming vector at the MBS and the passive beamforming vectors at all the IRSs. Additionally, an element clustering scheme is developed to reduce computation and control complexity, in which each element cluster works like a unit and all clusters can collaborate to communicate with users. Extensive simulations are conducted to evaluate the achievable communication performance and to verify the feasibility of the proposed IRS backscatter enabled downlink multi-cell MIMO network.

Resource Allocation for RSMA-Based Coordinated Direct and Relay Transmission

In this letter, we investigate a rate splitting multiple access (RSMA) based coordinated direct and relay transmission (CDRT) system, where a base station (BS) serves two users using the rate splitting strategy, and a decode-and-forward (DF) relay aids the BS in establishing a communication link with a far user. We focus on a max-min fairness problem aiming at maximizing the minimum achievable rate of two users. The precoding vectors of the BS and the relay, the common rate of each user and the time allocation coefficients are jointly optimized under the constraint of limited system resources. Unfortunately, the optimization problem is non-convex due to the coupled optimization variables and the non-convex objective. Therefore, we transform the original problem into a difference of convex (DC) program and obtain a sub-optimal solution by adopting an iterative constrained concave convex procedure (CCCP) based algorithm. Simulation results demonstrate substantial performance gains of our proposed RSMA-CDRT over the conventional CDRT strategies and the flexibility in adapting to various channel environments.

Heterogeneous Computational Resource Allocation for NOMA: Toward Green Mobile Edge-Computing Systems

Mobile Edge Computing (MEC) is a viable solution in response to the growing demand for broadband services in the new-generation heterogeneous systems. The dense deployment of small cell networks is a key feature of next-generation radio access networks aimed at providing the necessary capacity increase. Nonetheless, the problem of green networking and service computing will be of great importance in the downlink, because the uncontrolled installation of too many small cells may increase operational costs and emit more carbon dioxide. In addition, given the resource and computational limitation of the user layer, energy efficiency (EE) and fairness assurance are critical issues in MEC-based cellular systems. Considering the user fairness criteria, this paper proposes a dynamic optimization model which maximizes the total UL/DL EE along with satisfying the necessary QoS constraints. Based on the non-convex characteristics of the EE maximization problem, the mathematical model can be divided into two separate subproblems, i.e., computational carrier scheduling and resource allocation. So that, a subgradient method is applied for the computational resource allocation and also successive convex approximation (SCA) and dual decomposition methods are adopted to solve the max-min fairness problem. The simulation results exhibit considerable EE improvement for various traffic models in addition to guaranteeing the fairness requirements. It also proved that the proposed computational partitioning scheme managed to significantly improve the total throughput for mobile computing services.

Max–Min Fairness Beamforming With Rate-Splitting Multiple Access: Optimization Without a Toolbox

We propose a max-min fairness (MMF) design method in a multi-antenna downlink network, where rate-splitting multiple access (RSMA) is adopted. A main aim in the considered MMF problem is providing uniformly good rates to users, by carefully controlling the rate of each private and common message, respectively. Solving this problem is challenging since multiple optimization variables, i.e., beamforming vectors and common message portions, are intricately intertwined in a non-tractable objective function. To resolve these obstacles, we first split a whole problem into two stages. In the first stage, we identify beamforming vectors given common message portion by exploiting the LogSumExp (LSE) approximation technique and the novel generalized power iteration (GPI) framework. In the second stage, we determine common message portions under fixed beamforming vectors. Iterating these two stages, we jointly design beamforming vectors and common message portion accordingly. Via simulations, we demonstrate that our method outperforms existing other frameworks in terms of the minimum rate, while requiring extremely small computational complexity.

Ultra-Low-Complexity Algorithms With Structurally Optimal Multi-Group Multicast Beamforming in Large-Scale Systems

In this work, we propose ultra-low-complexity design solutions for multi-group multicast beamforming in large-scale systems. For the quality-of-service (QoS) problem, by utilizing the optimal multicast beamforming structure obtained recently in [2], we convert the original problem into a non-convex weight optimization problem of a lower dimension and propose two fast first-order algorithms to solve it. Both algorithms are based on successive convex approximation (SCA) and provide fast iterative updates to solve each SCA subproblem. The first algorithm uses a saddle point reformulation in the dual domain and applies the extragradient method with an adaptive step-size procedure to find the saddle point with simple closed-form updates. The second algorithm adopts the alternating direction method of multipliers (ADMM) method by converting each SCA subproblem into a favorable ADMM structure. The structure leads to simple closed-form ADMM updates, where the problem in each update block can be further decomposed into parallel subproblems of small sizes, for which closed-form solutions are obtained. We also propose efficient initialization methods to obtain favorable initial points that facilitate fast convergence. Furthermore, taking advantage of the proposed fast algorithms, for the max-min fair (MMF) problem, we propose a simple closed-form scaling scheme that directly uses the solution obtained from the QoS problem, avoiding the conventional computationally expensive method that iteratively solves the inverse QoS problem. We further develop lower and upper bounds on the performance of this scaling scheme. Simulation results show that the proposed algorithms offer near-optimal performance with substantially lower computational complexity than the state-of-the-art algorithms for large-scale systems.

Cell-Free mmWave Massive MIMO Systems With Low-Capacity Fronthaul Links and Low-Resolution ADC/DACs

In this paper, we consider the uplink channel estimation phase and downlink data transmission phase of cell-free millimeter wave (mmWave) massive multiple-input multiple-output (MIMO) systems with low-capacity fronthaul links and low-resolution analog-to-digital converters/digital-to-analog converters (ADC/DACs). In cell-free massive MIMO, a control unit dictates the baseband processing at a geographical scale, while the base stations communicate with the control unit through fronthaul links. Unlike most of previous works in cell-free massive MIMO with finite-capacity fronthaul links, we consider the general case where the fronthaul capacity and ADC/DAC resolution are not necessarily the same. In particular, the fronthaul compression and ADC/DAC quantization occur independently where each one is modeled based on the information theoretic argument and additive quantization noise model (AQNM). Then, we address the codebook design problem that aims to minimize the channel estimation error for the independent and identically distributed (i.i.d.) and colored compression noise cases. Also, we propose an alternating optimization (AO) method to tackle the max-min fairness problem. In essence, the AO method alternates between two subproblems that correspond to the power allocation and codebook design problems. The AO method proposed for the zero-forcing (ZF) precoder is guaranteed to converge, whereas the one for the maximum ratio transmission (MRT) precoder has no such guarantee. Finally, the performance of the proposed schemes is evaluated by the simulation results in terms of both energy and spectral efficiency. The numerical results show that the proposed scheme for the ZF precoder yields spectral and energy efficiency 28% and 15% higher than that of the best baseline.

Fast First-Order Algorithm for Large-Scale Max-Min Fair Multi-Group Multicast Beamforming

We propose a first-order fast algorithm for the weighted max-min fair (MMF) multi-group multicast beamforming problem in large-scale systems. Utilizing the optimal multicast beamforming structure obtained recently, we convert the nonconvex MMF problem into a min-max weight minimization problem and show that it is a weakly convex problem. We propose using the projected subgradient algorithm (PSA) to solve the problem directly, instead of the conventional method that requires iteratively solving its inverse problem. We show that PSA for our problem has closed-form updates and thus is computationally cheap. Furthermore, PSA converges to a near-stationary point of our problem within finite time. Simulation results show that our PSA-based algorithm offers near-optimal performance with considerably lower computational complexity than existing methods for large-scale systems.

Impact Analysis of Emerging Semantic Communication Systems on Network Performance

With the paradigm shift from Shannon’s legacy, semantic communication (SC) is emerging as one of the promising next-generation communication technologies. The new paradigm in communication technology allows the meaning of transmitted messages to be successfully delivered to a receiver. Hence, the semantic communication focuses on the successful delivery of transmitted messages such as human language communication. In order to realize such new communication, both transmitter and receiver should share the same background knowledge with each other. Recently, several researchers have developed task-specific SC systems by exploiting astonishing achievements in deep learning, which can allow the same knowledge to be shared between them. However, since such SC systems are specialized to handle specific applications, not all users can be serviced by the SC systems. Therefore, a network will face a coexistence of an SC system and a traditional communication (TC) system. In this paper, we investigate how introducing emerging SC systems affects the performance of the TC system from a network perspective. For analysis, we consider the signal-to-noise ratio (SNR) differently for the user served by an SC system and the user served by a TC system. Then, by using two different SNR equations, we formulate a max-min fairness problem in the coexistence of SC and TC systems. Via extensive numerical results, we compare the network performance of TC and SC users with and without SC systems, and then confirm that SC systems are indeed a promising next-generation communication alternative.

Joint Design of Hybrid Beamforming and Reflection Coefficients in RIS-Aided mmWave MIMO Systems

This paper considers a reconfigurable intelligent surface (RIS)-aided millimeter wave (mmWave) downlink communication system where hybrid analog-digital beamforming is employed at the base station (BS). We formulate a power minimization problem by jointly optimizing hybrid beamforming at the BS and the response matrix at the RIS, under the signal-to-interference-plus-noise ratio (SINR) constraints at all users. The problem is highly challenging to solve due to the non-convex SINR constraints as well as the unit-modulus phase shift constraints for both the RIS reflection coefficients and the analog beamformer. A two-layer penalty-based algorithm is proposed to decouple variables in SINR constraints, and manifold optimization is adopted to handle the non-convex unit-modulus constraints. We also propose a low-complexity sequential optimization method, which optimizes the RIS reflection coefficients, the analog beamformer, and the digital beamformer sequentially without iteration. Furthermore, the relationship between the power minimization problem and the max-min fairness (MMF) problem is discussed. Simulation results show that the proposed penalty-based algorithm outperforms the state-of-the-art semidefinite relaxation (SDR)-based algorithm. Results also demonstrate that the RIS plays an important role in the power reduction.

Rate-Splitting Multiple Access for Multigateway Multibeam Satellite Systems With Feeder Link Interference

This paper studies the precoder design problem of achieving max-min fairness (MMF) amongst users in multigateway multibeam satellite communication systems with feeder link interference. We propose a beamforming strategy based on a newly introduced transmission scheme known as rate-splitting multiple access (RSMA). RSMA relies on multi-antenna rate-splitting at the transmitter and successive interference cancellation (SIC) at the receivers, such that the intended message for a user is split into a common part and a private part and the interference is partially decoded and partially treated as noise. In this paper, we formulate the MMF problem subject to per-antenna power constraints at the satellite for the system with imperfect channel state information at the transmitter (CSIT). We also consider the case of two-stage precoding which is assisted by on- board processing (OBP) at the satellite. Numerical results obtained through simulations for RSMA and the conventional linear precoding method are compared. When RSMA is used, MMF rate gain is promised and this gain increases when OBP is used. RSMA is proven to be promising for multigateway multibeam satellite systems whereby there are various practical challenges such as feeder link interference, CSIT uncertainty, per-antenna power constraints, uneven user distribution per beam and frame-based processing.

Closed-form solution for the max-min fairness problem in non-orthogonal multiple access systems

Non-orthogonal multiple access (NOMA) can improve both the spectrum efficiency and the number of users in wireless communication systems. In the downlink of NOMA, the base station superimposes multiple data flows in the power domain and the users decode the information using successive interference cancellation SIC. The performance of downlink NOMA systems is highly dependent on the power allocation scheme for all users. This paper investigates the max-min fairness problem that maximizes the minimum achievable user rate, aiming to ensure fairness for all users in downlink NOMA systems. Although the max-min fairness problem in downlink NOMA systems is non-convex, we obtain its closed-form optimal solution in this paper. This result will be useful for the analysis and design of future NOMA systems. Numerical results validate the correctness and effectiveness of our closed-form optimal solution.

Joint Power Control and LSFD for Wireless-Powered Cell-Free Massive MIMO

This paper considers wireless uplink information and downlink power transfer in cell-free massive multiple-input multiple-output systems. The single-antenna user equipments (UEs) utilize the energy harvested in the downlink to transmit uplink pilot and information signals to the multiple-antenna access points (APs). We consider Rician fading and maximum ratio processing based on either linear minimum mean-squared error (LMMSE) or least-squares (LS) channel estimation. We derive the average harvested energy by using a practical non-linear energy harvesting circuit model for both coherent and non-coherent transmission schemes. Furthermore, the uplink spectral efficiency (SE) is derived for all the considered methods and the max-min fairness problem is cast where the optimization variables are the AP and UE power control coefficients together with the large-scale fading decoding vectors. The objective is to maximize the minimum SE of the UEs’ under APs’ and UEs’ transmission power constraints. A novel alternating optimization algorithm with guaranteed convergence and improvement at each step is proposed to solve the highly-coupled non-convex problem.

Rate Splitting for Multi-Group Multicasting With a Common Message

In this letter, precoding for max-min fairness (MMF) for multi-group multicasting with a common message is studied. The MMF problem is converted into a weighted mean square error minimization problem. A rate-splitting solution is proposed. In rate-splitting, multicast messages for each group are divided into private and common parts, and these common parts, together with the original common message are combined as a super common message. This super common message is superposed on or concatenated to the private multicast data vector, or it is transmitted via a mixed scheme. Simulations show that RS demonstrates significant gains especially in overloaded systems.

Edge Cloud-Enabled Radio Resource Management for Co-Operative Automated Driving

Co-operative automated driving (CAD) is a key fifth generation mobile networks (5G) use case in which autonomous vehicles communicate over vehicle-to-vehicle (V2V) links requiring a wide range of rate-reliability-delay performance. One key 5G enabler for CAD sidelink radio resource management (RRM) in a multi-operator environment is the virtualization of RRM at the cloud server. This, however, is challenging due to an increase in control plane delay, signaling overhead and complexity. This paper introduces an edge cloud-enabled end-to-end vehicle-to-everything (V2X) architecture to support sidelink RRM in CAD scenarios. Analyzing the problem of a cloud-based sidelink resource allocation for CAD, a utility-based multi-objective optimization problem is described and is translated to three tasks: 1) a vehicle cluster formation as a solution to the clique partitioning problem ensuring vehicle reachability on the control plane, 2) an inter-cluster resource block pool (RB-pool) allocation as a solution to a max-min fairness problem and 3) an intra-cluster resource allocation. The proposed solution framework aims to achieve high modularity, low complexity and decouples cluster formation and RB-pool assignment from the intra-cluster optimum resource allocation, which may be performed on different time scales at different edge cloud entities. Simulation results in a realistic vehicular deployment show significant gains in terms of sidelink throughput and delay while maintaining high link quality.

Physical Layer Multicasting in Massive MIMO Systems With Statistical CSIT

We present a transmit design for physical layer multicasting in single-cell massive multiple-input-multiple-output (MIMO) systems using statistical channel state information at the base station (BS). We first establish the relationship between the transmit design problems under the quality of service (QoS) and max-min fair (MMF) criteria. According to the relationship between the QoS and MMF problems, we only focus on the transmit covariance optimizations under the latter criterion. We show that when the uniform linear array is equipped at the BS, the eigenvectors of the optimal transmit covariance are given by columns of the discrete Fourier transform matrix, which reveals the optimality of the beam domain transmission in massive MIMO multicasting. A dual algorithm together with stochastic programming is proposed to specify the eigenvalues of the transmit covariance. To reduce the complexity involved in stochastic programming, we further formulate two simplified MMF problems by using the deterministic equivalents and upper bound to approximate the ergodic achievable rate, respectively. We show that the optimality of the beam domain transmission still holds for the two simplified MMF problems. Then we present two low-complexity transmit designs. Simulation results demonstrate the performances of the proposed algorithms.

A QoS-Oriented Trajectory Optimization in Swarming Unmanned-Aerial-Vehicles Communications

This letter aims to present a novel approach for unmanned aerial vehicles (UAV)’ path planning with respect to certain quality of service requirements. More specifically, we study the max-min fairness problem in an air-to-ground communication system where multiple UAVs and multiple ground stations exist. We jointly optimize the UAVs trajectories and power allocation as well as the user scheduling. To this end, we propose an effective iterative algorithm that relies on the successive convex approximation and the block coordinate descent techniques.

Max-Min Energy-Efficient Resource Allocation for Wireless Powered Backscatter Networks

In this letter, we present the first attempt to solve an energy efficiency (EE) based max-min fairness problem for a wireless powered backscatter network where a power beacon (PB), which is a dedicated radio frequency (RF) power resource, and multiple backscatter devices work in the same frequency band. Each backscatter transmitter harvests energy from the signal transmitted by the PB, modulates its own information on the received signal, and backscatters the modulated signal to its associated receiver. We propose to ensure max-min fairness among the backscatter links by jointly optimizing the PB transmission power and the backscatter reflection coefficients. For analytical tractability, we solve the optimization problem for the case of two co-channel backscatter links by employing Lagrange dual decomposition when it is convex, and analyzing the monotonicity of the constraints when it is non-convex. Based on the obtained closed-form expressions of the optimal PB transmission power and the optimal backscatter reflection coefficients, we propose an iterative algorithm for max-min EE resource allocation. Simulation results show that the proposed iterative algorithm converges very fast and achieves a much fairer EE performance among backscatter links than maximizing the system EE of the network.

Constrained Partial Group Decoding With Max–Min Fairness for Multi-Color Multi-User Visible Light Communication

Consider a fixed orientation multi-user visible light communication (VLC) system with multi-color light emitting diodes (LEDs) where each transmitter serves a user with limited coordination impeding transmitter-side beamforming. In this paper, a multi-layer coding and constrained partial group decoding (CPGD) method is proposed to tackle strong color interference and increase the system throughput. After channel model formulation, user information rates are allocated and decoding order for all the received data layers is obtained by solving a max-min fairness problem using a greedy algorithm. An achievable rate is derived under the truncated Gaussian input distribution. To reduce the decoding complexity, a map on the decoding order and rate allocation is constructed for all positions of interest on the receiver plane parallel to the transmitter plane, and its size is reduced by a clustering algorithm. Meanwhile, the symmetrical geometry of LED arrays is exploited. Finally, the transmitter-user association problem is formulated and solved by a genetic algorithm. It is observed that the system throughput increases as the receivers are slightly misaligned with corresponding LED arrays due to the reduced interference level, but decreases afterwards due to the weakened link gain.

Multi-Group Multicast Beamforming: Optimal Structure and Efficient Algorithms

This paper considers the multi-group multicast beamforming optimization problem, for which the optimal solution has been unknown due to the non-convex and NP-hard nature of the problem. By utilizing the successive convex approximation numerical method and Lagrangian duality, we obtain the optimal multicast beamforming solution structure for both the quality-of-service (QoS) problem and the max-min fair (MMF) problem. The optimal structure brings valuable insights into multicast beamforming: We show that the notion of uplink-downlink duality can be generalized to the multicast beamforming problem. The optimal multicast beamformer is a weighted MMSE filter based on a group-channel direction: a generalized version of the optimal downlink multi-user unicast beamformer. We also show that there is an inherent low-dimensional structure in the optimal multicast beamforming solution independent of the number of transmit antennas, leading to efficient numerical algorithm design, especially for systems with large antenna arrays. We propose efficient algorithms to compute the multicast beamformer based on the optimal beamforming structure. Through asymptotic analysis, we characterize the asymptotic behavior of the multicast beamformers as the number of antennas grows, and in turn, provide simple closed-form approximate multicast beamformers for both the QoS and MMF problems. This approximation offers practical multicast beamforming solutions with a near-optimal performance at very low computational complexity for large-scale antenna systems.

Joint admission control and beamforming in max–min fairness networks

The max–min fairness (MMF) strategy has been widely employed to manage wireless networks since it guarantees fairness among users. However, with a large number of users awaiting service, the network tends to be congested and the quality-of-service (QoS) will degrade substantially. This motivates us to study the MMF problem jointly with the consideration of admission control. Specifically, the authors consider a downlink network consisting of a multi-antenna base station (BS) and multiple single-antenna users. By jointly optimising the admissible users and the BS transmit beamformers, they aim to maximise the minimum signal-to-interference-plus-noise-ratio of the admissible users, such that high QoS and fairness can be guaranteed simultaneously for them. This problem is essentially NP-hard, and hence they pursue an efficient approximate solution to it. To this end, they first reformulate this problem from the perspective of sparse optimisation, and then develop a low-complexity algorithm to iteratively solve the approximate problem. Moreover, to facilitate the algorithm's implementation, they further recast the subproblem in each iteration, such that it fits into the framework of the alternating direction methods of multipliers. Finally, an efficient distributed algorithm is designed, with each step being simply computed in a closed form.