Max-min Fairness Research Articles

Maxmin Fairness for UAV-Enabled Proactive Eavesdropping With Jamming Over Distributed Transmit Beamforming-Based Suspicious Communications

Unmanned aerial vehicle (UAV) plays an important role in wireless communication systems, due to the additional degree of freedom realized from its flexible deployment. Driven by this advantage and considering the security issue, this paper aims to investigate UAV-enabled proactive eavesdropping over distributed transmit beamforming-based suspicious communications. Specifically, for the suspicious system, there are multiple suspicious clusters aiming to communicate with the suspicious destination (D) using mutually orthogonal frequency bands, and distributed transmit beamforming is exploited by each cluster to strengthen the signal receiving quality at D. For the legitimate party, the full-duplex UAV exploits one antenna to jam D and uses the other antenna to overhear the signals of the suspicious clusters concurrently. By resorting to the Laguerre series approximation and the central limit theorem, we first characterize, in closed form, the approximated distributions of the receiving signal-to-interference-noise ratio (SINR) at D and the UAV, which are shown to be very tight. Based on this analysis and considering that the suspicious system works in the delay-limited transmission mode or the delay-sensitive transmission mode, we aim to maximize the minimum eavesdropping success probability of the UAV for those suspicious communications links, by jointly adjusting the UAV’s deployment and jamming power allocations over different frequency bands. The problem is highly non-convex. To tackle this, we develop an alternative optimization framework and further a novel and low-complexity solution in the high SNR regime to the optimization problem. Simulation results show the effectiveness of our proposed schemes compared to competitive benchmarks.

Polynomial-time Combinatorial Algorithm for General Max–Min Fair Allocation

Polynomial-time Combinatorial Algorithm for General Max–Min Fair Allocation

Research on Power Allocation in Multiple-Beam Space Division Access Based on NOMA for Underwater Optical Communication.

To meet the transmission requirements of different users in a multiple-beam access system for underwater optical communication (UWOC), this paper proposes a novel multiple-beam space division multiple access (MB-SDMA) system by utilizing a directional radiation communication beam of the hemispherical LED arrays. The system's access users in the different beams are divided into two categories: the users with a single beam and the users with multiple beams. We also propose a power allocation algorithm that guarantees the quality of service (QoS) for single beam and multiple beam access, especially the QoS for edge users, and fairness for all users. An optimization model of power distribution under the constraints of specific light-emitting diode (LED) emission power is established for two scenarios, which ensure the user QoS for edge users and the max-min fairness for fair users. Using the Karush-Kuhn-Tucker (KKT) condition and the bisection method, we obtain the optimal power allocation expression for the two types of users in the optimization model. Through simulation, we verify that the proposed user classification and power allocation method can ensure the fairness of fair users on the premise of ensuring the QoS of edge users. At the same time, we know that the number of users will affect the improvement of the minimum rate, and the throughput of the non-orthogonal multiple access (NOMA) system is greatly improved compared with the traditional orthogonal multiple access (OMA) systems.

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.

Space-Terrestrial Cooperation Over Spatially Correlated Channels Relying on Imperfect Channel Estimates: Uplink Performance Analysis and Optimization

A whole suite of innovative technologies and architectures have emerged in response to the rapid growth of wireless traffic. This paper studies an integrated network design that boosts system capacity through cooperation between wireless access points (APs) and a satellite for enhancing the network’s spectral efficiency. <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">As for our analytical contributions</i> , upon coherently combing the signals received by the central processing unit (CPU) from the users through the space and terrestrial links, we first mathematically derive an achievable throughput expression for the uplink (UL) data transmission over spatially correlated Rician channels. Our generic achievable throughput expression is applicable for arbitrary received signal detection techniques employed at the APs and the satellite under realistic imperfect channel estimates. A closed-form expression is then obtained for the ergodic UL data throughput, when maximum ratio combining is utilized for detecting the desired signals. <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">As for our resource allocation contributions</i> , we formulate the max-min fairness and total transmit power optimization problems relying on the channel statistics for performing power allocation. The solution of each optimization problem is derived in form of a low-complexity iterative design, in which each data power variable is updated relying on a closed-form expression. Our integrated hybrid network concept allows users to be served that may not otherwise be accommodated due to the excessive data demands. The algorithms proposed allow us to address the congestion issues appearing when at least one user is served at a rate below his/her target. The mathematical analysis is also illustrated with the aid of our numerical results that show the added benefits of considering the space links in terms of improving the ergodic data throughput. Furthermore, the proposed algorithms smoothly circumvent any potential congestion, especially in face of high rate requirements and weak channel conditions.

Distributed RIS-assisted mmWave multi-user MIMO beamspace system

We are considering a novel distributed reconfigurable intelligent surfaces assisted (RIS-assisted) millimeter-wave (mmWave) multi-user multi-input multi-output (MIMO) beamspace system. Beamspace systems offer a low-scattering communication to users through beams. To enrich the propagation environment, multiple reconfigurable intelligent surfaces are installed on top of the surrounding buildings to provide an additional communication link, between the base station and users, by introducing phase shifts in the incoming signal arriving at it. Such systems allow the selection of two distinct beams for each user. The first beam is directly steered towards the user and the second beam is steered to the user via RIS. The selection of desirable beams is required to reduce the number of radio frequency (RF) chains at the transmitter. In this paper, we propose a beam selection algorithm that can assign two distinct and unshared beams to each user after optimally adjusting the phases of each RIS. Additionally, we propose a max–min fairness power allocation scheme to obtain a minimum achievable rate for each user. Simulation results compare the sum-rate performance with the existing beam selection algorithms.

SWIPT-Enabled NOMA in Distributed Antenna System With Imperfect CSI for Max-Sum-Rate and Max–Min Fairness

Motivated by the fact that the energy harvesting (EH) of simultaneous wireless information and power transfer (SWIPT) and the system throughput of nonorthogonal multiple access (NOMA) can be greatly increased with the help of the distributed antenna system (DAS), we present a framework for applying the DAS to SWIPT-enabled NOMA. In this article, we jointly optimize power splitting (PS) for SWIPT and power allocation for NOMA signaling in SWIPT-enabled NOMA helped by the DAS for two different following goals: 1) sum-rate maximization; and 2) achieving max–min fairness. Also, we analyze the impact of imperfect channel state information (CSI) on power splitting and power allocation of SWIPT-NOMA with the DAS in both problems. Due to the nonconvexity of the joint optimization problem, we first obtain the optimal PS ratios and use them to convert the problem to a single-variable problem. The joint optimal solution is then obtained in the closed-form by finding and comparing all local extrema of the objective function using the first-order derivative. Numerical results were used to validate the theoretical findings and demonstrate that the proposed framework of using SWIPT-enabled NOMA in DAS achieves higher data rates than the existing SWIPT-enabled NOMA while guaranteeing minimum harvested energy and data rate requirements.

Max-Min Fairness Precoder Design for Rate-Splitting Multiple Access: Impact of Imperfect Channel Knowledge

Rate-splitting multiple access (RSMA) is a key enabling technology for beyond 5G networks due to its robustness against imperfect channel knowledge. In this paper, we consider both the imperfect channel state information (CSI) at the receiver (CSIR) and imperfect CSI at the transmitter (CSIT) and propose a max-min fairness optimization framework relying on RSMA to guarantee each user's minimum level of quality of service (QoS). First, we formulate the max-min fairness optimization problem that has non-convexity. To transform the non-convex problem into a convex problem, we apply the semi-definite relaxation (SDR) and convex-concave procedure (CCP) to the proposed algorithm. From simulation results, we confirm that RSMA is still a robust scheme over conventional multiple access schemes for both imperfect CSIT and CSIR.

On Optimal Power Allocation in Multibeam Multicast NOMA for Satellite Communication Systems

This paper addresses two key challenges in the multibeam multicast non-orthogonal multiple access (MB-MC-NOMA) scheme and respective beamforming design problems in satellite systems. Achieving the max-min fairness (MMF) and maximum sum-rate among multiple multicast groups of users are jointly considered in a theoretical information framework. It is assumed that each frame contains information of multiple users in multicast transmission. Therefore, contrary to the unicast linear precoding, we have developed the multicast linear precoding with mapping function considering trade-offs to deal with the lack of the spatial degree of freedom. In our proposed scheme, each beamforming vector conveys information to more than one group of users in a NOMA framework, relying on the superposition techniques at the transmitters and successive interference cancellation (SIC) at the receivers. We have derived the capacity rates achievable in each beam, proposing the methods to maximize the minimum rate and weighted sum-rate. Considering the dependency of the broadcasting power and the respective achievable rates, the equivalent channel and water-filling algorithm for the MB-MC-NOMA is developed; as such, the optimal transmit power density for the groups of users within multiple beams are efficiently computed. The extensive simulation results confirm the proposed theoretical findings, providing a considerable boost in both minimum-rate and sum-rate with respect to state-of-the-art multibeam multicast satellite systems.

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.

User Subgrouping and Power Control for Multicast Massive MIMO Over Spatially Correlated Channels

Massive multiple-input-multiple-output (MIMO) is unquestionably a key enabler of the fifth-generation (5G) technology for mobile systems, enabling to meet the high requirements of upcoming mobile broadband services. Physical-layer multicasting refers to a technique for simultaneously serving multiple users, demanding for the same service and sharing the same radio resources, with a single transmission. Massive MIMO systems with multicast communications have been so far studied under the ideal assumption of uncorrelated Rayleigh fading channels. In this work, we consider a practical multicast massive MIMO system over spatially correlated Rayleigh fading channels, investigating the impact of the spatial channel correlation on the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">favorable propagation</i> , hence on the performance. We propose a subgrouping strategy for the multicast users based on their channel correlation matrices’ similarities. The proposed subgrouping approach capitalizes on the spatial correlation to enhance the quality of the channel estimation, and thereby the effectiveness of the precoding. Moreover, we devise a max-min fairness (MMF) power allocation strategy that makes the spectral efficiency (SE) among different multicast subgroups uniform. Lastly, we propose a novel power allocation for uplink (UL) pilot transmission to maximize the SE among the users within the same multicast subgroup. Simulation results show a significant SE gain provided by our user subgrouping and power allocation strategies. Importantly, we show how spatial channel correlation can be exploited to enhance multicast massive MIMO communications.

Handling Interference in Integrated HAPS-Terrestrial Networks Through Radio Resource Management

Vertical heterogeneous networks (vHetNets) are promising architectures to bring significant advantages for 6G and beyond mobile communications. High altitude platform station (HAPS), one of the nodes in the vHetNets, can be considered as a complementary platform for terrestrial networks to meet the ever-increasing dynamic capacity demand and provide sustainable wireless networks for future. However, the problem of interference is the bottleneck for the optimal operation of such an integrated network. Thus, designing efficient interference management techniques is inevitable. In this letter, we aim to design a joint power-subcarrier allocation scheme in order to achieve fairness for all users. We formulate the max-min fairness (MMF) optimization problem and develop a rapid converging iterative algorithm to solve it. Numerical results validate the superiority of the proposed algorithm and show better performance over other conventional network scenarios.

Rescaled Brownian Motion of Molecules and Devices in Three-Dimensional Multiuser Mobile Molecular Communication Systems

This paper considers a three-dimensional anomalous-diffusive mobile molecular communication (MC) channel. Herein, the communicating devices, i.e., point transmitter (Tx) and passive receiver (Rx) can also move anomalously with the information-carrying molecule (ICM). In order to incorporate the anomalous diffusion phenomenon, the concept of rescaled-Brownian motion is explored. Two different scenarios, named point-to-point and multi-user MC systems, are considered for the analysis. First, considering the point-to-point scenario, the expressions for the channel impulse response (CIR) incorporating static and mobile Tx and Rx are derived. Further, the expressions for the peak time of CIR and the corresponding peak value are also derived. Furthermore, the point-to-point MC system is exploited in terms of bit-error-rate (BER), minimum BER, maximum mutual information, and throughput. A multi-user MC system is considered in the second scenario, and a molecular division multiple access (MDMA) method is used. The system is analyzed in terms of BER and throughput. Further, the system performance is optimized using two schemes known as min-max fairness for error probability and max-min fairness for throughput. Furthermore, we use best-to-best and best-to-worst assignment strategies to allocate different types of ICMs for each Rx. Subsequently, the optimal allocation for the number of ICMs is obtained when specific ICMs are assigned to all users/receivers for a two-user scenario. All the channel metrics are verified through particle-based and Monte-Carlo simulations.

Max-Min Rate Optimization for Uplink IRS-NOMA With Receive Beamforming

This letter addresses an intelligent reflecting surface (IRS) to the uplink nonorthogonal multiple access (NOMA) served by a multiantenna receiver for effective data collection from massive devices. We aim to achieve max-min fairness of the network by optimizing receive beamforming, IRS reflection, and transmit power allocation (PA) of the devices. For this purpose, first, we design a block coordinate descent (BCD) algorithm that reduces the complexity of a conventional IRS reflection optimization. Next, we design a nonlinear optimization (NLO) problem solvable with the limited-memory Broyden-Fletcher-Goldfarb-Shanno bounded (L-BFGS-B) algorithm, which is renowned for handling large-scale problems, to cope with large IRS elements and devices. The problem is formed with a smooth but complex objective function that depends on the IRS phase shift and PA vectors for which the gradient is derived in a computationally efficient form. The results reveal that the proposed BCD and proposed NLO with the L-BFGS-B outperform the conventional BCD in performance and complexity, where the NLO approach offers a substantial complexity reduction.

Switching in the Rain: Predictive Wireless x-haul Network Reconfiguration

4G, 5G, and smart city networks often rely on microwave and millimeter-wave x-haul links. A major challenge associated with these high frequency links is their susceptibility to weather conditions. In particular, precipitation may cause severe signal attenuation, which significantly degrades the network performance. In this paper, we develop a Predictive Network Reconfiguration (PNR) framework that uses historical data to predict the future condition of each link and then prepares the network ahead of time for imminent disturbances. The PNR framework has two components: (i) an Attenuation Prediction (AP) mechanism; and (ii) a Multi-Step Network Reconfiguration (MSNR) algorithm. The AP mechanism employs an encoder-decoder Long Short-Term Memory (LSTM) model to predict the sequence of future attenuation levels of each link. The MSNR algorithm leverages these predictions to dynamically optimize routing and admission control decisions aiming to maximize network utilization, while preserving max-min fairness among the nodes using the network (e.g., base-stations) and preventing transient congestion that may be caused by switching routes. We train, validate, and evaluate the PNR framework using a dataset containing over 2 million measurements collected from a real-world city-scale backhaul network. The results show that the framework: (i) predicts attenuation with high accuracy, with an RMSE of less than 0.4 dB for a prediction horizon of 50 seconds; and (ii) can improve the instantaneous network utilization by more than 200% when compared to reactive network reconfiguration algorithms that cannot leverage information about future disturbances.

Mirror Prox Algorithm for Large-Scale Cell-Free Massive MIMO Uplink Power Control

We consider the problem of max-min fairness for uplink cell-free massive multiple-input multiple-output (MIMO) subject to per-user power constraints. The standard framework for solving the considered problem is to separately solve two subproblems: the receiver filter coefficient design and the power control problem. While the former has a closed-form solution, the latter has been solved using either second-order methods of high computational complexity or a first-order method that provides an approximate solution. To deal with these drawbacks of the existing methods, we propose a mirror prox based method for the power control problem by equivalently reformulating it as a convex-concave problem and applying the mirror prox algorithm to find a saddle point. The simulation results establish the optimality of the proposed solution and demonstrate that it is more efficient than the known methods. We also conclude that for large-scale cell-free massive MIMO, joint optimization of linear receive combining and power control provides significantly better user fairness than the power control only scheme in which receiver coefficients are fixed to unity.

ADMM Based Symbol-Level Precoding for MU-MISO Downlink With Low-Resolution DACs

In this letter, we investigate the problem of symbol-level precoder design with low-resolution digital-to-analog converters (DACs) to implement wireless multiuser multiple-input single-output (MISO) downlink communications. Specifically, we aim to maximize the minimum distance between the noise-free received signal and its decision boundaries via a min-max fairness design. Due to the nondifferentiable objective and finite-alphabet constraint, the problem is NP-hard and difficult to tackle. To handle this problem, we first reduce the dimension of the variables by solving a relaxed problem. Then, the problem is transformed to a smoothed form which can be efficiently solved using the alternative direction method of multipliers (ADMM)-based framework. In addition, we propose a closed-from solution based on majorization-minimization method to provide a low-complexity near-optimal solution. We further provide the convergence and computational complexity analyses, and validate the performance by simulations.

MinMax fairness: from Rawlsian Theory of Justice to solution for algorithmic bias

This paper presents an intuitive explanation about why and how Rawlsian Theory of Justice (Rawls in A theory of justice, Harvard University Press, Harvard, 1971) provides the foundations to a solution for algorithmic bias. The contribution of the paper is to discuss and show why Rawlsian ideas in their original form (e.g. the veil of ignorance, original position, and allowing inequalities that serve the worst-off) are relevant to operationalize fairness for algorithmic decision making. The paper also explains how this leads to a specific MinMaxfairness solution, which addresses the basic challenges of algorithmic justice. We combine substantive elements of Rawlsian perspective with an intuitive explanation in order to provide accessible and practical insights. The goal is to propose and motivate why and how the MinMaxfairness solution derived from Rawlsian principles overcomes some of the current challenges for algorithmic bias and highlight the benefits provided when compared to other approaches. The paper presents and discusses the solution by building a bridge between the qualitative theoretical aspects and the quantitative technical approach.

Optimization-Based Predictive Congestion Control for the Tor Network: Opportunities and Challenges

Based on the principle of onion routing, the Tor network achieves anonymity for its users by relaying user data over a series of intermediate relays. This approach makes congestion control in the network a challenging task. As of this writing, this results in higher latencies due to considerable backlog as well as unfair data rate allocation. In this article, we present a concept study of PredicTor, a novel approach to congestion control that tackles clogged overlay networks. Unlike traditional approaches, it is built upon the idea of distributed model predictive control, a recent advancement from the area of control theory. PredicTor is tailored to minimizing latency in the network and achieving max-min fairness. We contribute a thorough evaluation of its behavior in both toy scenarios to assess the optimizer and complex networks to assess its potential. For this, we conduct large-scale simulation studies and compare PredicTor to existing congestion control mechanisms in Tor. We show that PredicTor is highly effective in reducing latency and realizing fair rate allocations. In addition, we strive to bring the ideas of modern control theory to the networking community, enabling the development of improved, future congestion control. Thus, we demonstrate benefits and issues alike with this novel research direction.

EECDN: Energy-efficient Cooperative DNN Edge Inference in Wireless Sensor Networks

Multi-access edge computing (MEC) is emerging to improve the quality of experience of mobile devices including internet of things sensors by offloading computing intensive tasks to MEC servers. Existing MEC-enabled cooperative computation offloading works focus on the optimization of total energy consumption but fail to exploit multi-relay diversity and min-max fairness of energy consumption on participated sensors. We explore a typical wireless sensor network with multi-source, multi-relay, and one edge server, where relay nodes can provide both cooperative communication and computation services. We divide the energy efficiency optimization problem into two sub-problems: One is to minimize the weighted average total energy consumption per time slot, and the other is to minimize the maximum weighted energy consumption. For the first sub-problem, we propose an optimal algorithm named as optimal weighted average total energy consumption algorithm (OTCA) based on bipartite matching. For the second sub-problem, greedy algorithm for fairness guarantee (GAF) is proposed with an approximation ratio of (1 + ε), where ε is a small positive constant. Extensive numerical results show that OTCA outperforms the baseline algorithms by 26.7–77.4% on the average total weighted energy consumption while GAF outperforms benchmark algorithms by 30.7–84.4%. NS-3 simulation experiments comply with numerical results.