Proportional Fairness Criterion Research Articles

Traffic Load Optimization for Multi-Satellite Relay Systems in Space Information Network: A Proportional Fairness Approach.

Backbone satellites in a space information network (SIN) can be used as air base stations or data relay satellites (DRSs) to realize cross-system, cross-network and long-distance relay transmission. In this paper, a traffic load optimization problem for multi-satellite relay systems in SIN is considered to achieve highly efficient cooperative transmission and improve resource utility. A model of SIN based on a distributed satellite cluster (DSC) is considered, and the characteristics of the model are analyzed. Based on this, a hybrid resource management architecture combining distributed and central resources control schemes is proposed to realize a centrally controllable and distributed optimization of resources to meet various comprehensive service requirements. Two scenarios of multi-satellite relay systems in SIN are given, and traffic load optimization problems with joint bandwidth and power allocation for these two scenarios are formulated based on proportional fairness (PF) criterion to achieve traffic load balancing with considerable system capacity. The optimization problems in these two scenarios are proved to be a convex optimization problem with mathematical analysis, and the closed-form solutions of two problems in their dual domain are derived by dual transformation. With the closed-form solutions, two iterative algorithms based on the subgradient method are designed under the proposed hybrid resource management architecture to solve the problems in this paper. Simulation results show that the proposed schemes can effectively improve the upper bound of system capacity by resource sharing and cooperative relay, and it can balance the traffic load well with guarantees of a reasonable level system capacity compared with existing methods.

A Sophisticated Anti-Eavesdropping Strategy

Wireless networks are susceptible to malicious attacks, especially those involving eavesdropping. In this letter, we consider a new type of anti-eavesdropping strategy which, beyond the basic goal of increasing the secrecy rate, also wants to achieve this in the most unpredictable way for the adversary. We model the problem by a non-zero sum game where a control center (called the transmitter) must communicate with a group of nodes allocated in security zone in the presence of an adversary intent on eavesdropping upon this communication. The transmitter wants to find a trade-off between two goals: (a) to increase the expected secrecy rate, and (b) to maintain such secret communication in the most unpredictable way for the adversary. As a metric for unpredictability of the transmitter we consider the Shannon entropy of its strategy. We model this problem by a nonzero-sum, two-player resource allocation game. The equilibrium is found in closed form, and its dependence on communication network parameters is illustrated. Finally, weighting coefficients for the basic and secondary goals of the transmitter are optimized based on proportional fairness criteria.

Proportionally fair and scalable EV charging under distribution line voltage constraints

The ever-increasing Electric Vehicle (EV) fleet will undoubtedly stress the power system that requires scalable solutions to ensure normal grid operation and seamless EV charging. Fairness of EV charging power allocation and alignment to voltage restrictions is also essential. Towards that end, this paper introduces an EV charging allocation framework that takes into account residential power needs, EV charging demand and distribution-line voltage constraints. Our approach breaks down the charging problem into two parts; firstly, it allocates power to distribution line buses according to the weighted proportional fairness criterion and takes into account their specific EV fleet demand. Secondly, as an outcome of a constrained least squares optimization process, each EVs charging power is assigned. Both problems are solved by centralized reference convex optimization algorithms as well as scalable distributed ones introduced to address the charging needs of large EV fleets and long infrastructures. Rigorous analysis proves that the solution of distributed algorithms is close to centralized reference ones. Daily EV charging simulation results indicate a more balanced EV charging power allocation when comparing proportional fairness to linear and quadratic power allocation approaches.

Optimal allocation of quantum resources

The optimal allocation of resources is a crucial task for their efficient use in a wide range of practical applications in science and engineering. This paper investigates the optimal allocation of resources in multipartite quantum systems. In particular, we show the relevance of proportional fairness and optimal reliability criteria for the application of quantum resources. Moreover, we present optimal allocation solutions for an arbitrary number of qudits using measurement incompatibility as an exemplary resource theory. Besides, we study the criterion of optimal equitability and demonstrate its relevance to scenarios involving several resource theories such as nonlocality vs local contextuality. Finally, we highlight the potential impact of our results for quantum networks and other multi-party quantum information processing, in particular to the future Quantum Internet.

Is Massive MIMO Robust Against Distributed Jammers?

In this paper, we evaluate the uplink spectral efficiency (SE) of a single-cell massive multiple-input-multiple-output (MIMO) system with distributed jammers. We define four different attack scenarios and compare their impact on the massive MIMO system as well as on a conventional single-input-multiple-output (SIMO) system. More specifically, the jammers attack the base station (BS) during both the uplink training phase and data phase. The BS uses either least squares (LS) or linear minimum mean square error (LMMSE) estimators for channel estimation and utilizes either maximum-ratio-combining (MRC) or zero-forcing (ZF) decoding vectors. We show that ZF gives higher SE than MRC but, interestingly, the performance is unaffected by the choice of the estimators. The simulation results show that the performance loss percentage of massive MIMO is less than that of the SIMO system. Moreover, we consider two types of power control algorithms: jamming-aware and jamming-ignorant. In both cases, we consider the max-min and proportional fairness criteria to increase the uplink SE of massive MIMO systems. We notice numerically that max-min fairness is not a good option because if one user is strongly affected by the jamming, it will degrade the other users’ SE as well. On the other hand, proportional fairness improves the sum SE of the system compared with the full power transmission scenario.

Fairness Optimization of Fixed-Rate Wireless Networks With RF Energy Harvesting Transmitters

The letter proposes two simple and yet effective resource allocation schemes for wireless powered communication networks based on static time division multiple access (TDMA). The energy harvesting users (EHUs) do not have channel state information (CSI) available and transmit at fixed power and fixed rate to the base station (BS). In order to facilitate fairness, the network employs either the proportional fairness criterion or the max-min criterion for the EHUs’ rates by optimizing the key system parameters: the BS transmit power, the durations of energy harvesting and information transmission phases, and the EHU’s rates. Unlike the existing schemes that adapt the system parameters in each channel fading state, our proposed schemes are much simpler for practical implementation.

Graph-based multi-user scheduling for indoor cooperative visible light transmission.

Recent progress in the indoor visible light communication (VLC) has shown promising signs of alleviating an increasing strain on the radio frequency spectrum and enhancing transmission capacity. Nevertheless, the indoor VLC usually suffers from inter-channel interference (ICI) due to the dense light-emitting diode (LED) deployment. The ICI is considered as a key factor affecting signal to interference and noise ratio (SINR) and spectral efficiency. To address this challenge, an efficient multi-user scheduling framework that employs interference coordination and cooperative transmission is investigated based on the graph theory. To effectively mitigate ICI and maximize benefit of the cooperative transmission, the cell-centric (CC) and user-centric (UC) clustering are introduced for cooperative transmission. For the CC clustering, the multi-user scheduling problem under the proportional fairness criterion is formulated to maximize spectral efficiency while ensuring user fairness. Such a problem is solved by linear programming and greedy algorithms after transforming it into a maximum weighted independent set problem with the aid of a modified interference graph. For the UC clustering, the multi-user scheduling problem under the max-min criterion is formulated and solved by a proposed heuristic approach based on the bipartite graph theory. Numerical results show that the proposed graph-based scheduling is capable of providing up to 7.7 dB gain in SINR over the non-cooperative transmission. The bipartite graph scheduling offers high spectral efficiency and service fairness index. In the worst case with an occlusion probability of 1, a small SINR penalty of up to 1 dB is observed with the greedy algorithm. It is shown that the graph-based scheduling is robust to receiver rotation and occlusion in terms of spectral efficiency, SINR, and user fairness.

Fairness-Aware Throughput Maximization Over Cognitive Heterogeneous NOMA Networks for Industrial Cognitive IoT

In this work, an uplink secondary Internet of Things (IoT) device scheduling and power allocation problem based on imperfect channel state information (CSI) and imperfect spectrum sensing is investigated for industrial cognitive IoT over cognitive heterogeneous non-orthogonal multiple access (NOMA) networks. The joint secondary IoT device scheduling and power allocation problem maximizes the network throughput subject to total power constraint at each secondary IoT device, proportional fairness transmission rate among different secondary IoT devices, maximum number of accessed secondary IoT devices for each subchannel, and interference power threshold constraint at each primary base station (BS). Firstly, successive convex approximation method is adopted to transform the original resource allocation problem into a bi-convex programming problem. Then, we employ the dual decomposition method to analyze the secondary IoT device scheduling criterion and obtain the power allocation close-form expression. Finally, a joint power allocation and secondary IoT device scheduling algorithm with the proportional fairness criterion is proposed. Numerical simulation results demonstrate that the throughput and fairness for the proposed algorithm are better than that of other resource allocation algorithm significantly.

Joint Optimization for User Association and Inter-Cell Interference Coordination Based on Proportional Fair Criteria in Small Cell Deployments

Joint Optimization for User Association and Inter-Cell Interference Coordination Based on Proportional Fair Criteria in Small Cell Deployments

Pricing-Based Semi-Distributed Clustering and Beamforming for User-Centric MIMO Networks

User-centric dynamic base station (BS) clustering can efficiently avoid cell edge effect, which results in overlapped clusters and introduces tremendous complexity in beamforming optimizations. However, existing works mainly focus on addressing the problem in a centralized manner. In this letter, a semi-distributed user-centric clustering and beamforming scheme for sum-rate maximization is proposed, where the optimization problem is split by introducing interference pricing and solved subsequently at the anchor of each cluster. Specifically, based on interference pricing, the problem is decomposed into parallel subproblems by decoupling interference constraints and power constraints, where beamforming matrices are optimized at the anchor of each cluster through generalized iterative minimization of mean-square error; besides, cluster size is controlled by taking power spent as penalizing term and minimum rate constraints are taken into consideration to guarantee the throughput of edge users. Simulation results show about $3\times $ gains in sum-rate criteria and $2\times $ gains in proportional fair criteria of the proposed scheme in terms of 5%-tile user throughput compared to BS-centric and centralized schemes.

Achieving Large Sum Rate and Good Fairness in MISO Broadcast Communication

A tradeoff between sum rate and fairness for multiple-input single-output (MISO) broadcast communication employing dirty paper coding or zero-forcing dirty paper coding at physical layer is investigated in this paper. The tradeoff is based on a new design objective termed “tri-stage” approach as well as a new $\ell _1$ -based fairness measure that is much more robust than the well-known Jain's index for comparing fairness levels achieved by various design objectives at a much finer resolution in high SNR regime. The newly proposed tri-stage design also introduces a new concept of statistical power allocation that randomly allocates power to users based on an optimal probability distribution derived from the tradeoff between sum rate and fairness. Simulation results show that the proposed approach can simultaneously achieve a larger sum rate and better fairness than the reputable proportional fairness criterion. A performance upper bound is also given in the paper to show the excellent performance of the proposed approach at moderate and high SNR regimes as well as some potential for further improvement in low SNR regime.

Energy-Efficient Joint User Association and Power Allocation in Relay-Aided Massive MIMO Systems

Energy efficiency is an important metric for downlink transmission in an amplify-and-forward relayaided massive multiple-input multiple-output system, but has not been well investigated. In this work, considering the characteristics of such a system and quality-of-service requirements of users, the energy-efficient joint user association and power allocation problem is studied. First, the closed-form expression of system energy efficiency under the proportional fairness criterion is derived. Then, the proportionally fair utility of system energy efficiency is maximized under constraints of minimum signal-to-noise ratio requirements of users and maximum transmit powers of the base station (BS) and relay stations. As it is difficult to solve this optimization problem directly due to its mixed-integer and non-convex features, the original problem is decomposed into a user association sub-problem and a power allocation sub-problem. For the former, optimum user association is determined by solving a Lagrangian dual problem with a sub-gradient algorithm; for the latter, optimum transmit powers of the BS and each relay station are determined by using Newton’s method. Finally, a sub-optimal solution of the original problem is obtained by a low-complexity iterative algorithm. Simulation results show that the proposed joint user association and power allocation algorithm can offload the traffic of the BS effectively, keep the BS and relay stations operate at low power levels, and improve the system energy efficiency significantly, compared with user association-only schemes.

Cellular-D2D resource reuse algorithms based on proportional fairness

Device-to-device (D2D) communication can improve coverage, spectrum efficiency, and energy efficiency based on the current cellular network architecture. The fair scheduling for D2D communication in the orthogonal frequency division multiple access-based cellular network is studied in this paper. Based on the proportional fairness criteria, the optimization objective is formulated to maximize the sum of the relative achievable rate of both cellular users (CUs) and D2D pairs. It is a hybrid optimization problem since it involves in both the resource reuse and the transmit power control. A practical proportional fairness scheduling (PFS) algorithm is proposed. Firstly, the admissible area is decided according to the transmit power limitation of terminals and the quality of service (QoS) requirement. Next, we seek the optimal transmit power combination for the CU and D2D pair in the admissible area and it is demonstrated that the optimal value can be selected from several points on the border of the admissible area. Lastly, when multiple subchannels can be employed for scheduling, based on the generated bipartite graph, Hungarian algorithm is adopted to realize maximum matching, i.e., select reusable CUs and D2D pairs to maximize the sum of the relative achievable rates. The simulation results show that PFS algorithm can guarantee the excellent performance of both throughput and fairness.

On the throughput performance of multirate IEEE 802.11 networks with variable-loaded stations: analysis, modeling, and a novel proportional fairness criterion

This paper focuses on multirate IEEE 802.11 Wireless LAN employing the mandatory Distributed Coordination Function (DCF) option. Its aim is threefold. Upon starting from the multi-dimensional Markovian state transition model proposed by Malone et.al. for characterizing the behavior of the IEEE 802.11 protocol at the Medium Access Control layer, it presents an extension accounting for packet transmission failures due to channel errors. Second, it establishes the conditions under which a network constituted by N stations, each station transmitting with its own bit rate, Rd(s), and packet rate, λs, can be assumed loaded. Finally, it proposes a modified Proportional Fairness (PF) criterion, suitable for mitigating the rate anomaly problem of multirate loaded IEEE 802.11 Wireless LANs, employing the mandatory DCF option. Compared to the widely adopted assumption of saturated network, the proposed fairness criterion can be applied to general loaded networks. The throughput allocation resulting from the proposed algorithm is able to greatly increase the aggregate throughput of the DCF, while ensuring fairness levels among the stations of the same order as the ones guaranteed by the classical PF criterion. Simulation results are presented for some sample scenarios, confirming the effectiveness of the proposed criterion for optimized throughput allocation.

Proportional Switching in First-in, First-out Networks

We consider a family of discrete time multihop switched queueing networks where each packet moves along a fixed route. In this setting, BackPressure is the canonical choice of scheduling policy; this policy has the virtues of possessing a maximal stability region and not requiring explicit knowledge of traffic arrival rates. BackPressure has certain structural weaknesses because implementation requires information about each route, and queueing delays can grow super-linearly with route length. For large networks, where packets over many routes are processed by a queue, or where packets over a route are processed by many queues, these limitations can be prohibitive. In this article, we introduce a scheduling policy for first-in, first-out networks, the ProportionalScheduler, which is based on the proportional fairness criterion. We show that, like BackPressure, the ProportionalScheduler has a maximal stability region and does not require explicit knowledge of traffic arrival rates. The ProportionalScheduler has the advantage that information about the network’s route structure is not required for scheduling, which substantially improves the policy’s performance for large networks. For instance, packets can be routed with only next-hop information and new nodes can be added to the network with only knowledge of the scheduling constraints.

Cloud Cooperated Heterogeneous Cellular Networks for Delayed Offloading using Millimeter Wave Gates

Abstract Increasing the capacity of wireless cellular network is one of the major challenges for the coming years. A lot of research works have been done to exploit the ultra-wide band of millimeter wave (mmWave) and integrate it into future cellular networks. In this paper, to efficiently utilize the mmWave band while reducing the total deployment cost, we propose to deploy the mmWave access in the form of ultra-high capacity mmWave gates distributed in the coverage area of the macro basestation (Macro BS). Delayed offloading is also proposed to proficiently exploit the gates and relax the demand of deploying a large number of them. Furthermore, a mobility-aware weighted proportional fair (WPF) user scheduling is proposed to maximize the intra-gate offloading efficiency while maintaining the long-term offloading fairness among the users inside the gate. To efficiently link the mmWave gates with the Macro BS in a unified cellular network structure, a cloud cooperated heterogeneous cellular network (CC-HetNet) is proposed. In which, the gates and the Macro BS are linked to the centralized radio access network (C-RAN) via high-speed backhaul links. Using the concept of control/user (C/U) plane splitting, signaling information is sent to the UEs through the wide coverage Macro BS, and most of users’ delayed traffic is offloaded through the ultra-high capacity mmWave gates. An enhanced access network discovery and selection function (eANDSF) based on a network wide proportional fair criterion is proposed to discover and select an optimal mmWave gate to associate a user with delayed traffic. It is interesting to find out that a mmWave gate consisting of only 4 mmWave access points (APs) can offload up to 70 GB of delayed traffic within 25 sec, which reduces the energy consumption of a user equipment (UE) by 99.6 % compared to the case of only using Macro BS without gate offloading. Also, more than a double increase in total gates offloaded bytes is obtained using the proposed eANDSF over using the conventional ANDSF proposed by 3GPP due to the optimality in selecting the associating gate.

A Novel Algorithm for Efficient Downlink Packet Scheduling for Multiple-Component-Carrier Cellular Systems

The simultaneous aggregation of multiple component carriers (CCs) for use by a base station constitutes one of the more promising strategies for providing substantially enhanced bandwidths for packet transmissions in 4th and 5th generation cellular systems. To the best of our knowledge, however, few previous studies have undertaken a thorough investigation of various performance aspects of the use of a simple yet effective packet scheduling algorithm in which multiple CCs are aggregated for transmission in such systems. Consequently, the present study presents an efficient packet scheduling algorithm designed on the basis of the proportional fair criterion for use in multiple-CC systems for downlink transmission. The proposed algorithm includes a focus on providing simultaneous transmission support for both real-time (RT) and non-RT traffic. This algorithm can, when applied with sufficiently efficient designs, provide adequate utilization of spectrum resources for the purposes of transmissions, while also improving energy efficiency to some extent. According to simulation results, the performance of the proposed algorithm in terms of system throughput, mean delay, and fairness constitute substantial improvements over those of an algorithm in which the CCs are used independently instead of being aggregated.

Fairness Resource Allocation for Parallel Multi-Radio Access in Cognitive Multi-Cell

The secondary users (SUs) in cognitive heterogeneous networks have the capability of utilizing the coexisting multi-radio access (MRA) networks to further improve network capacity as well as user satisfaction. In this paper, we focus on multi-radio resource management for the parallel multi-radio access technology in a cognitive multi-cell, where SUs have different services demands, including real-time (RT) services and best-effort (BE) services. Since the interference introduced to the primary users must be considered carefully in order to forbid their performance degradation, the proposed resource management strategy jointly handles the interference problem and the varied resource constraints caused by MRA networks simultaneously. Additionally, because all the users expect to be allocated a fair amount of resource and gain a same level of QoS, the proportional fairness criterion is introduced and aims at all the SUs. Therefore, the proposed strategy can achieve the fairness between RT SUs and BE SUs when the residual resource is sufficient after satisfying the target rate of the RT SUs. Since the formulated problem is NP-hard, a novel algorithm based on genetic algorithm is addressed to solve it. Finally, extensive simulations are presented to verify the performance improvement of the proposed strategy.

Decentralized control and fair load-shedding compensations to prevent cascading failures in a smart grid

Abstract Evidence shows that a small number of line contingencies in power systems may cause a large-scale blackout due to the effects of cascading failures. With the development of new technologies and the growing number of heterogeneous participants, a modern/smart grid should be able to self-heal its internal disturbances by continually performing self-assessment to deter, detect, respond to and restore from unpredictable contingencies. Along this line, this research focuses on the problem of how to prevent the occurrence of cascading failures through load shedding by considering heterogeneous shedding costs of grid participants. A fair load-shedding algorithm is proposed to solve the problem in a decentralized manner, where a load-shedding participant need only monitor its own operational status and interact with its neighboring participants. Using an embedded feedback mechanism, the fair load-shedding algorithm can determine a marginal compensation price for each load-shedding participant in real time based on the proportional fairness criterion, without knowing the shedding costs of the participants. Such fairly determined compensations can help motivate loaders/generators to actively participate in the load shedding in the face of internal disturbances. Finally, the properties of the load-shedding algorithm are evaluated by carrying out an experimental study on the standard IEEE 30 bus system. The study will offer new insights into emergency planning and design improvement of self-healing smart grids.

A Suboptimal Multiuser-Pairing Algorithm With Low Complexity for Virtual MIMO Systems

In virtual multiple-input-multiple-output (V-MIMO) systems, employing a user-pairing algorithm can significantly improve system capacity and spectral efficiency using multiuser diversity. The optimal pairing algorithm can achieve optimal system performance, but it is not feasible to implement in practice due to its huge complexity. To solve the problem, an efficient suboptimal pairing algorithm with lower complexity is proposed, which maximizes the system throughput by selecting users one by one. Furthermore, to achieve a good balance between throughput and user fairness, a novel pairing algorithm is derived, which combines the advantages of the suboptimal pairing algorithm and proportional fair (PF) criteria. Simulation results show that the proposed algorithm achieves better fairness and higher system throughput than the double PF (D-PF) algorithm, and has much lower complexity than the optimal pairing algorithm.