Proportional Fairness Research Articles

Joint Optimization of User Association, Subchannel Allocation, and Power Allocation in Multi-Cell Multi-Association OFDMA Heterogeneous Networks

Heterogeneous network is a novel network architecture proposed in Long-Term-Evolution~(LTE), which highly increases the capacity and coverage compared with the conventional networks. However, in order to provide the best services, appropriate resource management must be applied. In this paper, we consider the joint optimization problem of user association, subchannel allocation, and power allocation for downlink transmission in Multi-cell Multi-association Orthogonal Frequency Division Multiple Access (OFDMA) heterogeneous networks. To solve the optimization problem, we first divide it into two subproblems: 1) user association and subchannel allocation for fixed power allocation; 2) power allocation for fixed user association and subchannel allocation. Subsequently, we obtain a locally optimal solution for the joint optimization problem by solving these two subproblems alternately. For the first subproblem, we derive the globally optimal solution based on graph theory. For the second subproblem, we obtain a Karush-Kuhn-Tucker (KKT) optimal solution by a low complexity algorithm based on the difference of two convex functions approximation (DCA) method. In addition, the multi-antenna receiver case and the proportional fairness case are also discussed. Simulation results demonstrate that the proposed algorithms can significantly enhance the overall network throughput.

Application-Aware Resource Allocation of Hybrid Traffic in Cellular Networks

The hybrid traffic, a composite of elastic and inelastic data generated by delay-tolerant and real-time applications respectively, forms the bulk of what is carried over modern cellular systems. Since a smooth performance of real-time and delay-tolerant applications is tied to their distinctive needs for resources, networks’ intelligence about representative characteristics of applications’ traffic, networks’ ability to prioritize subscribers, and networks’ sophistication to cope with temporal variations in traffic amounts from the real-time and delay-tolerant applications can help efficiently assign resources accordingly to the preceding issues and consequentially elevate the quality-of-experience. To this end, the manuscript at hand aims at concocting a convex proportional fairness resource allocation method for cognitive cellular systems equipped with the intelligence to consider the traffic type, its temporal variations, and user prioritization. The devised method is formalized as mathematically equivalent centralized and distributed formulations with provided solution algorithms and convergence conditions. It is proved that the centralized approach has a lower transmission overhead, whose some lower bounds are derived for the centralized and distributed methods. Analyses of the sensitivity to changes of user equipments quantity and of application usage are presented under a variation of bidding scenarios in the face of the system dynamics.

Neighbors-Aware Proportional Fair scheduling for future wireless networks with mixed MAC protocols

In this paper, we consider a beyond-5G scenario, where two types of users, denoted as scheduled and uncoordinated nodes, coexist on the same set of radio resources for sending data to a base station. Scheduled nodes rely solely on a centralized scheduler within the base station for the assignment of resources, while uncoordinated nodes use an unslotted Carrier Sense Multiple Access (CSMA) protocol for channel access. We propose and evaluate through simulations: (a) a novel centralized resource scheduling algorithm, called Neighbors-Aware Proportional Fair (N-PF) and (b) a novel packet length adaptation algorithm, called Channel-Aware (CA) Packet Length Adaptation algorithm for the scheduled nodes. The N-PF algorithm considers the uplink channel state conditions and the number of uncoordinated nodes neighboring each scheduled node in the aggregate scheduling metric, in order to maximize packet transmission success probability. The CA algorithm provides an additional degree of freedom for improving the performance, thanks to the fact that scheduled nodes with lower number of hidden terminals, i.e., having higher packet capture probability, are assigned longer packet transmission opportunities. We consider two benchmark schemes: Proportional Fair (PF) algorithm, as a resource scheduling algorithm, and a discrete uniform distribution (DUD) scheme for packet lengths distribution. Simulation results show that the proposed schemes can result in significant gain in terms of network goodput, without compromising fairness, with respect to two benchmark solutions taken from the literature.

A Novel Resource Allocation and Power Control Mechanism for Hybrid Access Femtocells

LTE Small cells like Femto cells are being deployed in enterprises and residential buildings to improve data rates of indoor users who experience low Signal-to-Interference plus Noise Ratio (SINR) from Macro Base Stations (MBSs). Deployment of Femto cells inside a building can lead to signal leakage at the edges/corners of the buildings. This causes cross-tier interference and degrades the performance of users in High Interference Zone (HIZone) around the building area, who are connected to one of the MBSs in LTE Heterogeneous Networks (HetNets). Hybrid Access Femto cells (HAFs) can ensure QoS for paid Subscriber Group (SG) users by giving them preferential access to resource blocks over non-SG (NSG) users and also improve the throughput of LTE HetNet system by serving nearby NSG users. In this work, we address various challenges involved in deployment and operation of HAFs in indoor environments by proposing an Optimal Placement of Femto cell (OPF) model, a dynamic Bandwidth Allocation (BWA) mechanism for splitting resource blocks between SG and NSG users, a dynamic power control mechanism to mitigate co-tier and cross-tier interference in HetNets and an Enhanced Priority (EP) scheduling mechanism to give more priority to SG users over NSG users.During peak traffic load scenarios, HAFs may not be able to guarantee QoS of both indoor and HIZone users connected to them. As HAFs are primarily meant for indoor users, HAFs employ an Optimal Power Control (OPC) mechanism to tune their transmit powers so that HIZone users are offloaded to near-by MBSs. Since the OPC is a Mixed Integer Non-linear Programming (MINLP) problem, we put forth a Sub-Optimal Power Control (SOPC) mechanism. The SOPC mechanism boosts the throughput of MBSs by almost 62% over the traditional 3GPP proposed enhanced Inter-Cell Interference Co-ordination (eICIC) mechanism for 300 users in the HetNet system. Also, the proposed EP scheduling mechanism maintains Jain’s fairness index of 0.99 for both SG and NSG users while providing a 40% higher per user throughput than that obtained with the legacy proportional fair and Priority Set schedulers.

Fair Dynamic Spectrum Allocation Using Modified Game Theory for Resource-Constrained Cognitive Wireless Sensor Networks

This paper considers the deployment of a cognitive radio scheme in wireless sensor networks to achieve (1) fair spectrum allocation, (2) maximum spectrum utilization, and (3) priority-based sensor transmissions, while (4) avoiding unnecessary spectrum handover (or handoff). This problem is modelled as a bi-objective optimization problem. We apply modified game theory and a cooperative approach to identify an approximate optimal solution in reasonable time. We perform a series of numerical experiments to show that our scheme achieves fair spectrum allocation (in terms of proportional fairness) while observing transmission priorities and minimizing unnecessary spectrum handover.

Proportional fairness analysis of massive MIMO Two-tier multiuser downlink with subchannel pairing

This paper presents a proportional fairness throughput analysis of a millimeter wave massive multiple-input multiple output (MIMO) small base station (SBS)-assisted downlink with subchannel (SC) pairing. We derive an analytical expression for evaluating the average logarithmic throughput with SC-pairing and proportional fairness in two-tier network with amplify-and-forward (AF) and decode-and-forward (DF) SBSs. Analytical expressions are derived for the probability density function (PDF) of logarithmic throughput, and the average logarithmic throughput with statistical channel state information (CSI) based gain at AF SBS. It has been shown that the percentage error between simulation and analytical results decreases with increase in number of SC N and number of antennas, and is upper bounded by 0.28% and 0.79% when N≥16 for AF and DF SBSs, respectively.

Maximizing Proportional Fairness in Wireless Powered Communications

This letter investigates the fundamental tradeoff between sum rate and fairness of a wireless-powered uplink communication system, consisting of one base station (BS) and multiple energy harvesting users, which are coordinated through the harvest-then-transmit protocol. To this end, the optimal rate and time allocation, when aiming to maximize the proportional fairness, is investigated. Two well known communication protocols are considered, namely, time division multiple access (TDMA) and nonorthogonal multiple access with time-sharing (NOMA-TS). It is shown that NOMA-TS outperforms the considered benchmark scheme, which is the NOMA with fixed decoding order and adaptive power allocation, while TDMA proves to be an appropriate choice, when all the users are located in similar distances from the BS.

Waterfilling-Based Proportional Fairness Scheduler for Downlink Non-Orthogonal Multiple Access

In this letter, a low-complexity waterfilling-based power allocation (PA) technique, incorporated within the proportional fairness scheduler, is proposed and applied to a non-orthogonal multiple access (NOMA) scheme in a cellular downlink system. The aim of the proposed joint PA and scheduling scheme is to maximize the achieved average throughput through a quasi-optimal repartition of the transmit power among subbands, while guaranteeing a high level of fairness in resource allocation. Extensive simulation results show that the proposed technique enhances both system capacity and user fairness, when compared to either orthogonal signaling or NOMA with static PA.

Low‐complexity user pairing and power allocation algorithm for 5G cellular network non‐orthogonal multiple access

Non-orthogonal multiple access (NOMA) is a candidate technology for the 5th generation cellular networks to reduce the big gap between network capacity and fast growing traffic. It applies superposition coding in transmitters and successive interference cancellation at the receivers to cancel intra-cell interference. The same frequency resource can be allocated simultaneously to multiple intra-cell users, holding large potentials on improving network performance. A major technical challenge of NOMA is on user pairing and power allocation (UPPA). Most of existing UPPA algorithms are based on exhaustive search with extensive computation. A new algorithm, which has the lowest computation complexity achievable for NOMA UPPA is proposed. The main idea is to pair the first users having the highest proportional fairness priority coefficient with potential second users having the highest channel conditions. A fixed power allocation strategy is adopted. The proposed algorithm is significantly faster than existing algorithms without sacrificing NOMA throughput gain.

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.

Virtualization of Wireless Sensor Networks Through MAC Layer Resource Scheduling

In this paper, we propose a joint throughput and time-resource allocation scheme for the virtualization of IEEE 802.15.4-based wireless sensor networks (WSNs). Virtualization is realized through utilization of the guaranteed time slot (GTS) mechanism of cluster-tree topology to schedule resources on a media access control (MAC) layer. We develop a scheduler that is located in the personal area network (PAN) coordinator and that virtualizes the network into an aggregate of independent profiles, assigning the available resources to each profile with end-to-end (ETE) delay guarantees. The scheduler solves the problem of managing resources available in the network in an optimization framework, taking into consideration the individual profile and sensor requirements. Moreover, it uses the proposed heuristic fair resource allocation (FRA) algorithm to derive the solution in polynomial time. We validate the scheduling performance via discrete event simulation (DES) and compare the proposed FRA algorithm with round robin (RR) and proportionally fair (PF) scheduling algorithms in several scenarios. The proposed scheme demonstrates efficient resource management while maintaining profile isolation in all cases, whereas other algorithms lead to increased latency and lower throughput in the network.

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.

Joint Demand-Side Management in Smart Grid for Green Collaborative Mobile Operators Under Dynamic Pricing and Fairness Setup

In this paper, the interactions between multiple mobile operators, owning heterogeneous cellular networks, and energy retailers existing in the smart grid are investigated. Energy procurement decisions of the cellular networks sharing common energy sources are jointly optimized while considering both dynamic energy pricing and varying pollution levels of energy sources. The objective is to enable collaboration among mobile operators in their demand-side management (DSM) to achieve economical and environmental goals. This is performed by solving a unified optimization problem aiming at maximizing a metric based on mobile operators’ profits while limiting the amount of carbon dioxide (CO2) emitted by all networks. In this paper, three utility metrics, namely, Sum, Max-min, and Proportional Fair utilities, are considered to reflect the degree of fairness among mobile operators in the optimized DSM. Closed-form expressions of the optimal procured energy from each retailer used to power the marcocell and active small cell base stations (BSs) are derived for pricing profiles and utility metrics. Furthermore, the BS sleeping strategy is applied, in a centralized or a decentralized manner, in order to reduce the network energy consumption during low traffic periods. Finally, the impact of renewable energy generation uncertainty on the energy procurement decision is examined. The behavior of the different actors in the energy procurement decision is investigated through simulations. Results show that significant CO2 emissions reduction can be achieved thanks to the optimized DSM and the BS sleeping strategy.

New Combined Downlink Scheduling Algorithm for LTE Networks

Considered as the 4th generation network, the LTE (Long Term Evolution) was defined by the 3GPP consortium as a succession of these predecessors, allowing the improvement of the QoS offered to the customers. Due to the limitations at the bandwidth, Radio Resource Management (RRM) remains one of the important aspects in cellular networks. The Packet Scheduling is an essential mechanism of the RRM procedure. It is used to define the distribution method of radio resources. The main objective of these mechanisms is the improvement of the performance of the LTE system for all users. This is why scheduling algorithms are of great importance in the resources management. And since they are not defined in 3GPP specifications, they become a vital subject of research. In this paper, we proposed a new downlink scheduling algorithm named Combined PF-MLWDF-EXP/PF (CPMEP) and we compared its performances in a Single Cell with Interference scenario with the well-known schedulers such as Proportional Fair (PF), Modified Largest Weighted Delay First (MLWDF) and Exponential Proportional Fairness (EXP/PF). The simulation results show that the combined algorithm is more efficient for different applications, despite it has limitations in terms of Fairness Index and Throughput for Non Real-Time services.

A Novel Description approach based on sorted rectangles for scheduling information bearing in OFDMA systems

Dynamic time/frequency resource allocation has been widely employed in wireless OFDMA systems. In such mechanisms, sophisticated scheduling decisions need to be conveyed to users and may lead to considerable signaling overhead. In this paper, a new efficient approach, namely, Sorted-Rectangle Description (SRD) is proposed for describing the scheduling decision in an OFDMA frame. SRD first partitions a frame into minimum number of rectangular polygons, namely, rectangular bursts (RB), in which each RB contains the resource units belonging to the same assignment. We show that each RB-partitioned frame is sufficient to be fully reconstructed by the top-left coordinates of each RB in a specific sorted order. Sorting and reconstructing algorithms with linear time complexity in the total number of RBs are also proposed. Simulations based on a multi-user OFDMA system with full-buffer or periodic small-data traffic model are conducted to evaluate the performance of the proposed SRD method under two representative scenarios. The simulation results show that, for the full-buffer traffic model with a proportional fair (PF) scheduler, the proposed description approach can achieve significant reduction of the overhead ratio compared to that of the existing systems and is expected to lead to considerable increase of system throughput. Meanwhile, for the periodic small-data traffic model, it is shown that the proposed description approach can greatly reduce the rate of packet loss due to timeout or buffer overflow and thus provides significant improvement of the system capacity.

Joint Downlink User Association and Interference Management in Two-Tier HetNets With Dynamic Resource Partitioning

We investigate a joint user association and interference management problem in two-tier downlink heterogeneous networks where pico base stations (BSs) are densely deployed in areas of high traffic demand. We employ macro almost blanking subframes (ABSs) to mitigate cross-tier interference. To manage co-tier interference among picocells, we introduce pico operation mode (POM): During each POM, a distinct subset of picocells serve users simultaneously; different POMs operate at different times at different durations. We formulate the problem as maximizing the network utility under proportional fairness with the optimization over user association and resource partitioning (RP) (including the macro ABS and the amount of time allocated to each POM). As an exhaustive search over all possible POMs in the optimization may become computationally infeasible, we propose a method of preselecting favorable POMs to reduce the dimension of the optimization. With the selected POMs, we explicitly examine the structure of the optimal solutions and show that 1) the optimal user association is load-aware and can be determined by rate bias values of each BS, and 2) all the POMs and the macro BSs have balanced load in the sense that the ratios of the number of associated users to the allocated time are the same. Based on the analysis, an alternating algorithm is developed to obtain the RP and the biases. We demonstrate through numerical examples that 1) the proposed POM selection method does not incur significant performance loss, compared with the case where all possible POMs are considered; 2) the alternating algorithm provides near-optimal cell association and RP solutions; 3) by applying the proposed framework, significant network performance improvement can be achieved with dense pico deployments, compared with baselines without co-tier interference management and baselines with sparse pico deployments.

Gibbs-Sampling-Based CRE Bias Optimization Algorithm for Ultradense Networks

Cell range expansion (CRE) is an effective technique in the ultradense network (UDN) to enlarge small cells' ranges and promote network utility such as system throughput, number of users lower than a rate threshold, and proportional fairness. Due to the coupled relationship of user association and scheduling in rate-related utility optimization, optimal cell-specific CRE bias is difficult to achieve. This paper first proposes a centralized CRE bias adjusting algorithm based on Gibbs sampling to achieve the optimal solution of cell-specific CRE bias based on global information. After that, a decentralized Gibbs-sampling-based CRE bias adjusting algorithm without the need for the entire knowledge of global channel gains is designed to deal with the computational complexity and message exchange overhead problem caused by scale expansion of UDN. Finally, to further reduce the increasing computational complexity, message exchange overhead, and time complexity caused by scale expansion of UDN, this paper constructs a neighbor graph based on the mutual bias influence among cells, develops a graph-coloring-based clustering algorithm to classify cells into groups, and proposes a central-aided distributed CRE bias adjusting algorithm to obtain the optimal solution to the rate-related utility optimization problem based on local information. In the central-aided distributed CRE bias adjusting algorithm, a central macrocell is used to collect the information from the small cells, and the small cells distributively determine their CRE bias based on shared central information. The optimality and complexity of the proposed algorithms are proven and analyzed. Numerical results show that, compared with existing schemes, the proposed Gibbs-sampling-based algorithms can achieve a larger utility function with less iteration time.

Comparative performance analysis of different resource scheduler and characterising the impact of proportional fair under different TTI feedback delay in EUTRA network

Evolved UMTS terrestrial radio access network (EUTRAN) offers high uplink and downlink throughput. In this paper, we investigate the performance of five different schedulers of media access control for resource allocation, such as round robin (RB), proportional fair (PF), best channel quality indicator (CQI), max transmission point (TP) and resource fair (RF). On comparing the performance of resource allocation schedulers in the indistinguishable arrangement, we found the proportional fair (PF) offers balance in terms of individual metrics. Furthermore, we analyse the effect of feedback transmission time interval (TTI) delay on two typical EUTRAN networks referred to as long term evolution (LTE) and LTE-Advance (LTE-A). We evaluate the performance of the PF scheduler for both networks under varying feedback delay in TTI. Simulated results show that the delay in TTI affects the performance of resource allocation. Feedback delay improves network performance by compensating effect of imperfect channel.

Comparative performance analysis of different resource scheduler and characterising the impact of proportional fair under different TTI feedback delay in EUTRA network

Evolved UMTS terrestrial radio access network (EUTRAN) offers high uplink and downlink throughput. In this paper, we investigate the performance of five different schedulers of media access control for resource allocation, such as round robin (RB), proportional fair (PF), best channel quality indicator (CQI), max transmission point (TP) and resource fair (RF). On comparing the performance of resource allocation schedulers in the indistinguishable arrangement, we found the proportional fair (PF) offers balance in terms of individual metrics. Furthermore, we analyse the effect of feedback transmission time interval (TTI) delay on two typical EUTRAN networks referred to as long term evolution (LTE) and LTE-Advance (LTE-A). We evaluate the performance of the PF scheduler for both networks under varying feedback delay in TTI. Simulated results show that the delay in TTI affects the performance of resource allocation. Feedback delay improves network performance by compensating effect of imperfect channel.

Joint Design of User Association and Power Allocation With Proportional Fairness in Massive MIMO HetNets

Although the massive MIMO enabled heterogeneous networks (HetNets) can intensify the spectral efficiency benefits, the proper user association and resource allocation are both crucial to achieve desirable performance since the power consumption of base station (BS) scales with the large number of antennas. This paper aims to investigate joint design of user association and power allocation with loads constraint and transmit power constraint for the massive MIMO HetNets by considering proportional fairness about the spectral efficiency under imperfect channel state information. First, we derive a closed-form lower bound on the ergodic spectral efficiency with linear zero-forcing beamforming, based on which, a mixed-integer nonlinear programming problem is formulated. It is difficult to efficiently obtain an exact solution since it is non-convex and combinational. To solve this NP-hard problem, an effective algorithm with guaranteed convergence is proposed, where the original problem is decomposed into the corresponding subproblems, which can be solved by low complexity approaches, respectively. Numerical results show that how the number of antennas and the number of BSs affect the spectral efficiency, and our proposed algorithm outperforms other algorithms in terms of the spectral efficiency and load balancing.