Proportional Fairness Research Articles

An Optimal Standard-Compliant MIMO Scheduler for LTE Downlink

Frequency domain packet scheduling (FDPS) problem is one of the crucial elements in the 3rd generation partnership project (3GPP) long term evolution (LTE) system, which has a tremendous impact on the LTE system performance. However, optimal resource allocation through FDPS is a complicated and challenging task when multiple input and multiple output (MIMO)-orthogonal frequency division multiple access (OFDMA) technology is adopted. In this paper, we propose a new FDPS scheme for the 3GPP LTE downlink channels that optimally assigns time-frequency resources to users based on the proportional fairness metric. The proposed scheme jointly considers multiple system constraints imposed by the 3GPP LTE standard that arise in the MIMO mode selection and modulation and coding scheme (MCS) selection. Such scheduling problem is considered to be among the most difficult optimization problems. Our major contribution in this paper is that we model the FDPS problem as a unique binary linear programming problem and prove that the problem is totally unimodular. With the total unimodularity property, we are able to solve the complicated FDPS problem using efficient linear programming problem solvers. Simulation results show that our proposed scheme outperforms the existing state-of-the-art MIMO proportional fair scheduling algorithms used in the FDPS problem.

Fairness-Based Resource Allocation with Minimum Rate Guarantee in a Multiuser OFDMA System

We propose a resource allocation scheme based on Proportional Fairness (PF) for minimum bit rate guarantee in a multiuser, frequency-selective frame-based OFDMA system. Instead of considering subcarrier-and-bit allocation, we consider a more realistic scheduling which is performed at the beginning of each frame, while allowing time-slots multiplexing among active users. Our scheme aims to guarantee different minimum bit rates to different users, while throughput fairness among users is maintained. We formulate the optimization problem based on a multichannel proportional fairness objective function. Minimum bit rate guarantee is taken as the constraint. The optimization problem is solved by using the Lagrange multiplier method. Then, we use our fast cross-layer approach integrated to our optimization solution to schedule packets from finitely backlogged queues. Simulations with user mobility are conducted. The results show that the proposed scheme can serve users with satisfied minimum bit rate requirement. Furthermore, the simulation results also confirm throughput fairness among users.

Optimization of Cyclic-Delay Diversity Aided Frequency-Selective Scheduling in OFDMA Downlink Systems

Cyclic-delay diversity (CDD)-aided frequency-selective scheduling has been known as an effective technique for increasing the system capacity of orthogonal frequency-division multiple-access (OFDMA) systems. By increasing the channels' frequency selectivity with different cyclic delays applied on transmit antennas, the merit of multiuser diversity can be more effectively exploited in the system. In this paper, we aim to optimize the design of the CDD-aided frequency-selective scheduling for OFDMA downlink systems. Optimization is done from two aspects: cyclic-delay search and scheduling-information feedback. In the optimization of cyclic-delay search, three new methods are proposed, including antenna-wise sequential search for frequency-nonselective (AWSS-FNS) channels, AWSS for frequency-selective (AWSS-FS) channels, and a genetic-algorithm-based search (GAS). AWSS-FNS achieves the optimal performance if a channel is frequency nonselective over a subchannel, whereas AWSS-FS and GAS provide good tradeoffs between system performance and complexity for channels that are frequency selective over a subchannel. In the optimization of scheduling-information feedback, a new channel-dependent feedback (CDF) method is proposed, where the feedback resource is allocated to users according to their frequency-selectivity rates and a principle of proportional fairness. The optimized scheduler is shown to provide significant improvement in both system sum rate and user fairness over previous methods under fixed feedback overhead.

Proportional Fair MU-MIMO in 802.11 WLANs

We consider the proportional fair rate allocation in an 802.11 WLAN that supports multi-user MIMO (MU-MIMO) transmission by one or more stations. We characterise, for the first time, the proportional fair allocation of MU-MIMO spatial streams and station transmission opportunities. While a number of features carry over from the case without MU-MIMO, in general neither flows nor stations need to be allocated equal airtime when MU-MIMO is available.

Optimal Algorithms in Wireless Utility Maximization: Proportional Fairness Decomposition and Nonlinear Perron-Frobenius Theory Framework

We study the network utility maximization problems in wireless networks for service differentiation that optimize the Signal-to-Interference-plus-Noise Radio (SINR) and reliability under Rayleigh fading. Though seemingly nonconvex, we show that these problems can be decomposed into an optimization framework where each user calculates a payment for a given resource allocation, and the network uses the payment to optimize the performance of the user. We study three important examples of this utility maximization, namely the weighted sum logarithmic SINR maximization, the weighted sum inverse SINR minimization and the weighted sum logarithmic reliability maximization. These problems have hitherto been solved suboptimally in the literature. By exploiting the positivity, quasi-concavity and homogeneity properties in these problems and using the nonlinear Perron-Frobenius theory, we propose fixed-point algorithms that converge geometrically fast to the globally optimal solution. Numerical evaluations show that our algorithms are stable (free of parameter configuration) and computationally fast.

A survey on resource allocation techniques in OFDM(A) networks

In this contribution, we present a survey on the radio resource allocation techniques in orthogonal frequency division multiplexing (OFDM) and orthogonal frequency division multiple access (OFDMA) systems. This problem goes back to 1960s and that is related to properly and efficiently allocate the radio resources, namely subcarriers and power. We start by overviewing the main open issues in OFDM. Then, we describe the problem formulation in OFDMA, and we review the existing solutions to allocate the radio resources. The goal is to discuss the fundamental concepts and relevant features of different radio resource management criteria, including water-filling, max–min fairness, proportional fairness, cross-layer optimization, utility maximization, and game theory, also including a toy example with two terminals to compare the performance of the different schemes. We conclude the survey with a review of the state-of-the-art in resource allocation for next-generation wireless networks, including multicellular systems, cognitive radio, and relay-assisted communications, and we summarize advantages and common problems of the existing solutions available in the literature. The distinguishing feature of this contribution is a tutorial-style introduction to the fundamental problems in this area of research, intended for beginners on this topic.

Energy-Efficient Resource Allocation in OFDM Systems With Distributed Antennas

In this paper, we develop an energy-efficient resource-allocation scheme with proportional fairness for downlink multiuser orthogonal frequency-division multiplexing (OFDM) systems with distributed antennas. Our aim is to maximize energy efficiency (EE) under the constraints of the overall transmit power of each remote access unit (RAU), proportional fairness data rates, and bit error rates (BERs). Because of the nonconvex nature of the optimization problem, obtaining the optimal solution is extremely computationally complex. Therefore, we develop a low-complexity suboptimal algorithm, which separates subcarrier allocation and power allocation. For the low-complexity algorithm, we first allocate subcarriers by assuming equal power distribution. Then, by exploiting the properties of fractional programming, we transform the nonconvex optimization problem in fractional form into an equivalent optimization problem in subtractive form, which includes a tractable solution. Next, an optimal energy-efficient power-allocation algorithm is developed to maximize EE while maintaining proportional fairness. Through computer simulation, we demonstrate the effectiveness of the proposed low-complexity algorithm and illustrate the fundamental tradeoff between energy- and spectral-efficient transmission designs.

Confederation Based RRM with Proportional Fairness for Soft Frequency Reuse LTE Networks

A new radio resource management (RRM) technique for improving the downlink performance in soft-frequency-reuse based long term evolution (LTE) networks is presented. In this RRM the resource is dynamically allocated in distributed and centralized manners such that spectral efficiency is maximized across the whole network. To achieve this a unique interference mapping strategy is implemented to assist in deciding whether a distributed or centralized mode is applicable per basestation. When a distributed approach is granted to a basestation it can use the entire spectrum while when a centralized approach is imposed on a basestation it will only be allocated a subset of the spectrum. The proposed then utilizes the confederation concept in the sense that once the allocation approach is determined the individual basestations can take control of their allocated resource. When combined with proportional fairness scheduling, this RRM can also benefit from multiuser diversity. It will be shown through mathematical analysis and computer simulations that this technique offers significant improvements in terms of sum rate and quality of service by increasing the guaranteed data rate per user.

A novel energy efficient packet-scheduling algorithm for CoMP

The increasing energy consumption driven by striking growths in the number of users and data usage has placed cost reduction and energy efficiency at the forefront of system design. As a step towards incorporating more energy friendly mobile platforms in future networks, 3GPP LTE-Advanced has adopted Coordinated Multi-Point (CoMP) transmission/reception due to its ability to mitigate and/or coordinate inter-cell interference (ICI). However, there is room for reducing energy consumption further by exploiting the inherent flexibility of the dynamic resource allocation (DRA) protocols. Pivotal to the DRA is the packet scheduler that plays central key role in determining the overall performance of the 3GPP long-term evolution (LTE) based on packet-switching operation and provide a potential research playground for optimizing energy consumption in future networks. In this paper, a novel energy-efficient scheduling (EES) is proposed that can achieve power-efficient transmission to the UEs while providing both system energy efficiency gain and fairness improvement. The proposed algorithm is based on a novel scheduling metric focusing on the ratio of the transmit energy per bit and allocates the Physical Resource Block (PRB) to the UE that requires the least ratio of the transmit energy per bit. Through computer simulation, the performance of the proposed EES packet-scheduling algorithm using mixed traffic is compared with the State-of-the-Art (SoTA) packet-scheduling algorithms such as Maximum Carrier-to-Interface ratio (MCI), Proportional Fairness (PF), and Round Robin (RR), which eventually shows the significant improvement.

A User Selection Algorithm Using Angle between Subspaces for Downlink MU-MIMO Systems

One of major issues in the efficient use of radio resource for multiuser multiple-input/multiple-output (MU-MIMO) systems is the selection of users to achieve the maximum system throughput. The optimal user selection algorithm, which requires exhaustive search, is prohibitive due to its high computational complexity where Block diagonalization (BD) method is applied and known as a suboptimal precoding technique for downlink MU-MIMO systems, which intents to perfectly eliminate inter-user interference. In this paper, we propose efficient, iterative user selection algorithms with low complexity, where the product of eigenvalues of effective channels is utilized as a selection metric by applying the concept of principal angles between subspaces. And, we further examined the applicability of the proposed algorithms to limited feedback systems and proportional fair (PF) scheduling. Through computational complexity analysis, we show that the proposed algorithm has low complexity with a little loss in throughput. Simulation results validate that the proposed algorithm achieves almost the same system throughput by a capacity-based algorithm under high SNR regime with considerable reduction in complexity.

AP Association for Proportional Fairness in Multirate WLANs

In this paper, we investigate the problem of achieving proportional fairness via access point (AP) association in multirate WLANs. This problem is formulated as a nonlinear programming with an objective function of maximizing the total user bandwidth utilities in the whole network. Such a formulation jointly considers fairness and AP selection. We first propose a centralized algorithm Non-Linear Approximation Optimization for Proportional Fairness (NLAO-PF) to derive the user-AP association via relaxation. Since the relaxation may cause a large integrality gap, a compensation function is introduced to ensure that our algorithm can achieve at least half of the optimal in the worst case. This algorithm is assumed to be adopted periodically for resource management. To handle the case of dynamic user membership, we propose a distributed heuristic Best Performance First (BPF) based on a novel performance revenue function, which provides an AP selection criterion for newcomers. When an existing user leaves the network, the transmission times of other users associated with the same AP can be redistributed easily based on NLAO-PF. Extensive simulation study has been performed to validate our design and to compare the performance of our algorithms to those of the state of the art.

Low complexity user scheduling algorithm for energy‐efficient multiuser multiple‐input multiple‐output systems

In downlink multiuser multiple-input multiple-output (MU-MIMO) systems, block diagonalisation (BD) is a well-known precoding technique that eliminates inter-user interference. The number of simultaneously supportable users with BD is limited by the number of base station transmit antennas and the number of user receive antennas. Traditional MU-MIMO scheduling algorithms focus on sum capacity. However, these user scheduling algorithms might not be optimal with respect to energy efficiency. Here, the authors consider the energy-efficient MU-MIMO scheduling that maximises the energy efficiency. The brute-force search for the optimal user set, however, is computationally prohibitive. Therefore they propose a low-complexity user scheduling algorithm for energy-efficient MU-MIMO systems. They first obtain an approximation expression for the energy efficiency by utilising the upper bound of the MU-MIMO system capacity. Then they show that the maximum energy efficiency can be achieved if the scheduling user set is selected to obtain the largest matrix volume. The numerical results show that the proposed algorithm achieves a good tradeoff between energy efficiency and computational complexity. They also consider the problem of maintaining fairness among users, and propose a simplified proportional fair (PF) scheduling algorithm.

On the Complexity of Joint Subcarrier and Power Allocation for Multi-User OFDMA Systems

Consider a multi-user Orthogonal Frequency Division Multiple Access (OFDMA) system where multiple users share multiple discrete subcarriers, but at most one user is allowed to transmit power on each subcarrier. To adapt fast traffic and channel fluctuations and improve the spectrum efficiency, the system should have the ability to dynamically allocate subcarriers and power resources to users. Assuming perfect channel knowledge, two formulations for the joint subcarrier and power allocation problem are considered in this paper: the first is to minimize the total transmission power subject to quality of service constraints and the OFDMA constraint, and the second is to maximize some system utility function (including the sum-rate utility, the proportional fairness utility, the harmonic mean utility, and the min-rate utility) subject to the total transmission power constraint per user and the OFDMA constraint. In spite of the existence of various heuristics approaches, little is known about the computational complexity status of the above problem. This paper aims to fill this theoretical gap, i.e., characterizing the complexity of the joint subcarrier and power allocation problem for the multi-user OFDMA system. It is shown in this paper that both formulations of the joint subcarrier and power allocation problem are strongly NP-hard. The proof is based on a polynomial time transformation from the so-called 3-dimensional matching problem. Several subclasses of the problem which can be solved to global optimality or $\epsilon$-global optimality in polynomial time are also identified. These complexity results suggest that there are not polynomial time algorithms which are able to solve the general joint subcarrier and power allocation problem to global optimality (unless P$=$NP), and determining an approximately optimal subcarrier and power allocation strategy is more realistic in practice.

A high-performance QoS-enhanced proportional fair scheduling algorithm over downlink OFDMA-based networks

OFDMA-based networks have been considered to be a promising solution to wireless networks especially for broadband multimedia mobile services. The major challenges pertaining to such OFDMA-based networks are to design a medium access control scheme that is expected to exploit multi-channel multi-rate diversity and with QoS provision. The previous existing scheduling algorithms either target at maximizing system throughput while starving the low-rate users, or focus on throughput fairness but seriously decreasing the system throughput. While proportional fair (PF) has emerged as a prominent candidate in wireless networks, as it achieves a good tradeoff between system throughput and fairness, PF still leads to low throughput of bad channel users, resulting in limiting the attainable QoS throughput for the entire system.In this paper, we propose a QoS-enhanced proportional fair (QEPF) scheduling algorithm, which aims at maximizing QoS throughput while still retaining fairness as well as maximizing system throughput in downlink OFDMA networks. QEPF proposes a QoS-enhanced PF-based utility function, which supports QoS and is a low-complexity algorithm for multi-channel OFDMA networks. We demonstrate via extensive simulation results, that QEPF outperforms PF in terms of system throughput and mean delay. The results illustrate that QEPF surprisingly attains great performance for poor channel users, while not sacrifices the performance of good channel users. Furthermore, the results show that QEPF well accommodates nearly twice the amount of high priority data than PF does.

Low Complexity in Exaggerated Earliest Deadline First Approach for Channel and QoS-aware Scheduler

Long Term Evolution (LTE) is a Quality of Service (QoS) provisioning wireless network for today’s technology and as well as for future demands. There is a high demand for better network performance over LTE network, either for real-time or non-real-time traffic. Specifically, the existing scheduling algorithms for real-time application, Exponential/Proportional Fair (EXP/PF), Proportional Fair (PF), and Modified-Largest Weighted Delay First (M-LWDF) have not fully optimized in LTE network. Hence, this paper aims to deliver new scheduling algorithm in the LTE network which overcomes several QoS and channel concerns. Several algorithms were studied, tested and compared which includes EXP/PF, PF, and M-LWDF, which are the popular scheduling algorithms for real-time application in today’s deployment. A typical LTE network is simulated and several experiments were conducted. Extensive simulation results showed that our proposed scheduling algorithm, Exaggerated Earliest Deadline First (E2DF), has outperformed the three existing scheduling algorithms. The proposed algorithm is a LTE compliance module and it able to provide great performance improvement as compared to the other algorithms for real-time application. 

Cross-Layer Scheduling and Resource Allocation for Heterogeneous Traffic in 3G LTE

3G long term evolution (LTE) introduces stringent needs in order to provide different kinds of traffic with Quality of Service (QoS) characteristics. The major problem with this nature of LTE is that it does not have any paradigm scheduling algorithm that will ideally control the assignment of resources which in turn will improve the user satisfaction. This has become an open subject and different scheduling algorithms have been proposed which are quite challenging and complex. To address this issue, in this paper, we investigate how our proposed algorithm improves the user satisfaction for heterogeneous traffic, that is, best-effort traffic such as file transfer protocol (FTP) and real-time traffic such as voice over internet protocol (VoIP). Our proposed algorithm is formulated using the cross-layer technique. The goal of our proposed algorithm is to maximize the expected total user satisfaction (total-utility) under different constraints. We compared our proposed algorithm with proportional fair (PF), exponential proportional fair (EXP-PF), and U-delay. Using simulations, our proposed algorithm improved the performance of real-time traffic based on throughput, VoIP delay, and VoIP packet loss ratio metrics while PF improved the performance of best-effort traffic based on FTP traffic received, FTP packet loss ratio, and FTP throughput metrics.

Resource Allocation Algorithm with Dynamic Subcarrier Assignment in OFDMA-based Wireless Networks

The allocation of available resources is one of the main issues in multi-user systems. Dependence of system capacity on radio link quality is an additional obstacle of efficient resource allocation in wireless networks. Combinations of two opposite approaches—fair resource allocation and system capacity maximization are used to solve this problem in practice.This paper proposes a resource allocation method that is primarily based on assigning almost an equal bandwidth to all users. System capacity maximization is achieved by selecting the subcarriers with the best SNR values. This algorithm was developed for orthogonal frequency division multiple access (OFDMA) wireless systems. Resource allocation is done at the subcarrier level according to the weight factor that had been calculated for each user. Frequency hopping was used to increase frequency diversity and to make the system more robust to disturbance. Frequency hopping pattern is determined dynamically on the basis of SNR value of each subcarrier.The results of the proposed algorithm are compared with the water filling (WF) and proportional fairness (PF) methods. The influence of various data traffic classes on system throughput and resource allocation is also described.

Fair Optimization of Video Streaming Quality of Experience in LTE Networks Using Distributed Antenna Systems and Radio Resource Management

Network quality of experience (QoE) metrics are proposed in order to capture the overall performance of radio resource management (RRM) algorithms in terms of video quality perceived by the end users. Metrics corresponding to average, geometric mean, and minimum QoE in the network are measured when Max C/I, proportional fair, and Max-Min RRM algorithms are implemented in the network. The objective is to ensure a fair QoE for all users in the network. In our study, we investigate both the uplink (UL) and downlink (DL) directions, and we consider the use of distributed antenna systems (DASs) to enhance the performance. The performance of the various RRM methods in terms of the proposed network QoE metrics is studied in scenarios with and without DAS deployments. Results show that a combination of DAS and fair RRM algorithms can lead to significant and fair QoE enhancements for all the users in the network.

Global proportional fairness scheduling algorithm based on spectrum aggregation in cognitive radio

In a cognitive radio system, it is still a problem that resource scheduling among secondary users (SUs) is distributed unfairly when spectrum aggregation technology is involved to support high-speed data transmission. A global proportional fair scheduling algorithm is proposed based on spectrum aggregation to solve the problem. This paper focuses on the relation between the fairness for SUs and spectrum aggregation. Throughput fairness can be guaranteed as much as possible after considering two parameters, the span of spectrum aggregation and the remaining data queue length of SUs. Simulation results show that the proposed scheduling algorithm takes advantage of fairness and the delay of system service as compared with the other two scheduling algorithms, max C/I and partial proportional fairness. Meanwhile, it is shown that the proposed scheduling algorithm has lower throughput shake to make sure of fairness among SUs and high efficiency of system.

A Fairness Relation Based on the Asymmetric Choquet Integral and Its Application in Network Resource Allocation Problems

The recent problem of network resource allocation is studied where pairs of users could be in a favourable situation, given that the allocation scheme is refined by some add-on technology. The general question here is whether the additional effort can be effective with regard to the user’s experience of fairness. The computational approach proposed in this paper to handle this question is based on the framework of relational optimization. For representing different weightings for different pairs of users, the use of a fuzzy measure appears to be reasonable. The generalized Choquet integrals are discussed from the viewpoint of representing fairness and it is concluded that the asymmetric Choquet integral is the most suitable approach. A binary relation using the asymmetric Choquet integral is proposed. In case of a supermodular fuzzy measure, this is a transitive and cycle-free relation. The price of fairness with regard to a wireless channel allocation problem taking channel interference into account is experimentally studied and it can be seen that the asymmetric on relation actually selects allocations that perform on average between maxmin fairness and proportional fairness, and being more close to maxmin fairness as long as channel interference is not high.