# A Gain-Computation Enhancements Resource Allocation for Heterogeneous Service Flows in IEEE 802.16 m Mobile Networks

Authors: Wafa Ben Hassen; Meriem Afif
Journal: International Journal of Digital Multimedia Broadcasting
 (2012)

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## Abstract

This paper deals with radio resource allocation in fourth generation (4G) wireless mobile networks based on Orthogonal Frequency Division Multiple Access (OFDMA) as an access method. In IEEE 802.16 m standard, a contiguous method for subchannel construction is adopted in order to reduce OFDMA system complexity. In this context, we propose a new subchannel gain computation method depending on frequency responses dispersion. This method has a crucial role in the resource management and optimization. In a single service access, we propose a dynamic resource allocation algorithm at the physical layer aiming to maximize the cell data rate while ensuring fairness among users. In heterogeneous data traffics, we study scheduling in order to provide delay guaranties to real-time
services, maximize throughput of non-real-time services while ensuring fairness to users. We compare performances to recent existing algorithms in OFDMA systems showing that proposed schemes provide lower complexity, higher total system capacity, and fairness among users.


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## Body

## 1. Introduction

In fourth Generation (4G) wireless cellular networks, increasing demands for higher speed data rates transmission, mobility, and multiservice access, have imposed staggering challenges. Therefore, IEEE 802.16 standards propose the use of Orthogonal Frequency Division Multiple Access (OFDMA) among multiple alternatives. OFDMA has become one of the most interesting developments in the area of new broadband wireless networks due to its powerful capability to mitigate Inter-Symbol Interference (ISI), provide high spectral efficiency and immunity of multipath fading.Looking at wireless networks literature, several researches focus on adaptive resource allocation algorithms for single service required by users, in order to achieve some objectives aimed either to minimize total power under data rate constraint, called Margin Adaptive (MA) problem [1–3], or to maximize the total system throughput under power constraints referred as Rate Adaptive (RA) problem [4–6]. However, in practice how to efficiently allocate resources in multiservice wireless networks is not well-explored, nowadays. To resolve this challenge, recent multiservice transmission researches in wireless networks are paid more attention [7–9]. To handle a multiservice access network of heterogeneous traffic, the resource management scheme that can efficiently allocate subchannels to different users and services is essential.The major characteristics of resource allocation algorithms consist of their running time, computational complexity, and efficiency. Generally, optimal resource allocation algorithms are classified as Nondeterministic Polynomial-time Hard (NP-Hard) problems, making them unsuitable for real-time applications such as video call. Therefore, literature tackles such problems by proposing suboptimal algorithms and heuristic methods in order to close optimal solution with low complexity and face real-time and channel variations constraints.In this work, we propose two complementary methods in order to guarantee an efficient resource allocation policy. The first method gives new approach, in context of contiguous subchannel method, for subchannel gain computation using frequency responses dispersion. Our goal in this study is to increase the number of bit per symbol subject to maintain lower BLoc Error Rate (BLER) in mobility and high-mobility context. The main objective in this second contribution is to resolve resource assignment to mobile users' problem, in order to take into account the trade-off between maximizing resources' use and fairness. In this context, a new dynamic heuristic algorithm is proposed. After that, we bring out multiservice feature of fourth generation wireless networks by proposing an adaptive resource allocation algorithm in OFDMA systems to support a variety of Quality-of-Service-(QoS-) sensitive applications such as streaming multimedia.The remainder of this paper is organized as follows, In Section2, system model is introduced and problem for resource allocation is formulated. In Section 3, a new method for subchannel gain is presented. Then, an adaptive subchannel allocation scheme is proposed. After that, a multi-QoS-based adaptive resource allocation algorithm is introduced in Section 5. Finally, numerical results are provided in Section 6.


## 2.  System Model and Problem Formulation

In this work, we consider an OFDMA system for mobile wireless networks, based on IEEE 802.16 m standard. The system consists of a single Base Station (BS) that serversK users and N represents the number of subchannels composed by a group of M adjacent subcarriers in a single subchannel with N=L/M and L is the total number of adjacent subcarriers. Considering hk,n as the channel gain of the kth user on nth subchannel, it following the complex Gaussian distribution and its magnitude, called fading factor, following Rayleigh distribution [10]. In fact, intercell interference occurs at a Mobile Station (MS), when the BSs of neighbouring cells transmit data over a subchannel used by its serving cell. The intercell interference phenomenon depends on user locations and mobilities, frequency reuse factor interfering cells as it is expressed by (2). We should notice that our considered cell in this work is not isolated. The downlink quality can be measured by the Signal-to-Interference plus Noise Ratio (SINR) and expressed as(1)SINRe,k=Pe(Ie,k+ΔfN0)|hk,n|2,
where Pe and Δf are, respectively, the total transmit power and subchannel spacing. N0 presents the Additive White Gaussian Noise (AWGN) variance. The average downlink interference per subchannel Ie,k for the MS k served by BS e [11] is expressed as follows:(2)Ie,k=∑s≠eΛ(e,s)χs(PsGs,kLs,k),
where  (i)
Ps is the transmit power per subchannel of BS s;(ii)
Gs,k is the antenna gain;(iii)
Ls,k is the path-loss between BS s and MS k;(iv)
χs is the probability that the same subchannel used by the mobile k is used in the same time by another MS served by the BS s;(v)
Λ(e,k) denotes the interference matrix, where the coefficient Λ(e,k) equals 1 if cells e and s use the same band and zero otherwise.The system capacity,Csyst, is given by the following equation:(3)Csyst=∑t=1T∑k=1K∑n=1Nαk,nCSCt,k,n.
If the subchannel n is allocated to user k at the subframe t,αk,n is equal to 1 and zero otherwise. The Parameter CSCt,k,n is the capacity of subchannel n allocated to user k at the subframe t and is presented by(4)CSCt,k,n=∑m=1MCsbcrm,
where Csbcrm is the transmitted information quantity of sub-carrier in a subframe time. Assuming that all sub-carriers in each subchannel use the same AMC, (4) becomes(5)CSCt,k,n=M⋅Csbcrm,Csbcrm=NAMCk,n⋅Nsym/SF,
where NAMCk,n and Nsym/SF represent, respectively, the number of bits per symbol and the number of symbols per subframe. They depend on the modulation choice type.Thus, the total system capacity is obtained as follows:(6)Csyst=∑t=1T∑k=1K∑n=1Nαk,n⋅M⋅NAMCk,n⋅Nsym/SF.
The Bit Error Rate (BER) for QPSK and M-QAM modulations are determined by formulas approximations presented in Table 1. In order to measure efficiency of the proposed method, we have introduced the Jain fairness index [13], given as(7)JFairIndex=(∑k=1KRk,mean)2K⋅∑k=1K(Rk,mean)2,
where Rk,mean is the mean data rate of user k in a simulation time. This indicator is given by the following formula: (8)Rk,mean=1b∑i=1b=T/TSFRk,i,
where Rk,i is the data rate of MS k in subframe i.Table 1
Approximate BER for coherent modulations [12].
ModulationFormulaQPSKPb≈Q(2γb)M-QAMPb≈4(M-1)Mlog2MQ(3γ̅blog2M(M-1))In this work, equal power is allocated to subchannels in downlink sense in order to reduce computational complexity. Having the target to maximize the system capacity, the objective function is formulated as follows:(9)MaximizeCsyst=∑t=1T∑k=1K∑n=1Nαk,n⋅M⋅NAMCk,n⋅Nsym/SFJFairIndex=(∑k=1KRk,mean)2K⋅∑k=1K(Rk,mean)2SubjecttoC1:αk,n∈{0,1},∀k∈Ψ,n∈ΓC2:∑k=1Kαk,n=1,∀n∈ΓC3:∑n=1Nαk,n≤1,∀k∈Ψ.The two constraints C1 and C2 are on subchannel allocation to ensure that each subchannel is assigned to only one user whereΨ and Γ denote, respectively, the set of active users and subchannels in the cell. The constraint C3 denotes that one MS could have only one subchannel at the same time.


## 3. Efficiency of Sliding Window Gain Computation Method

In IEEE 802.16 m systems, the total sub-carriers of one bandwidth are grouped into subchannels in order to reduce the computational complexity and the signalling overhead [14–16]. Each subchannel is presented by a global channel gain that has a crucial role in the subchannels allocation policy in the case of multiuser wireless OFDMA systems.In order to compute the global subchannel gain, different methods are described in [17–19]. In [18], a conservative estimation at the channel quality is made by choosing the most unfavorable channel of each group to represent that group's channel quality. Similarly, in [20, 21], the minimum channel gain approach is selected and considered as intuitive from an information-theoretic framework to ensure error-free transmission on all sub-carriers contained in the subchannel. However, if there are several sub-carriers with high channel gain, then the minimum sub-carriers gain method degrades the total system capacity and the maximum subchannel capacity is not being reached. In other works, the subchannel is denoted by an average channel gain for the corresponding set of sub-carriers. In [17], the channel magnitude response for each user is divided into a number of partitions where each partition is represented by the average channel gain. The same approach is adopted in [22] that allocates a subset of blocks with highest average channel gains to the corresponding user. In this case, sub-carriers with high channel gain are penalized by those with bad channel gain even though these sub-carriers represent a minority compared to those with high channel gain. Then, existing methods degrade the total system capacity.In this section, we propose a new method to compute the subchannel's gain depending on frequency responses. The idea here is to close the channel quality based on dispersion probability and average channel gain. We can define the sub-carrier gain array as(10)H=(h1,1h1,2⋯h1,Lh2,1h2,2⋯h2,L............hK,1hK,2⋯hK,L),
where K and L represent, respectively, the number of users and the number of available sub-carriers in the system. hk,l is the channel gain of the lth sub-carrier for the kth user. We assume that a subchannel is composed by M adjacent sub-carriers where N=L/M. When sub-carriers are grouped into subchannels, the subchannel gain array is obtained as(11)H′=(h1,1′h1,2′⋯h1,N′h2,1′h2,2′⋯h2,N′..⋅...⋅...⋅.hK,1′hK,2′⋯hK,N′).
Our proposed “Sliding Window” method is a recursive scheme that depends on the average of sub-carriers gain and the dispersion probability. It gathers sub-carriers into three groups presented by a quality coefficient Q that may vary from a type of service to another with 0.5≤Q≤1. (i)
The number of sub-carriers with high channel gain is greater than that with bad channel gain:P>Q.(ii)
The number of sub-carriers with bad channel gain is greater than that with high channel gain:P<(1-Q).(iii)
The number of sub-carriers with bad and high gain is almost the same:P∈[1-Q,Q].Our proposed method is described as in Algorithm1.Algorithm 1:Our sliding window scheme.
BEGINfork=1 to Kdoforn=1 to Ndo(i)Initializationvect←{hk,1,hk,2,…,hk,M};∀l∈{1,2,…,L};∀m∈{1,2,…,M}; vectmax←ϕ; vectmin←ϕ.(ii)Subchannel Gain ComputationStep  (1):Calculate the average channel gainavg based onthe sub-carriers frequency responses whereavg←average(vect).Step (2):Calculate the probabilityp where p←∑m=1Mxm/M, with∑m=1Mxm≤M andxm={1ifhk,m>avg,0ifnot.ifp>Qthenform=1 to Mdoifhk,m>avgthenvectmax=vectmax+{hk,m}.end  ifend foriflength(vectmax)=1thenreturngain←vectmax(1).elsevect←vectmax; Jump to Step (1).end ifend ififp<(1-Q)thenform=1 to Mdoifhk,m<avgthenvectmin=vectmin+{hk,m}.end  ifend foriflength(vectmin)=1thenreturngain←vectmin(1).elsevect←vectmin; Jump to Step (1)end  ifend  ififp∈[1-Q,Q]thenform=1 to Mdoifhk,m<avgthenvectmin=vectmin+{hk,m}.end   ifend  foriflength(vectmin)=1thenreturngainmin←vectmin(1).elsevect←vectmin; Jump to Step (1)end  ifform=1 to Mdoifhk,m>avgthenvectmax=vectmax+{hk,m}.end  ifend  foriflength(vectmax)=1thenreturngainmax←vectmax(1).elsevect←vectmax; Jump to Step (1).end  ifreturngain←average(gainmax,gainmin).endifh′k,n←gain.end forend forENDAfter computing the available subchannels gain, let us move to the subchannel allocation scheme in a single-service context.


## 4. A New Heuristic Method for Subchannel Allocation in Loaded System

In a loaded system, the number of usersK is greater than the number of available subchannels N. Here, the BS may assign to each user only one subchannel and a subchannel is allocated to only one user during a subframe. Our proposed resource allocation scheme consists of 3 steps: (1)Initialization step. Vectors and matrices that will be used later in the algorithm are initialised. (2)Users ordering step. Users are sorted in decreasing order depending on their best subchannel gain given by Algorithm 1. (3)Subchannels allocation step. Here, two cases are defined as it is depicted in Algorithm 2. Firstly, if only the selected user has this order, then we verify if its best subchannel is free. If yes, we allocate it and update the rate. If not, we search for the next free and best subchannel. Secondly, if two users or more have the same order, we verify if they require the same subchannel. If yes, we choose the user with the minimum second subchannel gain because it has a low chance to get a good subchannel (Algorithm 2).Algorithm 2:An adaptive resource allocation scheme.
BEGIN(i)InitializationEqual power is allocated to groupsΓ={1,2,…,N}; Ψ={1,2,…,K}; hk,n,∀k∈Ψ,∀n∈Γ; αk,n=0,∀k∈Ψ,∀n∈Γ; Rk=0,∀k∈Ψ.(ii)Users Orderingfork=1 to KdoSorthk,n in decreasing order.Order userk according to its best channel gain  hk,1.end for(iii)Subchannels Allocationfork=1 to K  where order(k)≤order(k+1)don← find the subchannel n where the user k has its bestchannel  gain.Step (1):if(uniqueorder=1)then{%onlyuserkhasthisorder}.Sub-step(1.a):ifα1→K,n=0then{% the subchanneln is not allocated}αk,n←1{%  allocate the subchannel n}Γ←Γ-{n}; Updated data rate Rkend  ifSub-step(1.b):ifα1→K,n=1then{ % the subchannel n is allocated}repeatj=j+1{% search the next free subchannel}untilα1→K,j=0orhk,j<hk*,j{k*  is the userless priority than the actual one andk*∈[k+1,K].}Jump to Sub-step (1.a)end  ifend  ifStep (2):if(uniqueorder=0)then{% two or more users have the same order}.Sub-step (2.a):if(uniquesubchannel=0)then{% users with the same order do not require thesame subchannel}jump to Sub-step (1.a) or Sub-step (1.b)end ifSub-step(2.b):if(uniquesubchannel=1)then{% these users require the same subchannel}ifα1→K,n=0thenk̂← determine the user that has the minimumsecond best sub-channe{ % this user has a lowchance to get a good subchannel}.Jump to Sub-step(1.a)end ififα1→K,n=1thenk̂← determine the user that has the minimumsecond best subchannel; Jump to Sub-step (1.b)end ifend ifend ifend forENDComputational Complexity
Let us recall thatK refers to the users number and N is the subchannels number. The users ordering step (2) sorts subchannels in descending order for each user. The sorting process requires (Nlog2(N)) operations for each user. Sorting subchannels in decreasing order for K users requires then KNlog2(N). Thus, the asymptotic complexity is O(KNlog2(N)). As proportional fairness method [23] includes a remaining subchannels allocation phase to ensure fairness criterion, computational complexity is equal to O(KNlog2(N)+K(N-K)log2(N-K)). Alternative factor method [24] includes two steps: (1) Subchannels ordering step requires KNlog2(N) operations. (2) Users ordering step requires Klog2(K) operations. Alternative factor computation requires (KN) operations. These steps pertain to subchannel allocation and the asymptotic complexity is equal to O(KNlog2(N)+Klog2(K)+(KN)). Then, we conclude that our suboptimal resource allocation scheme provides lower complexity than other existing methods and may be adopted for real-time applications. However, the key feature of 4G mobile network is its capability to support multiservice access when a user requires different service types, as it is well underlined in the next section.


## 5. Multi-QoS-Based Adaptive Resource Allocation Algorithm

We consider three Classes of Service (CoS) which are real-time Polling Service (rtPS), non-real-time Polling Service (nrtPS), and Best Effort (BE). For each CoS, the QoS satisfaction has a distinct definition [7]. The proposed algorithm consists of three steps: resource distribution step, calculation of each user's priority step, and resource allocation step.


### 5.1. Resource Distribution

We assume thatNrtPs,NnrtPs, and NBE represent, respectively, the number of subchannels reserved to rtPS, nrtPS, and BE classes and are determined by the following equations: NrtPs=αN,  NnrtPs=βN, and NBE=γN, where α,β and γ∈[0,1] and α+β+γ=1. Let NCrtPS,NCnrtPS,NCBE represent and, respectively, rtPS connections number, nrtPS connections number and BE connections number, and NC denotes the total connections number. Proportional parameters are initially determined by α=(NCrtPS/NC), β=(NCnrtPS/NC), and γ=(NCBE/NC). They are dynamically updated depending on the system availability. If necessary, a class, as rtPS-class, may reserve free subchannels from lower prior classes as nrtPS and BE classes and the opposite case is not allowed.


### 5.2. Calculation of User's Priority

For each user, a queue is used for buffering arrival packets in the proposed BS scheduler. We design the scheduling priority of each connection based on its channel quality, QoS satisfaction and service type priority.


#### 5.2.1. Real-Time Traffic

For rtPS traffic of userk on subchannel n, the scheduling priority Pk,n is defined as [25](12)Pk,n={βrtPS(Rk,nRmax⁡)(1Fk)ifFk>1,Rk,n≠0,βrtPS(Rk,nRmax⁡)ifFk≤1,Rk,n≠0,0ifRk,n=0,
where βrtPS∈[0,1] is the rtPS class coefficient as defined in [25] and Fk is the delay satisfaction indicator and is defined as(13)Fk=Tk-2TFWk,
where  (i)
Rk,n is the information bits that can be carried by user k on the subchannel n in one OFDM symbol,(ii)
Rmax is the most bits per symbol that can be allocated when the most efficient AMC mode is selected,(iii)
Wk is the longest packet waiting time of user k,(iv)
Tk is the maximum packet latency of user k,(v)
TF is the frame duration.We should notice that in this rtPS-class, the packet should be immediately sent if its deadline expires before the next frame is totally served. The ratio(Rk,n/Rmax) denotes the normalized channel quality. If Wk≥Tk-2TF we set the highest priority to the corresponding packet. When Rk,n=0, the channel is in deep fade and this connection should not be served.


#### 5.2.2.  Non-Real-Time Traffic

For the nrtPS connection of userk on subchannel n, the scheduling priority is defined as [25](14)Pk,n={βnrtPS(Rk,nRmax⁡)(1Fk)ifFk≥1,Rk,n≠0,βnrtPS(Rk,nRmax⁡)ifFk<1,Rk,n≠0,0ifRk,n=0,
where βnrtPs∈[0,1] is the nrtPS class coefficient as defined in [25] and Fk is the ratio of the average transmission rater̅k over minimum reserved rate rk, representing the rate satisfaction indicator. If Fk≥1 the rate requirement is satisfied. If not, representing the case within the queue will be full, packets of user k should be then sent as soon as possible.


#### 5.2.3. Best Effort Traffic

For the BE service of userk on subchannel n, the scheduling priority is defined as [26](15)Pk,n=βBE(Rk,nRmax⁡),
where βBE∈[0,1] is the BE-class coefficient as defined in [25]. In fact for the BE service, the scheduling priority depends only on the channel quality.We should notice that the role ofβrtPS,βnrtPS, and βBE, is to provide different priorities for different QoS classes, then βrtPS>βnrtPS>βBE [25]. The purpose behind this idea is that the QoS of connections in a high-priority QoS class can be satisfied prior to those of low-priority QoS class.After calculating the priority of each userk on each subchannel n, we define a Priority Function that represents the user's priority and is described as(16)Pk=max⁡Pk,n,∀n∈{1,…,N}.


### 5.3. Resource Allocation Scheme

We should notice that in this study, each user requires a single service at the same time and packets buffered in the same queue follow a First In First Out (FIFO) scheduler. Letk* denote the selected serving user, where(17)k*=max⁡Pk,∀k∈{1,…,K}.
After that, the user k* picks its best subchannel n* where(18)n*=max⁡(Rk*,nRmax⁡),∀n∈{1,…,N}.
The number of OFDMA symbols allocated for each user is calculated under the assumption that the minimum reserved rate rk and maximum latency Tk should be satisfied for rtPS-class and only the minimum reserved rate rk for nrtPS-class. For each connection, a minimum data rate rk should be guaranteed and expressed by the following inequality:(19)rk≤r̅k(m+1),
where r̅k(m+1) is the average service data rate of user k at frame (m+1). It is estimated over a windows size Tc as [26](20)r̅k(m+1)=r̅k(m)(1-1Tc)+Δk(m+1)/TFTc,
where Δk(m+1) is the number of information bits that should be sent during the frame (m+1) of user k, where [26](21)Δk(m+1)={(rk-r̅k(m))Tc+r̅k(m)TFifr̅k(m)<rk.0ifr̅k(m)≥rk.The number of slots required to carryΔk(m+1) information bits on subchannel n equals (22)Nsub,k(m+1)=⌈Δk(m+1)M⋅Rk,n⌉.
For rtPS connection, there is one more step to calculate the number of information bit to be sent. We examine the waiting time of packets in the queue of connection from the head of line until the first packet whose waiting time is longer than (Tk-2TF) is encountered. We denote Δk′(m+1) the sum of bits of packets from the head of line to the finding packet. The number of information bits allocated to rtPS connection of user k is given by [26](23)Δ̂k(m+1)=max⁡{Δk(m+1),Δk′(m+1)}.
The number of slots required to carry Δ̂k(m+1) information bits on subchannel n equals (24)Nsub,k(m+1)=⌈Δ̂k(m+1)M⋅Rk,n⌉.
If the available slot on subchannel n is less than Nsub,k, the second best subchannel for that user is selected and the remaining bits are allocated.


## 5.1. Resource Distribution

We assume thatNrtPs,NnrtPs, and NBE represent, respectively, the number of subchannels reserved to rtPS, nrtPS, and BE classes and are determined by the following equations: NrtPs=αN,  NnrtPs=βN, and NBE=γN, where α,β and γ∈[0,1] and α+β+γ=1. Let NCrtPS,NCnrtPS,NCBE represent and, respectively, rtPS connections number, nrtPS connections number and BE connections number, and NC denotes the total connections number. Proportional parameters are initially determined by α=(NCrtPS/NC), β=(NCnrtPS/NC), and γ=(NCBE/NC). They are dynamically updated depending on the system availability. If necessary, a class, as rtPS-class, may reserve free subchannels from lower prior classes as nrtPS and BE classes and the opposite case is not allowed.


## 5.2. Calculation of User's Priority

For each user, a queue is used for buffering arrival packets in the proposed BS scheduler. We design the scheduling priority of each connection based on its channel quality, QoS satisfaction and service type priority.


### 5.2.1. Real-Time Traffic

For rtPS traffic of userk on subchannel n, the scheduling priority Pk,n is defined as [25](12)Pk,n={βrtPS(Rk,nRmax⁡)(1Fk)ifFk>1,Rk,n≠0,βrtPS(Rk,nRmax⁡)ifFk≤1,Rk,n≠0,0ifRk,n=0,
where βrtPS∈[0,1] is the rtPS class coefficient as defined in [25] and Fk is the delay satisfaction indicator and is defined as(13)Fk=Tk-2TFWk,
where  (i)
Rk,n is the information bits that can be carried by user k on the subchannel n in one OFDM symbol,(ii)
Rmax is the most bits per symbol that can be allocated when the most efficient AMC mode is selected,(iii)
Wk is the longest packet waiting time of user k,(iv)
Tk is the maximum packet latency of user k,(v)
TF is the frame duration.We should notice that in this rtPS-class, the packet should be immediately sent if its deadline expires before the next frame is totally served. The ratio(Rk,n/Rmax) denotes the normalized channel quality. If Wk≥Tk-2TF we set the highest priority to the corresponding packet. When Rk,n=0, the channel is in deep fade and this connection should not be served.


### 5.2.2.  Non-Real-Time Traffic

For the nrtPS connection of userk on subchannel n, the scheduling priority is defined as [25](14)Pk,n={βnrtPS(Rk,nRmax⁡)(1Fk)ifFk≥1,Rk,n≠0,βnrtPS(Rk,nRmax⁡)ifFk<1,Rk,n≠0,0ifRk,n=0,
where βnrtPs∈[0,1] is the nrtPS class coefficient as defined in [25] and Fk is the ratio of the average transmission rater̅k over minimum reserved rate rk, representing the rate satisfaction indicator. If Fk≥1 the rate requirement is satisfied. If not, representing the case within the queue will be full, packets of user k should be then sent as soon as possible.


### 5.2.3. Best Effort Traffic

For the BE service of userk on subchannel n, the scheduling priority is defined as [26](15)Pk,n=βBE(Rk,nRmax⁡),
where βBE∈[0,1] is the BE-class coefficient as defined in [25]. In fact for the BE service, the scheduling priority depends only on the channel quality.We should notice that the role ofβrtPS,βnrtPS, and βBE, is to provide different priorities for different QoS classes, then βrtPS>βnrtPS>βBE [25]. The purpose behind this idea is that the QoS of connections in a high-priority QoS class can be satisfied prior to those of low-priority QoS class.After calculating the priority of each userk on each subchannel n, we define a Priority Function that represents the user's priority and is described as(16)Pk=max⁡Pk,n,∀n∈{1,…,N}.


## 5.2.1. Real-Time Traffic

For rtPS traffic of userk on subchannel n, the scheduling priority Pk,n is defined as [25](12)Pk,n={βrtPS(Rk,nRmax⁡)(1Fk)ifFk>1,Rk,n≠0,βrtPS(Rk,nRmax⁡)ifFk≤1,Rk,n≠0,0ifRk,n=0,
where βrtPS∈[0,1] is the rtPS class coefficient as defined in [25] and Fk is the delay satisfaction indicator and is defined as(13)Fk=Tk-2TFWk,
where  (i)
Rk,n is the information bits that can be carried by user k on the subchannel n in one OFDM symbol,(ii)
Rmax is the most bits per symbol that can be allocated when the most efficient AMC mode is selected,(iii)
Wk is the longest packet waiting time of user k,(iv)
Tk is the maximum packet latency of user k,(v)
TF is the frame duration.We should notice that in this rtPS-class, the packet should be immediately sent if its deadline expires before the next frame is totally served. The ratio(Rk,n/Rmax) denotes the normalized channel quality. If Wk≥Tk-2TF we set the highest priority to the corresponding packet. When Rk,n=0, the channel is in deep fade and this connection should not be served.


## 5.2.2.  Non-Real-Time Traffic

For the nrtPS connection of userk on subchannel n, the scheduling priority is defined as [25](14)Pk,n={βnrtPS(Rk,nRmax⁡)(1Fk)ifFk≥1,Rk,n≠0,βnrtPS(Rk,nRmax⁡)ifFk<1,Rk,n≠0,0ifRk,n=0,
where βnrtPs∈[0,1] is the nrtPS class coefficient as defined in [25] and Fk is the ratio of the average transmission rater̅k over minimum reserved rate rk, representing the rate satisfaction indicator. If Fk≥1 the rate requirement is satisfied. If not, representing the case within the queue will be full, packets of user k should be then sent as soon as possible.


## 5.2.3. Best Effort Traffic

For the BE service of userk on subchannel n, the scheduling priority is defined as [26](15)Pk,n=βBE(Rk,nRmax⁡),
where βBE∈[0,1] is the BE-class coefficient as defined in [25]. In fact for the BE service, the scheduling priority depends only on the channel quality.We should notice that the role ofβrtPS,βnrtPS, and βBE, is to provide different priorities for different QoS classes, then βrtPS>βnrtPS>βBE [25]. The purpose behind this idea is that the QoS of connections in a high-priority QoS class can be satisfied prior to those of low-priority QoS class.After calculating the priority of each userk on each subchannel n, we define a Priority Function that represents the user's priority and is described as(16)Pk=max⁡Pk,n,∀n∈{1,…,N}.


## 5.3. Resource Allocation Scheme

We should notice that in this study, each user requires a single service at the same time and packets buffered in the same queue follow a First In First Out (FIFO) scheduler. Letk* denote the selected serving user, where(17)k*=max⁡Pk,∀k∈{1,…,K}.
After that, the user k* picks its best subchannel n* where(18)n*=max⁡(Rk*,nRmax⁡),∀n∈{1,…,N}.
The number of OFDMA symbols allocated for each user is calculated under the assumption that the minimum reserved rate rk and maximum latency Tk should be satisfied for rtPS-class and only the minimum reserved rate rk for nrtPS-class. For each connection, a minimum data rate rk should be guaranteed and expressed by the following inequality:(19)rk≤r̅k(m+1),
where r̅k(m+1) is the average service data rate of user k at frame (m+1). It is estimated over a windows size Tc as [26](20)r̅k(m+1)=r̅k(m)(1-1Tc)+Δk(m+1)/TFTc,
where Δk(m+1) is the number of information bits that should be sent during the frame (m+1) of user k, where [26](21)Δk(m+1)={(rk-r̅k(m))Tc+r̅k(m)TFifr̅k(m)<rk.0ifr̅k(m)≥rk.The number of slots required to carryΔk(m+1) information bits on subchannel n equals (22)Nsub,k(m+1)=⌈Δk(m+1)M⋅Rk,n⌉.
For rtPS connection, there is one more step to calculate the number of information bit to be sent. We examine the waiting time of packets in the queue of connection from the head of line until the first packet whose waiting time is longer than (Tk-2TF) is encountered. We denote Δk′(m+1) the sum of bits of packets from the head of line to the finding packet. The number of information bits allocated to rtPS connection of user k is given by [26](23)Δ̂k(m+1)=max⁡{Δk(m+1),Δk′(m+1)}.
The number of slots required to carry Δ̂k(m+1) information bits on subchannel n equals (24)Nsub,k(m+1)=⌈Δ̂k(m+1)M⋅Rk,n⌉.
If the available slot on subchannel n is less than Nsub,k, the second best subchannel for that user is selected and the remaining bits are allocated.


## 6. Simulation Results

In this work, the channel is modelled as a Rayleigh Channel with four multipaths. The simulated system consists of a single cell that uses 1024 sub-carriers for communications. In order to consider the mobility, the channel state changes every subframe delay and the simulation window is equal to 10000 subframes. Simulation parameters are described in Table2.Table 2
OFDMA parameters for IEEE 802.16 M.
ParameterSymbolValueSubchannels numberN48Subcarriers number per subchannelM18Number of subframes per frame7Sub-carriers spacingΔf7.813 KHzSuper frame delay20 msFrame delayTF5 msSubframe delay714,286μs


### 6.1. Proposed Sliding Window Method Performances

We show the performance of our sliding window method compared to the minimum [18] and average [19] method.Figure1 compares the average spectral efficiency per subcarrier versus the number of users. The total spectral efficiency is determined by (6).Figure 1
Total spectral efficiency versus the number of users in loaded systems.Table3 shows variation intervals in terms of total spectral efficiency. Let TSEVIPag and TSEVIPmi denote the total spectral efficiency for different variation user intervals. These values are computed based on, respectively, the mean difference between sliding window and average channel gain method and the mean difference between sliding window and minimum channel gain method. As TSEVIPag>0   and   TSEVIPmi>0, for all intervals, it is obvious that the proposed method provides greater spectral efficiency, because it computes a subchannel gain that closes the channel quality. Figure 2 illustrate the average Bloc Error Rate (BLER) versus the number of users.Table 3
Variation intervals in terms of total spectral efficiency.
[48,75[[75,100[[100,125[[125,150]TSEVIPag(bit/sym)0.1970.1930.2500.246TSEVIPmi(bit/sym)1.8231.8831.8991.923Figure 2
BLoc Error Rate (BLER) versus the number of users.Table4 shows variation intervals in terms of BLER. Let BVIPag and BVIPmi denote the average BLER for different variation user intervals. These values are computed based on, respectively, the mean difference between sliding window and average channel gain method and the mean difference between sliding window and minimum channel gain method. As BVIPag<0  and  BVIPmi≤0, for all intervals, our proposed method provides lower BLER than the average gain method and quasisimilar BLER compared to minimum gain method, because our scheme closes the channel quality.Table 4
Variation intervals in terms of BLER.
[48,75[[75,100[[100,125[[125,150]BVIPag10-4(dB)−5.718−5.320−4.724−4.535BVIPmi10-6(dB)−1.371−3.870−2.233−0.977


### 6.2. Proposed Subchannels Allocation Algorithm Performances in a Single Service Context

Our proposed resource allocation algorithm is compared with the suboptimal existing solutions [23, 24]. The reason for this comparison is as follows. Shen et al. [23] formulates the problem of maximizing the total system capacity with proportional rate constraints. It uses the subchannel with high SINR for each user. Hwang et al. [24] proposes a heuristic for channel allocation. In this work, an alternative factor is defined for subchannel allocation. It aims to increase the downlink system capacity while maintaining sufficient fairness.Figure3 compares the average spectral efficiency per sub-carrier versus the number of users.Figure 3
Total spectral efficiency in loaded systems.Table5 shows variation intervals in terms of total spectral efficiency. Let SEVIPAF and SEVIPPF denote the average spectral efficiency in different variation user intervals. These values are computed based on, respectively, the mean difference between proposed scheme and alternative factor method [24] and the mean difference between proposed scheme and proportional fairness method [23]. As SEVIPAF>0 and SEVIPPF>0, when the number of users K∈ ]60,150], our proposed method provides greater spectral efficiency, because it covers the loaded system case when the number of available resources is lower than the number of users requiring access to the cell. However, when K∈[50,60], the proposed scheme provides lower SE than the proportional fairness method as SEVIPPF<0. Hence, the contribution of our proposed scheme performs better when the number of users in the cell is important which is close to the practical case.Table 5
Variation intervals in terms of total spectral efficiency.
[50,60]]60,75[[75,100[[100,125[[125,150]SEVIPAF(bit/s)1.311.381.511.601.70SEVIPFF(bit/s)−0.110.260.721.191.55To better examine the fairness of these algorithms for different number of users, their performance is shown in Figure4. The Jain Fairness Index is expressed by (7). It is obvious that the proposed method provides a fairness index close to 1.Figure 4
Jain Fairness Index versus the number of users in loaded systems.Table6 shows variation intervals in terms of average Jain Fairness Index. Let JFIVIPAF and JFIVIPPF denote the Jain Fairness Index for different variation user intervals. These values are computed based on, respectively, the mean difference between proposed scheme and alternative factor method described in [24] and the mean difference between proposed scheme and proportional fairness method proposed in [23]. As JFIVIPAF>0 and JFIVIPPF>0, for all intervals, it is obvious that the proposed method provides more fairness among active users than the alternative factor and proportional fairness method as each user may reserve only a single subchannel at any given time as it is expressed by constraint C3 in our optimisation problem formulation.Table 6
Variation intervals in terms of Jain Fairness Index.
[50,75[[75,100[[100,125[[125,150]JFIVIPAF0.1830.4200.5490.639JFIVIPPF0.0570.1030.1280.145Figure5 shows the outage probability versus the number of users where the outage probability represents the rejected users percentage. When a user does not get its required subchannel, the number of rejected users increases by one. Then, the outage probability is the ratio of the number of rejected users and the total number of active users in a loaded system.Figure 5
Outage probability versus the number of users in loaded systems.Table7 shows variation intervals in terms of outage probability. Let OPVIPAF and OPVIPPF denote the Outage probability for different users variation intervals. These values are computed based on, respectively, the average of difference between proposed scheme and alternative factor method described in [24] and the average of difference between proposed scheme and proportional fairness method proposed in [23]. As OPVIPAF<0 and OPVIPPF<0, for all intervals, it is obvious that the proposed scheme provides lower outage probability than other methods. We should notice that in this case, as it is shown by Table 7, the difference between the proposed heuristic and existing methods [23, 24] increases when the number of users rises, meaning that the proposed scheme satisfies a greater number of users than other existing methods [23, 24] in a loaded system case, because it covers the inefficiency resource case by allocating to each user its second best and free subchannel.Table 7
Variation intervals in terms of outage probability.
[50,75[[75,100[[100,125[[125,150]OPVIPAF(%)−0.943−2.156−2.809−3.247OPVIPPF(%)−3.772−8.626−11.236−12.991For unloaded system case, the performance of our proposed algorithm is compared with the algorithms proposed in [23, 27]. The reason for this comparison is as follows. Authors in [23] aim to maximize the total system capacity while maintaining proportional fairness among active users. The principle of this suboptimal subchannel algorithm is to use the subchannels with high SINR for each user. For remaining subchannels, the user with the lowest proportional capacity has the option to pick which subchannel to use in order to achieve proportional fairness. Resource allocation algorithm proposed in [27] aims to assign to each user a subchannel in which the user has the best channel conditions. For the remaining subchannels, the user with the lowest amount of capacity is selected and its best subchannel is allocated to him in order to reach a sufficient fairness among users.Figure6 compares the average spectral efficiency per sub-carrier versus the number of users.Figure 6
Total spectral efficiency versus the number of users in unloaded systems.Table8 shows variation intervals in terms of total spectral efficiency for proposed. Let USEVIPMM and USEVIPPF denote the average total spectral efficiency for different users variation intervals in unloaded systems. These values are computed based on, respectively, the mean difference between proposed scheme and max-min method described in [27] and the mean difference between proposed scheme and proportional fairness method proposed in [23]. As USEVIPMM>0 and USEVIPPF>0, when K∈ ]12,30], it is obvious that the proposed method provides greater spectral efficiency than the max-min and proportional fairness method. We should notice that in this case, as it is shown by Table 8, the difference between the proposed method and existing methods [23, 27] increases when the number of users rises. Then, the proposed method operates well the multiusers diversity. However, when K≤12, the existing method in [23, 27] provides better performance in terms of total spectral efficiency as USEVIPMM<0 and USEVIPPF<0 when K∈[10,12], because they introduce a remaining subchannel allocation phase. So, one user may have more than one subchannel as it is described above. Hence, the contribution of our proposed scheme performs better when the number of users in the cell is important which is generally close to the practical case when good subchannels are not yet available.Table 8
Variation intervals in terms of total spectral efficiency in unloaded systems.
[10,12]]12,15[[15,20[[20,25[[25,30]USEVIPMM(bit/s)−0.2310.2370.6871.1231.458USEVIPPF(bit/s)−0.0870.2650.7091.1321.466


### 6.3. Proposed Subchannels Allocation Scheme Performances in a Heterogeneous Traffics System

The performance of the Multi-QoS-based adaptive resource allocation proposed algorithm is compared to two existing algorithms that are proposed in [28, 29] in terms of rtPS average Packet Loss Rate (PLR)and nrtPS Packet Satisfaction Ratio (PSR). On one hand, Maximum-Carrier-to-Interference and Noise Ratio (MAX-CINR) scheme [28] allocates resources to the user with the maximum receiver CINR and then only the users' link qualities are concerned and the QoS requirements are totally ignored. On the other hand, Modified Proportional Fair (MPF) scheduling algorithm proposed in [29] is taken into account with QoS guaranteed to users in the system. In order to evaluate the performance of various QoS services, we use the Near Real Time Video (NRTV) traffic model for rtPS service, FTP model for nrtPS service [30]. Here we heuristically define length of rtPS packets 1024 bits, nrtPS 2048 bits, and BE 4096 bits and we set the QoS class coefficients as βrtPS= 1.0, βnrtPS= 0.8 and βBE= 0.6. Moreover, we assume that packet arrival process is Poisson distributed, each connection with its own average arrival rate. We suppose that there are 150 users in the system where each one requires a single service at the same time. For rtPS connection, the minimum reserved rate and maximum latency of each connection are set to 500kbps and 20ms, respectively. For nrtPS connection, the minimum reserved rate is set as 1 Mbps. For BE connection, the buffer size is 5000 packets with 512 bytes each.Figure7 shows the average Packet Loss Ratio (PLR) of the rtPS connection across different number of users. The average PLR is defined as the ratio of the number of the lost rtPS packets to the total packets' number.Figure 7
Average rtPS packet loss ratio versus the number of users.Table9 shows variation intervals in terms of rtPS Packet Loss Ratio. Let HPLRVIPMCI and HPLRVIPMPF denote the PLR in different variation user intervals in heterogeneous services system. These values are computed based on, respectively, the average of difference between proposed scheme and MAX-CINR method described in [28] and the average of difference between proposed scheme and modified proportional fairness method proposed in [29]. As HPLRVIPMCI<0  and  HPLRVIPMPF<0, for all intervals, it is obvious that the proposed method satisfies more rtPS users than the MAX-CINR and modified proportional fairness method, because our scheduler gives the priority to rtPS-class to ensure an adequate resource allocation.Table 9
Variation intervals in terms of rTPS packet loss ratio.
[50,75[[75,100[[100,125[[125,150]HPLRVIPMCI(%)−20.88−13.78−9.204−8.351HPLRVIPMPF(%)−24.84−16.72−14.21−10.33In Figure8, we investigate the average nrtPS Packet Satisfaction Ratio (PSR) which is defined as the ratio of the number of the connections guaranteeing the minimum reserved rate to the total connections number. Table 10 shows variation intervals in terms of nrtPS Packet Satisfaction Ratio. Let HPSRVIPMCI and HPSRVIPMPF denote the PSR in different variation user intervals in heterogeneous services systems. These values are computed based on, respectively, the mean difference between proposed scheme and MAX-CINR method [28] and the mean difference between proposed scheme and modified proportional fairness method [29]. As HPSRVIPMCI>0 and HPSRVIPMPF>0, for all intervals, it is obvious that the proposed method satisfies more nrtPS users than the MAX-CINR and MPF method, due to our proposed reservation phase that reserves subchannels to rtPS, nrtPS, and BE services according to proportional parameters depending on system resources availability. For other methods, there are no resource reservation phase, which can increase the nrtPS calls rejection.Table 10
Variation intervals in terms of nrTPS packet satisfaction ratio.
[50,75[[75,100[[100,125[[125,150]HPSRVIPMCI(%)9.0785.9945.7403.631HPSRVIPMPF(%)27.2118.3215.5711.32Figure 8
Average nrtPS packet satisfaction ratio versus the number of users.


### 6.4. Concluding Remarks

Simulation results demonstrate that our sliding window method increases the system capacity and decreases the BLER effectively compared the minimum and the average channel gain methods. In loaded systems, simulation results show that the proposed algorithm permits to achieve a better trade-off between fairness and efficiency use of resources compared to other recent methods [23, 24]. Moreover, our proposed resource allocation scheme proves efficient in unloaded system than other existing methods. In addition to this contribution, the new heuristic algorithm present a low complexity and may be adopted for real-time and mobile applications. In a heterogeneous services context, simulation results illustrate that our proposed scheme can simultaneously satisfy the QoS requirements of various classes services: rtPS, nrtPS, and BE.


## 6.1. Proposed Sliding Window Method Performances

We show the performance of our sliding window method compared to the minimum [18] and average [19] method.Figure1 compares the average spectral efficiency per subcarrier versus the number of users. The total spectral efficiency is determined by (6).Figure 1
Total spectral efficiency versus the number of users in loaded systems.Table3 shows variation intervals in terms of total spectral efficiency. Let TSEVIPag and TSEVIPmi denote the total spectral efficiency for different variation user intervals. These values are computed based on, respectively, the mean difference between sliding window and average channel gain method and the mean difference between sliding window and minimum channel gain method. As TSEVIPag>0   and   TSEVIPmi>0, for all intervals, it is obvious that the proposed method provides greater spectral efficiency, because it computes a subchannel gain that closes the channel quality. Figure 2 illustrate the average Bloc Error Rate (BLER) versus the number of users.Table 3
Variation intervals in terms of total spectral efficiency.
[48,75[[75,100[[100,125[[125,150]TSEVIPag(bit/sym)0.1970.1930.2500.246TSEVIPmi(bit/sym)1.8231.8831.8991.923Figure 2
BLoc Error Rate (BLER) versus the number of users.Table4 shows variation intervals in terms of BLER. Let BVIPag and BVIPmi denote the average BLER for different variation user intervals. These values are computed based on, respectively, the mean difference between sliding window and average channel gain method and the mean difference between sliding window and minimum channel gain method. As BVIPag<0  and  BVIPmi≤0, for all intervals, our proposed method provides lower BLER than the average gain method and quasisimilar BLER compared to minimum gain method, because our scheme closes the channel quality.Table 4
Variation intervals in terms of BLER.
[48,75[[75,100[[100,125[[125,150]BVIPag10-4(dB)−5.718−5.320−4.724−4.535BVIPmi10-6(dB)−1.371−3.870−2.233−0.977


## 6.2. Proposed Subchannels Allocation Algorithm Performances in a Single Service Context

Our proposed resource allocation algorithm is compared with the suboptimal existing solutions [23, 24]. The reason for this comparison is as follows. Shen et al. [23] formulates the problem of maximizing the total system capacity with proportional rate constraints. It uses the subchannel with high SINR for each user. Hwang et al. [24] proposes a heuristic for channel allocation. In this work, an alternative factor is defined for subchannel allocation. It aims to increase the downlink system capacity while maintaining sufficient fairness.Figure3 compares the average spectral efficiency per sub-carrier versus the number of users.Figure 3
Total spectral efficiency in loaded systems.Table5 shows variation intervals in terms of total spectral efficiency. Let SEVIPAF and SEVIPPF denote the average spectral efficiency in different variation user intervals. These values are computed based on, respectively, the mean difference between proposed scheme and alternative factor method [24] and the mean difference between proposed scheme and proportional fairness method [23]. As SEVIPAF>0 and SEVIPPF>0, when the number of users K∈ ]60,150], our proposed method provides greater spectral efficiency, because it covers the loaded system case when the number of available resources is lower than the number of users requiring access to the cell. However, when K∈[50,60], the proposed scheme provides lower SE than the proportional fairness method as SEVIPPF<0. Hence, the contribution of our proposed scheme performs better when the number of users in the cell is important which is close to the practical case.Table 5
Variation intervals in terms of total spectral efficiency.
[50,60]]60,75[[75,100[[100,125[[125,150]SEVIPAF(bit/s)1.311.381.511.601.70SEVIPFF(bit/s)−0.110.260.721.191.55To better examine the fairness of these algorithms for different number of users, their performance is shown in Figure4. The Jain Fairness Index is expressed by (7). It is obvious that the proposed method provides a fairness index close to 1.Figure 4
Jain Fairness Index versus the number of users in loaded systems.Table6 shows variation intervals in terms of average Jain Fairness Index. Let JFIVIPAF and JFIVIPPF denote the Jain Fairness Index for different variation user intervals. These values are computed based on, respectively, the mean difference between proposed scheme and alternative factor method described in [24] and the mean difference between proposed scheme and proportional fairness method proposed in [23]. As JFIVIPAF>0 and JFIVIPPF>0, for all intervals, it is obvious that the proposed method provides more fairness among active users than the alternative factor and proportional fairness method as each user may reserve only a single subchannel at any given time as it is expressed by constraint C3 in our optimisation problem formulation.Table 6
Variation intervals in terms of Jain Fairness Index.
[50,75[[75,100[[100,125[[125,150]JFIVIPAF0.1830.4200.5490.639JFIVIPPF0.0570.1030.1280.145Figure5 shows the outage probability versus the number of users where the outage probability represents the rejected users percentage. When a user does not get its required subchannel, the number of rejected users increases by one. Then, the outage probability is the ratio of the number of rejected users and the total number of active users in a loaded system.Figure 5
Outage probability versus the number of users in loaded systems.Table7 shows variation intervals in terms of outage probability. Let OPVIPAF and OPVIPPF denote the Outage probability for different users variation intervals. These values are computed based on, respectively, the average of difference between proposed scheme and alternative factor method described in [24] and the average of difference between proposed scheme and proportional fairness method proposed in [23]. As OPVIPAF<0 and OPVIPPF<0, for all intervals, it is obvious that the proposed scheme provides lower outage probability than other methods. We should notice that in this case, as it is shown by Table 7, the difference between the proposed heuristic and existing methods [23, 24] increases when the number of users rises, meaning that the proposed scheme satisfies a greater number of users than other existing methods [23, 24] in a loaded system case, because it covers the inefficiency resource case by allocating to each user its second best and free subchannel.Table 7
Variation intervals in terms of outage probability.
[50,75[[75,100[[100,125[[125,150]OPVIPAF(%)−0.943−2.156−2.809−3.247OPVIPPF(%)−3.772−8.626−11.236−12.991For unloaded system case, the performance of our proposed algorithm is compared with the algorithms proposed in [23, 27]. The reason for this comparison is as follows. Authors in [23] aim to maximize the total system capacity while maintaining proportional fairness among active users. The principle of this suboptimal subchannel algorithm is to use the subchannels with high SINR for each user. For remaining subchannels, the user with the lowest proportional capacity has the option to pick which subchannel to use in order to achieve proportional fairness. Resource allocation algorithm proposed in [27] aims to assign to each user a subchannel in which the user has the best channel conditions. For the remaining subchannels, the user with the lowest amount of capacity is selected and its best subchannel is allocated to him in order to reach a sufficient fairness among users.Figure6 compares the average spectral efficiency per sub-carrier versus the number of users.Figure 6
Total spectral efficiency versus the number of users in unloaded systems.Table8 shows variation intervals in terms of total spectral efficiency for proposed. Let USEVIPMM and USEVIPPF denote the average total spectral efficiency for different users variation intervals in unloaded systems. These values are computed based on, respectively, the mean difference between proposed scheme and max-min method described in [27] and the mean difference between proposed scheme and proportional fairness method proposed in [23]. As USEVIPMM>0 and USEVIPPF>0, when K∈ ]12,30], it is obvious that the proposed method provides greater spectral efficiency than the max-min and proportional fairness method. We should notice that in this case, as it is shown by Table 8, the difference between the proposed method and existing methods [23, 27] increases when the number of users rises. Then, the proposed method operates well the multiusers diversity. However, when K≤12, the existing method in [23, 27] provides better performance in terms of total spectral efficiency as USEVIPMM<0 and USEVIPPF<0 when K∈[10,12], because they introduce a remaining subchannel allocation phase. So, one user may have more than one subchannel as it is described above. Hence, the contribution of our proposed scheme performs better when the number of users in the cell is important which is generally close to the practical case when good subchannels are not yet available.Table 8
Variation intervals in terms of total spectral efficiency in unloaded systems.
[10,12]]12,15[[15,20[[20,25[[25,30]USEVIPMM(bit/s)−0.2310.2370.6871.1231.458USEVIPPF(bit/s)−0.0870.2650.7091.1321.466


## 6.3. Proposed Subchannels Allocation Scheme Performances in a Heterogeneous Traffics System

The performance of the Multi-QoS-based adaptive resource allocation proposed algorithm is compared to two existing algorithms that are proposed in [28, 29] in terms of rtPS average Packet Loss Rate (PLR)and nrtPS Packet Satisfaction Ratio (PSR). On one hand, Maximum-Carrier-to-Interference and Noise Ratio (MAX-CINR) scheme [28] allocates resources to the user with the maximum receiver CINR and then only the users' link qualities are concerned and the QoS requirements are totally ignored. On the other hand, Modified Proportional Fair (MPF) scheduling algorithm proposed in [29] is taken into account with QoS guaranteed to users in the system. In order to evaluate the performance of various QoS services, we use the Near Real Time Video (NRTV) traffic model for rtPS service, FTP model for nrtPS service [30]. Here we heuristically define length of rtPS packets 1024 bits, nrtPS 2048 bits, and BE 4096 bits and we set the QoS class coefficients as βrtPS= 1.0, βnrtPS= 0.8 and βBE= 0.6. Moreover, we assume that packet arrival process is Poisson distributed, each connection with its own average arrival rate. We suppose that there are 150 users in the system where each one requires a single service at the same time. For rtPS connection, the minimum reserved rate and maximum latency of each connection are set to 500kbps and 20ms, respectively. For nrtPS connection, the minimum reserved rate is set as 1 Mbps. For BE connection, the buffer size is 5000 packets with 512 bytes each.Figure7 shows the average Packet Loss Ratio (PLR) of the rtPS connection across different number of users. The average PLR is defined as the ratio of the number of the lost rtPS packets to the total packets' number.Figure 7
Average rtPS packet loss ratio versus the number of users.Table9 shows variation intervals in terms of rtPS Packet Loss Ratio. Let HPLRVIPMCI and HPLRVIPMPF denote the PLR in different variation user intervals in heterogeneous services system. These values are computed based on, respectively, the average of difference between proposed scheme and MAX-CINR method described in [28] and the average of difference between proposed scheme and modified proportional fairness method proposed in [29]. As HPLRVIPMCI<0  and  HPLRVIPMPF<0, for all intervals, it is obvious that the proposed method satisfies more rtPS users than the MAX-CINR and modified proportional fairness method, because our scheduler gives the priority to rtPS-class to ensure an adequate resource allocation.Table 9
Variation intervals in terms of rTPS packet loss ratio.
[50,75[[75,100[[100,125[[125,150]HPLRVIPMCI(%)−20.88−13.78−9.204−8.351HPLRVIPMPF(%)−24.84−16.72−14.21−10.33In Figure8, we investigate the average nrtPS Packet Satisfaction Ratio (PSR) which is defined as the ratio of the number of the connections guaranteeing the minimum reserved rate to the total connections number. Table 10 shows variation intervals in terms of nrtPS Packet Satisfaction Ratio. Let HPSRVIPMCI and HPSRVIPMPF denote the PSR in different variation user intervals in heterogeneous services systems. These values are computed based on, respectively, the mean difference between proposed scheme and MAX-CINR method [28] and the mean difference between proposed scheme and modified proportional fairness method [29]. As HPSRVIPMCI>0 and HPSRVIPMPF>0, for all intervals, it is obvious that the proposed method satisfies more nrtPS users than the MAX-CINR and MPF method, due to our proposed reservation phase that reserves subchannels to rtPS, nrtPS, and BE services according to proportional parameters depending on system resources availability. For other methods, there are no resource reservation phase, which can increase the nrtPS calls rejection.Table 10
Variation intervals in terms of nrTPS packet satisfaction ratio.
[50,75[[75,100[[100,125[[125,150]HPSRVIPMCI(%)9.0785.9945.7403.631HPSRVIPMPF(%)27.2118.3215.5711.32Figure 8
Average nrtPS packet satisfaction ratio versus the number of users.


## 6.4. Concluding Remarks

Simulation results demonstrate that our sliding window method increases the system capacity and decreases the BLER effectively compared the minimum and the average channel gain methods. In loaded systems, simulation results show that the proposed algorithm permits to achieve a better trade-off between fairness and efficiency use of resources compared to other recent methods [23, 24]. Moreover, our proposed resource allocation scheme proves efficient in unloaded system than other existing methods. In addition to this contribution, the new heuristic algorithm present a low complexity and may be adopted for real-time and mobile applications. In a heterogeneous services context, simulation results illustrate that our proposed scheme can simultaneously satisfy the QoS requirements of various classes services: rtPS, nrtPS, and BE.


## 7. Conclusion

In order to reduce the OFDMA system complexity, available sub-carriers are grouped into equal groups of contiguous sub-carriers, where each group is called a subchannel. The adaptive modulation and coding scheme, AMC, is used in order to maximize the number of bit per symbol. In this paper, we have firstly proposed a new method for subchannel gain computation based on the frequency responses dispersion. Secondly, we have proposed a new heuristic method for subchannels allocation problem in the context of WiMAX release 2.0, IEEE 802.16 m. An adaptive method for subchannels allocation was necessary in order to exploit the multi-user diversity, to respect real-time constraints and to maximize the system capacity. The idea of this method was based on the statistic parameters, mean, variance, root mean square, or RMS of the frequency response channel gain for every mobile station. Finally, we proposed a multi-QoS-based resource allocation algorithm for OFDMA systems. We defined a priority function for each user according to the QoS satisfaction degree and its corresponding subchannel qualities. Simulation results showed that proposed algorithms provide a better trade-off between total system capacity, fairness, and complexity compared to other existing methods. For future work, we are interested to validate the present proposition in a multiservice context in order to develop an efficient radio resources management policy for Long-Term Evolution (LTE) network.



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*Source: 431958-2012-02-09.xml*