Yosra Abbes, Sameh Najeh, Hichem Besbes

Research Laboratory COSIM, Sup’Com, University of Carthage, Tunisia

I. INTRODUCTION

Fifth Generation (5G) networks are expected to provide users with a variety of heterogeneous services such as high resolution and 3D video streaming, tactile Internet, interactive games and remote monitoring which require high data rate demands as well as guaranteed QoS. This challenging dilemma is also faced by the limitation of the available radio resources (Bandwidth and Power) at the Base Station (BS). Therefore, the need for an efficient allocation of these scarce resources among different users in the cell to deliver the most adequate QoS with the minimum cost is crucial. Hence, incorporating an admission control strategy could be an efficient way to tackle the problem of overloaded situations and balance the goal of maximizing the number of supported users while ensuring the efficiency of the resource utilization.

In [1], authors provide an analysis framework for admission control in OFDMA systems by applying channel-dependent resource assignment. The assignment algorithm framework performs admission control to allow the prediction of achievable rates given a certain amount of resources and a certain set of requests. As a result, there is a significant improvement for the admission control schemes in the assignment algorithm in terms of data capacity. Unfortunately, due to the NP-hard nature of the optimization problem,the proposed framework neglect the overall performance enhancement fulfilled by the exploitation of the multiuser diversity in the OFDMA systems. Since fourth generation cellular networks utilize a frequency reuse of one, especially terminals at the cell edge suffer from inter-cell interference. In order to provide them with rates that guarantee specific QoS parameters without reserving too many resources, a good prediction of their possible rates is needed. Thus, an accurate performance model of a dynamic OFDMA system is required which take the effect of interference from adjacent cells into account. The work proposed in [1] was extended in [2] where authors propose a framework that permits to quantify the number of VoIP calls that can be supported in downlink of interference-limited systems purely based on the average SINR per terminal. It was shown that cell performance is not simply governed by average SINR but the received power of the signal of interest is much more important (together with the received interference power). The weakness of this work is that only one co-channel neighbor cell is considered.

In this paper, the authors proposed a complete framework for admission control in the downlink of OFDMA system to guarantee the required QoS performance.

In [3], authors propose a dynamic admission control and a bandwidth reservation schemes for WiMAX network. The presented strategy aims to provide an adaptive QoS for admitted users according to the network load and the various classes of scheduling services.In addition, it proposes a dynamic adjustment of the reserved bandwidth for better resource utilization.

The degree of user satisfaction with an allocated amount of resource can also be depicted by utility functions which are developed using mathematical models. So, the admission control strategy can be also modeled based on maximizing the utility function which determines the user service satisfaction. This approach is discussed in [4, 5]. Authors propose in [4] a mechanism of joint admission control and resource block allocation in a time slot aiming to satisfy the bit rate demands of user applications. The proposed schemes take into account the relative rate requests in addition to the relative channel conditions of the users.The proposed problem is simplified based on a relaxation bound to be solved as weighted sum rate maximization problem. Numerical results show that the schemes behave well in situations of high network load.

In [5], resource allocation and admission control strategies for OFDMA systems are proposed providing both QoS-constrained user services and best-effort services. The proposed strategy aims to maximize the total network utility of the BE users while satisfying the QoS request for maximum number of High Priority (HP) users having strict requirement on packet loss rate and delay tolerance. It was shown that the feasibility of the resource allocation problem depends on the number of HP users in the network. Mixed integer linear program (MILP) formulation of the joint admission control and resource allocation problem for multimedia streaming in mobile networks was presented in [6]. The proposed solution derived using simple LP formulation and binary search exploits system state prediction to guarantee the required QoS for the set of admitted users. The admission control problem is further investigated in multi-tier network.In [7] authors suggested an admission and power control algorithm for two-tier small cell networks. Noting that the number of small cell users that can be admitted at their outage probability specifications is maximized and their total transmit power is minimized and this without violating the outage probability specification of the macrocell user. Since the formulated joint admission and power control problem is NP-hard, convex relaxation is applied to obtain approximate solutions. Authors in [8] proposed a distributed admission control mechanism for load balancing among sub-carriers with multiple QoS classes. In addition,small cells mitigate co-tier and cross-tier interferences using slot allocation of different traffic streams among different sub-carriers.However, no power allocation was performed.

Most of the admission control technique focuses only on maximizing the number of admitted users. However, unfairness between served users can be a greatest weakness of the proposed admission control policy. In fact,promoting users with the best radio conditions can lead to an excessive transmission delay and so causing sever performance deterioration [9]. Furthermore, providing users with the required service even those having bad radio channel conditions is crucial for the service provider.

In homogeneous network, network capacity can be expanded by either increasing the bandwidth or improving link efficiency through the use of MIMO, OFDM and other advanced signal processing techniques. The SC is one of PHY layer technique that permits to further exploit the radio resources as so to improve the system capacity. This concept was introduced by Costa in 1983 [10] and known as “writing on dirty paper” which suggests that the addition of a sequence in the channel known only to the transmitter does not change the link capacity. So, it allows to send an additional stream to a user having good radio channel condition on a subcarrier initially allocated to a user having poor radio channel condition. The superposition coding for the throughput-optimal network configuration is studied in [11]. However, scheduling is not considered in [11]. Authors in [12] formulated a joint routing and scheduling flow-based problem of finding jointly optimal parameters for superposition coding for the maxmin throughput in order to ensure fairness between different users. This work shows that the combination of superposition coding with interference cancellation allows a network to double the maximum throughput in wireless mesh networks. In [13], a superposition coding/decoding scheme was proposed permitting the use of one subcarrier by at most two users.This superposition coding scheme is used to allocate the radio resources while ensuring fairness among users. In [14] analyzed the performance of the gains offered by multiple users scheduling via superposition coding with successive interference cancellation in comparison with the conventional single user scheduling for three operating points, namely hard fairness, proportional fairness and fixed weights. The authors in [14] showed that the superposition coding with the successive interference cancellation can achieve a 10%or higher gain than the single user scheduling, so it may be feasible in some scenarios.Authors in [15] provided a suboptimal scheduling scheme which combines the two users with the maximum weighted instantaneous rate using superposition coding. The instantaneous rate and power allocation are derived in closed-form as there are only two users for superposition coding, while the long term rate of each user is derived in integral form for all channel distributions. The proposed scheme significantly reduces feedback overhead and computational complexity as compared to the optimal superposition scheme with successive interference cancellation.

Motivated by the performance enhancement offered by the superposition coding concept[16], we aim to propose in this work three different admission control policies based on optimization problems to guarantee the desired QoS for all users admitted in the cell:

● Opportunistic approach (OPSC) favoring users having good radio channel conditions for the benefit of other users.

● Great Fairness approach (GFSC) based on absolute fairness between users in the cell.

● Proportional Fairness approach (PFSC)allowing to create a compromise between fairness and efficiency.

These strategies are based on a new sufficient condition which depends on the user channel’s condition and the required bit rate.

The remainder of this paper is organized as follows. In Section II, we describe the system model and assumptions. Moreover, we formulate a reduced Channel Quality Information to predict the channel behavior during a frame.Section III deals with the proposed superposition coding strategy to be applied in the admission control process. Section IV introduces the proposed admission control strategies.Simulation results are presented in Section V.Finally, Section VI concludes this paper.

II. SYSTEM MODEL AND ASSUMPTIONS

2.1 System model

The admission control strategies are performed over a frame ofLtime slots in the downlink of wireless OFDMA network. Each time slot is constituted ofJPhysical Resource Block(PRBs). The same spectrum bandwidthBis equally divided intoJPRBs.

The received signal at the “k” user side on the “j” PRB during thenthtime slot is given by:

whereh(k,j,n) is the channel gain,s(k,j,n) is the transmitted signal andw(k,j,n) represents the contribution of noise and interference, which is modeled as an Additive White Gaussian Noise (AWGN) having a variance equal to σ2.

The number of bits that we can allocate to thekthuser on thejthPRB at time slotnis given by:

whereQ( . ) is a quantization function allowingb(k,j,n,pk) to be in {0.5,1,1.5,...,6} ,pkis the transmitted power and γ(k,j,n) is the normalized channel to noise ratio given by:

Γ is the normalization parameter which depends on the desired bit error rate performance at the receiver side and on the used forward error correction scheme.

In order to compute (2) and (3), we need to have the Channel Quality Information (CQI)for all users and on all the PRBs, which will increase the overhead. To make it tractable, we propose to introduce a partial state information concept, which will be discussed in the next section.

2.2 Reduced channel quality information

When the number of users increases, there is a higher possibility to increase cell throughput.However, channel feedback from the user to the BS incurs high overhead especially in the case of transmission over multiple channel like OFDMA systems. Several techniques were proposed in the literature to reduce CQI feedback overhead and to escalate the uplink resources [17].

To reduce the quantity of feedback information without significant throughput degradation, a practical strategy that consists on delivering feedback on a partial set of channels with the best channel quality was proposed in [1]. It was shown in [1] that the density function of the set of the best-subchannels permit to obtain a better channel characteristic behavior than a random channel. Based on this feedback analysis, we propose in this section,to solve the problem of the large feedback of channel quality information overhead by using best-m feedback reduction scheme.

Based on this feedback analysis, we define for each userk:We define for each user :

We consider the case where we allocate the maximum powerPmaxon all the PRBs.Assuming that during the frame period the channel experience a slow fading, in another word, channel coherence time is considered to be much longer than the frame length.. Hence,γSM(k,n) are invariant during each frame and is given as follows:

Moreover, the variation of set of theMbest PRBsSM(k,n) are almost constant, soMis equal to:

and the corresponding number of bits(k,n) remains constant, even though the set of theMbest PRBsSM(k,n) changes from one time slot to another. That’s to say:

Users who experience slow fading channel,can achieve the same average throughput in the long term and the feedback information remains almost the same for a number of consecutive slots. Thus, users can report their feedback periodically. Finally, we assume that all users transmit to the base station through a control channel the information aboutis considered as the CQI metric instead of received SNR.

2.3 Users classification

Three classes of users are proposed in this work, depending on their radio channel’s condition [9].

III. THE SUPERPOSITION CODING CONCEPT

In the novel multimedia mobile services, providing the network access is not enough. The operators must guarantee for the consumers high data rate and different QoS requirements such as bandwidth, delay, jitter and packet loss. The total network accessibility is constrained by the lack of radio resources availability and load network. To overcome this issue, an efficient admission control must be applied to maximize the overall system utility while respecting the resource availability constraint and providing user’s QoS expectation.Since its capability to improve the whole system performance in terms of throughputs [13],mean transfer times and blocking probabilities[18], the superposition coding is a worthy candidate to be deployed by the 5G systems. We aim in this section to introduce the proposed superposition coding concept that will be used by the different admission control strategies aiming at simultaneously improve the efficiency utilization of network resources and guaranteeing QoS for the admitted users.

3.1 The proposed superposition coding strategy

The SC is a simultaneous transmission of a two signals sent to different users, over a common frequency band (subchannel) [19].In fact, this strategy allows the sharing of the radio resources: power and subchannels, between users having different radio channels conditions. Users situated close to the BS called “Potential” users as they have good radio channel conditions. Users located farther away from their served BS are denoted as “degraded” users since he experiences low SNR. Potential user could send his stream on a subcarrier that was initially allocated to carry an original stream to a degraded user while transmitting a very small amount of power.

Let us consider, without loss of generality,that the potential users is assigned 16-QAM constellations for this example (see fig.1,right) and that the degraded user is assigned 4-QAM constellation (see fig.1, left). The superposition coding allows the BS to send over one subcarrier the combination of the two signals using 64-QAM constellation, as shown infig.2.

To decode their signals, potential users employs Successive-Interference Cancellation(SIC) approach [19, 13]. First, potential user decodes the signal of the degraded user and then subtracts its from the received signal to extract his own data [19, 20]. Due to the low amount of power allocated to the potential user, the degraded user could then decode his signal. Moreover, authors in [13] proposed a simple SC scheme which verifies that there is almost no error propagation during the decoding operation only if the SNRs of the potential and degraded users are higher than SNRs thresholds. Doing so, we guarantee no degradation of a degraded user’s performance.Hence, SC allows to increase the spectral efficiency by exploiting the multiuser diversity,yielding a higher overall system capacity,without any extra power cost.

In the literature, most of the works that studied the use of superposition coding focused solely on the subcarrier and power optimization, improving BER performance,coding and decoding as well as scheduling.Hence, we aim in this work to explore the benefit of the superposition coding in the admission control.

3.2 The sufficient constraint based on the superposition coding concept

Based on the user classification described in Section 2, users in the cell are categorized into three types:Crusers,Cmusers andCpusers.Moreover, as we use the SC concept, we assume that the potential userkpotenjoying favorable channel radio conditions belong to the set of rich usersCrand the degraded userkdeghaving low radio channel condition belong to the set of poor usersCpand is considered as poor user.

Applying the SC concept, the orthogonality constraint when allocating the radio resources could be removed. So, potential userkpotcould sent his data stream over the same PRB initially allocated to the degraded userkdegwithout affecting the rate of the degraded user and without any increase in the power budget.We assume the presence of a high number of users in the cell and a suitable power budgetPmaxto ensure more superposition opportunities between potential and degraded users. In addition, we assume that the degraded user’s SNR is higher than an SNR threshold allowing the use of the SIC technique at the potential user side and to ensure that there is no error propagation during the decoding operation.

Fig. 1. 4-QAM constellation (left) 16-QAM constellation (right).

Fig. 2. The derived Superposition coding constellation.

We define the total number of admittedCrusersuras follows:

wherethe number of potential users using SC andis the number of the admitted users belonging to the rich class and without using the SC.

In order to guarantee the system stability and the required QoS of the potential userkpot, the allocated datarkpotshould be equal to the average bit rate θkpotas it is given in the following

whereNis the total number of PRB in a frame,Bdenotes the total bandwidth ,is the number of allocated PRBs for the potential userkpotduring a frame andis the average number of bit allocated to each potential user.

From equation (8), we note that the average number of PRBs allocated to the potential userkpotto meet the QoS constraint is given by:

To simplify the concept, we assume that the same throughputris allocated to all users independently of the class that they belong to.

The total number of PRBs allocated to the potential users is equals to

Applying the same line of thought used in(8) to the class of poor users, we can deduce thatthe average number of PRBs allocated to theCpusers is equal to:

Hence,Mpthe total number of PRBs allocated toCpusers (degraded users) to fulfill the QoS requirement can be derived by:

whereupis the total number of admittedCpusers.

Lemma 1.A sufficient condition that should be respected to ensure for each user k the desired data rater to ensure stability, can be derived by

where ∈ is a margin parameter introduced to tackle the channels variation during the frame duration. The margin parameter ∈ can also be defined to allow some room to prioritized new coming to joint the network [21].

Proof.Since each allocated PRB will be shared by the degradedCpuser,kdegand the potential user,kpot, the total number of allocated PRBs to the degraded users is equals to the number of PRBs allocated to the potential users,Mp=. We can deduce from equations (10) and (12) that

Then, we derive from equation (12), thatMr, the total number of PRBs allocated to theCrusers is equals to

Moreover, the total number of PRBs allocated to theCmusers,Mmis equals to:

Since the total number of PRBs during a frame shouldn’t surpassNL, and using equations (12), (16) and (15) we have:

Using the equations (7) and (14), we obtain

Applying equation (18) into the statement(17), the proposed condition to meet the required QoS based on the superposition coding concept is then derived.

Using the stability condition defined by equation (13), we can estimate whether the available resources can support the rate requirements of all the presentUusers(K=U). If the stability condition is respected we will admit all theKusers. In the other case, a strategy of the admission control should be established which is the subject of the next section.

IV. ADMISSION CONTROL POLICIES BASED ON THE SUPERPOSITION CODING TECHNIQUE

This section will handle the explanation of three different admission control policies using the superposition coding concept explained previously:

1. an Opportunistic approach allowing to serve initially users having the best radio channel conditions.

2. a Great Fairness admission control policy which offers absolute fairness between the different class of users to the access to the network.

3. a Proportional Fairness strategy which represents proportionally the three users’ classes in the system.

To simplify the concept, and to respect fairness among users in terms of the offered data rate, we assume that the same throughputris allocated among all users independently of the class that he belongs to.

GivenUr,UmandUp, the total number of users from each class. We defineucthe number of admitted users from each class of users,

where λcdenotes the proportion of admitted users from rich, medium and poor class respectively.

4.1 Opportunistic admission control strategy

Opportunistic downlink scheduling has gained much attention in designing the existing wireless scheduling policies. Such opportunistic scheduling mechanisms can result in higher spectrum utilization, and increased system throughput. These facts motivate us to consider the opportunistic scheduling paradigm in the admission control process. The proposed opportunistic policy aims to serve the maximum number of users. The radio resources are allocated to the user who would benefit the most from the opportunity to transmit. Thus,we start by fulfilling the requirement of rich users who have good channels’ condition. If all these users are admitted and condition (7)is satisfied, the rest will be given to the second class and so on and so forth. Based on this strategy, when the total number of users demanding access to the network is huge or the required rates are very important, users having bad channel conditions are excluded.

To maximize the total number of served users under the stability constraint, we formulate the following optimization problem:

The constraint (20a) refers to the stability constraint. The constraint (20b) indicates that the proportion of the admitted users from each class is higher or equal to 0 and couldn’t surpass 1.

The objective function of the problem (20)is concave. Since the constraints are all linear, (20) is a convex optimization problem.Therefore, this optimization problem can be efficiently solved using convex-simplex algorithms or reduced gradient algorithm.

The proposed opportunistic strategy may cause unfairness situation between users since most of the radio resources are monopolized by rich users. To this end, we propose a great fairness admission control approach in the next section.

4.2 Great fairness admission control strategy

The goal of this strategy is to guarantee the admission of users from different classes to ensure absolute fairness while maximizing the total number of admitted users. In this strategy all users:r,mandphave the right to access to the network. Moreover, all admitted users should be granted “equal ”QoS (bit rate,delay,...). If the proportions of admitted users from each class are equals,λ= λr= λm=λp,the absolute fairness case is achieved. In fact,this admission control objective function ensures non-zero admitted users for all classes.Therefore, the corresponding scheme attempts to increase the number of admitted poor user up in order to increase the admission rate for the other classes (mandr).

To ensure absolute fairness between users,the number of admitted users from each class can be determined via the following optimization problem:

The constraint (21a) refers to the stability constraint. The constraint (21b) indicates that the proportion of the admitted users from each class is higher or equal to 0 and couldn’t surpass 1. The last constraint (21c) expresses the total equity between the admitted users from each class.

Lemma 2.The optimization problem formulated in(21)has a unique solution given by

Proof.The details of the proof are given in“Appendix A”.

After this procedure, we draw randomly from these classes the respective computed number of usersur,umandupthat can be admitted:

Rather than the opportunistic approach, the great fairness strategy allows the allocation of radio resources to the poor users which can leads to the waste of a certain portion of resources. To escape from the “optimality-fairness” dilemma, we propose in the next section a proportional fairness admission control strategy.

4.3 Proportional fairness admission control strategy

A good trade-off between fairness and throughput can be obtained by utilizing the proportional fair scheduler, which utilizes the instantaneously achievable data rate divided by its time average as a decision variable.Such a scheduling rule leads to resource fairness since all users asymptotically get equal access to the channel. Their throughput, however, depend on their positions.

The Proportional Fairness admission control strategy aims to simultaneously improve the efficiency of the resource utilization and establish a certain fairness level between users. In this strategy, a proportional coefficient should be defined in order to provide fairness between the different users. To determine the number of users from each class of users, we propose to solve the following optimization problem:

The constraint (24a) refers to the stability constraint. The constraint (24b) indicates that the proportion of the admitted users from each class is higher or equal to 0 and couldn’t surpass 1.

We can determine the number of users per class that can be admitted applying the Proportional Fairness Admission Control Algorithm(PFACA) algorithm given in Algorithm (1).

Thus, based on the solution of the previous optimization problem given by equation (22),we aim to determinethe proportional coefficient from each class of users. The number of users is increased gradually while respecting the stability constraint expressed by equation(24a) and the proportionality constraint defined by equation (24b).

V. SIMULATIONS RESULTS

In this section, we investigate the performance of the proposed admission control strategies OPSC, GFSC and PFSC in terms of the mean of served VoIP users, the dropping user’s rate and the average of the VoIP packet transmission delay.

5.1 Simulations parameters

To validate the effectiveness of our proposed algorithms, we consider a single cell where each user’s location is randomly generated and evenly distributed over the cell. The number of VoIP users varies from 100 to 500 in increment of 50 where 50% areCrusers, 30% areCmusers and 20% areCpusers. User data rate arrival is according to a Poisson process with raterkfor each userk. We consider the path loss, shadowing and flat fading in the channel propagation model. For path loss, we use the modified Hata urban propagation model [23]. The shadowing component follows a log-normal distribution with mean value of 0 and standard deviation of 8dB. The VoIP traffic generates a 40-byte VoIP packet every 10 ms. To meet the QoS requirement, the maximum queuing delay is set to 20 ms [24]. We perform Monte-Carlo simulations over 103realizations. Simulations parameters are summarized in Tab.I.

5.2 Simulations results

We conduct simulations to corroborate the effectiveness of the assumptions considered in this work. We depict in figures 3 and 4, the behavior of(k) and γSM(k,n) versustime, when M=10 while considering indoor environment and outdoor environment. We consider the maximum user’s velocity equals to 1km/h and 30km/h for the indoor and outdoor environment respectively. We consider in this simulation 10 frame where each one contains 20 time slots.(k) is estimated as the value of γSM(k,n) during the first time slot. It is interesting to note that, in the worst case, the difference between the estimated and the real value of(k) remain less than 0.2 dB in the case of the indoor environment and 1.2 dB in the case of the outdoor environment.This will not affect too much the result since it will be compensated over time. Moreover, the mentioned results depict the evolution of the CQI on the weakest PRB from the set of the M best PRBs. However, users may be assigned other PRBs which have better radio channel conditions. So, this channel state estimation allows to match the current channel condition of each user as if a full feedback channel estimation is used. Finally, the proposed reduced CQI permits to reduce the amount of feedback information necessary at the BS especially when the number of users increases consuming non-negligible amount of radio resource.

Algorithm 1. Proportional fairness admission control algorithm (PFACA).

Table I. Simulations parameters.

Fig. 3. Evolution of γSM (k, n ) versus time slot number (Indoor environment).

Fig. 4. Evolution of γ (k, n ) versus time slot number (Outdoor environment).

Fig. 5. Mean of served VoIP users versus the initial number of users.

For the welfare of performance comparison,Cluster Allocation SubProblem (CASP) based on the Modified Chinneck Search algorithm proposed in [5]is also evaluated. CASP aims to maximize the utility of BES users while providing HP users with their needed rate. CASP can be infeasible when the QoS requirements of HP users exceed the instantaneous achievable channel capacity. So, a subset of HP users should be identified for which the feasibility of CASP is ensured. Several heuristic solutions were proposed by introducing elastic Linear Problem (LP) in order to determine the number of served HP users. We have chosen to evaluate from the proposed heuristics the Modified Chinnek Algorithm. The Superposition Coding is not supported in this scheme.

● Mean of served VoIP users

To measure the efficiency of the proposed approaches, we depict in fig.5 the evolution of the means of served VoIP users and the dropping user’s rate while increasing gradually the initial number of users presented before the AC process.

It is clearly notable that the OPSC and PFSC approaches can admit over 250 VoIP users with an admission rate equals to 100% and the GFSC and CASP approaches can support over 150 VoIP users also with an admission rate equals to 100%. As soon as the initial number of VoIP increases, we detect that the OPSC approach has the highest mean of admitted users (admission rate equals to 63%for 500 VoIP users) followed by the PFSC approach (48%), the GFSC strategy (44%)and finally the CASP approach (38%). We can note that the performance of the proposed approaches outperform the CASP admission control policy proposed in [5]. In fact, as they use the superposition coding concept, the proposed admission control strategies allows to further improve the number of admitted users exploring the benefit of the multiuser diversity.

● Dropping user’s rate

Figure 6 draws the dropping user’s rate in terms of the initial number of users. The dropping rate is estimated as the average of the rejected users over the total number of present users during the admission control process.We choose to evaluate this metric to measure the fairness between user’s classes. As the fairest policy, the GFSC admission control strategy achieves almost identical dropping user’s rate for the three user’s classes as it is shown in fig.6. Yet, for the OPSC strategy, the class of poor users Cp has the most important dropping user’s rate since it tends to favor users having the best radio channel conditions.For the PFSC approach, the highest dropping user’s rate belongs to the C p user’s class then the C r class and finally the C m class. Finally,since CASP algorithm doesn’t matter about user’s classes and aims to find a subset of users having the maximum cardinality from all user’s subsets, the dropping user’s rate is proportional to the number of users of each class.

In summary, the OPSC approach is more efficient in the use of the radio resources since they preferably serve users having the best radio channel conditions which don’t need a large amount of resources to reach the desired QoS and this can explain the highest admission rate. Moreover, the performance of the PFSC strategy is net superior than the GFSC strategy (about 80% for the PFSC strategy and 73% for the GFSC strategy for an initial number of users equals to 300). Indeed, The GFSC approach keeps special attention on fairness than efficiency by guaranteeing an equal share of the resources between the different classes of users which reduce the admission rate for the GFSC strategy.

● Average of the VoIP packet transmission delay

Fig. 6. The dropping user’s rate per class in terms of the initial number of users.

Fig. 7. Average VoIP packet transmission delay versus the initial number of VoIP users.

We plot in figure 7 the evolution of the average of the VoIP packet transmission delay in terms of the number of users presented in the cell before the admission control process. The packet transmission delay is defined as the delay between the transmissions of the first bit of the packet to the transmission of the last bit.We believe that the average packet transmission delay is an important metric to evaluate the QoS of the proposed approaches. It is clear that in all cases, CASP strategy achieve the lowest transmission delay (about 0.5ms when the total number of users is equals to 500)since it achieve the lowest user’s admission rate. We note then that PFSC strategy allows the minimum transmission delay (less than 0.5 ms) than the GFSC and OPSC approaches.The GFSC approach presents a higher transmission delay than the PFSC approach when the number of users reaches 150. This can be explained by the highest number of servedCpusers by the GFSC strategy which requires more resource to fulfill the desired QoS contrary to the OPSC approach which presents the highest transmission delay (about 0.6 ms for a number of users equals to 500).

● Total throughput

Figure 8 shows the effect of the load increasing on the total throughput. It is clearly noticeable that the total throughput increases with the increase of the load in the network. For a total load higher than 10 Mbps, the OPSC, PFSC and GFSC outperform the CASP algorithm.This can be explained by the increase of the system capacity exploiting the mutiuser diversity while applying the SC concept.

Fig. 8. Total throughput in terms of the total load.

From the system utility point of view, the opportunistic approach is optimal since it permits to maximize the number of served users so it allows to increase the total throughput of the cell (total throughput about 18 Mbps for a total load of 32 Mbps). Despite efficiency,such approach is far from being fair and can cause abusive situations in the distribution of radio resources since it deprives mobile users constantly endure bad radio conditions from the needed resources. The proposed GFSC admission control strategy permits to serve different user’s class. However, this policy may penalize users with better radio conditions and reduce the system’s utility. Indeed, serving a mobile user suffering from bad radio conditions is a waste of precious radio resources.

The proposed proportional fairness approach permits to ensure the admission of the three users’s class according to the user’s configuration in the cell. It was shown that this strategy is effective in terms of not only individual mobile user satisfaction but also the overall system performance (total throughput equals to 14 Mbps for a total load of 16 Mbps).

We have shown by several simulations results the capability of our proposed schemes in operating in high load network while taking into account the QoS needed by each users.So, the proposed admission control policies could be efficiently applied in the case of crowded events [25] when real-time services like voice calls which require a greater concern of QoS, is demanded by a large number of users. Finally, the proposed admission control strategies are complexity effective and can be applied in 5G network to provide QoS guarantee for the offered services.

VI. CONCLUSION

In this paper, we have proposed a complete framework for admission control in the downlink of OFDMA system to guarantee the required QoS performance. We have developed a joint superposition coding and admission control formalism to determine the number of users that can be served without surpassing the cell radio resource availability. The proposed admission control strategies are formulated based on three different optimization problems(GFSC, PFSC and OPSC). Firstly, we have developed an Opportunistic approach (OPSC)which serves initially users having the best radio channel conditions. The inherent drawback of this strategy is the lack of fairness and the poor users may be completely shut off during the admission control process. Secondly we proposed a Great Fairness (GFSC) admission control strategy. Besides, policies that provide absolute fairness penalize users with better condition and reduce the system capacity.After, we proposed a Proportional Fairness(PFSC) admission control approach which permits to admit proportionally the three user’s classes permitting to fulfill a trade-off between efficiency and fairness. Simulation results have shown the efficiency of the OPSC strategy in increasing the number of served users in the system (about 320 VoIP users), the fairness in the user’s admission offered by the GFSC approach and the compromise efficiency-fairness and the and the transmission delay reduction fulfilled by the PFSC strategy (less than 0.5 ms).

Appendix A (proof of Lemma1)

We consider the optimization problem formulated in (21). If the problem formulated has a unique solution, applying the logarithmic function onto the objective function of (21)converts (21) into a convex optimization problem that also has a unique solution. The objective function of the problem (21) is a log-concave function. The first derivative ofln(uc)is a monotonic decreasing function. Moreover,the second derivative ofln(uc) is a strictly negative function. So the objective function of(21) is a log-concave function.

The problem (21) can be converted to:

Ignoring the constraint (25.b) , the Lagrangian is formulated as

where μ is the Lagrangian multiplier. We take the derivative ofL(λc, μ ) with respect to λcand equate it to zero to obtain

Tacking the derivative ofL(λc, μ ) with respect to μ and equate it to zero we get

using (27) into the equation (28),

So,is derived as

Sinceλr= λm= λp, we can deduce that

This completes the proof.

[1] J. Gross, “Admission control based on OFDMA channel transformations, ”in IEEE International Symposium on a World of Wireless, Mobile and Multimedia Networks (WoWMoM), pp. 1-11,Kos, June 2009.

[2] F. Naghibi and J. Gross, “How bad is interference in IEEE 802.16e systems?”in Proc. of the European Wireless Conference (EW), Lucca, Italy,April 2010.

[3] C. Wang, W. Yan, and H. Lo, “Dynamic admission control and bandwidth reservation for IEEE 802.16e mobile WiMAX networks,”EURASIP J.Wireless Commun. Netw., vol. 2012, no. 143,April. 2012.

[4] V. Venkatkumar, T. Haustein and M. Faulkner,“Joint Admission Control and Resource Allocation for Multiuser Loading in LTE networks,”Smart Spaces and Next Generation Wired/Wireless Networking , Lecture Notes in Computer Science, vol. 6294/2010, pp. 421-435, 2010.

[5] S. Bashar and Z. Ding , “Admission control and resource allocation in a heterogeneous OFDMA wireless network,”in IEEE Transactions on Wireless Communications, vol. 8, no. 8, pp. 4200-4210, Aug. 2009.

[6] N. Bui, I. Malanchini and J. Widmer, “Anticipatory Admission Control and Resource Allocation for Media Streaming in Mobile Networks,”in Proc.of MSWiM ’15, pp.255-262, November 2015.

[7] S. E. Nai, T. Quek, M. Debbah, and A. Huang,“Slow admission and power control for small cell networks via distributed optimization, ”in IEEE Wireless Communications and Networking Conference (WCNC), 2013 , pp. 2261-2265,2013.

[8] S. Namal, K. Ghaboosi, M. Bennis, A. MacKenzie,and M. Latva-aho, “Joint admission control and interference avoidance in self-organized femtocells,”in Conference Record of the 44th Asilomar Conference on Signals, Systems and Computers(ASILOMAR) 2010, pp. 1067-1071, 2010.

[9] Y. Abbes, H. Besbes, “VAE VICTIS and Democratic Admission Control Strategies for OFDMA Network”,In Proc. of IWCMC 2012, pp. 1191-1196, August 2012.

[10] M. Costa, “Writing on dirty paper,”IEEE Trans.Info. Theory, vol. 29, no. 3, pp. 439-441, May 1983.

[11] R. H. Gohary and T. J. Willink, “Joint routing and resource allocation via superposition coding for wireless data networks,”IEEE Transactions on Signal Processing, vol. 58, no. 12, Dec. 2010.

[12] S. Shabdanov, P. Mitran, and C. Rosenberg,“Cross-layer optimization using advanced physical layer techniques in wireless mesh networks,”IEEE Transactions on Wireless Communications,vol. 11, no. 4, pp. 1622-1631, Apr. 2012.

[13] S. Najeh and H. Besbes, “A Simple Superposition Coding Scheme for Optimizing Resource Allocation in Downlink OFDMA Systems”,Wireless Personal Communications, pp. 237-260, Jan.2010.

[14] A. Zafar, M. Shaqfeh, M.-S. Alouini, and H. Alnuweiri, “On multiple users scheduling using superposition coding over rayleigh fading channels,”IEEE Commun. Lett.,vol.17,no.4, Apr.2013.

[15] A. Zafar, M. Shaqfeh, M.-S. Alouini, and H. Alnuweiri, “A suboptimal scheme for multi-user scheduling in Gaussian broadcast channels,”IEEE Signal Process. Lett., vol. 22, no. 2, pp. 136-140, Feb. 2015.

[16] Y. Abbes, S. Najeh and H. Besbes, “Joint proportional fairness admission control and superposition coding for OFDMA networks”,In Proc. of ICT 2013, pp.1-5, May 2013.

[17] H. Ganapathy and C. Caramanis, “Queue-based Sub-carrier Grouping For Feedback Reduction In OFDMA Systems,”IEEE INFOCOM2012, pp.1098 - 1106, March 2012.

[18] A. Jdidi and T. Chahed, “Flow-level performance of proportional fairness with hierarchical modulation in ofdmabased networks,”Comput. Netw.,vol. 55, pp. 1784–1793, June 2011.

[19] Tse D, Viswanath P. Fundamentals of Wireless Communication. Edited by Cambridge University press, 2005.

[20] T. M. Cover, “Broadcast Channels”,in Proc. IEEE Trans. Inform. Theory, vol. 18, no. 1, pp. 2-14,Jan. 1972.

[21] Delgado O, Jaumard B. Joint admission control and resource allocation with GoS and QoS in LTE uplink. In Proc. of IEEE Globecom 2010 Workshop on Broadband Wireless Access, Miami,December 2010; 829-833.

[22] D. Julian, M. Chiang, D. O’Neill, and S. Boyd,“QoS and fairness constrained convex optimization of resource allocation for wireless cellular and ad hoc networks,”in Proc. 2002 IEEE INFOCOM

[23] A. Medeisis and A. Kajackas, “On the use of the Universal Okumura-Hata Propagation Prediction Model in Rural Areas,”In Proc. of the IEEE Vehicular Technology Conference (VTC Spring),vol. 3, pp. 450 - 453, May 2000.

[24] B. Huang, J. Li and T. Svensson, “A Utility-Based Joint Resource Allocation Approach for Multi-Service in CoMP Networks”,Wireless Personal Communications, pp. 1633-1648, May 2013.

[25] M. Zubair Shafiq, Lusheng Ji, Alex X. Liu, Jeffrey Pang, Shobha Venkataraman, and Jia Wang,“A First Look at Cellular Network Performance during Crowded Events,”in Proc. of the ACM International Conference on Measurement and Modeling of Computer Systems (SIGMETRICS),Pittsburgh, PA, June 2013.