Cédric Gueguen
email: cedric.gueguen@irisa.fr

Mahdi Ezzaouia
email: mahdi.ezzaouia@irisa.fr

Mohamad Yassin
email: mohamad.yassin@irisa.fr

Inter-Cellular Scheduler for 5G Wireless Networks

Keywords: Wireless Networks, 5G, Scheduling, Quality of Experience, Quality of Service

Enhancing the Quality of Experience (QoE) in wireless networks is a crucial issue. Many acknowledged works focus on intra-cellular scheduling. They have shown that when the channel impairment is taken into consideration by the opportunistic scheduling approaches, it allows to reach higher throughputs and, for the most efficient ones, a higher fairness. However, if some of these works provide results near to optimum considering a single cell, high QoE cannot be guaranteed for scenarios where the cells are overloaded. In this article, we propose a new intercellular scheduler able to help the overloaded cells thanks to a dynamic cell bandwidth allocation. Our resource allocation technique is based on an adequate emergency parameter called Mean Cell Packet Delay Outage Ratio (MCPDOR). Performance evaluation shows that the proposed scheduler widely outperforms existing solutions in various scenarios. A variant of our solution that does not consider MCPDOR is also proposed and evaluated.

I. INTRODUCTION

Providing mobile multimedia transmission services with an adequate Quality of Service (QoS) is very challenging. In contrast with wired communications, wireless transmissions are subject to many channel impairments such as path loss, shadowing and multipath fading [START_REF] Proakis | Digital Communications[END_REF][START_REF] Steele | Mobile Communications[END_REF][START_REF] Goldsmith | Wireless Communications[END_REF][START_REF] Parsons | The Mobile Radio Propagation Channel[END_REF]. These phenomena severely affect the transmission capabilities and in turn the QoS experienced by applications, not only in terms of data integrity but also in terms of the supplementary delays or packet losses that appear when the effective bit rate at the physical layer is low. The past decades have witnessed intense research efforts on wireless digital communications. Among all the studied transmission techniques, Orthogonal Frequency Division Multiplexing (OFDM) [START_REF] Hanzo | MIMO-OFDM for LTE, WiFi and WIMAX: Coherent Versus non-Coherent and Cooperative Turbo-Transceivers[END_REF] has clearly emerged for future broadband wireless multimedia networks (4G [START_REF] Dahlman | 4G LTE and LTE-Advanced for Mobile Broadband[END_REF] and 5G [START_REF]5G White Paper[END_REF] systems). It is already widely implemented in the most recent wireless systems like 802.11a/g or 802. [START_REF] Fodor | Intercell interference coordination in ofdma networks and in the 3gpp long term evolution system[END_REF]. The basic principle of OFDM for fighting the negative impact of multipath propagation is to divide the available channel bandwidth into several subfrequency bands, such that their width is less than the coherence bandwidth of the channel (inverse of the delay spread). The transmission of a high speed signal on a broadband frequency selective channel is then substituted by the transmission of slow speed signals on multiple subcarriers, which are immune to intersymbol interference and subject to flat fading. This subdivision of the overall bandwidth into multiple channels provides frequency diversity. This frequency diversity, along with the time and the multiuser diversity result in a very spectrally efficient system subject to an adequate scheduling.

In this context, much interest has recently been given to the design of intra-cellular scheduling algorithms that improve the performance of multiuser OFDM systems [START_REF] Domenica | A Radio Resource Management Scheduling Algorithm for Self-Organizing Femtocells[END_REF][START_REF] Chandrasekhar | Spectrum Allocation in Tiered Cellular Networks[END_REF][START_REF] Ramachandran | Frequency Selective OFDMA Scheduler with Limited Feedback[END_REF][START_REF] Yoon | Interference Mitigation in Heterogeneous Cellular Networks of Macro and Femto Cells[END_REF]. Opportunistic scheduling techniques take advantage of multiuser diversity by preferably allocating the resources to the active mobile(s) with the most favorable channel conditions at a given time. This technique was first explored in single carrier communications [START_REF] Knopp | Information capacity and power control in single-cell multiuser communications[END_REF]. More recently, opportunistic scheduling has been exploited in multicarrier systems [START_REF] Wong | Multiuser OFDM with adaptive subcarrier, bit, and power allocation[END_REF][START_REF] Wang | An OFDM-TDMA/SA MAC protocol with QoS constraints for broadband wireless LANs[END_REF]. These schemes are derived from the Maximum Signal-to-Noise Ratio 1 (MaxSNR) technique that allocates the resource at a given time to the active mobile with the greatest SNR. Dynamically adapting the modulation and coding allows then to always make the most efficient use of the radio resource and come closer to the Shannon limit. This maximizes the system capacity from an information theory point of view. However as much efficient the intra-cellular scheduler is, QoS and QoE cannot be guaranteed when the considered cell is overloaded. Consequently, 5G systems require new strategies in order to avoid cell overloading.

The 5G network should be able to serve massive number of UEs in the extreme cases. For instance, data rates of several tens of Mbit/s should be supported for tens of thousands of UEs in crowded areas, such as stadiums or open-air events [START_REF]5G White Paper[END_REF]. Another example is providing 1 Gbit/s simultaneously to tens of UEs in the same office floor. 5G deals with a very large number of connections per square meter, and a huge traffic density. Moreover, it should be able to provide 10 ms end-to-end latency in general, and 1 ms end-to-end latency for the use cases that require extremely low latency [START_REF] Metis D6.6 | Final Report on the METIS 5G System Concept and Technology Roadmap[END_REF]. Thus, more sophisticated techniques are required to manage the available spectrum efficiently and to satisfy these QoS requirements.

In this article, we propose an inter-cellular scheduler for efficient support of multimedia services in multi-user 5G wireless networks. Our solution is called Inter-cellular Bandwidth Fair Sharing scheduler (IBFS). It dynamically allocates the available bandwidth between the cells, taking into account their relative difficulties to ensure high QoS. The concept is to help the overloaded cell by allocating the potential useless part of bandwidth of its neighbors to it. Consequently, more subcarriers are allocated to the overloaded cell, which helps it to absorb its traffic congestion and decrease user dissatisfaction without penalizing the donor cells that keep only the optimal quantity of radio resource units to ensure QoS to their own users.

This article also deals with the metric used to select the best candidate cell to receive additional bandwidth from its neighbors. Indeed, the logical metric could be to base our approach on the global cell traffic load, but we will show that it is not the optimal metric. Indeed, cell's mobiles have no reason to use the same data rate profiles (less or more elastic) and the same applications with the same delay constraints. Intra-cellular schedulers of the cells with more elastic traffic profile or more restrictive QoS constraints have a more difficult task to ensure QoS. They could require more bandwidth than the schedulers of other cells with higher global throughput but less restrictive QoS constraints or lower peak data rate demands. Consequently, the IBFS scheduler should be based on a reliable metric, which is a crucial issue for its performance. Our second contribution is to propose an adequate metric in order to select the best cell to help. This metric, called Mean Cell Packet Delay Outage Ratio (MCPDOR), measures the cell emergency to access to more radio resources, and it allows to always select the appropriate cell to help.

The rest of this article is organized as follows. Section II describes the state-of-the-art techniques, including methods that consider the inter-cellular scheduling approaches. Section III describes the IBFS solution, and gives details about our proposed algorithm. In Section IV, we present a detailed performance evaluation of our proposed solution through a simulation study. Section V concludes the article and summarizes our contributions.

II. RELATED WORK

Rather than promoting standardized Inter-Cell Interference Coordination (ICIC) techniques, the Third Generation Partnership Project (3GPP) provides support for proactive and reactive schemes, and it allows constructors and operators to configure a wide range of non-standardized ICIC techniques [START_REF] Fodor | Intercell interference coordination in ofdma networks and in the 3gpp long term evolution system[END_REF][START_REF] Asheralieva | Resource Allocation for LTE-Based Cognitive Radio Network with Queue Stability and Interference Constraints[END_REF][START_REF] Chen | Fast Efficient Spectrum Allocation and Heterogeneous Network Selection Based on Modified Dynamic Evolutionary Game[END_REF]. We classify these techniques into centralized, decentralized, and hybrid schemes.

The centralized approach requires the existence of a central management entity. It collects information related to channel quality and UE throughput demands. Then, it finds the optimal resource allocation between the existing base stations, and it also performs resource allocation among UEs (scheduling). Although the centralized approach offers the optimal resource allocation, a large amount of signaling messages is generated. The decentralized approach allows each cell to determine its own resource allocation, without the need to cooperate with other cells. This approach does not generate any additional signaling overhead, and it is characterized by a low implementation complexity. However, it does not guarantee the optimal resource allocation. Hybrid approaches are proposed as a compromise between centralized and decentralized approaches. In these schemes, a centralized control entity collects channel quality information and UE throughput demands in order to adjust resource allocation between the network cells, while RB allocation to the active UEs is locally performed by each base station.

The frequency reuse-N model, Fractional Frequency Reuse (FFR), and Soft Frequency Reuse (SFR) techniques [START_REF] Yassin | Survey of ICIC Techniques in LTE Networks under Various Mobile Environment Parameters[END_REF] have been widely suggested to minimize interference between adjacent cells. Traditionally, adjacent cells of a mobile network are grouped into clusters where only a portion of the available spectrum is used in each cell. Therefore, interference is reduced since frequency resources are not simultaneously used by adjacent base stations. If g is the number of cells within a cluster (also called: cluster size), then 1 g of the available subcarriers are used in each cell according to frequency reuse-g model. Figure 1 illustrates a mobile network where the frequency reuse-3 model is used to manage frequency resources distribution between the different cells.

Fig. 1: Frequency reuse-3 model FFR and SFR are not able to dynamically adapt to situations where throughput demands or UE positions are not homogeneously distributed between the different cells. To improve the performance of FFR, resource allocation and interference coordination problems are jointly considered in [START_REF] Assaad | Optimal fractional frequency reuse (ffr) in multicellular ofdma system[END_REF]. The proposed scheme searches for the optimal dimensions of cell-center and cell-edge zones as well as the optimal frequency reuse factor. In [START_REF] Gonzalez | Optimization of Soft Frequency Reuse for Irregular LTE Macrocellular Networks[END_REF], a multi-objective algorithm for improving SFR performance is proposed. It addresses the tradeoff between enhancing network capacity and improving cell-edge performance.

A matrix-based scheduling method is proposed in [START_REF] Ramachandran | Frequency Selective OFDMA Scheduler with Limited Feedback[END_REF], where the objective is to guarantee proportional fairness among the different UEs. In fact, UEs with good channel conditions and low average past throughputs are allowed to receive more resources. However, this technique does not modify resource allocation between network cells. Thus, inter-cell interference problems are not alleviated.

In this context, we introduce a heuristic resource allocation algorithm that aims at reducing Inter-Cell Interference (ICI) and improving user satisfaction. The proposed IBFS scheduler is a hybrid ICIC approach that consists of two phases: in the first phase, bandwidth sharing between the different cells is adjusted by a central controller that manages a multi-cell cluster after receiving the necessary information from the different cells. In the second phase, resource allocation is delegated to the base stations, and UE scheduling is performed locally for each cell. It is a cooperative algorithm that dynamically adjusts resource allocation among the adjacent cells according to user satisfaction in each cell.

III. INTER-CELLULAR BANDWIDTH FAIR SHARING SCHEDULER (IBFS)

In this Section, we describe the core of the proposed IBFS algorithm. IBFS consists in fair sharing of the bandwidth between the different cells. We propose two versions: IBF S load that helps the cell having the highest traffic load (defined as the total amount of data that users of the cell want to receive and transmit), and IBF S M CP DOR that helps the cell characterized by the highest MCPDOR. In sub-section III.A, we will describe the global IBFS mechanism, and the different parameters used across this article are defined in table I. Discussion about M CP DOR and why IBF S M CP DOR outperforms IBF S load will be given in sub-section III.B.

A. IBFS algorithm

Our proposed IBFS mechanism (Fig. 2) operates as follows:

• Step 1: For each cell of the system, the inter-cellular scheduler refreshes the values of MCPDOR for IBF S M CP DOR and respectively the traffic load for IBF S load . IBFS goes to the next step.

• Step 2: IBFS selects the cell that has the highest MCPDOR value for IBF S M CP DOR , with the highest traffic load for IBF S load . This cell is denoted r. r will be the cell to help in this scheduling occurrence. All the cells in its neighborhood are potential donor cells. IBFS goes to the next step.

• Substep 3: Among all the k cells in the neighborhood of r and for each group of band g different than the group of r, IBFS determines the leader donor cell d g that has the highest portion W g(r) (k) of the band g r . This step allows to detect and select a donor cell that could have received previously the highest part of bandwidth from r in order to restitute it. If W g,k is not null, IBFS goes to step 3.1. Otherwise, this group has no leader donor cell and the inter-cell scheduler goes to step 3.2.

-Substep 3.1: For each leader donor's group, IBFS restitutes from d g a total amount of frequency equal to Q transf er to r. This restitution is also made from d g to the cells of the same groups of r neighboring d g . This avoids future potential frequency blocking. In addition, if the cells in the neighborhood of r and of the same group d g used frequency included in this restitution, IBFS also restitute them following the same rules. IBFS goes to step 4.

-Substep 3.2: If IBFS reaches this substep, this is because IBFS tries to help r not thanks to bandwidth restitution, but taking the own bandwidth of donor cells (frequency of their band W g(k) (k)) for the frequency transfer. This requires some additionnal verification. Even in the case of a cell that has no users in its coverage zone, we consider that this cell must never lend the totality of its bandwidth to its neighbors otherwise the cell disapears. We define a minimum bandwidth W min which represents the part of the bandwidth that a cell must never lend to the other cells in order to always be able to offer a minimal service. Thanks to W min , if a new user appears, he will always have minimal radio resource units available to get connected (if W min is not enough, IBFS will adequalty share the available bandwidth between the cells in the next occurrence, and it will allocate more frequency resources to this cell). Consequently, for each group of band g and for each potential donor cell k of the considered group, IBFS checks whether the total bandwidth W g(k) (k) minus Q transf er is greater than or equal to W min . If this condition is respected2 , IBFS transfers Q transf er from all the donor cells to the cell r and their respective neighbors included in the band g r . Otherwise, helping r from this group of band is impossible, and the scheduling process ends for this group without any transfer. IBFS goes to step 4.

• Step 4: End of the scheduling process. In order to conclude this section, we would detail one point that merit more explanation. IBFS helps cells that experience difficulties by taking frequency resources from its neighborhood. As we described in step 3, restitution (step 3.1) must be always favored when possible. Indeed, it is less costly for the system compared to the simple transfer (step 3.2). For example, if g max = 3, giving Q transf er to help a cell means taking Q transf er from three cells in the neighborhood of r, while restitution means taking Q transf er from the leader donor and less than or equal to Q transf er from the two other concerned cells.

B. Cell selection metric

Considering that the cell to help is always the cell with the highest traffic load (IBF S load solution) is not always optimal. Indeed, the crucial objective of IBFS is to fully support 5G multimedia transmission services, including the widest range of services [START_REF] Metis D1.1 | Scenarios, Requirements and KPIs for 5G Mobile and Wireless System[END_REF]: VoIP, videoconference, email, file transfer... This requires the coexistence of delay sensitive flows with tight delay constraints and elastic traffic pattern as well as non real time traffic with looser delay constraints. For the intracellular scheduler, the most difficult flows to manage are unquestionably the delay sensitive flows. Since cells of the 5G system will manage users with different services, it appears that the cell having the highest traffic load is not the one that experiences the worst Quality of Experience (QoE). Another cell with less traffic load can have users with more delay sensitive and more elastic flows. In this case, the IBF S load solution will not help the cell in need.

The best solution is to select the cell that has the highest difficulties to satisfy its users. However measuring user satisfaction is a very difficult task in modern networks. The used applications are more and more varied, and require different management techniques with different QoS constraints such as jitter, mean delay, or guaranteed data rate. Considering the diversity of all the applied applications, measuring if the application is satisfied or not is really challenging. In this article, an additional contribution is to propose a new metric (the Mean Cell Packet Delay Outage Ratio M CP DOR) to measure cells users satisfaction in a generic approach, which takes into account all the potential QoS constraints to be satisfied in a simple step. M CP DOR does not provide feedbacks about the nature of the problem that the applications can meet in the cell, but it alerts whether the applications of the cell users have their QoS constraints satisfied in the network or not. IBF S M CP DOR protocol selects the cell to help thanks to MCPDOR. This will avoid making mistakes in the cell selection, and it allows to always help the one that has the most of difficulties.

MCPDOR of the cell i is the average of the Packet Delay Outage Ratio (PDOR) of all the users' service flows in this cell: M CP DOR i = P DOR Total number of user's service flows in the cell .

We define a service flow as a traffic stream and its QoS profile, in a given transmission direction. A mobile may have multiple service flows both in the uplink and in the downlink. An application may also use several service flows enabling for instance the implementation of Unequal Error Protection schemes in the physical layer. Each service flow possesses its own transmission buffer. The QoS profile is defined as the set of parameters that characterizes the QoS requirements of a service flow mainly in terms of data integrity and delay. In the following, data integrity requirements are specified by a Bit Error Rate (BER) target, which we denote by BER target . Delay requirements are specified at the packet level. We assume that traffic streams are organized at the MAC level in blocks of bits of constant size that we call packets. The packet delay is defined as the time between the arrival of the packet in the transmission buffer and the time of its reception by the mobile or the access point. This delay is roughly equal to the packet waiting time in the service flow transmission buffer neglecting the transmission and propagation delays. The packet delay can be directly calculated in the downlink by the access point. In the uplink, this information is known by the user that computes the PDOR and regularly signals it to the access point for the IBF S P DOR bandwidth management. Adequately specifying the delay requirements is challenging. We believe that the meaningful constraint is a limitation of the occurrences of large delay values. By analogy with the concept of outage used in system coverage planning, we define the concept of delay outage.

A service flow is in delay outage when its packets experience a delay greater than a given application specific threshold denoted T h. We define the Packet Delay Outage Ratio (P DOR) experienced by each service flow as the percentage of packets that do not meet the delay threshold T h among the total number of transmitted packets:

P DOR = Total flow's packets not transmitted/received on time (after th) Total packet transmitted/received .

(

) 2
The experienced PDOR value is tracked all along the lifetime of the service flows: at each transmission of a packet of service flow, the total number of packets whose delay exceeds the delay threshold T h divided by the total number of packets transmitted since the beginning of the connection is computed. Additionally, we define the Packet Delay Outage Ratio target, denoted P DOR target3 , as the maximum ratio of packets that may be delivered after the delay threshold. This characterizes the delay requirements of any service flow in a generic approach. Figure 3 illustrates an example cumulative distribution of the packet delay of service flow at a given time.

The objective of the IBF S M CP DOR protocol is to regulate the experienced PDOR along with the lifetime of the service flow such that its value stays below the target PDOR in each cell. This ensures the satisfaction of the delay requirements at a short time scale.

IV. PERFORMANCES EVALUATION

A. Simulation setup and assumptions

Performance evaluation results are obtained using discrete event simulations. We consider Orthogonal Frequency Division Multiplexing (OFDM) transmission technique that has clearly emerged for future broadband wireless multimedia networks (4G and 5G systems) and is already widely implemented in most recent wireless systems like 802.11a/g or 802. [START_REF] Fodor | Intercell interference coordination in ofdma networks and in the 3gpp long term evolution system[END_REF]. Traffic load and channel conditions vary independently over the time for each user in each cell. The channel gain model on each subcarrier considers free space path loss and multipath Rayleigh fading [START_REF] Proakis | Digital Communications[END_REF][START_REF] Steele | Mobile Communications[END_REF][START_REF] Goldsmith | Wireless Communications[END_REF][START_REF] Parsons | The Mobile Radio Propagation Channel[END_REF]. We assume that mobiles run videoconference applications. This demanding type of applications generates a high volume of data with high sporadicity and requires tight delay constraints which substantially complicates the task of the scheduler. We assume that each mobile has only one service flow with a traffic composed of an MPEG-4 video stream [START_REF] Baey | Modeling MPEG4 video traffic based on a customization of the DBMAP[END_REF] and an AMR voice stream [START_REF] Brady | A model for generating on-off speech patterns in two-way conversation[END_REF] with a BER target taken equal to 10 -3 and a delay threshold T h equal to 100 ms. The IBFS algorithm is proposed for a generic reuse-g deployment and it will be compared to the traditional REUSE-3 model. The cell numbers in a cluster are defined following Fig. 4. In 5G wireless context, for each cell, users can have different traffic profiles. In this scenario, we assign users with high variable bit rate to the cell number 1 , while all the other cells (cell 2, 3, 4, 5, 6 and 7) have users with less variable traffic. In addition, the global traffic load of these cells is 15% higher than that of the cell 1. In this context, even with less global traffic load, cell 1 is the cell that will experience more difficulties, since high data burst can appear due to more elastic traffics that cause high delay peaks and high users dissatisfaction.

In this context, the frequency reuse-3 model provides a MCPDOR equal to 9% in cell 1, while the other cells have MCPDOR near to 0%. This leads to high mobile dissatisfaction in cell 1. This bad result is due to the fact that reuse-3 never helps a cell that is in difficulties so this leads to the highest global mean packet delay (Fig. 5(a)), highest MCPDOR (Fig. 5(b)) and highest user dissatisfaction (Fig. 5(c)) in the system.

IBF S load slightly solves this problem. It takes bandwidth from other cells when cell 1 experiences high data rate burst that overpasses other cell traffic load, in order to help it to ensure user QoE. However, sometimes, IBF S load can make some sub-optimal decisions. The cell that is selected to receive bandwidth (cell with the highest traffic load) may not be the cell that has the highest difficulties. It could appear that this cell has not the worst radio conditions or its delay sensitive flows are not the hardest to satisfy in the system. Based on the MCPDOR, the selection is more accurate with IBF S M CP DOR that outperforms IBF S load and widely outperforms the frequency reuse-3 model (Fig. 5(c)).

C. Scenario 2: overloaded cells

In this subsection we compare the performance of IBFS with that of the well-known reuse-3 technique in a scenario that illustrates a special event occurrence (like sport event, protest march, etc.). We consider exceptional gathering of users in a cell (Fig. 6). They stay in cell number 1 during a certain time, then they move to another cell (cell number 2) and come back (Fig. 7 7(c) represents the mean traffic load of the other cells of the system that have the same mean traffic load over time. We notice that following the users moves, cell 1 is overloaded, then cell 2 and, once again cell 1.

During the first period, the cell 1 experiences high difficulties to guarantee high QoS and QoE to its users due to the high load. Figure 8 shows the average radio resources used by each solution over time. The frequency reuse-3 model does not provide any aid to the overloaded cells. Consequently, with reuse-3, the cell 1 uses a large amount of its bandwidth (Fig. 8(a)) and sometimes has a lack of available radio resources to manage the burst of data. This induces high delay peaks as shown Fig. 9(a). On the contrary IBFS solution supports cells that experience difficulties. IBF S load takes bandwidth from the cells that have few data to manage in order to give radio resources to the cell that has more load. IBF S M CP DOR applies the same principle by selecting the cell that has the highest number of packet in delay outage in order to give it more radio resources from the other cells that experience no difficulties. According to the two solutions, more bandwidth is allocated to the cell 1 when it is overloaded, and it has consequently more capacity to absorb the data burst (Fig. 8(a)). This allows IBF S load and IBF S M CP DOR to highly reduce peak of delay (Fig. 10(a), 11(a)) with a mean average packet delay in all the system equal to 23 ms and 22.75 ms, respectively. However, the frequency reuse-3 technique provides a mean average packet delay equal to 67.25 ms.

Figure 12 shows the global results of the system for the cells 1 and 2 that experience high traffic load period and for the other cells, that are represented here by the cell 4. The frequency reuse-3 model failed to ensure high QoE. 24% of the packets of the cell 1 did not have their QoS constraints satisfied (Fig. 12(a)) and this results in 37% of dissatisfaction ratio (Fig. 12(b)). This performance is slightly the same for cell 2 that experiences smaller traffic congestion over the time. On the contrary, we note that cell 4 (representative of all similar other cells that have not experienced congestion) easily succeeds to provide high QoE to its users since its available bandwidth is widely outsized. This over provisioning of useless bandwidth for the cell that does not experience difficulties to ensure QoE is a waste. If offered to overloaded cells, this bandwidth could offer high breathing space allowing to increase QoE in the system. IBFS adequately adapts bandwidth sharing between the cells that require more radio resources. This scheduler widely decreases the global amount of packets that arrive in delay outage in the period of cell overloading (Fig. 12(a)). This leads to dividing the global users dissatisfaction in cells 1 and 2 by more than 2 without penalizing the donor cells (Fig. 12(b)). In addition, these results show that the metric used to select the cell to help is crucial. They underline that IBF S M CP DOR outperforms IBF S load despite its good performance (Fig. [START_REF] Hanzo | MIMO-OFDM for LTE, WiFi and WIMAX: Coherent Versus non-Coherent and Cooperative Turbo-Transceivers[END_REF][START_REF] Domenica | A Radio Resource Management Scheduling Algorithm for Self-Organizing Femtocells[END_REF][START_REF] Chandrasekhar | Spectrum Allocation in Tiered Cellular Networks[END_REF][START_REF] Ramachandran | Frequency Selective OFDMA Scheduler with Limited Feedback[END_REF][START_REF] Yoon | Interference Mitigation in Heterogeneous Cellular Networks of Macro and Femto Cells[END_REF][START_REF] Knopp | Information capacity and power control in single-cell multiuser communications[END_REF]. This is due to the fact that high traffic load is a good indication to find the cell that might require the more assistance, but this is not sufficient enough, nor it is efficient in realistic wireless context. Delay constraints, jitter and BER must be also considered. MCPDOR verifies if these parameters are respected or not, and it is a better candidate than cell traffic load to estimate whether the scheduler succeeds or not in supporting users' traffic. The next scenario will provide complementary results that will reinforce this conclusion.

D. Scenario 3: cells with different radio conditions

In this scenario, we consider that all the cells have the same mean traffic load with an average of eight users per cell that are active at the same time. However, we assume that a cell (cell 1) is characterized by worst radio conditions in comparaison with other cells for a same path loss to users. For example, this can be due to a more dense/urban environment for this cell than the others which increases shadowing and multipath fading effects. Consequently, it is expected that users are more unsatisfied in cell 1 than in the other cells.

Figure 13 shows the users dissatisfaction results: in cell 1 that provides poor radio condition (Fig. 13(a)), in all other/normal cells (Fig. 13(b)) and the average in all the system (Fig. 13(c)). Since all the cells have the same global bandwidth with Reuse-3, we notice that with this method the users of the cell 1 (that represents extremely urbanized zone) are highly penalized with 19.5% of dissatisfaction versus 0.09% in the other cells.

Despite of the good results of IBF S load in previous scenarii, it is interesting to observe that, in this scenario, IBF S load is not efficient. Since this algorithm helps the cell that has the highest traffic load and since all the cells have globally the same traffic load, it allocates the same priority and the same mean amount of bandwidth to each cell. Consequently, IBF S load fails to help the cell 1 to manage its users. This is not due to the fact that the principle of IBFS is inefficient in this context but just that the metric chosen for selecting the cell to help is not adequate.

Indeed, on the contrary, IBF S M CP DOR succeeds to help users of cell 1. Due to bad radio conditions, their PDOR quickly increases and the MCPDOR of the cell 1 surpasses the MCPDOR of normal cells. Thanks to MCPDOR, IBF S M CP DOR adequately detects that the cell 1 needs more bandwidth than the other cells even if the traffic load is globally the same and efficiently shares the radio resources between the cells. The result is a dissatisfaction ratio equal to 7.12% for the users of cell 1 (dissatisfaction divided by 2.74 compared to the frequency Reuse-3 model), while the dissatisfaction of users of the other cells stays bellow 1% (results are 0.4% which can be neglected). Focusing on the global results in Fig. 13, the global user dissatisfaction is highly reduced.

V. CONCLUSION

Many works in intra-cellular scheduling have been done in order to increase system throughput, QoS and QoE. However, in 5G networks, many events can lead to a cell overloaded scenarii where all the current solutions fail to guarantee high user satisfaction. This article proposed a new inter-cellular MAC scheduling scheme in order to enhance the Quality of Experience in 4G and 5G wireless networks. It dynamically selects the cells that experience the highest difficulties in order to give them more radio resources from the cells that do not need them. Our solution is proposed in two versions. It helps the cell that has the highest traffic load, and the obtained results widely outperform traditional solutions. However, we are convinced that traffic load is not the most efficient criteria in order to select the cell that will receive more frequency resources. Consequently, a second contribution of this article is to take into consideration a new parameter able to always make the best decision. Simulation results and performance evaluations confirm this choice, and system performance is further improved. In future works, we will search for the optimal value of minimal bandwidth to guarantee to each cell. We will also search for the best tradeoff about the amount of bandwidth to take to the donor cell in order to optimize the beneficiary cell help, without decreasing the donor cell's QoE.

Fig. 2 :

 2 Fig. 2: IBFS scheduling algorithm flow chart.

Fig. 3 :

 3 Fig. 3: Example packet delay CDF and experienced PDOR.

Fig. 4 :

 4 Fig. 4: Cluster illustration.

  (a) Mean packet delay in the system. (b) Mean Packet delay Outage. (c) Mean users dissatisfaction over the time.

Fig. 5 :

 5 Fig. 5: Simulation resuts of the first scenario

  (a) and 7(b)). Cells 3, 4, 5, 6 and 7 experience normal traffic load, and have the same global cell throughput (Fig. 7(c)).

Fig. 6 :

 6 Fig. 6: performance evaluation scenario.

  (a) Traffic load of cell 1. (b) Traffic load of cell 2 (c) Traffic load of cell 3, 4, 5, 6, 7.

Fig. 7 :

 7 Fig. 7: System cells traffic load.

Figure

  Figures 7(a), 7(b) respectively show the traffic load over time for cell 1 and 2.Figure7(c) represents the mean traffic load of the other cells of the system that have the same mean traffic load over time. We notice that following the users moves, cell 1 is overloaded, then cell 2 and, once again cell 1.During the first period, the cell 1 experiences high difficulties to guarantee high QoS and QoE to its users due to the high load. Figure8shows the average radio resources used by each solution over time. The frequency reuse-3 model does not provide any aid to the overloaded cells. Consequently, with reuse-3, the cell 1 uses a large amount of its bandwidth (Fig.8(a)) and sometimes has a lack of available radio resources to manage the burst of data. This induces high delay peaks as shown Fig.9(a). On the contrary IBFS solution supports cells that experience difficulties. IBF S load takes bandwidth from the cells that have few data to manage in order to give radio resources to the cell that has more load. IBF S M CP DOR applies the same principle by selecting the cell that has the highest number of packet in delay outage in order to give it more radio resources from the other cells that experience no difficulties. According to the two solutions, more bandwidth is allocated to the cell 1 when it is overloaded, and it has consequently more capacity to absorb the data burst (Fig.8(a)). This allows IBF S load and IBF S M CP DOR to highly reduce peak of delay (Fig.10(a), 11(a)) with a mean average packet delay in all the system equal to 23 ms and 22.75 ms, respectively. However, the frequency reuse-3 technique provides a mean average packet delay equal to 67.25 ms.Figure12shows the global results of the system for the cells 1 and 2 that experience high traffic load period and for the other cells, that are represented here by the cell 4. The frequency reuse-3 model failed to ensure high QoE. 24% of the packets of the cell 1 did not have their QoS constraints satisfied (Fig.12(a)) and this results in 37% of dissatisfaction ratio (Fig.12(b)). This performance is slightly the same for cell 2 that experiences smaller traffic congestion over the time. On the contrary, we note that cell 4 (representative of all similar other cells that have not experienced congestion) easily succeeds to provide high QoE to its users since its available bandwidth is widely outsized. This over provisioning of

  (a) Mean Bandwidth usage ratio for cell 1. (b) Mean Bandwidth usage ratio for cell 2. (c) Mean Bandwidth usage ratio for cell 3, 4, 5, 6, 7.

Fig. 8 :

 8 Fig. 8: REUSE3 and IBFS Bandwidth usage ratio sharing comparaison.

Fig. 9 :

 9 Fig. 9: System cells mean delay with REUSE3.

Fig. 10 :

 10 Fig. 10: System cells mean delay with IBF S load .

Fig. 11 :

 11 Fig. 11: System cells mean delay with IBF S M CP DOR .

Fig. 12 :

 12 Fig. 12: Analysis of the respect of QoS constraints.

Fig. 13 :

 13 Fig. 13: Comparaison of users dissatisfaction for REU SE3, IBF S load and IBF S M CP DOR .

TABLE I :

 I List of Symbols

i index of the cell gi group of the cell i g index of the group of cells in a cluster (i.e. g is the number of different bandwidth groups in a cluster Reuse-g) gmax maximum number of different groups dg leader donor cell of group g k index of the cells in a specific group r cell selected to receive help from donor cell W g(i) (k) quantity of bandwidth, originally of the group g of cell i, and currently owned by the cell k Wmin quantity of the bandwidth that a cell cannot lend to other cells

also known as Maximum Carrier to Interference ratio (MaxC/I).

Note that in order to avoid interference, a cell can only use frequency given by its neighbors in the case where this cell has received this one from all its neighbors that are included in the band that originally contains this frequency.

a user can be considered as dissatisfied when its PDOR overpasses 5%, so P DORtarget is fixed to this value in this article.


Cédric Gueguen
email: cedric.gueguen@irisa.fr

Opportunistic Energy Aware Scheduler For Wireless Networks

Keywords: Wireless Network, Green Networking, Energy Consumption, Opportunistic Scheduling, Multiuser diversity

In the last decade, many research efforts have been done in order to increase the spectral efficiency of wireless communications. From now on, opportunistic resource allocations have emerged as the best way to reach this objective. They take into consideration the radio conditions in the allocation process. This allows to guarantee high system throughput and high Quality of Service (QoS). However, today, it is not sufficient anymore. Many climate problems have been underlined by the majority of world scientists and decreasing world greenhouse gas emission has become a necessity for the world's environment preservation. This requires to also reduce energy consumption in as much sectors as possible including wireless communication networks. This paper proposes to extend the opportunistic approach with the proposition of a new scheduling solution enables to significantly decrease the system energy consumption. Performance evaluations will show that the global energy consumption can be divided by 2 compared to existing schedulers without jeopardizing system efficiency.

I. INTRODUCTION

Wireless networks have become a key of the society development. However, in contrast with wired communications, wireless transmissions are subject to many channel impairments such as path loss, shadowing and multipath fading [START_REF] Goldsmith | Wireless Communications[END_REF]. These phenomena severely affect the transmission capabilities and in turn the energy consumption. In this context, the conventional access methods like Round Robin (RR) [START_REF] Nagle | On packet switches with infinite storage[END_REF] and Random Access (RA) are obsolete. They are not adapted to the wireless environment and providing poor throughput. The past decades have witnessed intense research efforts on wireless digital communications. Among all the studied resource allocation aproaches, one major has emerged and appeared in literature as the reference: opportunistic scheduling. Opportunistic schedulers preferably allocate the resources to the user(s) with the most favourable channel conditions at a given time. Taking benefit of time, multiuser and frequency diversity, they are able to maximize the system throughput. In this paper, two opportunistic schemes will be considered as references: Maximum Signal-to-Noise Ratio scheduler (MaxSNR) and Weighted Fair Opportunistic scheduler (WFO).

In MaxSNR, priority is given at each scheduling event to the users which have the greatest signal-to-noise ratio (SNR) [START_REF] Wong | Multiuser OFDM with adaptive subcarrier, bit, and power allocation[END_REF], [START_REF] Wang | An OFDM-TDMA/SA MAC protocol with QoS constraints for broadband wireless LANs[END_REF]. It dynamically adapts the modulation and coding. Taking profit of multiuser and frequency diversity, this allows to always make the most efficient use of the radio resource and coming closer to the Shannon limit.

MaxSNR strongly increases the system throughput. However, it manages any service differentiation and shows a severe lack of fairness in regards to users with different positions [START_REF] Gueguen | Scheduling in OFDM wireless networks without tradeoff between fairness and throughput[END_REF], different types of traffic, etc. Many works have been done in order to correct these problems with the proposition of a new opportunistic scheduler called WFO [START_REF] Gueguen | A fair opportunistic access scheme for multiuser OFDM wireless networks[END_REF]. This scheduler extends the classical cross-layer approach taking into account both the physical layer specificities (transmission conditions) and the higher layer constraints (traffic patterns, QoS constraints, Bit Error Rate...).This results in an efficient scheme which guarantees the high service differentiation required by all multimedia networks. Providing a same spectral efficiency than MaxSNR but with more fairness, WFO bandwidth management is able to ensure great Quality of Experience (QoE) for a very large amount of wireless network users.

Despite that these two acknowledged schemes provide high spectral efficiency and, for the WFO, high QoS: this is not sufficient anymore. Today, the world's growing population and the growing global energy demands bring to a critical situation. They generate unsustainable development both environmental and economical. Consequently, reducing power consumption has become a necessity including in wireless networks and resources allocation process. This paper brings a new solution called "Opportunistic Energy Aware" scheduler (OEA). It proposes to radically change the classical opportunistic radio resource mapping. Built in an extended cross layer approach, its main principle is to minimize energy consumption exploiting active-sleep mode and channel condition together. Physical layer information is used in order to take advantage of time, frequency and multi-user diversities. Like previous opportunistic schemes, this will allow to reach high system capacity. Higher layer information are take into account in order to achieve the QoS requirements, in particular the Bit Error Rate (BER target ). At the MAC level, users buffer occupancy and device power consumption information are exploited in order to compress transmission time (i.e, active mode) acknowledged to be highly greedy in energy. At each scheduling event, OEA determines the best transmission opportunities and finds the most profitable resource mapping in terms of number of transmitted bits per Watt. Maximizing the sleeping-time duration while taking into account the channel conditions in the allocation process, OEA allows to make a better usage of radio resources than previous scheme, reaching high spectral efficiency and greatly reducing energy consumption.

The remainder of this paper is organized as follows. Section 2 provides a description of the system under study. Section 3 describes our proposition. Section 4 presents a detailed performance evaluation and Section 5 concludes the paper.

II. CONTEXT DESCRIPTION

In this paper, we consider a centralized and synchronized approach [START_REF] De Beek | A time and frequency synchronization scheme for multiuser OFDM[END_REF] and we focus on the allocation of radio resources among the set of users situated in the coverage zone of an access point. We focus our study in Multiple Input Multiple Output (MIMO) -OFDM technology which is acknowledged for outperforming other strategies in terms of spectral efficiency [START_REF] Jayaweera | Energy analysis of mimo techniques in wireless sensor networks[END_REF]. This allows to make a more efficient use of the scarce bandwidth since it offers the possibilities to take a maximal benefit of the frequency diversity in the opportunistic scheduling. The total available bandwidth is divided in subfrequency bands, i.e. subcarriers. The radio resource is further divided in the time domain in frames. Each frame is itself divided in Time Slots (TS) of constant duration. The TS duration is an integer multiple of the OFDM symbol duration. The number of subcarriers is chosen so that the width of each sub-frequency band is less than the coherence bandwidth of the channel. Moreover, the frame duration is fixed to a value much smaller than the coherence time of the channel. With these assumptions, the transmission on each subcarrier is subject to flat fading with a channel state that can be considered static during each frame. However, the transmissions performed on different subcarriers by different users are assumed to have independent channel state values [START_REF] Andrews | Providing quality of service over a shared wireless link[END_REF]. In addition, the elementary resource unit (RU) is defined as any (subcarrier, TS) pair. Each of this RU may be allocated to any user with a specific modulation order. On each RU, the modulation scheme is QAM with a modulation order adapted to the channel state between the access point and the user to which it is allocated. This provides the flexible resource allocation framework required for opportunistic scheduling.

III. OPPORTUNISTIC ENERGY AWARE SCHEDULER

The OEA scheduler, located in the access node, grants RUs to each user as a function of: its QoS profile (BER target...), its different energy consumption mode (in active mode and sleep mode), its traffic backlog, its channel state... The QoS profile is signaled in the connection establishment phase. Additionally, knowledge of the channel state is supposed to be available at the receiver [START_REF] Li | Channel estimation for OFDM systems with transmitter diversity in mobile wireless channels[END_REF]. It is estimated by the access node based on the SNR of the signal sent by each user during the signaling phase. Assuming that the channel state is stable on a scale of 50 ms [START_REF] Truman | A measurement-based characterization of the time variation of an indoor wireless channel[END_REF], and using a frame duration of 2 ms, the users shall transmit their control information alternatively on each subcarrier so that the access node may refresh the channel state information once every 25 frames.

The OEA scheduling algorithm relies on weights that set the dynamic priorities for allocating the radio resources. These weights are built in order to satisfy two major objectives: system throughput maximization and energy consumption minimization as explained below.

A. System Throughput Maximization

In wireless communication systems, the resources are limited. The frequency of commercial cellular systems are mostly obtained through the purchase which is always very expensive and scarce. Moreover, the infrastructure and equipment of wireless communication system are also very expensive. Therefore, a major problem of system design and optimization is to take full advantage of limited frequency and hardware resources in wireless communication systems and to ensure Quality of Service under the premise of providing the highest possible capacity. To achieve this goal, the resource management is the very important part.

The OEA optimizes the system throughput in a MAC/PHY opportunistic approach. Data integrity requirements of users are enforced considering each user independently adapting the modulation and the transmit power to the user specific channel state. At each scheduling epoch, the scheduler computes the maximum number of bits m k,n that can be transmitted in a TS of subcarrier n if assigned to user k, for all k and all n. This number of bits is limited by two main factors: the data integrity requirement and the supported modulation orders.

The bit error probability is upper bounded by the symbol error probability [START_REF] Wong | Multiuser OFDM with adaptive subcarrier, bit, and power allocation[END_REF] and the TS duration is assumed equal to the duration T s of an OFDM symbol. The required received power P r (q, k) for transmitting q bits in a RU while keeping below the data integrity requirement BER target,k of user k is a function of the modulation type, its order and the singlesided power spectral density of noise N 0 . For QAM and a modulation order M on a flat fading channel [START_REF] Proakis | Digital Communications[END_REF]:

P r (q, k) = 2N 0 3T s erf c -1 BER target,k 2 2 (M -1), (1)
where M = 2 q and erf c is the complementary error function. P r (q, k) may also be determined in practice based on BER history and updated according to information collected on experienced BER. The transmit power P k,n of user k on subcarrier n is upper bounded to a value P max which complies with the transmit Power Spectral Density regulation:

P k,n ≤ P max . (2)
Given the channel gain a k,n experienced by user k on subcarrier n (including path loss and Rayleigh fading):

P r (q, k) ≤ a k,n P max . (3)
Hence, the maximum number of bits q k,n of user k which can be transmitted on a TS of subcarrier n while keeping below its BER target is:

q k,n ≤     log2   1 + 3P max × T s × a k,n 2N 0 erf c -1 BER target,k 2 2         . ( 4
)
We further assume that the supported QAM modulation orders are limited such as q belongs to the set S = {0, 2, 4, . . . , q max }. Hence, the maximum number of bits m k,n that will be transmitted on a TS of subcarrier n if this RU is allocated to the service flow k is:

m k,n = max {q ∈ S, q ≤ q k,n } . ( 5
)
MaxSNR based schemes allocate the RU to the flows which have the greatest m k,n values. This bandwidth allocation strategy maximizes the bandwidth usage efficiency but highly suffers of a inefficient energy management. In order to provide energy consumption minimization while preserving the system throughput maximization, a new parameter is introduced. It will modulate these pure opportunistic resource allocations.

B. Energy consumption minimization

The second major objective of the OEA is to provide efficient energy management in addition to the system throughput optimization. Existing opportunistic resource mapping (as MaxSNR or WFO for example) are basically horizontals. Due to flat fading during a frame, often a same user strictly experienced the greatest channel condition on each TS of a subcarrier. Consequently, with classical opportunistic schedulers, a same user often receives all the TS of a subcarrier and need to stay in active mode during a long time. Note that we can potentially have one different selected user on each available subcarrier. Consequently, during all TS, many selected users can not be set in sleep mode. They consume many power for transmitting few bit during a long time (with many allocated TS but on few subcarriers). To conclude, opportunistic scheduling is acknowledged as the best way to manage wireless resources, maximizing the system capacity and providing QoS but they need to be more energy efficient.

The OEA scheduler proposes to drastically minimize the energy consumption in particular in increasing the sleeping mode duration. This is done while trying to preserve the benefit of opportunistic strategies on system capacity. In order to achieve this goal, our proposition is to extend the classical opportunistic cross-layer design to obtain a new vertical opportunistic resource mapping (Fig. 1(b)). When a user is in active mode, OEA tries to benefit from its activation in order to compress its time of activity and to transmit more bit per "used" TS. Like this, OEA allows to significantly increase sleeping mode duration and energy preservation. OEA scheduler computes an "Energy Transmission Cost" (ET C k ) parameter (in Watt). It is based on the energy cost of user k to transmit on a RU:

ET C k = A k * Cn k + (1 -A k ) * C1 k , (6)
When the user k is in active mode, A k = 1 else, A k = 0 (i.e. sleep mode). In addition, Cn k and C1 k are two constants (in Watt). C1 k represents the energy needed to wake up the user k from the sleep mode to the active mode and to transmit on its first allocated subcarrier. Cn k represents the energy needed to transmit on a n th allocated subcarrier (the user is already awake). Cn k value is lower than C1 k since the cost to transmit some suplementary bits is lower than the cost to move to sleep mode to active mode 1 .

The OEA scheduling principle is then to allocate a TS of subcarrier n to the user k which provides the best "Bit Transmission Profitability" ("BT P k,n " in bit/Watt) such as:

BT P k,n = m k,n /ET C k (7)
This dynamic priorities allows to significantly reduce energy consumption while optimizing the global system throughput. Indeed, OEA is designed to found, in the resource allocation, the user which provides the best trade-off between these two objectives : transmitting the maximum number of bit and consuming the less energy than possible. This provides the most profitable allocation in term of bit/Watt.

Thanks to the BT P k,n parameters, higher priority are given to the users already awake but also to the users able to transmit the higher number of bit on the considered RU. Since Cn k << C1 k , it is often more profitable in terms of energy consumption to continue to allocate the subcarriers to a same user rather to choose a new one for a negligible throughput gain. This allow to compress the user active mode session, maximizing the sleeping session duration and helping to reduce the energy consumption. However, if the active users experience poor radio condition, it will be more profitable to take benefit of the good potential throughput of a sleeping user which could experienced really better radio conditions due to low multipath fading. In this case, OEA scheduler set this user in active mode and allocate to him the considered RU since it can provide a better ratio of transmitted bits by Watt, i.e a better bit transmission profitability.

IV. PERFORMANCE EVALUATIONS

A. Context and simulation setup

Performance evaluation results are obtained using OPNET discrete event simulations [START_REF]OPNET simulator[END_REF]. In the simulations, we assume a total number n sub of 16 subcarriers and a total number n ts of 50 TS in a frame. In addition, C1 k and Cn k are fixed respectively equal to 157 mW and 46.8 mW, for all k in accordance with measured hardware consumption. The channel gain model on each subcarrier assumes free space path loss and multipath Rayleigh fading [START_REF] Goldsmith | Wireless Communications[END_REF].The BER target is taken equal to 10 -3 and the average bit rate of each Variable Bit Rate (VBR) source is assume equal to 150 Kbps.

B. Radio resources managements

Fig. 2 shows the behaviours of each scheduler in the resource allocation. Fig. 2(a) represents the average number of TS used by each user in each frame. A TS is considered as "used" by a user if the user receive at least one RU of this TS in a frame and consequently that the user can not be set in sleep mode during this one. The higher this value, the more will be users active mode duration (greedy in energy) and the more will be the energy consumption. Fig. 2(b) represents the mean number of allocated subcarrier to a same user per allocated TS (this value is range between 1 and 16). Fig. 2(c) shows the average global amount of RUs allocated to each user in a frame.

First, we can observe that with each scheduler, if we have only one user in the system, this user is not in competition with other and it receives all the subcarrier of the first TS of the frame (n max = 16, Fig. 2(b)). In average, after the allocation of all the subcarrier of approximately 5 TS (Fig. 2(a)), the user throughput requirement is satisfied and no more allocation has been done. Note that for only 1 user in the sytem, each scheduler also provides the same allocation results since opportunistic scheduling show their benefits only if multiuser diversity exists.

Then, we can observe that, when the number of user increase, RR share the subcarrier of each TS with fairness between all users. This is due to the nature of the RR scheduling with alternativly serve user in RUs. Having less subcarrier per TS. Each user need to use more TS which will induce more energy consumption. If we increase the number of user more than 9 (Fig. 2(a)), the system capacity is exceeded and each user used the maximum available TS in the system (t max = 50).

Regarding MaxSNR and WFO results, we can observe that, like with RR, the subcarriers of each TS are shared between users (Fig. 2(b)). The higher the number of user, the less is the number of subcarrier allocated to a user in a TS and the more is the number of TS needed by the users. However few differences exist with RR results. First, the MaxSNR and WFO curve are above RR curve (Fig. 2(b)). In addition, the gradient of the curve is lower than the RR curve (Fig. 2(a)). Indeed, with these schedulers, the RUs are not simply shared between user but opportunistically allocated to the users with the best radio conditions during a frame and it is statistically possible to have a same user with good condition on many subcarrier in a same frame. In addition, results of Fig. 2(c) show that MaxSNR and WFO take advantage of the multiuser diversity to maximise the number of bit transmitted per RU. Higher the number of users in the system, the more efficient is the allocation process in term of system throughput since less RU are need by user.

OEA encourages vertical resource mapping. This explains why the OEA curve is below the others in fig 2(a) and above in Fig. 2(b). This shows that very few user are simultaneously in active mode. OEA wakes up only the adequate number of user in order keep good spectral efficiency. Consequenlty, the TS's subcarriers are shared between user but only if necessary for the transmission profitability. This will ensure a good trade-off between throughput and energy consumption.

C. Energy consumption

Fig. 3(a) and Fig. 3(b) respectively show the user and the global energy consumption. Focusing on RR curves, we can observe that, between 1 and 9 users, the mean user's energy consumption increases with the number of users. This is due to the sharing of the TS's subcarrier between users (Fig. 2(b)) which induces the active mode duration increase (Fig. 2(a)). With more of 9 users, the system is overloaded and RR fails to provide the sufficient amount of RUs required by each user. They are often forced to stay in sleep mode even with data to transmit due to the lack of RUs. More often in sleep mode, the user consumed less energy over the time. This explains why with more than 9 user, the RR curve decrease (Fig. 3(a)).

Like RR, MaxSNR and WFO share the TS's subcarriers between users which provides an energy consumption increase with the traffic load. However this share is less fair since it is statistically possible to have a same user with good condition on many subcarrier in a same frame. This corresponds to a more vertical allocation than RR. In addition, the usage of multi-user diversity allows to use less RUs by user when their number increase. This allows to reduce the user active mode duration and consequently the energy consumption. This explain why opportunistic scheduler curves grow more slowly than RR.

Then, let's focuses on OEA energy consumption results. We can observe that, instead to use all the multiuser diversity in order to exclusively improve system capacity, OEA uses it in order to also reduce energy consumption. Higher the number of users in the system, the more thrifty is the allocation process. In addition, when the system capacity is exceeded with OEA (more than 12 users), it is interresting to note that the global energy consumption is stabilized to a low level. Contrary to other schedulers which wake up many users in order to transmit few bits simutanously on many TS's subcarriers, OEA prefers to maximize the RUs utility (i.e. the number of bits transmitted per Watt consumed). Whatever the traffic load considered, few, but always the sufficient number of users, are simultaneously activate in order to provide good, but not energy expensive, spectral efficiency. Increasing the sleep mode duration, OEA provides an important energy gain if compared to other schedulers.

D. Spectral efficiency

Highly relies on Fig. 2(c), the Fig. 4 shows the spectral efficiency of each allocation and their abilities to optimized or not the system capacity. MaxSNR and WFO are acknowledged as the best schedulers regarding this network performance criterion. The OEA, which besides minimizes energy consumption, can not ensure the same level of throughput optimization but it is interesting to note that this strategy stay opportunistic and thoughput efficient. Indeed, OEA scheduler takes benefit of radio conditions and multi-user diversity. This provides a throuhput gain which is nevertheless significant compared to RR scheduler.

V. CONCLUSION

The OEA scheduler is a part of sustainable development approach. Maximizing the number of bits transmitted per Watt consumed, the OEA scheduler allows to reduce energy consumption of wireless communication networks without compromising too much their effectiveness characterized has high spectral efficiency. This proposed research can have several impacts: environmental and economicals. First, OEA allows significant reduction of the energy footprint of wireless computer equipment. Consequently, it helps to decrease the alarming world greenhouse gas emissions. Then, OEA increases the lifetime of our equipment on battery. This allows reducing electrical load time and lowering operating costs. Future works will focus on OEA improvements. We will try to minor the existing trade-off between throughput maximization and energy consumption decrease.

  (a) Classical and horizontal opportunistic management of RUs. (b) Vertical Opportunistic Energy Aware management of RUs.

Fig. 1 .

 1 Fig. 1. Conceptual scheduling strategies.

  (a) TS allocations per frame. (b) Subcarriers allocations per TS.(c) Global RUs allocations.

Fig. 2 .Fig. 3 .

 23 Fig. 2. Schedulers radio resources managements.

Fig. 4 .

 4 Fig. 4. System capacity study.

C k >> Cn k , i.e. energy needed to be active >> energy required to transmit on an additionnal RU if user already set in active mode