Filippo Rebecchi
email: filippo.rebecchi@lip6.fr

Lorenzo Valerio
email: lorenzo.valerio@iit.cnr.it

Raffaele Bruno
email: raffaele.bruno@iit.cnr.it

Vania Conan
email: vania.conan@thalesgroup.com

Marcelo Dias De Amorim

Andrea Passarella
email: a.passarella@iit.cnr.it

A Joint Multicast/D2D Learning-Based Approach to LTE Traffic Offloading

Keywords: Cellular multicast, mobile data offloading, device-to-device communications, reinforcement learning, multi-armed bandit

Multicast is the obvious choice for disseminating popular data on cellular networks. In spite of having better spectral efficiency than unicast, its performance is bounded by the user with the worst channel in the cell. To overcome this limitation, we propose to combine multicast with device-to-device (D2D) communications over an orthogonal channel. Such a strategy improves the efficiency of the dissemination process while saving resources at the base station. It is quite challenging, however, to decide which users should be served through multicast transmissions and which ones should receive the content via D2D communications. The progress of content dissemination through D2D communications depends on how users meet while on the move. The optimal decision for each content depends both on the status of the LTE channel (when the multicast transmission is executed) and on the evolution of the mobility process of the nodes from there on. We propose a learning solution based on a multi-armed bandit algorithm that dynamically selects the best allocation of users between multicast and D2D to guarantee the timely delivery of data. Numerical evaluations are performed to compare our proposal with the state-of-the-art scheme and an optimal but unfeasible strategy. We confirm that a proper mix of multicast and D2D helps operators save resources at the base station and that the learning algorithm can autonomously find a near-optimal configuration in a reasonable time.

Introduction

Long Term Evolution (LTE) and LTE-A offer significant higher rates than their preceding technologies -up to 100 Mbps for LTE, and 500 Mbps for LTE-A [START_REF] Dahlman | 4G: LTE/LTE-advanced for mobile broadband[END_REF]. Despite these numbers, delivering large amounts of data over cellular networks remains a challenge, with the radio access being the bottleneck. The situation will also be exacerbated by the predicted spectacular increase in mobile data demand for the coming years. It is foreseen that the demand for mobile data will grow at an exponential rate (57% compound annual growth rate between 2014 and 2019), while capacity will not match this pace (increasing only by a factor of 2 in the same time frame) [START_REF]Cisco. Cisco visual networking index: Global mobile data traffic forecast update[END_REF]. Therefore, it is of paramount importance to find alternative solutions to reduce the burden on the cellular network.

It is possible to save considerable amount of cellular resources when one needs to distribute the same piece of data to a community of interested users grouped in a limited geographical area (i.e., when data requests are spatially and temporally correlated). In such situations, two possible approaches may address effectively the needs of cellular operators: cellular multicast 1 and mobile data offloading.

Lately, field trials for video service during crowded sport events like the super-bowl or soccer matches have tested the effectiveness of cellular multicast [START_REF] Tim | LTE Broadcast is coming, the new generation mobile TV[END_REF][START_REF] Honig | Verizon demonstrating LTE Multicast during Super Bowl XLVIII[END_REF]. By exploiting the broadcast nature of the wireless channel, multicast benefits from a single unidirectional link, shared among several user equipments (UEs) inside the same radio cell. This permits, in principle, a more efficient use of network resources with respect to the case where each UE is reached through dedicated unicast transmissions. However, despite its attractive features, cellular multicast presents intrinsic and still unresolved issues that limit its exploitation: (i) the rate of adaptation to the worst channel user and (ii) the lack of reliability. The reasons behind these inefficiencies are investigated in detail in Section 2.

On the other hand, re-routing part of the traffic to other types of network represents a very promising alternative to reduce the burden on the cellular network infrastructure [START_REF] Barbera | Data offloading in social mobile networks through {VIP} delegation[END_REF][START_REF] Han | Mobile data offloading through opportunistic communications and social participation[END_REF][START_REF] Rebecchi | DROiD: Adapting to individual mobility pays off in mobile data offloading[END_REF]. Data offloading is considered as one of the key enabling technologies for 5G cellular network architectures [START_REF] Gpp | TSG SA: Feasibility study for proximity services (ProSe) (release 12)[END_REF][START_REF] Rebecchi | Data offloading techniques in cellular networks: A survey[END_REF]. In this paper, we consider one type of data offloading based on opportunistic networks leveraging direct device-to-device (D2D) communications between mobile devices. While opportunistic networks offer additional capacity that can be leveraged to reduce congestion on the cellular network, timely delivery of content is an issue, due to the variability of human mobility and the resulting stochastic nature of forwarding events. When data must be delivered within a mandatory deadline, we need offloading solutions that reduce as much as possible the traffic carried by the cellular network, meeting at the same time the deadline.

In this paper, we explore the combination of opportunistic offloading and multicasting. Well-positioned UEs can participate in mitigating the inefficiencies of cellular multicast (where the UE with the worst radio conditions inherently limits the efficiency) by handing over content to nodes with bad cellular channel through opportunistic transmissions. Despite the benefits of this hybrid distribution strategy are evident, in its design, we faced several challenges specific to the opportunistic and wireless domains: (i) performance of the opportunistic delivery hinges on the mobility pattern of users, (ii) opportunistic networks can only guarantee a probabilistic assurance of data reception, and (iii) understanding which fraction of UEs to reach through multicast and D2D transmissions is vital to offer a minimal QoS while guaranteeing resource savings.

Since a truly optimal solution is not conceivable without precise knowledge of future contact patterns, we attack the problem from a more practical point of view. We apply a Reinforcement Learning (RL) approach to decide which fraction of UEs should be reached through a multicast transmission and which should be served using opportunistic communications. A central controller installed at the eNB (evolved Node B) decides, for each packet of a content item to be disseminated, which fraction of users to reach with a multicast transmission. Each decision results in a certain use of the cellular network resources, which generates a reward associated to that choice. This reward is then used to guide (probabilistically) the future choices of the controller. Due to the many similarities in the formulation, we adopt the well-known multi-armed bandit technique to implement this algorithm [START_REF] Sutton | Introduction to reinforcement learning[END_REF].

To fully understand the performance of this joint multicast/D2D approach, it is necessary to evaluate the amount of radio resources consumed at the base station. This motivates us to introduce a finer model of radio resource consumption with respect to those used in the literature. While this is well understood in the literature on physical aspects of cellular communications, existing proposals for opportunistic offloading do not consider heterogeneous channel conditions, assuming that delivering a given amount of data (i.e., a fixed size packet) to different users has always the same cost for the operator [START_REF] Li | Multiple mobile data offloading through disruption tolerant networks[END_REF][START_REF] Han | Mobile data offloading through opportunistic communications and social participation[END_REF]. Such an assumption does not hold in reality, as resource consumption varies according to the channel condition experienced by each user. In other words, transmitting the same piece of content to users with different channel conditions does lead to uneven costs at the eNB. To the best of our knowledge, we are the first to evaluate this aspect in the context of data offloading.

As a summary, the main contributions of this paper are:

• Joint offloading strategy. Our strategy employs direct D2D opportunistic communications to assist the cellular distribution via multicast.

• RL-based multicast selection. The multicast emission is driven by a RL algorithm. Exploiting the knowledge of past rounds, the algorithm tunes the set of nodes to be reached via multicast, allowing substantial savings at the cellular base stations.

• Fine-grained resource consumption analysis.

We evaluate resource consumption employing the smallest radio resource unit that can be assigned to users for data transmission. This analysis shows that existing macroscopic techniques fail to capture actual system behaviors.

• Performance evaluation. The RL strategy permits saving consistent amount of radio resources at the eNB (up to 90% for different mobility models and short delay-tolerances). Even in the worst case, the RL approach approximates an unfeasible strategy that picks the best fixed fraction of multicast users after exhaustive search.

The remainder of the paper is organized as follows. We first present the motivation of our work in Section 2. Two different multi-armed bandit approaches are described along the joint distribution strategy in Section 3. We evaluate the proposed system using a realistic packet-level simulator in Section 4. We postpone the discussion on the related work to Section 5 so that the reader has enough material to capture our original contribution. We finally conclude the paper and identify topics for future research in Section 6.

Background and motivation

Opportunistic networks are self-organizing mobile networks where the existence of simultaneous end-to-end paths between nodes is not taken for granted, while disconnections and network partitions are the rule [START_REF] Pelusi | Opportunistic networking: data forwarding in disconnected mobile ad hoc networks[END_REF] Apart from unicast transmissions, new LTE releases propose also an optimized broadcast/multicast service through eMBMS (enhanced Multimedia Broadcast Multicast Service), a point-to-multipoint specification to transmit control/data information from the cellular base station (eNB) to a group of user entities (UEs) [START_REF] Lecompte | Evolved multimedia broadcast/multicast service (eMBMS) in LTE-advanced: overview and rel-11 enhancements[END_REF]. UEs interested in receiving multicast transmissions can subscribe -granted they are authorized -to the eMBMS service. After the announcement of all the existing services, subscribed UEs can join one or more multicast group(s) of interest, following the procedure detailed in [START_REF] Araniti | Resource management of multicast services over LTE. Convergence of Broadband[END_REF]. All the users belonging to the same multicast group receive the same transmission. Channel heterogeneity (time varying and user-dependent) reduces the effectiveness of multicast because the eNB uses a single MCS for the entire multicast group. The selected MCS should be robust enough to ensure the successful reception and decoding of the data-frame for each UE in the multicast group. Thus, the worst channel among all the receivers dictates performance. It follows that an increase in the number of users in the multicast group boosts the probability that at least one user experiences bad channel conditions, degrading the overall throughput [START_REF] Bhatia | ICAM: integrated cellular and ad hoc multicast[END_REF].

To exemplify the influence of poor quality users, we simulate a 500 × 500 m 2 single LTE cell with an increasing number of randomly located receivers using the ns-3 simulator [START_REF]Network simulator[END_REF]. Fig. 1 presents the minimum average channel quality in terms of CQI, reported at the eNB by users. In this configuration, users are static, and their location is uniformly distributed inside the eNB coverage area. From Fig. 1, we highlight two aspects. The first one is that, when users are uniformly placed, there is a high chance of having at least one user experiencing a poor channel quality (e.g., even with only 10 users in the cell, we still have the worst CQIs not greater than about 4). The second point is that this behavior worsens as more users are added in the area. The result is that augmenting the number of multicast receivers clearly affects the attainable cell throughput. Table 1 shows also that an UE with the best CQI could theoretically receive 37 times the throughput of a user with the lowest index. This greatly motivates us to investigate methods to cope with the inefficiencies of multicast. We exploit the presence of alternative direct connectivity options available at UEs to relieve the cellular infrastructure load, while reducing the influence of users experiencing poor radio conditions.

A reinforcement learning approach for data dissemination

3.1. Content dissemination strategy and problem formulation We address the dissemination of popular content to a set of N mobile UEs inside a single LTE cell. Each UE is a multi-homed device that embeds both a LTE interface and a short-range technology that allows D2D communications. In simulation, we consider IEEE 802.11g, however, the future integration of D2D capabilities within the LTE standard could be employed as well [START_REF] Doppler | Device-to-device communication as an underlay to lte-advanced networks[END_REF] 2 . We want to transmit content with a guaranteed maximum reception delay D, at the smallest cost for the cellular infrastructure, i.e., using the minimum number of RBs. To this end, we exploit the possibilities offered by D2D connectivity and store-andcarry forwarding. In the following, we assume standard epidemic dissemination as far as opportunistic communications are concerned. Specifically, instead of addressing all interested UEs with a single multicast transmissionfollowing the discussion in Section 2, this will likely result in a high cost in terms of used RBs -we address only a subset of the UEs (those in better channel quality), and exploit opportunistic D2D communications to reach the others. The challenging issue is that opportunistic dissemination is, by definition, unreliable, as it depends on many factors outside of the control of the cellular infrastructure (e.g., movement pattern of nodes, variable density of opportunistic neighbors, or interference on the D2D channel). Using only opportunistic communications it is thus impossible, in general, to guarantee the maximum reception delays to all the nodes. To achieve guaranteed delivery, we consider an acknowledgment mechanism, and panic zone retransmissions similarly to the proposition in [START_REF] Whitbeck | Push-and-track: Saving infrastructure bandwidth through opportunistic forwarding[END_REF]. Accordingly, all UEs that receive the required content send an acknowledgment to the central controller situated at the eNB through LTE. When the reception delay reaches its maximum value D, the central controller instructs the eNB to push all the missing data to UEs that have not been served yet using unicast transmissions. Of course, unicast transmissions represent the last opportunity to assure data reception 3 . In this scheme, the cost of disseminating content to interested UEs comes from i) the cost of the initial multicast transmission, and ii) the cost of the unicast transmissions in the panic zone.

Fig. 2 offers a representative example of the proposed dissemination strategy. To avoid the penalty due to the 2 D2D communications will be soon possible within the LTE technology (and spectrum). However, in the proposed LTE-D2D extension, the eNB decides, as part of its scheduling process, which devices should communicate directly, not exploiting future direct communication opportunities enabled by nodes mobility. 3 The need for a guaranteed reception method is a common issue for multicast due to its shared nature. UEs have no assurance of reception because the radio channel could suddenly degrade during data reception (e.g., due to fast fading or mobility). For this reason, mechanisms similar to panic retransmission are considered in several works in the literature [START_REF] Tan | Towards optimum hybrid arq with rateless codes for real-time wireless multicast[END_REF][START_REF] Rahman | Hybrid multicast-unicast streaming over mobile networks[END_REF]. presence of UEs experiencing severe channel conditions, the eNB emits at a modulation that leaves them in outage. This is equivalent to restrict the access to the multicast group only to those UEs in "relatively" good channel conditions.

In the opportunistic dissemination phase, outaged UEs benefit from nearby nodes, fetching data through out-ofband D2D transmissions. This cooperative strategy is expected to be more efficient in terms of cellular resource consumption than multicast alone, given that the cellular rate increases and the D2D links typically exploit a much larger bandwidth than cellular communications. Finally, panic injections assure data reception to all users. It is clear that such a scheme admits an optimal operating point. Reducing the set of UEs reached via the initial multicast transmission results in a lower cost for the multicast transmission. However, this may be paid with an additional cost for unicast transmissions in the panic zone, if the remaining UEs are not reached quickly enough through opportunistic dissemination. The challenge to identify this optimal operating point is that the cost of each possible configuration depends on future mobility of nodes, which is unknown at the time the multicast transmission needs to be configured.

More precisely, the problem we address is the following: how to select the initial set of (seed) users to be reached using multicast transmissions with the objective of minimizing the total number of physical resource blocks (RBs) needed for content dissemination.

In our scheme, we employ a single parameter I 0 to address this problem. I 0 is the fraction of UEs that should be reached via the initial multicast transmission. Assuming that, when the multicast transmission is configured, UEs are ranked by decreasing value of CQI, this means that the eNB reaches at least the best I 0 UEs in terms of channel quality. Optimally configuring I 0 is not trivial, because, while the cost of the multicast transmission is deterministic at the time when it is configured, the cost of the needed unicast transmissions in the panic zone is a stochastic variable, which depends on the pattern of mobility of UEs in the next D seconds.

We model this problem as a multi-armed bandit problem and we solve it through a Reinforcement Learning (RL) approach. As explained in detail in the rest of the section, our scheme is able to learn autonomously the best value of I 0 by observing the effect of different configurations on the resulting cost of disseminating a given content. Assuming that multiple content items need to be disseminated over time to a given set of UEs, our scheme actually learns the best probability distribution over the possible values of I 0 , that results in the minimum cost in terms of RBs for a given stochastic mobility pattern of UEs. Without prior knowledge on the mobility patterns, and given that mobility is stochastic, learning the best distribution of I 0 is the only practical choice for a learning framework.

Multi-armed bandit background

Let us now briefly introduce the general formulation of a multi-armed bandit problem (bandit for short). In the simplest case, there is a set of K unknown probability distributions F D1 , ..., F D k with associated expected values µ 1 , ..., µ k and variances σ 2 1 , ..., σ 2 k . For the sake of illustration, let us assume that F Di describes the distribution of the outcomes of the i th arm on a slot machine (the bandit); the player is viewed as a gambler whose goal is to collect as much money as possible by pulling these arms over many turns. Initially, the distributions F Di are completely unknown to the player. At each turn, t = 1, 2, ..., the player selects an arm, with index j(t), and obtains a reward r(t) ∼ D j(t) . Since the player does not know in advance the distribution F Di , it has to explicitly test the i th action with a trial-and-error search. Therefore, the player has two conflicting objectives: on the one hand, finding out which distribution has the highest expected value (or explore the distribution space); on the other hand, gaining as much rewards as possible while playing (or exploit its knowledge). Reinforcement Learning algorithms specify a probabilistic strategy by which the player should choose an arm j(t) at each turn. Clearly, the effectiveness of the solution depends on how the gambler handles the exploration/exploitation dilemma when testing the different arms iteratively. Exploitation maximizes its reward at present time; at the same time, exploration may lead to a greater total reward in the future.

Learning algorithm

The general multi-armed bandit formulation can be specialized as follows. First of all, in our problem each arm of the bandit corresponds to a different I 0 threshold (recall: the fraction of UEs that receive a packet via the multicast emission). Thus, K is the number of different thresholds chosen for multicast emission. It follows that F Di is the distribution of the amount of RBs employed during the entire dissemination process when I 0 = i is used as threshold. More precisely, D i = m i + X i , where m i represents the amount of RBs necessary for a multicast transmission at the MCS needed to reach only the best I 0 ranked UEs, and X i is the random variable that models the RBs used for the unicast transmissions during the panic zone. Note that, while m i is fixed and known in advance, X i depends on many factors, including the set of seeds that are activated, the network topology and node mobility, as well as the dissemination strategy. In our case, each turn corresponds to the dissemination of a content composed of a multitude of packets that are transmitted independently. After the deadline, the reward for each threshold is updated based on the outcome of the dissemination of each packet composing the content. Assuming that I 0 = i was used for the n th multicast transmission, the obtained reward is computed as:

µ i (n) = 1 m i + x i (n) , (1)
where x i (n) is the number of RBs that are used for the unicast transmissions in the n th panic zone. Note that the higher the number of used RBs and the lower the reward. To dynamically estimate the average reward µ i (n) for each value of I 0 we use a classical exponential moving average with rate α:

µ i (n) = αµ i (n -1) + (1 -α)µ i (n). (2)
Now, we must define the policy to select at time n+1 the next I 0 value given the knowledge of the average rewards estimated at time n. Different learning methods have been proposed in the literature for the armed bandit problems.

The simplest one is the -greedy algorithm that selects with probability (1 -) the value of I 0 with the maximum accumulated reward (greedy action), while it selects with probability one of the remaining I 0 values at random (with uniform probability) independently of the reward estimates (exploration action). More formally, let π i(n) be the probability to set I 0 = i for the transmission of the n th packet, and i * (n) = argmax i µ i (n -1). Then, in the -greedy algorithm it holds that π i * (n) = 1 -.

Another class of learning algorithms is known as pursuit methods, in which the π probabilities are selected to strengthen the last greedy selection. Specifically, let i * (n) be the greedy value of I 0 defined above. Then, just prior to selecting the CQI for the transmission of the n th packet, the greedy probability is reinforced as follows

π i * (n) (n) = π i * (n) (n-1)+β[π M AX -π i * (n) (n-1)], (3)
while all the non-greedy probabilities are updated as follows

π i(n) (n) = π i(n) (n-1)+β[π M IN -π i(n) (n-1)], i = i * .(4)
Here π M AX , π M IN are respectively the upper and the lower bound that the probability π i(n) (n) can take ∀i, n. In equations 3 and 4 the greedy choice is increased, but never more than π M AX , and each non-greedy choice is reduced, but no less than π M IN . This guarantees that the pursuit method is able to cope with the possible non-stationarity of the problem we are considering, i.e. the distribution of rewards can change over time due to the underlying mobility. Compared to the pursuit method, the -greedy strategy presents a threshold effect by which the choice that has the maximum accumulated reward immediately gets the highest probability. In the pursuit method, the likelihood of the same option gradually increases by a factor β proportional to the distance to the maximum bound π M AX (similar remarks hold for the non greedy choices). So in pursuit the evolution of the distribution over the possible choices is less drastic and more gradual.

Wrap-up of the dissemination strategy

As a summary, the key principles behind the joint multicast/D2D approach are: i) at initial time, the eNB sends data to the best I 0 CQI-ranked UEs through a single multicast emission. A RL algorithm is employed to learn the experimental distribution (π i * (n)) for the I 0 parameter; ii) the UEs that have received the data through the multicast emission start disseminating it in a D2D (epidemic) fashion; iii) before the maximum deadline D, we define a time interval, a panic zone where all the nodes that have not yet retrieved the content (either with the initial multicast emission or in D2D fashion) receive it through unicast cellular retransmissions. The proposed scheme allows all UEs to receive data by the deadline (as long as the panic zone is sufficiently large). It adapts to different deadlines -the larger ones allowing for more D2D dissemination. Its performance relies on the RL algorithm that permits the cellular base-station to learn by experience the best transmission rate for each multicast emission.

Performance Evaluation

In this section, we analyze the offloading performance of the proposed RL algorithms while distributing popular content under different UEs mobility and density configurations.

ns-3 implementation

We implemented the multi-armed bandit algorithm using ns-3, a packet-level network simulator which implements the full LTE and Wi-Fi stacks, allowing for very realistic simulations [START_REF] Baldo | The ns-3 lte module by the lena project[END_REF][START_REF] Azzarelli | Description and development of moto simulation tool environment release b[END_REF]. Since ns-3 does not natively support cellular multicast, we modified it by implementing an additional module that interacts with the packet scheduler to emulate single-cell multicast. The multicast module decides, upon each transmission, the fraction of UEs to be reached directly, i.e. the I 0 parameter, based on the multi-armed bandit algorithm presented in Section 3. It receives the CQI from the standard LTE modules, and sets the MCS of the multicast transmission to reach the intended UEs. We fix the bandwidth allocated for the multicast service at 5 MHz. 3GPP standard recommends not to reserve more than 60% of RBs to multicast [START_REF] Lecompte | Evolved multimedia broadcast/multicast service (eMBMS) in LTE-advanced: overview and rel-11 enhancements[END_REF], so a 5 MHz value could represent respectively 50% or 25% of RBs in a typical 10 or 20 MHz deployment. The other simulation parameters for the LTE cell are listed in Table 2. Additionally, we implemented DTN store-carry-forward routing mechanism at UEs to support D2D opportunistic communications. This is an implementation of the conventional epidemic forwarding mechanism [START_REF] Vahdat | Epidemic routing for partially connected ad hoc networks[END_REF]. Regardless of its reception method, an unexpired packet can be forwarded on the Wi-Fi interface upon meeting with neighbors. Neighbor discovery is implemented through a beaconing protocol. UEs periodically (every 250 ms) broadcast beacon messages containing their identifier and the list of buffered packets. Upon beacon reception, UEs update their vicinity information and can transmit packets opportunistically.

Implementation assumptions: In simulation we made the following simplifications:

• HARQ-level retransmissions and RLC-level feedback are disabled in multicast. This is a reasonable assumption: otherwise the eNB should merge the ack/nack messages received from all the UEs, and decide which is the best retransmission strategy. Instead, we guarantee the maximum content delivery time D with panic zone retransmissions.

• The PUCCH channel is employed to acknowledge data reception towards the eNB. Panic zone retransmissions are then triggered looking at the list of received acknowledgments.

• The RL algorithm proposed in Section 3.3 acts as a packet scheduler. It employs a cross-layer design at the eNB. By exploiting signaling from physical layer (i.e., the amount of RBs consumed and the CQI for each UEs are used to evaluate the reward), the algorithm decides the MCS of each multicast transmission.

We are aware that our simulation-based evaluation has some limits. First, we consider a simplified version of the eMBMS standard. The proposed approach requires deeper integration with the eNB scheduler. Moreover, we leave out the discussion on incentives that are vital to convince users to agree to spend their battery and storage resources to relay data to someone else. This is an orthogonal prob-lem addressed in the opportunistic networking literature through appropriate mechanisms (see, for example, [START_REF] Zhuo | Win-Coupon: An incentive framework for 3G traffic offloading[END_REF]).

Experimental setup

In evaluation, we consider a single eNB, a remote server that provides the content, and several LTE multicast capable UEs implementing also the DTN routing mechanism. To assess the capability of the RL strategies to save resources at the eNB in a high load scenario, we consider all the UEs connected to the same eNB as requiring the content. Simulations are conducted in pedestrian scenarios such as a shopping mall or a crowded touristic landmark. Possible contents of interest include location based broadcasting with advertisement, geo-relevant data, alerts, public utility information and over-the-air software updates.

Each content of interest is formed by a UDP constant bit-rate downlink flow, with packet size of 2048 bytes and a total size of 8 MB (in total, 4000 packets). Each packet is distributed independently using the RL algorithm described in Section 3. The traffic has a loose QoS guarantee on a per-content basis (meaning that individual packets can be delayed, but the entire content must reach the user within the given deadline D).

We implement the mobility of UEs according to two models: Random Way Point (RWP) and SMOOTH [START_REF] Munjal | Smooth: a simple way to model human mobility[END_REF]. First, we evaluate the RWP model, where UEs move over the simulation area with speed falling between 1 and 2.5 m/s (pedestrian speed). 4 In this scenario, the eNB is placed in the center of the cell. Next, using SMOOTH, we focus on scenarios where the average distribution of the UEs is uneven across the cell. Apart from providing very realistic mobility, SMOOTH makes it possible to define landmark locations of different weights, where nodes head with variable probabilities. User density depends on the location, and we have a strong correlation between user positions (namely, around popular landmarks where contacts are frequent). Fig. 3, shows a synthetic map of waypoints generated with SMOOTH employing the parameters listed in Table 3. Taking advantage of this trace, we target two separate scenarios: one where the eNB is close to the most popular landmark (150,50), and the other, where the eNB is placed near the landmark with the lower weight (50,150). We test our RL algorithms in these two extreme scenarios with different correlations of movements.

All the simulation results are averages over 10 independent runs of 1 hour duration. Unless otherwise stated, confidence intervals are not shown, as they are very tight (usually in the order of 5% of the average value). We assess the performance for different values of N (the number of users inside the cell) and D (the maximum reception delay), so as to evaluate performance under different loads. 4 While the realism of the RWP model is questionable in general, it has been demonstrated that it realistically reproduces movement patterns of groups of users moving in a confined physical area [START_REF] Boldrini | HCMM: Modelling spatial and temporal properties of human mobility driven by users social relationships[END_REF]. Therefore, we consider it appropriate for simulation in our target scenario. 3. eNB location for SMOOTH-A is set at (150, 50) and eNB location for SMOOTH-B is set at (50,150)

Reference strategies

We compare our proposal with four different strategies for content delivery. The main performance indexes we consider are (i) the number of RBs used by the eNB to deliver the content by the stated deadline, and (ii) the offloading ratio, i.e. the fraction of UEs that are served via D2D opportunistic communications with respect to the case where only multicast is used. Additionally, we are also concerned about the convergence time of the bandit algorithm. The considered strategies are the following ones:

• Multicast-only is the basic strategy, where UEs have no other means than the cellular network to receive data. In this case, the eNB always schedules multicast transmissions to reach all UEs. Unicast transmissions in the panic zone are used to guarantee the delivery of lost packets.

• Fixed-best maintains a static allocation of multicast users (I 0 is fixed during all the simulation duration).

Since the best value of I 0 is unknown, we ran extensive simulations to find experimentally the I 0 value that minimizes the total number of RBs used for disseminating all contents. This strategy is clearly unfeasible in practice, but is used as a benchmark for the rest of the strategies, that are based on learning methods.

• -greedy implements the epsilon greedy version of the multi-armed bandit algorithm described in Section 3. It selects the greedy value of I 0 following Eq. 2. In our implementation, we selected = 0.05 and α = 0.5. We motivate this choice as a trade-off between different requirements. We need to maintain the exploration phase active in order to counter the possible non-stationarity of the underlying process. However, transmitting with a wrong MCS (i.e., giving too much weight to the exploration phase) can lead to significant efficiency loss (due to the panic re-transmissions).

• Pursuit selects the I 0 transmission probability following Eqs. 3 and 4. In this case, the transmission probability pursues the greedy action by adapting the likelihood of emission to the temporal evolution of the system. For fairness, we employed the same update value of the -greedy strategy for α. Moreover, we fixed β = 0.3, π M IN = 0.01, π M IN = 0.95. We will explain better these choices later on.

Finally, both RL strategies are initialized very conservatively, with 95% of multicast emissions targeting all the present UEs. Specifically, considering N UEs in the system, we have that Π i=N (0) = 0.95, and Π i =N (0) = 0.05/(N -1).

Fixed allocation vs. learning algorithms

Fig. 4 provides a summary of the simulation results in terms of RB savings (aggregate over 1 hour of simulation, and at the end of 1h of learning) for the two considered algorithms, related to the basic Multicast-only approach and the RWP scenario. In general, the RL solution to the joint multicast-D2D problem approaches and even surpasses Fixed-best in more than one occasion. For instance, the pursuit method allows saving up to 88% of RBs for the 90s scenario. This result confirms that the right synergy in the utilization of multicast and D2D resources allows for significant resource savings at the eNB. Even with shorter deadlines, the pursuit method performs consistently, saving at least 54% of RBs after the training phase. The -greedy method instead, while behaving well in most cases, suffers from short deadlines and many UEs.

RL strategies can autonomously find the trade-off between multicast and D2D transmissions in a reasonable time (always less than 1 hour) -without extensively search all the entire parameter space (as Fixed-best does). The behavior of the bandit methods (pursuit and -greedy) and Fixed-best differs significantly. Our evaluation is based on the RBs usage at the eNB (Fig. 5), and on the reception method (Fig. 6). We fix the deadline, varying the number of multicast UEs in the cell from 10 to 50. Intuitively, increasing the number of UEs demanding for the same content should require more infrastructure resources. On the other hand, the number of contact opportunities increases as well, offering more possibilities to offload the network. We analyze the detailed evolution of our strategy considering only the shorter deadline (30 s) that represents the worst-case scenario. A similar analysis can be done with the longer deadlines (plotted in Appendix A).

Unlike many other works in the offloading literature, that focus on savings in terms of messages, the use of the ns-3 simulator allows us to evaluate precisely the amount of radio resources consumed at the eNB. As a qualitative example, Fig. 5 depicts the learning process compared to fixed allocations for the tightest deadline considered (30 sec). Pursuit and -greedy strategies need time to learn the most appropriate distribution for I 0 . Once trained, their performance is often on par or even better than the best fixed-value strategy represented by Fixed-best, where the value of I 0 is fixed and pre-computed in advance. In this latter strategy, performance is stable over all the dissemination periods, but this figure is the outcome of an extensive trial and error simulation phase. Another advantage of the RL techniques is that, even when trained, they continue to explore the solution space, being able to cope with the possible non-stationarity of the contact process that rules the opportunistic diffusion. Conversely, Fixed-best is locked to a static value of the parameter I 0 and insensitive to mobility pattern variations.

Comparison between -greedy and pursuit method

The -greedy method, owing to the hard selection of the greedy value of I 0 , does not fit well scenarios where the underlying opportunistic diffusion process has significant variability. In these cases, pursuit is a better match. On the other hand, if performance of the opportunistic diffusion Time (min) Resource blocks x 1000 q q q q q q q q q q q q q q q q q q q q q q q q q q 0 5 10 15 20 [START_REF] Spinella | Integration of ad-hoc networks with infrastructured systems for multicast services provisioning[END_REF] Resource blocks x 1000 q q q q q q q q q q q q q q q q q q q q q q q q q q 0 5 10 15 20 [START_REF] Spinella | Integration of ad-hoc networks with infrastructured systems for multicast services provisioning[END_REF] Resource blocks x 1000 q q q q q q q q q q q q q q q q q q q q q q q q q q 0 5 10 15 20 [START_REF] Spinella | Integration of ad-hoc networks with infrastructured systems for multicast services provisioning[END_REF] Time (min) fraction of delivered packets q q q q q q q q q q q q q q q q q q q q q q q q q q 0 5 10 15 20 [START_REF] Spinella | Integration of ad-hoc networks with infrastructured systems for multicast services provisioning[END_REF] Time (min) fraction of delivered packets q q q q q q q q q q q q q q q q q q q q q q q q q q 0 5 10 15 20 [START_REF] Spinella | Integration of ad-hoc networks with infrastructured systems for multicast services provisioning[END_REF] Time (min) fraction of delivered packets q q q q q q q q q q q q q q q q q q q q q q q q q q 0 5 10 15 20 [START_REF] Spinella | Integration of ad-hoc networks with infrastructured systems for multicast services provisioning[END_REF] process is stable -i.e., in case of larger deadlines --greedy allows for quicker convergence times (e.g., Fig. 5(a)). In many cases, even when -greedy fails to converge, pursuit approaches the behavior of the fixed-best strategy. This depends on the fact that -greedy always selects the value of I 0 that maximizes the expected rewards. Instead, pursuit has an indirect selection method that better adapts to the temporal evolution of the system. The added complexity is however beneficial, as it translates into improved performance (Fig. 5(b) and Fig. 5(c)). The reinforcement given by Eq. 3, allows smoothing out the inherent variations in epidemic diffusion that prevent the proper prediction in the -greedy method. The effect appears when the number of targeted UEs increases while keeping a tight deadline (i.e., 30 s in our evaluations). In those scenarios, the variability in performance of the opportunistic diffusion prevents the -greedy method to learn properly the best distribution for selecting I 0 . An example of this effect is illustrated in Fig. 5(c). In that case, the pursuit method succeeds in matching the fixed-best strategy. The -greedy method instead diverges nearly instantaneously, failing to learn an appropriate policy.

Detailed evaluation of the pursuit method

Considering the same deadline, increasing the number of UEs has the effect of reducing the share of D2D transmissions. We plot in Fig. 6 the fraction of packets partitioned by their reception method for the pursuit method. While a larger number of UEs should multiply the contact opportunities, many of them are not adequately exploited because UEs can transmit only to one neighbor at a time. The result is that fixing the deadline, the share of UEs addressed through D2D transmissions is upper bounded. Note, however, that for a larger number of UEs, even though the fraction of UEs addressed through D2D transmission is limited (e.g., 20% in the case of 50 UEs), the resulting advantage in terms of RB saving is much higher (around 55% for that case, from results in Fig. 4). In this case, the learning algorithm understands that it is better to serve the 20% of the UEs that are experiencing bad cellular quality through D2D. Serving them through multicast is expected to result in a too high cost in terms of RBs, due to the need of reducing too much the MCS. On the other hand, decreasing too much the share of UEs served by the multicast transmission brings the opposite effect, with a considerable amount of RBs spent for unicast transmissions in the panic zone.

Focusing on the convergence time, we note that there is a discrepancy between Fig. 5 and Fig. 6. Looking at Fig. 6, it seems that the convergence time is less than 10 minutes. Instead, the real convergence time, in terms of RBs, happens much later in time, and depends on the fine-tuning of I 0 . The anomaly is justified by the fact that even a minimal amount of unicast retransmissions in the panic zone (such as those that may happen before finding Time (min) Expected rewards q q q q q q q q q q q q q q q q q q q q q q q q q q q I0 > 0.8 0.8 > I0 > 0.6 0.6 > I0 > 0. Expected rewards q q q q q q q q q q q q q q q q q q q q q q q q q q q I0 > 0.8 0.8 > I0 > 0.6 0.6 > I0 > 0. Expected rewards q q q q q q q q q q q q q q q q q q q q q q q q q q q I0 > 0.8 0.8 > I0 > 0.6 0.6 > I0 > 0. the best value for I 0 ) consumes much more resources than a single multicast emission.

In two scenarios out of three (namely for 10 and 50 UEs), there is a set of values for I 0 that performs clearly better than the others do. In the 25 UEs scenario instead, the distribution of I 0 is more spread out. There is a clear tendency to prefer higher values of I 0 though, in the range between 0.2 and 0.6. Considering the detailed mechanisms of the pursuit method described in Sec. 3.3, Fig. 7 compares the average reward µ i . We quantized the values of I 0 to form five levels. The best I 0 value is the one that is not affected too much by the loss in spectral efficiency due to the reduced multicast rate, but at the same time can guarantee a low penalty due to unicast panic re-injections. In the 10 UEs scenario, emitting with a multicast rate that targets one or two users (I 0 ≤ 0.2) is sufficient to achieve high efficiency. On the other hand, we note that increasing the multicast group size, the best distribution of I 0 shifts towards higher values. Intuitively, the penalty due to panic re-injections is extremely severe in these cases and the pursuit algorithm tends to allocate more seeders in the opportunistic domain. Finally, the emission probability follows the pattern of the rewards with the exception that the greedy probability is always reinforced until the value π M AX and the non-greedy probabilities are reduced until π M IN .

Correlated mobility patterns

In order to better understand the performance of our RL approach, we evaluated the two SMOOTH scenarios introduced in Section 4.2. First, we ran the SMOOTH-A scenario with reception delay of 30 s, then, we switched to the SMOOTH-B scenario, maintaining the simulation parameters unchanged. We are interested in how our system reacts under different UEs densities in various locations and realistic mobility patterns. Figs. 8 and9 propose the simulation results respectively for the SMOOTH-A and the SMOOTH-B scenarios with 25 UEs. As an initial consideration, if we focus only on the baseline Multicast-only strategy, we notice that the resource consumption is around three times higher than in the RWP case. The explanation for this observation lies in the fact that in both SMOOTH scenarios the eNB is skewed from the center of the mobility area (as it was in RWP). It follows that edge-located UEs are farther away from the eNB than in the RWP scenario (from Fig. 3 and Pythagoras' theorem, the additional distance between a UE and the eNB can be up to 70 m), worsening the overall transmission efficiency and increasing the amount of resources consumed at the eNB. This motivates even more the needs for efficient offloading strategies, since slight deterioration in channel quality brings large spikes in resource usage. Instead, since in the SMOOTH-A and SMOOTH-B scenarios the eNB location is symmetrical with respect to the center, we cannot perceive appreciable differences between the baseline RB consumption in these two scenarios.

In the SMOOTH-A scenario both RL algorithms converge towards an optimal level of resource usage very quickly (as shown in Fig. 8). Offloading savings due to D2D transmissions top a stunning 92% against the classic multicast-only mechanism. Indeed, the density of UEs around the eNB permits, most of the time, a resourceefficient multicast emission (i.e., with very high MCS) that covers at the same time a large part of requests. This is illustrated in Fig. 8(b), where we can appreciate that the larger fraction of packets are received through multicast. UEs heading towards distant waypoints are likely reached with D2D transmissions (representing around 40% of packet receptions). We notice that, in this scenario, -greedy benefits from its simple update strategy, showing a faster convergence time than pursuit.

Fig. 9 depicts the simulation results for the SMOOTH-B scenario. Evaluation outcomes differ sensibly from the prior scenario. This is a very demanding use case, with the majority of the UEs located at the edge of the cell. Consequently, most of the interactions between UEs take place further away from the eNB. Considering the reception methods, interestingly, D2D transmissions have a larger share. This is in line with our expectations: the multicast emission does not cover as many users as before, due to their distance from the eNB. The larger share of D2D transmissions is a direct consequence of this, along with the increased resource requirements for data dissemination due to a less efficient multicast emission. Also, Time (min) Resource blocks x 1000 q q q q q q q q q q q q q q q q q q q q q q q q q q 0 5 10 15 20 [START_REF] Spinella | Integration of ad-hoc networks with infrastructured systems for multicast services provisioning[END_REF] Time (min) fraction of delivered packets q q q q q q q q q q q q q q q q q q q q q q q q q q 0 5 10 15 20 [START_REF] Spinella | Integration of ad-hoc networks with infrastructured systems for multicast services provisioning[END_REF]

Time (min)

Resource blocks x 1000 q q q q q q q q q q q q q q q q q q q q q q q q q q 0 5 10 15 20 [START_REF] Spinella | Integration of ad-hoc networks with infrastructured systems for multicast services provisioning[END_REF]

(a) Resource blocks

Time (min) fraction of delivered packets q q q q q q q q q q q q q q q q q q q q q q q q q q 0 5 10 15 20 [START_REF] Spinella | Integration of ad-hoc networks with infrastructured systems for multicast services provisioning[END_REF] there are some fluctuations in the reception methods of the Fixed-best strategy (dashed lines in Fig. 9(b)), due to the non-stationarity of the underlying opportunistic diffusion process. The pursuit strategy works well, allowing discovering the optimal operating point and reaching a satisfactory trade-off between multicast and D2D transmissions. Despite the increased amount of panic zone retransmissions, they are kept to a reasonable level by pursuit -recall that panic zone retransmissions are unicast, thus they demand many resources. Similarly to the case with RWP and 50 UEs, the -greedy strategy is not plotted in Fig. 9. Indeed, it fails learning the appropriate policy. The choice that -greedy considers as the best one fluctuates a lot and does not stabilize. Therefore, the -greedy's simple selection strategy fails to fill the gap with the fixed-best allocation. This forces many transmissions to the panic zone, resulting into an increased resource consumption. This argues in favor of the pursuit strategy, which at the price of a possibly longer convergence time, constantly converges, scoring better offloading performance. Finally, by comparing Figure 8 and 9 we may appreciate that in SMOOTH-B, as expected, the amount of resources employed is higher for fixed best and pursuit (as the density of nodes is higher far away from the eNB). In any case, the use of D2D transmissions coupled with multicast still brings a very significant advantage over the multicast-only strategy.

Related work

Mobile data offloading. D2D communications have been the target of intensive studies as a method to relieve the pressure on the cellular infrastructure. Typically only unicast transmissions are considered. For instance, Han et al. identified the opportunity to save infrastructure data exploiting the social ties between users, proposing a subset selection mechanism based on contact history [START_REF] Han | Mobile data offloading through opportunistic communications and social participation[END_REF].

Similarly, Li et al. analytically formulated the problem of traffic offloading of multiple contents in a mobile environment. Under the assumption of Poisson contact, the optimal subset selection problem is solved under multiple constraints [START_REF] Li | Multiple mobile data offloading through disruption tolerant networks[END_REF]. Barbera et al. analyzed contacts between end-nodes in order to select a subset of socially important VIP users, which are turned into data forwarders [START_REF] Barbera | Data offloading in social mobile networks through {VIP} delegation[END_REF].

The above-mentioned works consider only the optimal selection of the initial seeder nodes and not the control of the dissemination process through injections. Whitbeck et al. proposed an injection algorithm that follows target objective functions [START_REF] Whitbeck | Push-and-track: Saving infrastructure bandwidth through opportunistic forwarding[END_REF]. Some of the authors of the present work proposed a simple re-injection based scheme that takes into account the evolution of the opportunistic dissemination [START_REF] Rebecchi | DROiD: Adapting to individual mobility pays off in mobile data offloading[END_REF]. Finally, a reinforcement learning algorithm to identify which users are good data carriers was proposed in [START_REF] Valerio | Adaptive data offloading in opportunistic networks through an actor-critic learning method[END_REF]. In all these works the principal metric is the amount of data (or messages) saved on the infrastructure link. While this is an influential driver for evaluation, it does not fully represent the real amount of saved resources at the base station. In addition, to the best of our knowledge, the interplay between multicast and D2D communications has not been addressed in this body of work.

D2D-aided multicast. Bhatia et al., proposed the use of D2D communications to improve performance of multicast in 3G cellular networks [START_REF] Bhatia | ICAM: integrated cellular and ad hoc multicast[END_REF]. A multihop ad hoc network is modeled analytically. A near-optimal discovery algorithm selects the best data forwarder for receivers with poor channel quality. The authors in [START_REF] Zhou | Intracluster device-todevice relay algorithm with optimal resource utilization[END_REF] devised an algorithm to figure out the optimal number of relays inside the cluster. The paper focuses on in-band D2D communications, such that considered in [START_REF] Gpp | TSG SA: Feasibility study for proximity services (ProSe) (release 12)[END_REF]. Similarly, in [START_REF] Spinella | Integration of ad-hoc networks with infrastructured systems for multicast services provisioning[END_REF], only the cluster head receives the content and is in charge of D2D retransmission inside its cluster. No hints are given on how clusters are created and discovered, and how these techniques can be applied to LTE networks to reduce the cellular resource usage. Huo et al., proposed a cooperative multicast scheduling for 802.16 networks. A two phase schema is proposed, and all successful recipients of multicast participate in data retransmission using in-band D2D links [START_REF] Hou | A cooperative multicast scheduling scheme for multimedia services in ieee 802[END_REF]. To the best of our knowledge, the only work in this area focusing on the data offloading problem with guaranteed delivery is [START_REF] Rebecchi | Flooding data in a cell: Is cellular multicast better than device-to-device communications?[END_REF], which however does not offer any mechanism to devise the correct allocation of users between multicast and D2D transmissions.

Conclusion

In this work, we have presented a hybrid distribution strategy, jointly leveraging LTE multicast and opportunistic D2D communications to distribute popular content with guaranteed delays. Multicast is an advantageous option to distribute popular data to users co-located inside a cell. However, it does not offer any reception guarantee, and the user with the worst channel quality inside the multicast group dictates overall performance. We proposed a framework that exploits D2D capabilities at UEs to counter the inefficiencies of cellular multicast.

The proper balance of multicast and D2D transmissions is achieved using a multi-armed bandit learning strategy.

We proposed and evaluated two different algorithms under variable multicast group size, reception deadlines and mobility patterns. Simulation results prove that D2D communications permit to configure multicast transmission in a more efficient way, saving more than up 90% of the radio resources at the base station. We have also shown that the tested learning algorithms are able to obtain performance comparable (and in several cases even superior) to the best possible strategy that uses a fixed split between multicast and D2D communications, which can only be identified after exhaustive search, and is thus practically unfeasible. On the other hand, the proposed learning algorithms are able to dynamically learn the best balance between multicast and D2D transmissions, and, to do so, need a reasonable learning time.

Time (min) PRBs x 1000 q q q q q q q q q q q q q q q q q q q q q q q q q q q 0 5 10 q q q q q q q q q q q q q q q q q q q q q q q q q q q 0 5 10 q q q q q q q q q q q q q q q q q q q q q q q q q q q 0 5 10 Time (min) fraction of delivered packets q q q q q q q q q q q q q q q q q q q q q q q q q q q 0 5 10 15 20 [START_REF] Spinella | Integration of ad-hoc networks with infrastructured systems for multicast services provisioning[END_REF] Time (min) fraction of delivered packets q q q q q q q q q q q q q q q q q q q q q q q q q q q 0 5 10 15 20 [START_REF] Spinella | Integration of ad-hoc networks with infrastructured systems for multicast services provisioning[END_REF] Time (min) fraction of delivered packets q q q q q q q q q q q q q q q q q q q q q q q q q q q 0 5 10 15 20 [START_REF] Spinella | Integration of ad-hoc networks with infrastructured systems for multicast services provisioning[END_REF] Time (min) PRBs x 1000 q q q q q q q q q q q q q q q q q q q q q q q q q q q q q 0 5 10 15 20 [START_REF] Spinella | Integration of ad-hoc networks with infrastructured systems for multicast services provisioning[END_REF] q q q q q q q q q q q q q q q q q q q q q q q q q q q q q 0 5 10 15 20 [START_REF] Spinella | Integration of ad-hoc networks with infrastructured systems for multicast services provisioning[END_REF] q q q q q q q q q q q q q q q q q q q q q q q q q q q q q 0 5 10 15 20 [START_REF] Spinella | Integration of ad-hoc networks with infrastructured systems for multicast services provisioning[END_REF] Time (min) fraction of delivered packets q q q q q q q q q q q q q q q q q q q q q q q q q q q q q 0 5 10 15 20 [START_REF] Spinella | Integration of ad-hoc networks with infrastructured systems for multicast services provisioning[END_REF] Time (min) fraction of delivered packets q q q q q q q q q q q q q q q q q q q q q q q q q q q q q 0 5 10 15 20 [START_REF] Spinella | Integration of ad-hoc networks with infrastructured systems for multicast services provisioning[END_REF] Time (min) fraction of delivered packets q q q q q q q q q q q q q q q q q q q q q q q q q q q q q 0 5 10 15 20 [START_REF] Spinella | Integration of ad-hoc networks with infrastructured systems for multicast services provisioning[END_REF]

Figure 2 :

 2 Figure2: UEs can decode data with a maximum modulation schema depending on their channel quality. The eNB may decide to multicast at higher rate. UEs unable to decode data are reached through out-of-band D2D links and final panic retransmissions.

Figure 3 :

 3 Figure 3: Synthetic map of waypoints generated for the SMOOTH-A and SMOOTH-B scenarios using the parameters listed in Table3. eNB location for SMOOTH-A is set at (150, 50) and eNB location for SMOOTH-B is set at(50,150)

Figure 4 :

 4 Figure 4: Cellular offloading ratio for the RWP scenario. Savings are referred to the multicast-only scenario (%): (a) considers the aggregate data savings over the entire 1 hour simulation; (b) considers only the final saving levels (after 1h of learning).

Figure 5 :

 5 Figure5: RWP scenario -RBs usage for Multicast-only (black), -greedy (blue), Fixed-best (green), and pursuit method (red). Content is divided into 4000 packets of 2048 bytes. Plots are averaged over 10 runs, 95 % confidence intervals are not plotted but are knit.

Figure 6 :

 6 Figure 6: RWP scenario -Pursuit method, reception method. Dashed lines are the objective ratio for Fixed-best. Content is divided into 4000 packets of 2048 bytes. Plots are averaged over 10 runs, 95 % confidence intervals are not plotted but are knit.

Figure 7 :

 7 Figure 7: RWP scenario -Pursuit method, average reward values for I 0 . Content is divided into 4000 packets of 2048 bytes. Plots are averaged over 10 runs, 95 % confidence intervals are not plotted but are knit.

Figure 8 :

 8 Figure 8: SMOOTH-A scenario, offloading performance for correlated mobility patterns with most of the waypoints near the eNB position.

Figure 9 :

 9 Figure 9: SMOOTH-B scenario, offloading performance for correlated mobility patterns with most of the waypoints far away from the eNB position.

Figure A. 10 :

 10 Figure A.10: RBs usage for Multicast-only (black), -greedy (blue), Fixed-best (green), and pursuit method (red). Plots are averaged over 10 runs, 95 % confidence intervals are not plotted but are knit.

Figure A. 11 :

 11 Figure A.11: Pursuit method, reception method. Dashed lines are the objective ratio for Fixed-best. Plots are averaged over 10 runs, 95 % confidence intervals are not plotted but are knit.

Figure A. 12 :

 12 Figure A.12: RBs usage for Multicast-only (black), -greedy (blue), Fixed-best (green), and pursuit method (red). Plots are averaged over 10 runs, 95 % confidence intervals are not plotted but are knit.

Figure A. 13 :

 13 Figure A.13: Pursuit method, reception method. Dashed lines are the objective ratio for Fixed-best. Plots are averaged over 10 runs, 95 % confidence intervals are not plotted but are knit.

Table 1 :

 1 CQI / MCS Table for LTE[START_REF]Evolved universal terrestrial radio access (e-utra); physical layer procedures[END_REF].

	CQI Modulation	code rate	Spectral Efficiency
	index	schema	x 1024	[bit/s/Hz]
	0		out of range
	1	QPSK	78	0.1523
	2	QPSK	120	0.2344
	3	QPSK	193	0.3770
	4	QPSK	308	0.6016
	5	QPSK	449	0.8770
	6	QPSK	602	1.1758
	7	16-QAM	378	1.4766
	8	16-QAM	490	1.9141
	9	16-QAM	616	2.4063
	10	64-QAM	466	2.7305
	11	64-QAM	567	3.3223
	12	64-QAM	666	3.9023
	13	64-QAM	772	4.5234
	14	64-QAM	873	5.1152
	15	64-QAM	948	5.5547

Table 2 :

 2 ns-3 simulation parameters.

	Parameter	Value
	Cellular layout	Isolated cell, 1-sector
	LTE downlink bandwidth	5 MHz (25 RBs)
	Frequency band	1865 MHz (Band 3)
	CQI scheme	Full Bandwidth
	eNb TX-power	51 dBm
	Pathloss	Cost 231
	Fast fading	Extended Pedestrian A (EPA) model
	Cell dimension	200 × 200 m 2
	eNb position	RWP (100, 100), SMOOTH A (150,50),
		SMOOTH B (50,150)
	eNb antenna height	30 m
	UE antenna height	1.5 m
	Multicast group size N	10, 25, 50 UEs
	Max reception delay D	30, 60, 90 s

Table 3 :

 3 SMOOTH-A and SMOOTH-B scenario parameters.

	Parameter	Value
	waypoints	1000
	range R	25 m
	clusters	5
	alpha	4.0
	beta	1.5
	min pause	1 (sec)
	max pause	60 (sec)

A more precise terminology would be "multicast/broadcast", because only a subset of nodes is concerned by the content (multicast), and the shared nature of the wireless medium (broadcast) is exploited to transmit data. For the sake of readability, in the following we will only employ the term "multicast".Preprint submitted to ElsevierDecember 1,

Acknowledgment

This work is partially supported by the European Commission in the framework of the FP7 Mobile Opportunistic Traffic Offloading (MOTO) project under grant agreement number 317959.

Appendix A. Additional figures

We include in the following page the figures for the simulations in the RWP scenario with deadline 60 and 90 seconds.


Pierre Ronco1

Hanna Debiec

Pierre Ronco
email: pierreronco@yahoo.fr

Membranous nephropathy: A fairy tale for immunopathologists, nephrologists and patients

This article reviews the considerable progress which has been made in the recent years in the understanding of the pathophysiology of membranous nephropathy, a model of organspecific auto-immune disease. It shows how experimental models developed more than 30 years ago have led to the identification of several human antigens including neutral endopeptidase in the neonate, phospholipase A2 receptor and thrombospondin 1 domain 7A in the adult, and cationic bovine serum albumin in children. Thanks to a successful GWAS performed in European Caucasians, the genetics of the disease begins to be understood.

These groundbreaking findings already have a major impact on patients' care owing to the development of reliable ELISA and immunofluorescence test for the detection of PLA2R antibodies and of PLA2R antigen screening in biopsies. This review will tell the story from the careful clinical observation of cases to the most recent therapeutic perspectives which have been made possible by these advances.

Advances in medical science often proceed by steps which are highly interdependent. New, groundbreaking findings with important clinical implications often result from the combination of faithful experimental models and careful clinical observations. This is well illustrated by the story of membranous nephropathy which started more than 50 years ago.

It is remarkable that in this disease, the experimental models predicted the pathophysiology of the human glomerulopathy. The stories that we will tell in this article are aimed at young clinical investigators who are sometimes reluctant to embark on research projects. We hope that they will convince them that bedside research performed with intellectual curiosity and a bit of chance can lead to significant progress in clinical medicine.

Presentation of the disease

Although membranous nephropathy (MN) is a rare disease, it is a major cause of nephrotic syndrome in the adult, which accounts for about 20% of cases, being only overpassed among non-diabetic glomerular diseases by focal segmental glomerulosclerosis (FSGS) in some ethnic populations (African and Hispanic Americans). MN annual incidence in the adult is 1 in 100,000, accounting for approximately 10,000 new cases in the EU each year [START_REF] Maisonneuve | Distribution of primary renal diseases leading to end-stage renal failure in the United States, Europe, and Australia/New Zealand: results from an international comparative study[END_REF]. The disease affects patients of all ages and ethnic and racial groups but is more common in men than in women (sex ratio, 2:1) with the peak incidence during the fourth and fifth decades of life [START_REF] Cattran | Idiopathic membranous glomerulonephritis[END_REF].

In the earliest stage, the glomeruli appear normal by light microscopy, and diagnosis relies only on immunofluorescence and electron microscopy. The next stage is characterized by homogeneous thickening of the capillary wall in sections stained with hematoxylin and eosin or with periodic acid-Schiff reagent. Early projections of the GBM between deposits may then be detected in a characteristic spike-like configuration by silver methenamine staining (Jones' stain). Later on, deposits are incorporated into the GBM and lucencies may appear as immune deposits are resorbed. Glomerular and tubulointerstitial fibrosis develop as the disease progresses. Deposits are formed of immune complexes and also contain C5b-9, the membrane attack complex of complement, which is the major mediator of proteinuria.

However, this common histopathological pattern does not refer to a single disease entity. MN can be "idiopathic" (iMN) or primary without any identified cause (70 to 80% of cases), or secondary to various clinical conditions including infections (for example hepatitis B and syphilis), autoimmune diseases (systemic lupus erythematosus), malignancy and drug intoxication [START_REF] Glassock | The pathogenesis of idiopathic membranous nephropathy : a 50-year odyssey[END_REF][START_REF] Ponticelli | Membranous nephropathy[END_REF].

For a long time, composition of immune complexes was unknown and the pathomechanism of the disease was poorly understood. The molecular pathomechanisms of human MN with the identification of several antigens are summarized on Figure 1A.

A single case can teach us more than large series of patients: from alloimmune neonatal

MN to Heymann nephritis and back

In 2000, the case of a neonate with MN was presented at our monthly clinico-pathological conference with pediatrician nephrologists [START_REF] Debiec | Antenatal membranous glomerulonephritis due to anti-neutral endopeptidase antibodies[END_REF]. Because of the early occurrence of the disease during antenatal life, it was tempting to speculate that the mother became immunized during pregnancy and that the nephritogenic antibodies had been transferred to the fetus. We suggested such a scenario because it reminded us of the passive model of experimental MN, called Heymann nephritis, which was the theme of the PhD thesis that of one of us (PR) had defended some 20 years earlier.

Actually, Heymann was a pediatrician from Cleveland (Ohio, USA), who established in 1959 a rat model of MN, which was induced by the immunization of Lewis rats with crude kidney extracts [START_REF] Heymann | Production of nephrotic syndrome in rats by Freund's adjuvants and rat kidney suspension[END_REF]. Because the disease was induced by fractions of renal brush-border membrane rather than by glomerular extracts, the deposits were initially believed to result from glomerular trapping of circulating immune complexes composed of brush-border-related antigens and the corresponding antibodies. Subsequently, however, the development of passive Heymann nephritis in rats injected with rabbit anti-rat brush-border antibodies, argued against a role for circulating immune complexes. With the use of ex vivo and isolated perfused kidney systems, Van Damme et al. and Couser et al. [START_REF] Van Damme | Experimental glomerulonephritis in the rat induced by antibodies directed against tubular antigens. V. Fixed glomerular antigens in the pathogenesis of heterologous immune complex glomerulonephritis[END_REF][START_REF] Couser | Experimental glomerulonephritis in the isolated perfused rat kidney[END_REF] demonstrated that antibrush border antibodies bound to an antigenic target located on podocytes, which indicated that the disease was caused by the in situ formation of immune complexes. The autoantigenic target in the rat disease was identified by Kerjaschki and Farquhar in the early 1980's (9, 10) as the podocyte membrane protein now called megalin.

We knew that megalin could not be responsible for human MN because neither megalin had been detected in subepithelial immune deposits, nor circulating anti-megalin antibodies had been found in patients with MN. The nature of the target antigen in our case was suspected by indirect immunofluorescence examination of rabbit and rat kidney sections incubated with the mother's or the infant's serum. The same pattern of fluorescence as in human kidneys was observed in the rabbit, whereas in the rat, staining was restricted to the cells of Bowman's capsule and to the brush-border of deep cortical segments of the proximal tubule. Because we had previously observed similar interspecies differences with antineutral endopeptidase (NEP) antibodies [START_REF] Ronco | Pathophysiology of the podocyte: A target and a major player in glomerulonephritis[END_REF], we suspected that NEP was the culprit.

Reactivity with NEP was confirmed by immunoprecipitation of rat brush-border extracts with the mother's serum [START_REF] Debiec | Antenatal membranous glomerulonephritis due to anti-neutral endopeptidase antibodies[END_REF][START_REF] Debiec | Role of Truncating mutations in MME gene in fetomaternal allo-immunization and neonatal glomerulopathies[END_REF]. Colocalization of NEP, IgG and C5-b9 within the human immune deposits and transfer experiments, in which a pregnant rabbit was injected with the IgG fraction from the mother, established that the disease was caused by anti-NEP antibodies [START_REF] Debiec | Antenatal membranous glomerulonephritis due to anti-neutral endopeptidase antibodies[END_REF][START_REF] Ronco | Molecular pathomechanisms of membranous nephropathy: from Heymann nephritis to alloimmunization[END_REF].

Because the mother did not show any renal manifestation even though she had persistently high titers of anti-NEP antibody, we hypothesized that she might be deficient in NEP. This hypothesis was supported by the lack of reactivity of her granulocyte extracts with a panel of anti-NEP antibodies [START_REF] Debiec | Antenatal membranous glomerulonephritis due to anti-neutral endopeptidase antibodies[END_REF]. Four additional families with materno-fetal alloimmune MN were identified. All immunized mothers were NEP deficient as a result of the same truncating mutation in exon 7 of the NEP gene [START_REF] Debiec | Role of Truncating mutations in MME gene in fetomaternal allo-immunization and neonatal glomerulopathies[END_REF][START_REF] Vivarelli | Genetic homogeneity but IgG subclass-dependent clinical variability of alloimmune membranous nephropathy with anti-neutral endopeptidase antibodies[END_REF]. In the first family, the mother was a compound heterozygote for this mutation and for another truncating mutation in exon 15.

Alloimmunization can be triggered by previous spontaneous miscarriages or by the ongoing pregnancy during which the mother's immune system is first exposed to the NEP of paternal origin on syncytiotrophoblastic cells. Thus, identification of this original mechanism of renal disease was made possible by our previous work on Heymann nephritis and the in-depth analysis of a clinical case which is the human counterpart to passive Heymann nephritis, which enabled us to bridge the gap between the experimental model and the human disease. Although the neonatal MN appears to be very rare, analysis of its pathogenic mechanisms provided the proof of concept that a podocyte antigen could be responsible for human MN, as is the case for megalin in the rat, and laid the foundation for the identification of the phospholipase A2 receptor (PLA2R) involved in adult forms of iMN.

From alloimmunity to autoimmunity and genetics: a two-way approach

The immunopathological approach

The search for antigens in iMN in the adult was unsuccessful for many years. We failed to identify a relevant antigen because we used differentiated human cultured podocytes as starting antigenic preparation and because our mass spectrometry analyser lacked sensitivity. In 2009 and 2014, using the same approach based on microdissection of human glomeruli, proteomic technology and mass spectrometry, two podocyte proteins were identified. The first major autoantigen is PLA2R [START_REF] Beck | M-type phospholipase A2 receptor as target antigen in idiopathic MN[END_REF]. Circulating autoantibodies to PLA2R

were detected in about 70% of patients with iMN. The second autoantigen is trombospondin type-1 domain-containing 7A (THSD7A), and circulating autoantibodies against this protein were detected in 5 to 10% of the anti-PLA2R negative patients [START_REF] Tomas | Thrombospondin type-1 domaincontaining 7A in idiopathic membranous nephropathy[END_REF]. PLA2R and THSD7A were detected in normal human glomeruli, in podocytes, and both antigens co-localized within subepithelial deposits with IgG4. Furthermore, IgG eluted from biopsy samples reacted with recombinant PLA2R or THSD7A. PLA2R and THSD7A have similar structural and biochemical properties. Autoantibodies to both proteins recognize their target antigens only under nonreducing conditions and are predominantly of the IgG4 subclass. Interestingly, the patients have an autoimmune response against either PLA2R1 or THSD7A, but not both. This suggests that PLA2R-and THSD7A-associated MN are two separate molecular entities and that these antigens are primary targets in this disease. An immunodominant epitope region was recently characterized in the 3 most N-terminal domains of PLA2R by two North-American [START_REF] Kao | Identification of the Immunodominant Epitope Region in Phospholipase A2 Receptor-Mediating Autoantibody Binding in Idiopathic Membranous Nephropathy[END_REF] and British (18) groups.

The genetic approach

At about the time when Beck et al described PLA2R, we were chasing gene variants that could explain predisposition to iMN in white Europeans by using a pangenomic approach.

We were the co-founders of a European MN consortium that collected patients with iMN in the UK, the Netherlands and France. We performed a genome-wide association study (GWAS) based on comparative hybridization of DNA from patients with iMN and from ethnically matched controls with chips featuring >300,000 SNPs. SNPs, which stand for single nucleotide polymorphisms, are single base changes in the DNA sequence that represent the most frequent polymorphism observed in humans. We found highly significant associations of iMN with a series of SNPs in the 6p21 HLA-DQA1 and 2q24 PLA2R1 loci [START_REF] Stanescu | Risk HLA-DQA1 and PLA(2)R1 alleles in idiopathic membranous nephropathy[END_REF].

The P values of the top (most significantly associated) SNPs reached 10-100 for HLA-DQA1 and 10-30 for PLA2R1 despite the small size of the cohorts. The success of this GWAS was explained by the homogeneous nature of the disease, as compared to many other conditions where histological lesions are diverse such as IgA nephropathy or even not defined such as chronic kidney disease in which thousands of patients are required to get significant gene associations. The ethnical match with the healthy controls is another requirement which should be carefully fulfilled.

Carrying the risk alleles of the two genes had an additive effect. Patients with all four risk alleles had an odds ratio close to 80 compared with individuals who had only the protective alleles. These data which were replicated in various cohorts from Europe [START_REF] Kanigicherla | Anti-PLA2R antibodies measured by ELISA predict long-term outcome in a prevalent population of patients with idiopathic membranous nephropathy[END_REF][START_REF] Bullich | HLA-DQA1 and PLA2R1 Polymorphisms and Risk of Idiopathic Membranous Nephropathy[END_REF], and Asia [START_REF] Lv | Interaction between PLA2R1 and HLA-DQA1 Variants Associates with Anti-PLA2R Antibodies and Membranous Nephropathy[END_REF][START_REF] Liu | Association of phospholipase A2 receptor 1 polymorphisms with idiopathic membranous nephropathy in Chinese patients in Taiwan[END_REF][START_REF] Kim | Single nucleotide polymorphisms in the phospholipase A2 receptor gene are associated with genetic susceptibility to idiopathic membranous nephropathy[END_REF], confirmed by an unbiased holistic approach that PLA2R, the antigen encoded by PLA2R1, was a key player in iMN. They further suggested that rare variants in PLA2R1 might account for a special conformation of the antigen triggering autoimmunity. However, sequence analysis of PLA2R1 coding sequence failed to identify rare polymorphisms or mutations specific for PLA2R-associated MN [START_REF] Coenen | Phospholipase A2 receptor (PLA2R1) sequence variants in idiopathic membranous nephropathy[END_REF]. It is remarkable that the most significantly associated SNPs in the GWAS are common alleles in the general population but it is still possible that a rare combination of these alleles may trigger the disease. More studies are needed to explain how alleles in the PLA2R1 and HLA-DQA1 loci interact with each other to increase susceptibility to MN.

Food and environmental antigens: not gone, just forgotten

An alternative model to Heymann nephritis first described in the rabbit by Border et al [START_REF] Border | Induction of membranous nephropathy in rabbits by administration of an exogenous cationic antigen[END_REF][START_REF] Adler | Electrical charge. Its role in the pathogenesis and prevention of experimental membranous nephropathy in the rabbit[END_REF] three decades ago and later in dogs, mice and rats [START_REF] Wright | Experimental immune complex glomerulonephritis in dogs receiving cationized bovine serum albumin[END_REF][START_REF] Kobayashi | Effects of FK506 on experimental membranous glomerulonephritis induced by cationized bovine serum albumin in rats[END_REF] was induced by injection of repeated doses of cationized bovine serum albumin (BSA) which serves as a planted antigen.

Border's experiments were driven by the hypothesis that antigen charge could be a key factor for the formation of sub-epithelial deposits, given the negative charge of the glomerular capillary wall. Only rabbits immunized with cationic BSA were found to have sub-epithelial deposits of IgG and C3, whereas those receiving anionic or native (neutral) BSA featured mostly mesangial deposits.

Based on these data, we speculated that in children with increased permeability of the intestinal barrier, cationic BSA (cBSA) could also serve as a target antigen for circulating anti-BSA antibodies after deposition in the glomerular capillary wall. We identified children less than 5 years of age with both high serum titre of anti-BSA antibodies (both IgG1 and IgG4) reacting primarily with one peptide region in BSA but not with the homologous peptide in human serum albumin, and elevated levels of circulating BSA which was shown to be cationic [START_REF] Debiec | Early childhood membranous nephropathy due to cationic bovine serum albumin[END_REF]. In these patients only, BSA could be detected in the absence of PLA2R in immune deposits. Although the source of cationic BSA remains obscure (milk formula, microbiota, intestinal cells), these data confirm the experimental model. Even if BSA is one of the more common diet antigens due to early exposure to cow and beef products, there are other dietary and environmental antigens that may lead to disease by similar mechanism. Other antigens such as hepatitis B and C viral antigens and enzymes used in replacement therapy may be involved in secondary MN [START_REF] Hunley | Nephrotic syndrome complicating alpha-glucosidase replacement therapy for Pompe disease[END_REF][START_REF] Debiec | Allo-immune membranous nephropathy and recombinant arylsulfatase replacement therapy: a need for tolerance induction therapy[END_REF][START_REF] Bhimma | Hepatitis B virus-associated nephropathy[END_REF].

Actually, there is a world-wide increasing prevalence of MN among the biopsied patients which is most likely related to pollution factors (Ronco, unpublished). Both air and water polluting compounds could be involved. Whether these compounds trigger auto-immunity against PLA2R or other antigens and whether these compounds could themselves serve as auto-antigens needs further investigations.

Complement activation in membranous nephropathy: still mysteries to be solved

Although MAC is a major mediator of proteinuria, the predominant T-helper-2 immune response leads to the production of IgG4 which do not activate complement by classical and alternative pathways [START_REF] Van Der Zee | Inhibition of complement activation by IgG4 antibodies[END_REF][START_REF] Aalberse | IgG4 breaking the rules[END_REF]. The classical pathway is most likely not a major player because of very low or undetectable amount of C1q in immune deposits, apart from exceptional cases [START_REF] Debiec | Recurrent membranous nephropathy in an allograft caused by IgG3κ targeting the PLA2 receptor[END_REF]. Mannan-binding lectin (MBL) has been identified in the glomeruli of patients with iMN [START_REF] Lhotta | Glomerular deposition of mannose-binding lectin in human glomerulonephritis[END_REF]. Preliminary studies indicate that anti-PLA2R IgG4 could bind MBL and activate the lectin pathway [START_REF] Ma | The role of complement in membranous nephropathy[END_REF]. Because MBL has been shown to bind N-linked sugars on IgG that lack terminal galactose [START_REF] Malhotra | Glycosylation changes of IgG associated with rheumatoid arthritis can activate complement via the mannose-binding protein[END_REF], it was suggested that the anti-PLA2R1 IgG4 antibodies might also lack galactose [START_REF] Ma | The role of complement in membranous nephropathy[END_REF]. However, we recently observed cases of iMN occurring in patients with complete MBL functional deficiency which was confirmed by genetic analysis (Bally and Debiec, unpublished observations), thus pointing to a major role of the alternative pathway as also attested by deposits of factor B [START_REF] Segawa | IgG subclasses and complement pathway in segmental and global membranous nephropathy[END_REF]. Genetic polymorphisms resulting in reduced activity of circulating or podocyte complement regulatory proteins as well as intrinsic or acquired defect of complement receptor-1 (CR1), could contribute as well to pathogenesis of MN and account for its varying severity.

Translational research in membranous nephropathy: fast, efficient and paradigm shifting in patient's care

The development of assays of circulating anti-PLA2R antibodies and their transfer to clinical practice has been amazingly fast, since the first immunofluorescence test was commercially available in 2011 (EUROIMMUN AG, Lübeck, Germany), less than 2 years after the description of anti-PLA2R antibodies. This test uses biochips coated with HEK293 cells transfected or not with the full-length human PLA2R1cDNA and incubated with the patients' sera [START_REF] Hoxha | An immunofluorescence test for phospholipase-A₂-receptor antibodies and its clinical usefulness in patients with membranous glomerulonephritis[END_REF][START_REF] Debiec | Nephrotic syndrome: A new specific test for idiopathic membranous nephropathy[END_REF]. The ELISA based on the extracellular domain of human PLA2R enables a more quantitative and faster determination of anti-PLA2R antibodies and shows a good correlation with the immunofluorescence test [START_REF] Hofstra | Antiphospholipase A2 receptor antibody titer and subclass in idiopathic membranous nephropathy[END_REF][START_REF] Dähnrich | Development of a standardized ELISA for the determination of autoantibodies against human M-type phospholipase A2 receptor in primary membranous nephropathy[END_REF] although the latter may be more sensitive.

Detection of PLA2R antigen in immune deposits in biopsy specimens is also possible with the use of commercial antibody after a retrieval step to unmask PLA2R epitopes [START_REF] Debiec | PLA2R autoantibodies and PLA2R glomerular deposits in membranous nephropathy[END_REF][START_REF] Svobodova | Kidney biopsy is a sensitive tool for retrospective diagnosis of PLA2R-related membranous nephropathy[END_REF]. These tests have induced a paradigm shift in the diagnosis, prognosis and patient monitoring [START_REF] Ronco | Pathophysiological advances in membranous nephropathy: time for a shift in patient's care[END_REF].

Studies performed in the last 3 years have shown that anti-PLA2R antibodies are specific and sensitive biomarkers of MN. In a recent meta-analysis including 2212 patients, specificity was 99% (95% CI: 96% to 100%) and sensitivity was 78% (95% CI: 66% to 87%) [START_REF] Du | The diagnosis accuracy of PLA2R-AB in the diagnosis of idiopathic membranous nephropathy: a meta-analysis[END_REF]. Anti-PLA2R antibodies are neither found in other nephropathies and auto-immune diseases nor detected in healthy individuals. They may occur with a low prevalence in secondary forms [START_REF] Hoxha | An immunofluorescence test for phospholipase-A₂-receptor antibodies and its clinical usefulness in patients with membranous glomerulonephritis[END_REF][START_REF] Qin | Anti-phospholipase A2 receptor antibody in membranous nephropathy[END_REF][START_REF] Knehtl | A case of phospholipase A₂ receptor-positive membranous nephropathy preceding sarcoid-associated granulomatous tubulointerstitial nephritis[END_REF] where it may be difficult to exclude a pure coincidence of MN with the associated disorder. Their prevalence seems higher in patients with hepatitis B and active sarcoidosis, which suggests that these two diseases may induce or enhance immune response against PLA2R [START_REF] Svobodova | Kidney biopsy is a sensitive tool for retrospective diagnosis of PLA2R-related membranous nephropathy[END_REF][START_REF] Larsen | Determination of primary versus secondary membranous glomerulopathy utilizing phospholipase A2 receptor staining in renal biopsies[END_REF][START_REF] Stehlé | Phospholipase A2 receptor and sarcoidosis-associated membranous nephropathy[END_REF]. PLA2R antigen can still be detected in deposits in the absence of circulating antibodies [START_REF] Debiec | PLA2R autoantibodies and PLA2R glomerular deposits in membranous nephropathy[END_REF], even in archival, paraffin-embedded kidney biopsies.

Conversely, in some patients, circulating anti-PLA2R antibodies are not associated with PLA2R deposits, suggesting that these antibodies may not be pathogenic. These results lead to recommend a combined serological (antibody) and biopsy (antigen) analysis in all patients with MN. Detection of antigen in immune deposits also is an important clue to the diagnosis of primary MN [START_REF] Debiec | Recurrent membranous nephropathy in an allograft caused by IgG3κ targeting the PLA2 receptor[END_REF] where PLA2R is often associated with predominant or exclusive IgG4 deposits [START_REF] Ronco | Pathogenesis of membranous nephropathy: recent advances and future challenges[END_REF]. However, presence of PLA2R in the deposits is commonly [START_REF] Svobodova | Kidney biopsy is a sensitive tool for retrospective diagnosis of PLA2R-related membranous nephropathy[END_REF][START_REF] Knehtl | A case of phospholipase A₂ receptor-positive membranous nephropathy preceding sarcoid-associated granulomatous tubulointerstitial nephritis[END_REF][START_REF] Larsen | Determination of primary versus secondary membranous glomerulopathy utilizing phospholipase A2 receptor staining in renal biopsies[END_REF].

Antibody levels also predict outcome since high titers are correlated with a lower risk of spontaneous [START_REF] Hofstra | Antiphospholipase A2 receptor antibody titer and subclass in idiopathic membranous nephropathy[END_REF] or immunosuppressant-induced [START_REF] Hoxha | Phospholipase A2 receptor autoantibodies and clinical outcome in patients with primary membranous nephropathy[END_REF][START_REF] Ruggenenti | Anti-PLA2R antibody titer predicts postrituximab outcome of membranous nephropathy[END_REF] remission and a higher risk of emergence of a nephrotic syndrome in non-nephrotic patients [START_REF] Hoxha | PLA2R antibody levels and clinical outcome in patients with membranous nephropathy and non-nephrotic range proteinuria under treatment with inhibitors of the renin-angiotensin system[END_REF] and of renal function deterioration [START_REF] Kanigicherla | Anti-PLA2R antibodies measured by ELISA predict long-term outcome in a prevalent population of patients with idiopathic membranous nephropathy[END_REF][START_REF] Hoxha | M-type phospholipase A2 receptor autoantibodies and renal function in patients with primary membranous nephropathy[END_REF]. The time interval from the start of immunosuppressive treatment to remission is significantly longer in patients with the highest antibody titers [START_REF] Hoxha | Phospholipase A2 receptor autoantibodies and clinical outcome in patients with primary membranous nephropathy[END_REF].

Last but not least, anti-PLA2R antibodies appear to be sensitive markers of treatment efficacy. Partial or complete depletion of anti-PLA2R antibodies precedes renal remission by several weeks or months [START_REF] Ruggenenti | Anti-PLA2R antibody titer predicts postrituximab outcome of membranous nephropathy[END_REF][START_REF] Oh | Autoantibodies against phospholipase A2 receptor in Korean patients with membranous nephropathy[END_REF], while re-emergence or increase of these antibodies precedes a renal relapse [START_REF] Ruggenenti | Anti-PLA2R antibody titer predicts postrituximab outcome of membranous nephropathy[END_REF]. The time lag of several months from immunological remission (depletion of antibodies) to renal remission is most likely accounted for by deposit remodeling and restoration of the glomerular capillary wall. Furthermore, antibody titer at the end of immunosuppressive treatment predicts occurrence of relpse (59). Because anti-PLA2R antibodies are much more sensitive markers than proteinuria for monitoring disease activity and outcome, they should play an essential part in therapeutic decisions and in the monitoring of patients. This is all the more important that immunosuppressive therapies may have toxic effects, including the risk of cancer in patients treated with alkylating agents (60). We think that the 2012 KDIGO guidelines (61) should be urgently revisited to include anti-PLA2R in the decision algorithm for patients with iMN. We recommend that antibodies be assessed every two months before starting immunosuppressive therapy to avoid unnecessary treatment in patients entering immunological remission, and every month afterward during the first 6 months of immunosuppression.

Therapeutic perspectives: A look into the future

Currently, only non-specific immunosuppressive treatments are proposed to patients with severe nephrotic syndrome persisting more than 6 months despite anti-proteinuric therapy because of frequent occurrence of spontaneous remission within 6 months to one year after diagnosis. New therapeutic options in patients with MN are presented on Figure 1B. Anti-CD20 antibody (rituximab) is a step in the right direction but still about a third of patients with persistent nephrotic syndrome will not respond [START_REF] Hoxha | Phospholipase A2 receptor autoantibodies and clinical outcome in patients with primary membranous nephropathy[END_REF], calling for more specific epitope-driven therapy based on specific immunoadsorption. Further knowledge of the molecular structure of the "nephritogenic" epitope will enable to design non-peptide antagonists that will serve as baits for antibody decay. However, efficacy of this therapeutic intervention might be limited by epitope spreading. Because proteinuria is partly caused by complement activation leading to podocyte injury, there is still a place for complement antagonists blocking MAC formation and effects, and for cytoprotective therapy favouring restoration of the glomerular capillary wall. Research in this field must certainly be strengthened.

Conclusion

Three ingredients of translational medicine in the field of immune-mediated glomerular diseases have remained constant over the years: the patients, the need for wellcharacterized relevant models of their diseases, and the contributions of physician-scientists who have accounted for most of the advances described in this issue. The patients and the need for animal models will remain, but the technology to study them will exponentially

Figure 1 .

 1 Figure 1. Mechanisms of immune mediated podocyte injury in MN and pathogenesis based therapeutic approach.

Acknowledgment: Research of the authors is supported by European Research Council Grant ERC-2012-ADG_20120314 (Grant Agreement 322947), Agence Nationale pour la Recherche Programme Blanc SVSE1 (2012) Decision ANR-12-BSE1-0002-01, Fondation pour la Recherche Médicale Equipe FRM 2012 grant, and 7th Framework Programme of the European Community Contract 2012-305608 (European Consortium for High-Throughput Research in Rare Kidney Diseases). None of the funding source played a role in the writing of the manuscript or the decision to submit it for publication. Special thanks to Mohammed DAHA for lively discussions often in the night during the preparation of EU applications and for his continuous friendship and support. This manuscript is dedicated to him!