Joint multicast routing and OFDM resource allocation in LTE-D2D 5G cellular network

Full text

Joint Multicast Routing and OFDM Resource
Allocation in LTE-D2D 5G Cellular Network
Safwan Alwan∗, Ilhem Fajjari†and Nadjib Aitsaadi‡
∗University Paris-Est, LiSSi EA 3956, UPEC, F94400, Vitry-sur-Seine, France
†Orange Labs, F92320, Chatillon, France
‡University Paris-Est, LIGM-CNRS UMR 8049, ESIEE Paris, F93160, Noisy-le-Grand, France
Emails: safwan.alwan@univ-paris-est.fr, ilhem.fajjari@orange.com, nadjib.aitsaadi@esiee.fr
Abstract—An offloading scheme based on LTE-D2D is pro-
posed in this paper to route the intracellular multicast traffic
via a network of D2D-enabled User Equipments (UEs). The
latter are ready to cooperate under the control of the eNodeB to
carry and deliver the traffic. In doing so, the UEs reuse uplink
resources granted by the eNodeB and thus, increasing the overall
spectral efficiency while reducing the traffic load on the eNodeB.
In this paper, we address the joint multicast routing and OFDM
resource allocation problem in the D2D network to accomplish
the offloading task. To do so, first we formulate the problem as
an Integer Linear Programming (ILP) model which takes into
account factors that limit spectrum reuse in addition to other
LTE-D2D limitations: half-duplex operation and contiguity in
resource block allocations. Then, we propose a novel scheme
named Joint Multicast Routing and Wireless allocation in D2D
communications (JRW-D2D-MC). The devised scheme consists
of two-stage algorithm which, first, performs a pre-admittance
filtering of flows that can be routed considering the current state
of the network. Then, it makes use of the branch-and-cut method
to solve the reduced ILP model. To evaluate effectiveness of our
proposal, we implement the LTE-D2D standard in a network
simulator NS-3. The results are very good in terms of flow-
acceptance rate and latency.
Index Terms—Multicast routing, Resource allocation, Offload-
ing, Device-To-Device LTE-D2D, Optimization
I. INTRODUCTION
According to Ciscos annual Visual Networking Index, over
the next five years (2016-2021), the number of connected
devices will exceed threefold the world population, by 2021.
The mobile data traffic, for its part, is expected to reach 48.3
exabytes per month by the same year, accounting for 17% of
the total traffic [1]. It is undeniable that this newly-arrived
zetabyte will inevitably be the catalyst of the telecommu-
nication infrastructures transformation. The democratization
of connected devices and the exponential growth of rich
multimedia services accentuate the cellular network ossifica-
tion. Therefore, networking vendors and telecommunication
operators make every effort to invent and adopt innovative
solutions.
In this context, the next generation of mobile standard
5G introduces several disruptive technologies to consolidate
the network infrastructure transformation. These innovative
solutions include: i) massive MIMO, millimeter-Wave antenna
systems, ii) Heterogeneous cellular deployment such as small
cells, Multiple Radio Access Technologies (Multi-RAT) and
iii) Device-to-Device (D2D) communications. The common
denominator between these technologies is their willpower to
enhance the network capacity. In doing so, high-throughput
data volumes and large number of connections can be flexibly
handled over the next generation Telecoms’ infrastructure.
D2D has become one of the 5G pillars that ensures an ex-
tended and controlled connectivity while reducing the network
deployment cost. Its main idea consists in giving to close user
terminals the ability to directly exchange data without passing
through the macro base-station. In doing so, D2D offers to the
network operators an enhanced cellular offloading technique
compared with existing techniques such as Wi-Fi offloading
and switching to femto-cells. However, the D2D raises new
challenges to deal with such as: the coexistence with conven-
tional communications mode (macro-cell), the spectrum reuse,
resource allocation and mode-switching, etc. [2], [3].
As a concrete step in adopting this paradigm, the D2D was
recently brought into LTE-A standards and, hence, commonly
called LTE-D2D. Besides its capability to enhance the overall
spectrum efficiency, D2D enables the LTE-A networks to
support new use cases such as: i) public safety scenarios,
ii) device-discovery for commercial applications, iii) D2D-
network relays, etc.
In this paper, we put forward a novel centralized approach
to deal with routing and resource allocation for flow-centric
multicast applications in relation to D2D offloading scenarios.
Our contribution is twofold: Firstly, a D2D based system is
designed and implemented to enable a multicast flow offload-
ing solution. Secondly, an advanced joint routing and resource
allocation strategy which harvests the D2D infrastructure to
extend the network capacity is proposed. Specifically, in the
context of one single cell, our central controller attempts to
offload the intra-cell emerging multicast flows while making
use of a D2D tier that relies on User Equipments (i.e.,
UEs) themselves. To do so, the proposed scheme exploits the
facilities of the LTE-D2D standard, as defined in its releases 12
and later, to implement the aforementioned D2D subnetwork.
This subnetwork is composed of a set of D2D links, called
also sidelinks (SL) in LTE-D2D terminology, that are used to
form a multicast distribution tree. This tree ensures the routing
of a given flow from the source UE to the destinations within
the cell. Besides, the proposed scheme relies on the controlled-
mode of D2D operation, which is one of the supported
modes in the LTE-D2D standard. According to this mode, the
D2D transmissions, scheduling, and resource allocation are
supervised by the base station (i.e. eNodeB).
It is worth noting that a SL shares the same physical resources
with the uplink (UL) (i.e., transceiver and spectrum). This
implies that a UE can be involved in a single kind of
communication which can be either SL or UL. Furthermore,
this implies that a UE cannot simultaneously transmit and
receive in SL. In other words, SL operates in half-duplex
mode. Accordingly, these restrictions make the D2D more
opportunistic compared to the conventional communication
especially in relation to scenarios where UEs are actively
connected to the eNodeB (i.e., eNB). It is worth noting that
the aforementioned technology restrictions have been taken
into consideration during the design of our system.
The main problem addressed in our work is to harness D2D
links to enhance wireless network capabilities. In doing so, the
congestion of conventional infrastructure is minimized and its
coverage is extended. To achieve our goal, we propose an ad-
vanced Joint Multicast Routing and Wireless allocation in D2D
communications strategy, named (JRW-D2D-MC). It operates
as follows: Firstly, it proceeds to control the admission of
978-1-5386-3416-5/18/$31.00 c
2018 IEEE

the newly-arrived multicast flows into the D2D subnetwork in
order to alleviate the conventional cellular network. Secondly,
our strategy selects the multicast routes to the destinations for
the admitted flows. Finally, it performs both the routing and
the resource allocation to handle the ongoing flows.
Our joint routing and resource allocation problem is formu-
lated as an Integer-Linear-Programming (ILP) model. Then
a two-stage algorithm is put forward to solve it. The initial
stage aims to reduce the complexity of the ILP model which
is subsequently solved using another sub-algorithm based on
the branch-and-cut algorithm. We perform extensive network
simulations in NS-3 simulator while considering the full
D2D protocol to gauge the performance of JRW-D2D-MC
algorithm. The results obtained are very satisfying.
The remainder of the paper is organized as follows: Sec-
tion II will succinctly summarize the related work dealing
with multicast routing in D2D infrastructures. In section III,
we will describe the design consideration and challenges for
the implementation of our multicast approach over LTE-D2D.
Then, we will give insights into our system model in sec-
tion IV. Next, we present our novel algorithm JRW-D2D-MC
in section V. Finally, the simulation environment and setup
together with results are presented and evaluated in section VI
with a concluding remarks in section VII.
II. RELATED WORK
Being a relatively new standard, extending D2D wireless
technologies to multicast routing scenarios has not been fully
explored yet and rare research work has been carried out to
address this issue in LTE-based infrastructures. In this section,
we summarize the most relevant related strategies found in
the literature tackling resource allocation in the context of
multicast in D2D systems.
In [4], the authors give insights into resource allocation
algorithms for multicast wireless OFDMA-based systems.
Besides, the work discusses various aspects of channel-aware
resource allocation of wireless multicast systems in addition
to multicast-related concepts such as group formation, single-
rate and multi-rate transmissions, etc. However, only multicast
transmissions carried in the downlink direction are tackled in
this paper. In other words, authors consider systems where
the origin of data is the base station and the cellular users in
multicast groups may act as forwarders.
In [5], the authors address the problem of power min-
imization in multicast multihop D2D networks through a
user grouping strategy. In their work, they circumvent the
NP-complete problem by proposing two greedy suboptimal
algorithms. However, the proposed scheme is limited to single
content delivery starting from the base station under some con-
sideration. The work also proceeds with generic assumptions
about the underlying D2D technology which is used to offload
the content delivery. Finally, the problem of resource allocation
is not tackled.
The work in [6] deals with multi-copy data dissemination
in the context of mobile opportunistic delay-tolerant networks
(DTN) where content delivery may last for days. The authors
put forward a probabilistically delay-constrained formulation
in order to discover the optimal multicast graph and minimize
the communication cost. The authors, then, proceed by propos-
ing a central algorithm and a distributed one which are then
simulated under real-world traces and random walk mobility
model.
In the same vein, the authors in [7] propose multicast archi-
tecture for D2D content delivery in cellular networks where
the content starts at the base station and the multicast relaying
is limited to a single hop. The work addresses primarily the
mode selection for content delivery (i.e., cellular or D2D) and
the caching strategy.
It is noteworthy that the previous proposals are not ap-
plicable in our context where the envisaged multicast traffic
is delay-constrained and starts and terminates at the user
equipments themselves. So unlike [4] and [5], we use the D2D
links to offload the multicast traffic. Contrary to [6], the traffic
in our proposal are delay-constrained. Compared to [7], our
proposal extends the relay operation to multihop. Furthermore,
unlike the previous cited works, the underlying optimization
problem in our proposal involves the routing and resource
allocation at the same time. To the best of our knowledge, we
are the first to address the joint routing and resource allocation
in context of offloading multicast traffic via a secondary tier
of multihop D2D communication network.
III. SYSTEM DESIGN:MOTIVATION AND CHALLENGES
In this section, we present the system design motivations
and challenges related to:
i) the resort to a centralized approach to handle the routing
and resource allocation operations, and
ii) the selection of the LTE-D2D as a multihop multicast
enabler and how to deal with certain implied limitations.
First, the design choice of implementing centralized con-
troller is motivated by the eNodeB ability to acquire a global
view of the D2D subnetwork state. The information related to
the characteristics of D2D links and the ongoing traffic and
queues can be collected by the eNodeB through periodic feed-
backs from UEs and/or short term estimations. Specifically,
the signal-to-interference-plus-noise ratio (SINR) characteris-
tics of D2D links can be calculated from the collected SL
measurements report and/or neighbor discovery reports from
the UEs. Moreover, the D2D queues for the traffic under
consideration are predictable, and hence, can be estimated
without resorting to buffer status reports. Second, in line
with the assumption of a well-behaved D2D topology (i.e.,
quasi-stationary UE nodes), the overall UE-to-eNB signaling
requirements can be further reduced. This is particularly true
for our design since the envisaged multicast communication
is connectionless-oriented by its nature and no feedback on
delivery is required. This is also true across all sublayers of the
D2D subsystem provided by the connectionless PC-5interface
of LTE-D2D:
The Packet Data Convergence Protocol (PDCP) sublayer,
responsible for the compression of the incoming IP header,
operates in unidirectional mode. Consequently, it requires no
feedback from the receiving entity.
The logical link sublayer, or the Radio-Link Control (RLC),
responsible for the segmentation, operates in the unacknowl-
edged mode.
Moreover, the MAC sublayer supports HARQ processes to
enhance the reliability of the SL operation. However, such a
mechanism is restricted to blind retransmissions, where the
same transport block (i.e., TB) is retransmitted three more
times without any feedback. Each TB carries its layer 2
identifiers: the source id and the destination group id.
At the physical layer SL, like to UL, SL transmission makes
use of the SC-OFDM modulation format using a resource-
block time-frequency grid. Each resource block (RB) occupies
a subframe (i.e., TTI) which lasts for 1ms and a bandwidth
of 12 sub-carriers (180 KHz) in frequency domain. But unlike
UL, SL allocations are organized in larger assignment time
units or SL frames, which can be set to values between 40

-1  +1
Time
Frequency
TSL
BSL
One SL Resource Block
One SL Frame
Flows arrived
during this SL frame are
evaluated for scheduling
on the next one
Fig. 1. Sidelink frame structure and scheduling
and 320 subframes. The frame structure and the resource grid
of SL is illustrated in Fig. 1.
IV. SYSTEM MODEL AND PROBLEM FORMULATION
In this section, we give insights into our offloading system
model for multicast intra-cell traffic based on LTE-D2D in-
frastructure. In line with our previous discussion, we consider
a set of UEs inside the coverage zone of a single LTE-A eNB.
We assume also that one-to-many (i.e., multicast) traffic flows
occur between these enhanced UEs supporting the LTE-D2D
protocol. The traditional delivery method for this kind of intra-
cell traffic relies on the conventional cellular infrastructure
using either the LTE-Broadcast (LTE-eMBMS) or the less
efficient multicast-to-unicast conversion.
However, under heavy traffic condition, we assume that a
secondary best-effort technique is provided to the eNB. This
approach makes use of UEs via multihop multicast transmis-
sion to achieve the one-to-many delivery. Relying on D2D sub-
network, the eNB carries out the detection and the evaluation
of multicast traffic flows that can be absorbed into and routed
over the D2D subnetwork. Moreover, the eNB implements
the decision algorithm related to the admission, multicast
routing and wireless OFDM resource allocation to maintain
the ongoing and incoming flows in this D2D subsystem.
A. System model
We model the topology of the D2D subnetwork, maintained
at the eNB’s central controller, as a symmetric directed graph
G=(V,E).Vrepresents the set of Nnodes corresponding
to UEs and the set Erepresents the formed lateral links (SLs)
between the UEs as edges in the graph. Note that an edge is
declared as a constituent link of the topology if the achieved
SNR over it exceeds a given threshold γTOPO. It means that the
Gis not necessarily (fully-)connected and can be in general
written as a disjoint union of connected subgraphs: G=G1∪
G2∪...∪GC.
We also refer to the multicast flows generated in the system
by the set F. Each flow fk∈Fhas its own source node
sk∈V, its destination group Dk⊆Vand its bit rate
assuming CBR applications. A flow bit rate is translated to
a specific demand in terms of OFDM resource blocks in the
SL assuming a baseline modulation and coding scheme (MCS)
and a given time period of TSL for the SL frame. That is to
say, the description of each flow fk∈F is augmented by its
demanded number Dkof RBs.
Conforming to the quasi-dynamic mode of routing, the
eNB’s endeavor to admit a flow fk∈F, into the D2D
subsystem, is embodied by constructing, if possible, a ded-
icated multicast (distribution) tree Tkfrom the available D2D
topology. An explanatory instance of this process is given in
Fig. 2. It should be noted that a non-leaf node and its children
represent a single D2D multicast hop (i.e., domain), where
h = 0
h = 1
h = 2
h=3
h = 4
R2R1
S
D4
R4
D3D2
D1
R3
R2R1
S
D4
R5
R4
D3
R6
D2
D1
Fig. 2. Multicast distribution tree constructed from a given topology
each transmission from the node is addressed to all children at
the same time. In other words, outgoing links from a node, in a
multicast tree, do not imply retransmissions for each individual
child. In LTE-D2D, each transmitted TB includes the source
and destination group addresses.
In addition, we assume that a node can use its D2D protocol
stack to send/receive at most one flow at a time, and therefore,
it cannot be involved in the routing of more than one flow si-
multaneously. This node-exclusivity assumption and the quasi-
dynamic routing imply that the multicast tree is dynamically
constructed based on the current state of D2D network (i.e.,
nodes and resource blocks available). It is worth noting that the
tree remains static during the whole flow lifetime. Besides, the
node-exclusivity implies that the simultaneous ongoing flows
in the system must have disjoint multicast trees.
Formally, the routing decision of our problem described
above is given by solving for the binary variable set xh,k
ij which
parallels the edge set E. Each variable xh,k
ij indicates whether
the corresponding link eij is selected or not to be a part of a
multicast tree Tkfor the flow fkat the tree level (hop) hfor
h=0,1,2,...,h
max. The solution space is constrained by the
following linear constraints:

eij ∈T (vn)
0≤h≤hmax,f k∈F
xh,k
ij ≤1∀vn∈V (1)
xh,k
ij ≤δh
0·δsk
vi+(1−δh
0)(1 −δsk
vi−δsk
vj)∀eij ∈E
∀0≤h≤hmax
∀fk∈F
(2)
xh,k
nm ≤
eij ∈T (vn)
xh−1,k
ij
∀enm∈E
∀1≤h≤hmax
∀fk∈F (3)

eij ∈T (vn)
0≤h≤hmax
xh,k
ij −
eij ∈O(vn)
0≤h≤hmax
xh,k
ij ≤Dk
vn
∀vn∈V
∀fk∈F (4)
tk
n≥
0≤h≤hmax
xh,k
nm
∀enm∈E
∀fk∈F (5)
tk
n≤
eij ∈O(vn)
0≤h≤hmax
xh,k
ij
∀vn∈V
∀fk∈F (6)

eij ∈T (vn)
0≤h≤hmax
xh,k
ij ≥Dk
vn·tk
sk
∀vn∈V
∀fk∈F (7)

fk∈F
tk
n≤1∀vn∈V (8)

fk∈F
δsk
vn+Dk
vn·tk
sk≤1∀vn∈V (9)
where each auxiliary variable tk
nis introduced to indicate

whether the node vnis acting as a sender in the multicast
tree Tkor not. The previous formulation includes the notation
1
Dk
vnfor indicator function of the set Dkwhich equals to 1 only
when vn∈D
k(i.e., the node is among the flow destinations).
For the sake of brevity, it also included the notation δp
qfor
the Kronecker delta function is 1 if its indexes p, q are equal,
and 0 otherwise. Furthermore the notations O(vn)and T(vn)
refer to the sets of outgoing edges from and incoming edges to
vnrespectively. Constraint (1) implies that a node has at most
one parent (i.e., one incoming link selected) in the multicast
tree of at most one flow. Constraint (2) ensures that only
links originating from the source node can be at the root of
the multicast tree. To ensure the tree structure, Constraint (3)
reflects the fact, that a link is declared to originate at some
level h of a tree, only if it has a parent at the previous level
h−1. To prevent the formation of unnecessary relay nodes,
Constraint (4) ensures that only a destination can be a leaf
in the tree. Note that, in our formulation, a node can be a
destination and a relay node for some flow. Constraints (5)
and (6) fix the value of the variable tk
nto show whether a
node vnis a sender in the flow fk’s multicast tree or not (i.e.,
only if there is at least one outgoing link selected or, in other
words, only if it is a non-leaf node in the tree Tk). Constraint
(7) stipulates that the multicast tree of some flow must span
all its destination(s) if the flow is decided to be admitted or
equivalently when its source node skhas at least an outgoing
link selected i.e. tk
sk=1. Following the node-exclusivity
assumption, Constraint (8) implies that a node can be a
sender (a non-leaf node) in at most one flow multicast tree.
In the same manner, Constraint (9) stipulates that admitted
simultaneous flows shall not contradict each other by sharing
nodes as roots or destinations in their multicast trees.
It is straightforward to prove the claim that the multicast
trees Tk={eij |eij ∈Eand xh,k
ij for some h}constructed
under the previous constraints are disjoint distribution trees
for their respective flows. First of all, if fkis admitted, (i.e.,
tk
sk=1), Tkis non-empty and has at least an outgoing edge
from the source node skat the level h=0where only those
outgoing edges are possible by Constraint (2). Hence Tkis
rooted. Moreover, by Constraints (3), and (1), a node other
than the root Tkhas only a unique directed path from the
root. In addition, Tkis cycle free. Any cycle that involves the
source node will invalidate Constraint (2) while other cycles
involving other nodes must have a directed path entering at
at least node leading two different paths to it, the other being
through the cycle. So cycles are not possible to appear in Tk.
Therefore, Tkis a connected directed graph with a unique
path from the source node vskand hence it is rooted directed
tree.
As for the resource allocation part of the problem, we
assume that the eNB must allocate sufficient resources to
the relay nodes, (i.e., internal nodes in a multicast tree), so
they can continuously retransmit as they receive without the
need for extra store-and-forward buffers. This is done to avoid
unnecessary UE-to-eNB reports on the status of intermediate
buffers. Let us represent the decision instants by:
t=τ·TSL for τ=0,1,2,...
where TSL is the SL frame duration which is the minimum
scheduling time unit in SL as illustrated in Fig. 1. That is to
say, a SL grant from eNB to a node to transmit on some RBs
will be valid for all the sub-frames within that interval. At
a given instant, we note that the nodes in the system can be
classified into sets:
V=VG∪V
D
where VGis the set of nodes actively engaged in the routing
of some ongoing flow and VDrepresents the remaining idle
nodes.
A node cannot use its D2D interface transmit and receive on
SL simultaneously as per the LTE-D2D standard. Therefore,
to deal with this half-duplex constraint, we assume that at
any moment the active nodes VGis divided into two half-
duplex sets, namely, V0
Gand V1
Gwhere the eNB schedule
each group to transmit in alternating manner in consecutive
SL frames e.g. depending on the parity of the SL frame
index τ. In other words, nodes in the same half-duplex set
are scheduled to transmit in one SL frame and then they are
allowed switch role to receive in next SL frame. The direct
implication of this half-duplex scheduling strategy together
with the previously mentioned no-extra-buffer arrangement is
that a node in multicast tree belongs to a half-duplex set
different than that of its children. Specifically, all nodes at
even-numbered levels in a multicast tree belong to the same
half-duplex set while those at odd-numbered levels belong to
the other set.
In addition to its assigned half-duplex set, a node need
OFDM resource blocks to transmit on SL. However, as per the
LTE-D2D standard, RBs in SL BSL are restricted to contiguous
allocations. This restriction limits the possible allocations to a
set of feasible allocation patterns for a given BSL. To represent
these allocations, we use an allocation matrix ZΩ×U=[zω,u]
whose columns represent the whole set of feasible allocations.
So, given a SL bandwidth BSL =ΩRBs, the number of
allocation patterns, (i.e., columns of the corresponding Z
matrix), is equal to U=1
2Ω(Ω + 1). An illustrative example
for this allocation matrix formulation, for Ω=4, follows:
Z4×10 =⎡
⎢
⎣
1000100101
0100110111
0010011111
0001001011
⎤
⎥
⎦
where the seventh column, e.g., represents two RBs are
allocated: namely the third and fourth ones.
Formally, the constraints for the resource allocation aspect
of the model are given by:

fk∈F
0≤h≤hmax
xh,k
ij ≤Hi+Hi∀eij ∈E (10)
2−
fk∈F
0≤h≤hmax
xh,k
ij ≥Hi+Hj∀eij ∈E (11)
U

u=1
yu,n ≤
fk∈F
tk
n∀vn∈V (12)
Bn≤Ω+(Dk−Ω) ·tk
n
∀vn∈V
∀fk∈F (13)
ΨσRω,p
ij +
n=i
gnj Ψt·φω,p
n,ij ≤gij Ψt
γRω,p
ij
∀eij ∈E
∀1≤ω≤Ω
∀p∈{ 0,1}(14)
where the binary variable Hnassigns the (active) node vn
to one of the half-duplex sets V0
Gand V1
Gand the variable
yu,n indicates if this node was allocated the RB pattern in the
column uof the matrix Z.
Constraints (10) and (11) ensure that a parent node and
a child node are assigned different half-duplex sets in accor-
dance to the previous discussion. On the other hand, Constraint

(12) implies that, at most, one allocation pattern from Zis
assigned to a node when it acts as a sender. On the other hand,
the allocated number of RBs, as indicated by the auxiliary
integer variable Bn, for a node vn, serving a flow fk, is limited
by the respective bound Dkas stated by Constraint (13).
Before commenting the constraint (14) which is related to
the management of wireless interference, we assume a flat
block-fading channel model. Following a per-RB treatment,
the overall SINR, on the link eij, is calculated within a certain
RB as: γij =gij Ψt,i

vn∈V
gnj Ψt,n +Ψ
σ
where Ψσand Ψt,n represent the spectral densities (per RB)
of the thermal noise and the transmission from vn, and gij is
the channel gain between the node pair (vi,v
j).
Constraint (14) ensures that the SINR is below a certain
threshold γconsidering all allocated RBs and taking into
account active nodes interfering in the same half-duplex set:
Vp
G. The auxiliary binary variable Rω,p
ij indicates that the link
eij is scheduled to transmit together with half-duplex set Vp
Gon
the RB number ω. In addition, the auxiliary binary variable
φω,p
n,ij indicates that the node vninterferes with the link eij
within the RB number ωand they are scheduled in the same
half-duplex set. The previous auxiliary variables are fixed by
the following constraints:
Bn
Ω

ω=1
Rω
n∀vn∈V (15)
Rω,p
ij Rω,p
i·Rij
∀eij ∈E
∀1≤ω≤Ω
∀p∈{ 0,1}(16)
φω,p
n,ij Rω,p
n·Rω,p
ij
∀vn∈V,∀eij ∈E
∀1≤ω≤Ω
∀p∈{ 0,1}(17)
Rω
n
U

u=1
yu,nzω,u ∀vn∈V
∀1≤ω≤Ω(18)
Rω,0
nRω
n−Rω,1
n;Rω,1
nHn·Rω
n∀vn∈V
∀1≤ω≤Ω(19)
Rij 
0≤h≤hmax
fk∈F
xh,k
ij ∀eij ∈E (20)
where a further step is needed to linearize the constraints con-
taining product terms by a standard technique by introducing
for each term x·yan additional auxiliary binary variable λxy
add three more linear constraints as follows:
λxy ≤x(a),λ
xy ≤y(b),λ
xy ≥x+y−1(c)(21)
The model constructed so far is an instance of Integer Linear
Programming (ILP) that compromises the joint routing and
resource allocation for the multicast scenario under consider-
ation. To solve this model, we propose a two-stage algorithm
given in the next section where we also propose the objective
function of optimization.
V. P ROPOSAL:JR-D2D-MC
We propose an incremental two-stage algorithm, with on-
line bulk strategy, to solve our joint routing and scheduling
problem (JR-D2D-MC). First, at each decision instant tτ, the
eNB classifies the total flows Finto:
i) Ongoing (scheduled) flows FSCHED: those flows which
have been already admitted to the system and not finished
yet.
ARRIVING
NON D2D
ROUTABLE
WAI TIN G
NO
YES
CANDIDATE
LEAVING
SCHEDULED
(ONGOING)
FINISHED
NO
YES
Pre-admiance
Filter
Is
admied?
Waiting timer
expired
Are destinations
graph-connected
to source?
Fig. 3. Flow state transition diagram
ii) Leaving flows: those flows which have waited more than
the maximum limit fixed by design. These flows will
exit unserviced from the system, heading for the primary
delivery method (i.e., the conventional communication).
iii) Finished flows: those flows whose last packet has been
received by all it destinations in the multicast group.
iv) Waiting flows FWAIT: those flows which are still in the
waiting queue including the newly-arrived during the
previous SL frame τ−1.
Obviously, the eNB will free the nodes and resources allocated
for the finished flows before solving the new decision problem
returning nodes to the idle set VD. Note that the eNB considers
only the flows which are D2D-routable (i.e., whose source and
destinations lie in the same connected component of the D2D
topology under consideration).
Instead of directly running the decision problem by solving
the ILP model to maintain the already admitted flows FSCHED
and all waiting flows FWAIT, the eNB carries out, first, an initial
stage of pre-admittance filtering for the waiting flows FWAIT .
The reason of running this initial stage is two fold: First, it
filters FWAIT to a set of candidate flows FCAND ⊆F
WAIT to
be considered in the ILP model of the next stage. Second, it
helps fixing the ILP model parameter hmax. In both cases, this
stage aims to reduce the complexity of the ILP model to allow
for rapid convergence and shorter solution time. The flow state
transition from the view point of the eNB is shown in Fig. 3.
The pre-admittance filtering algorithm (PREFILT) is given, in
details, in Algorithm 1. It takes as inputs the current set of idle
nodes VD, the multicast trees of the ongoing flows and the wait
flows in the system, and produced as outputs a set of candidate
flows for the current scheduling SL frame and the value for the
parameter hmax. The algorithm proceed as follows: For each
waiting flow fk, it tries to construct breadth-first-traversal tree
that originates from it source node and spans all destinations
traversing the currently idle nodes in the system. Note that
the tree construction stops once all destinations are visited.
If such prebft tree 
Tkexists then the flow fkis added to
the set of candidate flows. On the other hand, a flow, for
which a prebft tree does not exists, would not be considered
for routing in the current SL frame since given the current
state of the D2D subnetwork no multicast distribution tree
can be formed. This is because either it source or one of
destinations is already using its D2D interface to route another
flow or all unavoidable relay nodes are exclusively involved
in other concurrent multicast trees. Therefore flows that fail
to pass this stage must not be considered in the ILP model
for the current SL frames wait for upcoming opportunity in
subsequent frames. It should be noted that the prebft trees
are constructed dynamically based on the current state of

Algorithm 1 pre-admittance filtering algorithm (PREFILT)
Inputs: VD,Tk∀fk∈F
SCHED ,FWAIT
Outputs: FCAND,h
max
1: FCAND ←∅,h←0,
h←0
2: for each fk∈F
SCHED do
3: if HeightOF Tk>hthen
4: h←HeightOF Tk
5: end if
6: end for
7: for each fk∈F
WAIT do
8: if {vsk}∪D
kVDthen go to 30
9: end if
10: Q←∅ new empty queue
11: push vskinto Q
12: S←{vsk}
13: LevelOF(vsk)←0
14: while Q=∅∧D
kSdo
15: vi←Q.pop()
16: if LevelOF(vi)>
hthen
17: 
h←LevelOF(vi)
18: end if
19: for each eij ∈O(vi)do
20: if vj/∈S∧vj∈V
Dthen
21: push vjinto Q
22: S←S∪{vj}
23: LevelOF(vj)←LevelOF(vi)+1
24: end if
25: end for
26: end while
27: if Dk⊆Sthen
28: FCAND ←F
CAND ∪{fk}
29: end if
30: end for
31: hmax ←max h, β ·
h
the nodes, and their primary purpose is early reject flows
in the joint routing and resource allocation before running
the decision problem involving the ILP model. Moreover, the
prebft trees are well-balanced as they exhibit tendency to be
short spanning trees due the breadth-first-traversal algorithm.
However, from the viewpoint of global topology, they also tend
to deviate from this preferred condition, as said before, based
on the dynamic state of the topology nodes. Fig. 4 illustrates
the concept of prebft trees and their deviation. In view of
the dynamic nature of prebft trees, Algorithm 1 goes a step
further and set the parameter value hmax of the subsequent ILP
problem based on the reported heights of these trees and the
actual heights of the concurrent multicast trees as follows:
hmax =max⎧
⎨
⎩max
fk∈
FSCHED
HTk,βmax
fk∈
FCAND
H
Tk⎫
⎬
⎭(22)
where H(·)refers to the height-of-tree operator and β≥1is
a “room-for-manoeuvre” factor allowing more possible multi-
cast trees to be explored during the ILP subsequent solution.
After determining the candidate flows and the parameter hmax,
the eNB proceeds by constructing an ILP as described in IV
considering only the flows F=FSCHED ∪F
CAND. Note that
the eNB adds additional constraints to restore the old routing
trees and half-duplex set assignments for FSCHED.
To solve the ILP, we propose the following objective func-
tion:
R1
S
D3
R4
D1 D2
R4
R2
R1
D3
D2
D1
S
R6
R3
R5
R7
S
R6
D3
D1 D2
R5
RBusy (active) relay
RIdle relay
R4
R3
Fig. 4. Prebft tree deviation.
Algorithm 2 ILP resolution
Input: ILP Model P0as defined in formula (23)
Output: Solution value for V∗as [x∗,H∗,y∗,...]
1: Push the initial problem P0onto the stack S
2: f∗←−∞ Initial value for Objective function
3: I←0Counter
4: while S =∅∧I≤Imax do
5: I←I+1
6: Pop a problem from Sas P
7: Let ˜
Pbe the relaxed form of Pwith continuous V∗
8: Solve ˜
Pusing simplex yielding
˜
Vand ˜
f
9: if not feasible or ˜
f≤f∗then go to 4
10: if
˜
Vare all integers then
11: V∗←
˜
V,f∗←˜
fand go to 4
12: else
13: Choose the closest variable to 0.5 as v†
14: Add a cut v†≤0to Pand push it onto S
15: Add a cut v†≥1to Pand push it onto S
16: end if
17: end while
18: return the solution value V∗
max
V∗αR
vn∈V
Bn+αA
fk∈F
tk
sk−αN
vn∈V
fk∈F
tk
n(23)
s.t. (1) – (20)
with αR1
Ω·|V|,α
A1
|FCAND|,α
N1
|V|
where the vector V∗=[x∗,H∗,y∗]represents the binary
decision variables defined earlier.
The proposed objective function is a weighted-sums for-
mulation of the following sub-objectives: 1) To maximize the
total number of allocated RBs in the system, 2) To maximize
the number of admitted flows, and 3) To minimize the number
of engaged nodes.
To solve the optimization problem described above, we
make use of Branch-and-Cut resolution method [8]. Algo-
rithms 3 and 2 illustrate the pseudo-code of our proposal
JRW-D2D-MC. Note that a bound on the number of recursive
iterations is introduced in order to limit the execution time.
VI. PERFORMANCE EVALUATION
In this section, we will evaluate the performance of the
proposed JRW-D2D-MC algorithm based on extensive sim-
ulations. First of all, we will briefly describe the network
simulation environment NS-3 which we augmented to sup-
port LTE-D2D protocol stack. Afterwards, we will detail the
studied scenario in this paper. Then, we will define the per-
formance metrics that we consider to evaluate JRW-D2D-MC.

Algorithm 3 JRW-D2D-MC pseudo-code
1: for each SL frame τdo
2: for each fk∈F
ARR do Arriving Flows
3: FWAIT ←F
WAIT ∪{fk}
4: end for
5: for each fk∈F
FIN do Finished Flows
6: VD←V
D∪NodesOF Tk
7: end for
8: Execute Algorithm 1
9: Construct the ILP model as in formula (23)
10: Solve the ILP model using Algorithm 2
11: for each fk∈F
CAND do
12: if Ak=1then
13: Configure Tkaccording to xh,k
ij
14: end if
15: end for
16: p←τmod 2
17: for each vn∈V
p
Gdo
18: Allocate RBs for vnaccording to yu,n
19: end for
20: end for
Finally, we will analyze the simulation results and discuss the
effectiveness of our proposal.
A. Network simulation environment
The NS-3 software package [9] is written in C++. It
provides powerful open-source tools to implement a wide
variety of network simulation scenarios and application using
different degrees of abstractions and reference technologies.
NS-3 provides substantial support for a variety conventional
3GPP LTE simulation scenarios through the module NS-
3/LTE [10]. Unfortunately, the latter does not support the LTE-
D2D standard. To the best of our knowledge, this is the case
for all available network simulators in this respect. This is, in
part, due to the fact that LTE-D2D is a relatively new standard.
To achieve our goal, we extended the NS-3/LTE modules
to include LTE-D2D protocol stack described in section III.
We developed the PHY, MAC and PDCP/RLC procedures
along with the signaling between the eNodeB and eUEs. The
signaling is necessary to i) configure the SL parameters, ii)
establish the SL radio bearers (SLRBs), and iii) exchange the
SL reports and grants.
B. Network simulation setup
In line with our formulation in section IV, we run extensive
simulations for a network of one macro-cell LTE-A with radius
Rcell =1km. The deployed UEs follows a Poisson Point
Process distribution with a density λUE nodes per km2for
values from {10,15,20,25,30,35,40 }. The LTE-A macro-
cell is configured to work with an UL/SL frequency of 1930
MHz and a bandwidth of 5MHz (i.e., 25 RBs). The eNB
configures SL to share the same reference bandwidth as UL
where only 14 RBs are set aside for the SL. In other words,
the actual SL bandwidth for the D2D operations corresponds
to Ω=14RBs. All UEs are configured to transmit on SL
with a common power density of Ψt=−4dBm/RB which
is equivalent to a maximum of 10 dBm over the whole 5
MHz. To model the SL path-loss, we make use of WINNER
II B2-LOS channel model [11]. The SL fame length is fixed to
40 milliseconds which corresponds to 40 subframes. However,
only 32 subframes are actually used for data transmission. The
subsequent subframes are used for SL control information. The
eNB builds the D2D network topology making using of SNR
TABLE I
SIMULATION PARAMETERS
Parameter Value
Cell Radius Rcell 1km
UL/SL Frequency fUL 1930 MHz
UL/SL (Reference) Bandwidth BUL 5 MHz (25 LTE RBs)
SL RBs Used Actually Ω14 LTE RBs
SL frame (LTE-D2D SC-Period) 40 subframes (40 ms)
Data Part in SL frame 32 subframes
UE SL Power Transmit Density Ψt-4 dBm/RB
Noise Spectral Density Ψn-121.45 dBm/RB
UE Density λUE {10,15,20,
25,30,35,40 }per km2
UE-UE SNR Threshold γTOPO 10 dB
Scheduling SINR Threshold γ6dB
Flow Simulation Period 10 seconds
Flow Arrival Process Poisson Process
Flow Arrival Rates λFLOW {5,10,15,20 }flows/second
Flow Duration Random Variable Exponential
Flow Duration Mean λDUR 1 second
Flow Bit Rate Classes {25,50,75,100,
125,150,175,200 }kbps
Node-Flow Interest Probability ρ0.1
hmax update factor β1.5
Max. Iterations to solve ILP Imax 10000
reports and estimations. A link of topology exists if and only
if the respective SNR is greater than a threshold γTOPO =10
dB. Simulated flows are generated following a Poisson process
with an arrival rate equals to λFLOW ∈{5,10,15,20 }flows
per second. On the other hand, flows are assumed to carry a
CBR traffic randomly selected from predefined Constant Bit
Rate (CBR) classes. Flow duration distribution is simulated to
follow an exponential random variable with a mean duration
of λDUR =1second. Sources of multicast flows are selected
according a random uniform distribution. As for destinations,
they are selected for a given source assuming a node-flow
interest probability of ρ=0.1. In other words, once a
flow source is selected, other nodes are evaluated for being
interested in receiving the flow using Bernoulli trials with a
success probability equals to ρ. TABLE I summarizes the main
parameters used in simulations. For evaluation purpose, the
confidence level is set to 95% when applicable.
C. Performance metrics
We consider the following metrics to evaluate our proposal:
1) S: is the ratio of the flows that are offloaded by the D2D
subnetwork.
2) A: is the maximum number of concurrent admitted flows
in the D2D subnetwork.
3) H: is the average height of multicast distribution trees in
each simulation run.
4) D: is the average packet’s transmission delay between the
source and the farthest destination in each simulation run.
D. Simulation results
To assess the robustness of our approach, we evaluate, first,
its ability to absorb the multicast flows with respect to the
arrival rate of the latter (i.e., λFLOW ), while increasing the
network density. As depicted, in Fig. 5a, the offload rate
slightly decreases when the density of the network increases
whatever the value of λFLOW. This can be explained mainly by
the way the flows are generated. We recall that we make use
of Bernoulli trials to generate the destinations. Consequently,
the number of interested destinations is correlated with the
density of the network. Besides, we notice that the offload
rate varies between 10% and 25% when λUE varies between
10 and 40. Moreover, it is worth noting that, when increasing
λFLOW, the gap between the offload rates lessens. This result
proves that our approach optimizes jointly the path selection

0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
5 10 15 20 25 30 35 40 45
Offloadingrate(S)
λUE
λFLOW=5
λFLOW=10
λFLOW=15
λFLOW=20
(a) Offloading rate
0
0.5
1
1.5
2
2.5
3
3.5
4
5 10 15 20 25 30 35 40 45
Maximumnumberofconcurrentflows(A)
λUE
λFLOW=5
λFLOW=10
λFLOW=15
λFLOW=20
(b) Maximum number of concurrent admitted flows
Fig. 5. Performance metrics w.r.t Sand A
and the resources allocation which ensures a stable offload rate
against an increasing traffic load.
Fig. 5b depicts the maximum number of flows that the
D2D subnetwork can simultaneously handle, with respect to
the deployment density of UEs. It is straightforward to see
that Aincreases as λUE increases. This is due to the fact that
denser topologies enable more routes. Indeed, more nodes are
available to route concurrent flows circumventing the node-
exclusivity restriction. Besides, we notice that JRW-D2D-MC
is able to handle more flows as the traffic load increases. In
fact, as depicted in Fig. 5b, the number of flows circulating
in the network doubles when λFLOW grows from 5to 20. The
obtained results corroborate the previous ones depicted and
confirm that our proposal is capable of absorbing the growing
traffic.
In order to gauge the efficiency of our multicast path
selection, we evaluate the average height of multicast trees
with respect to the UEs deployment. Fig. 6a shows that H
linearly increases as the density of D2D nodes increases. In
fact, it rises threefold for a λUE varying between 10 and 40.
This is due mainly to the high interference level caused by
close UEs. Consequently, our approach selects longer paths to
alleviate interference effects and hence ensures a higher offload
rate. Besides, it is clear to see that our approach is still stable
while λFLOW grows from 5to 20. Such result is expected,
since JRW-D2D-MC aims to maximize the number of D2D
flows while minimizing the number of forwarding nodes. By
doing so, the allocation of wireless resources is optimized and
consequently, the interferences are minimized.
Fig. 6b depicts the average packet transmission delay, D,
measured between the source and the destinations of flows
0
1
2
3
4
5
6
7
8
5 10 15 20 25 30 35 40 45
Averageheightofmulticasttree(H)
λUE
λFLOW=5
λFLOW=10
λFLOW=15
λFLOW=20
(a) Average height of multicast tree
0
50
100
150
200
250
300
5 10 15 20 25 30 35 40 45
Averagepackettransmissiondelay(D)ms
λUE
λFLOW=5
λFLOW=10
λFLOW=15
λFLOW=20
(b) Average packet transmission delay
Fig. 6. Performance metrics w.r.t Hand D
with respect to λUE. It is clear to see that the delay slightly
increases when the topology becomes denser. This result
confirms those obtained for the height measurement of mul-
ticast trees. It is straightforward to see that multicast trees’
height directly impacts the transmission delay of packets.
Besides, it is clear to see that the delay is still stable whatever
the values of λFLOW. The obtained results confirm that our
proposal alleviates network delay, and hence enhances network
performance. Note that the obtained maximum delay is about
250 ms which satisfies the end-user performance expectations
for conversational services such as voice conversation, video
telephony and interactive games [12].
VII. CONCLUSION
In this paper, we addressed the problem of joint multicast
routing and OFDM resource allocation in LTE-D2D multihop
networks. We considered LTE-D2D-specific constraints: half-
duplex D2D operation in LTE-D2D and the contiguous RB al-
locations. An offloading application for intracellular multicast
traffic was conceived as use case where data from flows are
routed over the D2D multihop subnetwork and the eNB hosts
the control plane. We proposed an ILP formulation for the
problem and novel scheme named JRW-D2D-MC composed
of two-stage algorithm to solve it. We validated our proposal
using NS-3 simulator after implementing the whole LTE-D2D
protocol stack. The evaluation showed satisfactory results in
terms of optimality, ratio of admitted D2D flows and latency.
Results also showed how successful our conceived offloading
system is, under our scenario assumptions which are not far
from realistic setups.

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