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2018 IEEE 43rd Conference on Local Computer Networks (LCN)
Joint Routing and Wireless Resource Allocation in
Multihop LTE-D2D Communications
Safwan Alwan*, Ilhem Fajjaril and Nadjib Aitsaadi^
*University Paris-Est, LiSSi EA 3956, UPEC, F94400, Vitry-sur-Seine, France
1Orange 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—5G aims to maximize the data rate and to handle the
billions of video, voice, data and IoT flows. For this reason, the
macro-cells will be very congested and may fail to satisfy the end-
users. In this context, data offloading scheme is conceived to route
intra-cell traffic among the D2D-enabled u ser equipments reusing
wireless uplink resources and thus incr easing the overall spectral
efficiency. In this paper, we address the jo int routing and OFDMA
resource allocation problem in D2D network. To do so, first we
formulate the problem as Mixed In teger Linear Programming.
The model takes into account factors that limit spectrum reuse
as well as other LTE-D2D technology constraints such as: half-
duplex operation and contiguity in resource block allocations.
Then, we propose a novel scheme named Joint Routing and
Wireless allocation in D2D communications (JRW -D2D) which
is based on the branch-and-cu t algorithm. In order to gauge the
effectiveness o f our proposal, we implement the standard LTE-
D2D protocol stack, including our scheme JRW-D2D, in the NS-3
network simulator. The results obtained are very promising in
terms of reliability, ratio of admitted D2D flows and latency in
comparison to other basic one-sided optimal strategies including
an interference-aware heuristic scheme.
Index Terms—Multihop routing, Resource allocation, Offload-
ing, Device-To-Device LTE-D2D, Optimization.
I. Int r o duc t io n
There is no denying that the Fourth Generation (4G) of
mobile cellular network, Long Term Evolution (LTE), held
the promise of higher data rate and enhanced the Quality of
Service (QoS). But, the growth of video-centric and social
media services has led to the explosion of traffic demand.
In addition, Internet o f things will exponentially increase the
number of flows in the cellular network. Consequently, current
operator infrastructures struggle to accommodate the required
network resources and link capacities. This trend is set to
continue and recent statistics highlight that the number of
connected devices is estimated to reach 50 billion by 2020
while the mobile data traffic is expected to grow to reach 49
exabytes per month by 2021 [1].
Therefore, discussions of a new standard have taken place
in both industry and academia to design the Fifth Generation
(5G) mobile cellular network architecture. The main objective
of 5G is to ensure the QoS satisfaction of the different
applications and to deal with diverse deployments in terms of
available resources and connected devices requirements. In this
context, 5G puts forward disruptive technologies making use
of i) massive MIMO and millimeter-Wave antenna systems, ii)
Multiple Radio Access Technologies (Multi-RAT), iii) small
cells deployment and iv) advanced Device-to-Device (D2D)
communications. All these techniques aim to increase the
capacity of networks in order to handle large number of
connections and data volume at high throughput and very low
latency.
The main idea behind D2D is to enable direct communi
cations between devices in close proximity and thus bypass
ing macro base-stations (eNodeB). D2D was incorporated in
LTE-A to increase the spectral efficiency of cellular systems
and to support new use cases such as: i) public safety scenar
ios, ii) device-discovery for commercial applications, iii) D2D-
network relays, etc. D2D is also one pillar of 5G architecture
enabling operators to ensure an extended and controlled con
nectivity while reducing the networks cost thanks to the traffic
offloading solutions. In doing so, the data plane is moved
from operator’s infrastructure (i.e., E-UTRAN and EPC) to
end-users’ devices (i.e., UE). However, the control plane is
managed by the operator and hosted in E-UTRAN. This will
alleviate the infrastructure’s load while enabling large numbers
of simultaneous connections with better QoS.
D2D raises several design challenges [2], [3] such as:
coexistence with conventional communications mode (macro
cell), spectrum reuse and resource allocation, mode-switching,
extending single-hop scenarios to multihop ones, etc. In this
paper, we address the routing and wireless resource allocation
problems in D2D communications. Multihop D2D seeks to
enhance the utility of D2D systems by increasing communi
cation range and reducing the load in the operator’s infras
tructure. Multihop D2D system must adopt various policies
with respect to the routing, resource allocation, interferences:
intra-mode (i.e., D2D links) and inter-mode (i.e., D2D and
conventional communications). Note that a sidelink communi
cation (i.e., D2D) uses the same physical resource (transceiver
and spectrum) of uplink communication. That means, UE
cannot simultaneously run both sidelink and uplink com
munications. In addition, UE cannot simultaneously transmit
and receive in the sidelink. Consequently, each link in the
D2D path is half-duplex and only non-critical (in terms of
latency and bandwidth) traffic can be handled. We formulate
the joint routing and resource allocation problem o f D2D
communications while considering: i) contiguity of OFDMA
resource block allocation, ii) interference and iii) half-duplex
mode of operation in LTE-D2D as a Mixed Integer Linear
Programming (MILP) problem. The objective is to maximize
the bandwidth of each flow (i.e., best effort).
To solve the above problem, we propose novel scheme,
based on the branch-and-cut algorithm [4], named Joint
Routing and Wireless allocation in D2D communications
(JRW-D2D). In this paper, we assume a dense deployment
of UEs in delimited area such as stadium. Consequently, the
UEs are not mobile. It is worth noting that the routes set up
for flows are semi-static paths. In other words, each path is
maintained for the whole period of communication to avoid
excessive signaling to reconfigure D2D links. On the other
hand, resource allocations are dynamically executed every
assignment interval to cater for flow arrivals and departures.
To assess the performance of our proposal JRW-D2D, w e
implemented the LTE-D2D protocol stack in the NS-3 network
simulator to support this standard. In doing so, the whole
protocol stack is simulated and hence the conclusions will be
more significant than the numerical simulations. The results
obtained demonstrate the effectiveness of JRW-D2D in terms
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2018 IEEE 43rd Conference on Local Computer Networks (LCN)
of the optimality, ratio of admitted D2D flows and latency. In
addition, we compared our proposal to other basic one-sided
optimal strategies and an interference-aware heuristic scheme.
One-sided optimal strategy is one which is optimal only in
one sense either in terms of routing or in terms o f resource
block allocation.
The remainder of this paper is organized as follows. In
section II, we will present an overview of existing literature
that deals with the issue of multihop D2D communications. In
section IV, we will describe in details our system model for
the offloading application and how we formulate the decision
problem as a MILP model that includes routing and resource
block allocation. Then, in section V, we will describe our pro
posal JRW-D2D used to solve the underlying problem. Next,
in section VI, we will present our evaluation methodology and
network simulation results. Finally, Section VII will conclude
the paper.
II. Rel at ed Work
D2D wireless communications in cellular networks is an
extremely challenging paradigm that has aroused the interest
of both industry and academia. In this section, we summarize
the most relevant related work that helped us to have an
insight into the multihop D2D routing and resource allocation
problems.
In [5], the authors propose D2D multihop communications
in cellular networks for a public safety scenario under partial
coverage. Using a homegrown 3GPP standard compliant sys
tem level, the authors claim to have demonstrate improvements
in both energy and spectral efficiency compared to conven
tional communications. However, the routing algorithm was
not introduced in their public safety scenario. In fact, only
predefined routes are used in to allow one far-away UE to
reach an active base-station using the other UEs as relays.
In [6], the authors put forward a two-stage method to
find multihop D2D paths under a limit on the maximum
interference incurring at conventional mobile users. Based on
numerical simulations, significant improvements in throughput
can be achieved using multihop paths compared to single-hop
D2D communication. However, the proposed method is highly
generic. Indeed, only one single assumption is considered by
the authors to apply their approach: downlink resources are
shared by D2D and conventional communication.
In [7], the authors study the optimal transmission scheduling
and congestion control in multihop D2D communications
underlaying cellular networks while taking into account: i)
interference situation for D2D mode and conventional cellular
mode and ii) QoS requirements o f each traffic flow. Making
use of Lyapunov optimization theory, the formulation con
siders the following problems in order to solve the global
problem in a sub-optimal way: i) end-to-end rate control, ii)
joint routing and channel assignment, and iii) power allocation.
It is worth pointing out that the proposed algorithm takes into
account also the stability o f queues in forwarding devices
since it adopts a dynamic routing where decision is done
on per-time-slot basis. Remarkably, the proposed algorithm
also makes a number of assumptions relevant to LTE-D2D: i)
D2D links share the uplink spectrum and ii) half-duplex nature
of D2D links. However, the spectrum allocation in terms of
resource block is not considered which renders it less realistic
in the view of LTE-D2D standard.
In our work, we address the joint optimization of resource
block allocation and routing for multihop communications.
Unlike [7], we adopt a semi-static routing where path es
tablishment takes into account the current state of interfering
UE2
Fig. 1. LT E-D2D protocol stack fo r direct communicat ions
links, but the path is held for the whole period of communi
cation. We also model the allocation problem to the resource
block level taking into account the fact that they are allocated
in contiguous manner (3GPP uplink constraint). Besides, we
notice that existing literature on multihop D2D communica
tions shows varying degree of relevancy to LTE-D2D standard
and lack of proposal validation using network simulators due
the support for D2D standards. To cope with this limitation,
we implemented in NS-3 the full 3GPP LTE-D2D protocol
stack to evaluate the performance of our proposal.
III. LTE-D2D Architecture
To support LTE-D2D, an enhanced user equipment (UE)
contains an additional protocol stack besides the conven
tional one. This new LTE-D2D stack provides the so-called
proximity-based services (ProSe) to the upper layer(s) [8].
ProSe includes: i) Direct Discovery: a service whereby a UE
is able to detects and identify other UEs in its proximity,
ii) Direct Communications: UEs can directly communicate
with each other bypassing the cellular infrastructure, and
iii) UE-to-Network Relay: remote UE uses another UE as a
relay in the network.
From an upper level perspective, ProSe are carried over a
new type of wireless link besides the conventional ones (i.e.,
DownLink (DL) and UpLink (UL)). This lateral link between
UEs is called SideLink (SL). In LTE-D2D, SL is configured
to use the same frequency resources as UL to increase the
overall spectral efficiency. It also reuses much of UL structure
and hardware to add another efficiency dimension. From the
lower layers perspective, SL presents its direct communication
services to the upper layers in terms of no-feedback SL Radio
Bearers (SLRBs). This is done to present a uniform support
for both unicast and multicast IP communications [8].
A. LTE-D2D protocol stack for direct communications
Fig. 1 depicts the LTE-D2D stack to support direct communi
cations. Hereafter, we provide a brief top-down description.
1) PDCP/RLC
Similar to their counterparts in the conventional LTE commu
nication stack, Packet Data Convergence Protocol and Radio
Link Control layers provide IP packet segmentation, header
compression and security procedures. A single SLRB is iden
tified by pair of PDCP/RLC entities connected in tandem at
the source UE and the corresponding pair(s) at the destination
UE(s). At the interface with incoming packets from the upper
IP layer resides an IP-flow classifier that directs each IP packet
to its corresponding SLRB PDCP/RLC entities.
2) MAC
It serves the upper layers by transmitting Transport Block
(TB) composed of RLC Protocol Data Units (PDU) from
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2018 IEEE 43rd Conference on Local Computer Networks (LCN)
namely i) the source ProSe-UE-ID and ii) the destination
ProSe-L2-Destination-ID. A TB is transmitted when a new SL
transmission opportunity arrives while Hybrid ARQ (HARQ)
operations in LTE-D2D is restricted to blind retransmissions
(i.e., with no feedback) to increase the reliability. Hence,
each TB is further retransmitted three times in the subsequent
transmission opportunities with different redundancy versions.
3) PHY
Similar to UL, SL transmission uses the SC-OFDM modu
lation format using the grid of resource blocks. The latter
occupies a subframe (i.e., TTI) which lasts for 1 ms and
a bandwidth of 12 sub-carriers (180 KHz) in frequency
domain. However, unlike UL, SL allocations are organized
in longer periodic intervals called SideLink control Periods
(SL-Periods), which can be configured between 40 and 320
subframes in length. As depicted in Fig. 2, a SL-Period
starts with a control part followed by a data part. However
the information, on which subframes and RBs are actually
available for the operation, is conveyed by a configuration
parameter called a resource pool.
A UE interested in SL reception continuously scans the
configured resource pool(s) (the control part of SL periods)
to check for incoming data. On the other hand, a UE wanting
to transmit on SL transmission part, may be configured to
go ahead and autonomously selects a subset RBs to use for
transmission from a resource pool configured for this mode
of operation. Even with in-coverage scenarios, the eNodeB
may configure this autonomous mode for its UEs. Another
possible option is to configure scheduled-resources pool to be
used in the scheduled mode which gives the eNodeB a finer
control over resource allocation. In this mode, a grant from
the eNodeB to the UE determines which RBs and subframes
to be used by the UE to transmit on SL. In this paper, we
assume the latter mode of resource allocation. In doing so,
the eNodeB has a total control on the resource allocation.
B. Synchronous operation of SL
Transmission and reception on SL are synchronous operations
that require a common synchronization reference for all parties
in the system. With in-coverage scenarios, where a UE is
inside the coverage zone of an eNodeB, the UE synchronizes
its SL operation to the timing of the related macro-cell which
acts as a synchronization reference. Further procedures and
provisions are given in the standard allowing some UEs to
relay timing reference to extend the synchronization zone even
under out-of-coverage scenarios [8].
C. Half-duplex operation o f SL
As per LTE-D2D standard, the duplex mode of SL is half
duplex meaning that a UE can not simultaneously both listen
and transmit on SL. However, the rules for role-switching are
not specified and left to the application under consideration. In
Fig. 3. Sid elink frame structure and scheduling
addition, UEs connected to the eNodeB (i.e., macro-cell) are
required by the standard to give their UL transmissions higher
priority over SL transmissions since both compete for the same
SC-OFdMA transmitter. So, whenever there are UL data or
reports (e.g., SRS, CQI, etc.), an ongoing SL subframe, if
any, must be dropped. These properties make SL transmissions
more opportunistic and intermittent and less reliable than UL.
IV. System Model and Probl em Formul ation
Our system model considers N UEs inside the coverage zone
of a single LTE-A eNodeB. These UEs, which are supposed
to support the LTE-D2D protocol, are willing to offload the
intra-cellular traffic between them when commanded to do so
by the central controller in the eNodeB. We also assumes that
these UEs are quasi-stationary nodes. The eNodeB supervise
the offloading operation over this D2D subnetwork by con
tinuously allocating radio resources in every SL frame with
decision instants given by:
t = t x TSl for t = 0,1, 2,3,...
where TSL is the duration of SL frame. The SL frame, or the
SL control period in LTE-D2D terminology, is the scheduling
time unit in SL which spans multiple one-millisecond time
slots (i.e., multiple TTIs). Fig. 3 illustrates the structure of SL
frame. The eNodeB models the D2D topology as a symmetric
directed graph G = (V, E). The set of vertices V and the set of
edges E represent the UE nodes and the links between the UEs
(i.e. SLs) respectively. Note that a link in topology is formed,
and hence an edge exists in G, only when the achieved SNR
is greater than a threshold 7topo. This means that G is not
(fully-)connected in the general case and can be expressed as
a union of connected subcomponents: G = G 1 UG2 U.. .UGC.
The problem of finding an offloading path for a flow fk £
F, whose source and destination are sk ,dk respectively, can
be formulated as follows: We introduce for each link ej a
binary variable xj to indicate whether it is selected to be a
part of some route. We also introduce for each node vn a
binary variable An that indicates whether it is associated with
the flow fk. In this formulation the offloading path for fk is
defined by the set of P k C E :
Pk = {ej e E \x j = 1 A Ak = Ak = 1 } (1)
However, in order for equation (1), to meaningfully define a
path, the solution space must respect some constrained defined
in the following.
First we impose that nodes are exclusive for concurrent
flows. In other words, a node can route at most one flow at a
time. Formally, this constraint is introduced as:
_ < 1 (2)
yvn e V , J2Akn < 1
f keF
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2018 IEEE 43rd Conference on Local Computer Networks (LCN)
In addition, if a node is associated with some flow it must
have exactly one incoming links selected except at the source
where there is none. This is formally imposed as:
yv n £ V , Xij = A kn (3)
eij ££\j=n f k ,vn=sk
Similarly, if a node is associated with some flow it must have
exactly one outgoing links selected except at the destination
where there is none, or:
Vvn £ V , ]T Xij = ]T Akn (4)
eij ££\i=n f k £F\vn=dk
Also, to ensure that node association is consistent with link
selection, the following constraint imposes that the ends of a
selected links are associated with the same flow:
y f k £ F , yeij £ E, Xij - 1 < Ak - A k < 1 - Xij (5)
It is straightforward to see that, if some flow fk is decided
to be admitted, which is indicated by Ahsk = 1, then P k, as
defined in equation (1) and under Constraints (2) to (5), must
contain only one simple path, which starts from sk to dk.
However these constraints do not rule out superfluous links
(and nodes) from appearing in P k forming simple isolated
cycles between them.
To exclude these isolated simple cycles from the decision
space, we propose the token-split method. If a pair of nodes
(vi, v j ) is selected to form a route, a token of one unit,
tij +tji =1, is unconditionally split between them such that
vi and vj receive tij and tji respectively. Note that the
only constraint on tij ,tji is that they are nonnegative reals.
However, to exclude the above-stated cycles, we impose that
each node must receive a total amount of tokens that is strictly
less than 1. To see how this works, suppose that we have a
cycle of m nodes and m links selected. Then, the total tokens
to be split among them equals exactly m. In this case it is
impossible to find a way to split tokens between consecutive
pairs in the loop such that each node receive strictly less than
1. To formulate such strict inequality by a non-strict one, a
threshold parameter 0 < e < 2 may be used. Then, the no
loop constraint can be stated as:
yvn £V , 'Yk tij < 1 - e
eij ££\i=n
However, we must also be sure that such restriction does not
rule out arbitrary paths in the solution space. Suppose that we
have a path of m > 3 nodes with m - 1 links selected. Then,
we show that it is possible to split the total m - 1 tokens
respecting the previous constraints if e < m. To prove this,
we can split the tokens such that the first m - 1 nodes receive
exactly 1 - e token each, and as a consequence, the last one
receives (m - 1) - (m - 1)(1 - e) or (m - 1) e token. This is
explained graphically as follows:
© 1-2E 2 e © (m-2)E©
© CH)
® 1-c c ® «?-3 c <V l * (m-l{?
To respect the no-cycle condition at the last node, we have
(m - 1)e < 1 - e which implies e < m which completes
the proof. To sum it all, if we set the parameter e = ^,
where \V\ is the total number of nodes, then all possible loops
are excluded from the solution space without excluding any
possible (simple) path from a source to a destination. Formally,
the no-cycle constraints are given by:
Veij £ E, Xij + Xji < 1 (6)
yeij £ E ,t ij + tji Xij + Xj i (7)
yvn £ V, tij < 1 - V (8)
eij ££\i=n
Given the half-duplex mode hardware constraint in D2D,
UEs cannot simultaneously transmit and receive on SL. There
fore, active nodes must switch back and forth between roles.
In order to reduce the end-to-end delay, we require all non
successive nodes in a path to transmit in one period while
their respective partners are listening to them, and on the next
period, they swap roles. This principle of operation forces
the links along a path to be scheduled in alternating manner.
The net effect of these assumptions is that the SL scheduler
switches every SL frame between two sets of active UEs in
order to maintain the ongoing flows. In other words, the active
nodes VH C V are divided into two sets: VH = {vn £ V \
Hn = 0} and VH = {vn £ V \ H n = 1} where Hn are binary
variables attached to the nodes. Hence a pair of nodes, having
an active link between them, cannot be in the same half-duplex
set (period):
y e j £ E, Xij < H i + Hj < 2 - X j (9)
In addition to its assigned half-duplex period, a transmitting
node needs also frequency resources. In line with LTE-D2D
standard, we assume a Frequency Division Duplex (FDD)
cellular network where we assign a bandwidth BSL, composed
of Q contiguous OFDMA RBs, to the SL operation. Note that
only contiguous RB allocations are feasible within this band
width because the SL has the same communication proprieties
as the UL [9]. We represent the allocated RBs for a node vn,
by a vector of 0-1 variables for w = 1,2, ••• Q, where the
variable R% indicates whether the RB number w is allocated to
vn. To formulate the contiguity constraints, we use the Ham
ming distance. The Hamming distance dH (V1, V2) between the
vectors V1 and V2 is the number of positions at which the two
vectors differ. The Hamming distance between two 0-1 vec
tors, Vi = [ViW2, ••• , Vin]T and V2 = [
V
is the sum of component-wise XoR operation between the
vectors (i.e. dH(V1,V2) = J2"=1 V{ ©V£). To check an alloca
tion vector [Rn, R2n , • •• , R 2 ]T for contiguity, we remark that
the Hamming distance between [R n , R ^ , • •• , R k - 1 ]T and its
shifted version [R2n, R 2n , • •• , R n f is less than 2 if the Rn = 0
and is less than 1 if Rn = 1 as illustrated as follows:
01100000 11100000 0000 1111 allocation vectors
0 100000 100000 0000 1
lshifted vers ions
1 0 [ r i^ 0T0TO roTom oToToT^ |0|0 |0 rri^ 0TO XO R operations
a) valid contiguous allocations
0| 000| 00| o o o o allocation vectors
100 0100 100 10 00 1l shifted versions
[U [1 - U p - CTTQTU l i u p u p u 3 H [ l H 0 [ i g X O R o p e r a ti o n s
b) invalid non-contiguous allocations
Formally, this constraint is express as:
n-1
yvn £ V ,Y ,R n ® Rn+1 < 2 - Rn (10)
W=1
In addition, RBs are allocated for some node vn only when the
node is a transmitter (i.e. one of its outgoing links is selected).
Formally:
n
yv n £ V , J 2 R " < Xij (11)
w=1 eij ££\i=n
To increase the reutilization of RBs and to reduce power
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2018 IEEE 43rd Conference on Local Computer Networks (LCN)
consumption, we require that nodes are not allocated RBs
beyond the request of the associated flow or formally:
n
yfk £ f , y vn £ V , Y,Rn < Q + D - Q) Akn (12)
w=1
Note that the relation between flow bit-rate Rk and the
respective demand for RBs Dk is defined by [9] as:
k TBS (MCS, Dk1
R = C[mbps] (13)
where TBS is the MAC transport block size function in bits as
defined in [9] considering a baseline Modulation and Coding
Scheme (MCS) for the SL. C is a constant equal to 1000.
In face of the reutilization o f RBs, system performance is
limited by interference caused by nodes transmitting using
the same RB. To deal with interference, we assume a fixed
power density scheme for the D2D emission. According to
this scheme, the total emission power Stx,n of a node is pro
portional to the number of allocated RBs E n=1 Rn. Formally,
n
Stx,n = * t,n • ^ Rn [mW] (14)
Furthermore, we assume a common emission power density,
*t,n [mW/RB], for all the D2D nodes (i.e., yvn £ V, * t,n =
* t ). Following the same per-RB treatment and assuming flat
block-fading channel model, the overall Signal-to-Interference-
plus-Noise Ratio (SINR) on the link eij is equal to:
Y .. = g ij (15)
li3 E 9nj * t,n + * « ( 5)
Vn EV
where and *t,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 ).
Furthermore, additional variables Rn,<0 and Rn1 are defined
to indicate whether the RB w is used by vn in VH or VH (i.e.
half-duplex set of frames), respectively. Formally,
y(vn, w) £V x [1, Q], R ^ 0 4 Rn - RE (16)
y(vn,w) £ Vx [1, Q ^ 1 ± HnRn (17)
An additional set of link-level auxiliary 0-1 variables are
introduced as follows:
y(eij,w ,p) £ Ex [1, Q]x{0 ,1},R j 4 Rn,p (18)
y(ei, ,w ,p ) £ E x[1, Q]x{0 ,1},rn% ^ R Y R ? (19)
where Rnf indicates if the RB w is used for the scheduled
ij
link eij during the pth half duplex set, 4^,% is an interference
indicator between node vn and link eij on the RB w.
To adhere to a linear formulation, further steps are needed
to linearize the XoR-terms in Constraint (10) and the product
terms in Constraints (17), (18) and (19).
We make use of a standard technique to linearize each XoR -
term X®y by introducing an additional auxiliary 0-1 variable
\fy add four more linear constraints as follows:
(>x - y ), (A% > y-x ) , (A% < x +y), (x Xy<2 - X - y) (20)
We use another standard technique to linearize each product
term X y by introducing an additional auxiliary 0-1 variable
\fy add four more linear constraints as follows:
(A®y<x), (X%<y), (X% >X+ y-1 ) (21)
To optimize the performances by minimizing interferences,
SINR must be upper-bounded by a common threshold y. To
formulate this constraint on RB allocations, we translate this
limit (i.e., SINR < 7) into the inequality N+I < P
r/y where
Pr is the received power.
Algorithm l JRW-D2D pseudo-code
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
for each SL frame
t
do
for each fk £FA do > Arriving flows
if sk and dk £ the same component of G then
Fw ^ Fw U {fk}
end if
end for
for each fk £ Ffin do > Finished flows
V
d ^V d U NodesOF (Pk)
end for
Construct the MILP model as in formula (23)
Solve the MILP model using Algorithm 2
for each fk £ F W do
if Ak, = 1 th en > Flow is admitted
Configure the path according to P k
end if
end for
p ^
t
mod 2
for each vn £ VHP do
Allocate RBs according to [
R,1n , R n, • • • , R n\T
end for
end for
y(eij ,n,p)E
Ex[1,n]x{0,1}, * Rn,P+ J2 gnj * t • 4n,p <-
n,ij —
n=i
gij * t
YRj (22)
As stated before, the function of our eNodeB is to schedule
the SL resources in order to support the ongoing (already-
admitted) flows and to handle newly-arriving flows trying to
admit some of them when possible. In doing so, the objective
is to maximize the overall utilization of system resources
(nodes and RBs) while serving the maximum possible number
of flows. To reach such objective, our utility function can be
decomposed into three goals: 1) maximizing the total number
of allocated RBs, 2) maximizing the number of admitted flows,
and 3) minimizing the total hop-count of the reserved paths.
We propose to formulate these goals as single objective-
function of weighted-sums to complete the MILP formulation,
developed so far, as follows:
max.
xij ,An ,tij
Hn,R“ ,...
«B EE Rnn + «A Ak.k - «N
Vn£V
nE [1,n] f kEF
A
k
n
Vn E V
f kEF
subject to:
(2) to (12), (16) to (19) and (22)
tij £ [0,1] c R, all other variables £ {0,1} (23)
where the normalizing factors defined by:
aB = q\v\, a A = \ F \,a N = V (24)
V. P roposal: jrw-d2d
In this paper, we propose novel strategy named Jo in t Rout
ing and Wireless allocation in D2D com munications
(JRW-D2D) to solve the optimization problem described
above. our proposal is based on Branch-and-Cut algo
rithm [4]. The latter is well-known optimization algorithm
and efficient to solve the general class of Mixed-Integer-
Linear-Programming (MILP) problems. JRW-D2D proceeds
as follow. First, the binary variables are relaxed by allowing
them to admit continuous values between 0 and 1. Then,
the relaxed problem is solved by simplex algorithm. If the
latter converges to an optimal solution with at least fractional
value for a variable, then a branch is introduced on that
variable. A branch means that two subproblem nodes are
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2018 IEEE 43rd Conference on Local Computer Networks (LCN)
Algorithm 2 MILP resolution
Input: MILP Model P0 as defined in formula (23)
Output: Solution value for V* as [Xij , A kn, t ij, H n , R n ,. .. ]
1: Push the initial problem P0 onto the stack S
2: f
* <
----
c» > Initial value for Objective function
3: I ^ 0 > Counter
4: while S = < Imax d o
5: I ^ I + 1
6: Pop a problem from S as P
7: Let P be the relaxed form of P with continuous V*
8: Solve P using simplex yielding V and f
9: if not feasible or f < f
* then go to 17
10: if V are all 0 or 1 except for tij then
11: V * ^ V , f
* ^ f and go to 17
12: else
13: Choose the closest variable to 0.5 as v1
14: Add a cut v1 < 0 t o P and push it onto S
15: Add a cut v1 > 1 t o P and push it onto S
16: end if
17: end while
18: return the solution value V*
scheduled to be solved recursively with additional cuts (i.e.,
additional inequality constraints). Each cut bounds the variable
in subproblems by 0 or 1. Each subproblem is, in its turn,
relaxed again and the whole process repeats until finding a
set of feasible integral solutions that includes the optimal one.
However, a scheduled problem node is pruned if its objective-
function value in the relaxed solution is worse than the best
integral solution found so far. Pruning a node means that the
latter cannot generate further subproblems. Hence, extensive
search for optimal integral solution is avoided. Algorithms 1
and 2 illustrate the pseudo-code of our proposal JRW-D2D. It
should be noted that we also introduce a bound on the number
of recursive iterations to limit the execution time.
VI. Performance Eval uation
In this section, we will gauge the performance of our proposal
JRW-D2D based on extensive simulations. First of all, we
will briefly describe the network simulation environment NS-
3 which we augmented to support LTE-D2D protocol stack.
Then, we will detail the studied scenario in this paper. After
wards, we will define the performance metrics. Finally, we will
analyze the simulation results and discuss the effectiveness of
our proposal.
A. Network simulation environment
The NS-3 software package [10], which is written in C++,
provides powerful open-source tools to implement a wide
variety of network simulation scenarios and application using
different degree of abstractions and reference technologies.
NS-3 provides substantial support for a variety conventional
3GPP LTE simulation scenarios through the module NS-
3/LTE. 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 the necessary LTE-D2D protocol stack. We developed
the PHY, MAC and PDCP/RLC procedures along with the
signaling between the eNodeB and UEs. The signaling is
necessary to i) configure the SL parameters, ii) establish the
SL radio bearers (SLRB), and iii) exchange the SL reports and
grants.
table i
Simu l a t io n Parameter s
Parameter Value
Cell Ra dius R cel l
UL/SL Frequency fuL
UL/S L (Refere nce) Ban dwidth Bul
SL RBs Used Actually Q
SL frame (LTE-D2D SC-Period)
Data Part in SL frame
UE SL Po wer Transmit Density
No ise Spectral Density
LTE MCS Index used in SL
Tkm
1930 MHz
5 MHz (25 LTE RBs)
14 LTE RBs
40 subf rames (40 ms)
32 subframes
-4 dBm/RB
-121.45 dBm/RB
9 (QPSK)
UE D ensity Aue
UE-U E SNR Threshold ttopo
Sched uling SIN R Threshold 7
{10,15, 20, 25,
30, 35, 40} per km2
10 dB
6 dB
Flow Simulat ion Period
Flow Arrival Process
Flow Arrival Rates Afl
Flow Duration Random Variable
Flow Duration Mean Adur
Flow Bit Rate Classes
10 seconds
Poisson Process
{10, 20} flows/sec ond
Exponen tial
1 se cond
{25, 50, 75,100, ,b
125,150,175,200} kbps
B. Network simulation setup
In line with our formulation in section IV, we run simu
lations for a network composed of one macro-cell LTE-A
with radius Rcell = 1 km. The geographical deployment
of UEs inside the cell follows a Poisson Point Process dis
tribution with a density AUE nodes per km2 for values in
the set {10,15, 20, 25,30,35 ,40}. The LTE-A macro-cell is
configured to work in FDD mode with an UL frequency
of 1930 MHz and a bandwidth of 5 MHz (i.e., 25 RBs).
The eNodeB configures SL bandwidth to share the same
as UL. However, The eNodeB allocates scheduled-resources
pool only Q = 14 RBs for the offloading operation over
SL. UEs are configured to transmit on SL with a common
power density of * t = - 4dBm/RB (i.e., maximum of 10
dBm over the whole 5 MHz). To model the SL path-loss,
we use the WINNER II B2-LOS channel model [11]. The
SL-Period (SL frame) is configured to be 40 milliseconds
(i.e., 40 subframes), which is the minimum possible value
in the standard, of which 32 subframes is used for the data
transmission. The eNodeB, using a SNR reports, builds the
D2D network topology. A link is considered part of the
network if the respective SNR is greater than pTOPO = 10 dB.
Traffic flows are generated according to a Poisson process with
an arrival rate AFL £ {10, 20} flows per second. On the other
hand, each flow is assumed to have a Constant Bit-Rate (CBR)
traffic randomly selected from predefined CBR classes. Flow
duration distribution is simulated to follow an exponential
random variable with a mean duration of ADUR = 1 second.
Sources and destinations are chosen from a random uniform
distribution. TABLE I summarizes the main parameters used
in our network simulation. For the evaluation of results, the
confidence level is set to 95%.
C. Performance metrics
We define the following metrics to evaluate our proposal:
1) S is the ratio of the flows offloaded by the D2D subnet
work.
2) A is the maximum number of scheduled flows simulta
neously.
3) L is the average of flow packet loss in each simulation
run.
4) H is the average number of hops in the offloading path
in each simulation run.
In addition we compare the performance of our proposal
JRW-D2D with the following alternative routing and resource
strategies:
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2018 IEEE 43rd Conference on Local Computer Networks (LCN)
^UE
(a) Afl = 10
^UE
(b) Afl = 20
Fig. 4. S w.r.t the nodes density Aue-
1) DJK-RRB: is a pure path strategy that aims to find the
optimal routing trees using Dijkstra algorithm and then,
allocates RB randomly.
2) RRT-ORB: is a pure resource block oriented strategy that
finds the routing trees randomly using random walk on
the topology graph, and allocates RB optimally.
3) IAR-ORB: is a heuristic scheme composed of inter
ference aware routing based on Dijkstra algorithm. In
this variant, the link costs to minimize are the total
interference level on the link taking into consideration the
actual state of network before accepting the new flows.
Then, the resource block allocations are done optimally.
D. Simulation results
First, we evaluate our algorithm JRW-D2D regarding its
offloading capability and in comparison with the alternative
strategies DJK-RRB, RRT-ORB, IAR-RRB. To do so, we cal
culate the ratio of the flows offloaded over D2D subnetwork.
Fig. 4 illustrates S with respect to the density of UEs and
under two traffic conditions AFL = 10 and AFL = 20 flows per
second. For small values of AUE, it is straightforward to see
that S increases in proportion to AUE. This means that as D2D
node density increases, more flows will succeed to be routed
through the D2D network. This is expected because, when the
density increases, the probability of forming reliable D2D links
rises accordingly. And as a consequence, the D2D network
capacity to absorb random flows also grows. We remark that
DJK-RRB outperforms the other schemes in general. This is
expected since DJK-RRB routes flows over the fewest possible
nodes. As a result, it allows for more flows to be admitted into
the network. Taking DJK-RRB as a baseline, we note that our
proposal JRW-DD has a flow acceptance rate of AS = 1%
less than the baseline DJK-RRB, in average, for AFL = 10
as depicted in Fig. 4a. o n the other hand, Fig. 4b shows the
^UE
(a) Afl = 10
5 10 15 20 25 30 35 40 45
^UE
(b) Afl = 20
Fig. 5. A w.r.t node density Aue-
situation under more traffic pressure, AFL = 10, where the
acceptance rate drops for all schemes while the performance
gap of JRW-DD increases to be around AS = 3% in average
with respect the leader DJK-RRB.
To complement the evaluation of the offloading capability,
we measure the degree concurrency in utilizing the D2D
subnetwork. To this end, we measure the average of the
maximum number of flows offloaded simultaneously over D2D
subnetwork. This measure is conveyed by the metric A, shown
in Fig. 5, which demonstrates to what degree the different
scheme are successful to utilize system resources concurrently.
In a manner consistent the evolution of S, the evolution of A
is depicted in Fig. 5 under the two traffic conditions AFL = 10
and A
fl = 20. We note that the metric A increases in
response to an increase in AUE. This reflect the fact that, in
a denser topology, more nodes are available in the network
to route concurrent flows circumventing the restriction due to
maximum one flow per node. Again, we note that DJK-RRB
is the leader of the group where the our scheme JRW-DD
was able to offload slightly fewer simultaneous flows than the
others with performances gaps AA < 0.25 simultaneous flows
as indicated in Fig. 5a and Fig. 5b.
To quantify the QoS presented to the offloaded flows we
focus on latency and packet loss rate. Fig. 6 illustrates the
performance in terms of H metric which count the number
of hops in the routing paths. This metric indicates the QoS
presented to flows in terms of latencies where shorter is better.
Specifically, the end-to-end and the average packet delays
are proportional to H x TSL. Fig. 6a and Fig. 6b point out
that the average number of hops increases almost linearly in
accordance with the density of nodes AUE. The figure reveals
that JRW-D2D leads to shorter paths in average than the
others. This seems paradoxical in particular when comparing
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2018 IEEE 43rd Conference on Local Computer Networks (LCN)
5 10 15 20 25 30 35 40 45
^UE
(a) Afl = 10
^UE
(a) Afl = 10
^UE
(b) Afl = 20
Fig. 6. H w.r.t node density Aue
to DJK-RRB. However lower values of H are an artifact of
JRW-D2D being biased to accept flows with shorter paths at
the expense of blocking some long path flows.
Moreover, to quantify the QoS in terms of the packet
error rate at the IP level, Fig. 7 illustrates the average
packet loss (L) in flows as a function of the UEs’ density
for A
fl = 10 and AFL = 20 conditions respectively. In
Fig. 7, it is straightforward to see that our scheme JRW -D2D
outperforms the other schemes thanks to their capability to
take into consideration interference in OFDMA RB blocks
allocation. However, RRT-ORB performs badly in general,
which may seem paradoxical. It is straightforward to see that
such a behavior will lead to higher transmission delays. Being
interference-aware in routing and resource allocation makes
JRW-D2D more robust against the packet loss. In fact, the
latter succeeds to maintain L below 0.13 and 0.14 for both
traffic conditions AFL = 10 and AFL = 20 flow per seconds
respectively as depicted in Fig. 7a and Fig. 7b.
In summary, network simulations show that JRW-D2D out
performs the variants in terms of reliability at the expense of
small performance gaps with respect to latency and offloading
capacity.
VII. Conclusion
In this paper, we addressed the problem of joint routing and
OFDMA resource allocation in LTE-D2D multihop networks,
considering LTE-D2D-specific constraints, namely, the half
duplex operation and the contiguity in RB allocations. An
offloading application, as a use case, was conceived where
data from the eligible flows are routed over the D2D multihop
network and the eNodeB host the control plane. We proposed
a MILP formulation for the problem and a novel scheme
named JRW-D2D based on the branch-and-cut algorithm. We
validated our proposal with simulating the whole LTE D2D
^UE
(b) Afl = 20
Fig. 7. L w.r.t node density Aue-
protocol stack in the NS-3 network simulator. The results
obtained are very satisfying in terms of optimality, ratio
of admitted D2D flows and latency in comparison to other
implemented basic one-sided optimal strategies and another
interference-aware heuristic scheme.
References
[1] Cisco Visual Net working, “Cisco Global C loud Index: Forecast and
Methodology, 2015-2020,” White paper, 2016.
[2] A. Asadi, Q. Wang, and V. Mancuso, “A Survey on Dev ice-t o-De vice
Commu nication in Cellular Netw orks,” IEEE Com munications Surveys
Tutorials, vol. 16, no. 4, pp. 1801-1819, Fourthquarter 2014.
[3] P. Gandotra and R. K. Jha, “Dev ice-t o-De vice Communic ation in
Cellular Network s: A Survey,” Journ al o f N etwork and Compute r
Applications, vol. 71, pp. 99-117, 2016.
[4] J. E. Mitchell, “Integer Programming: Branch and Cut Algorith ms.” in
Encyclop edia o f Optimization, C. A. Floudas and P. M. Pardalos, Eds.
Springer, 2009, pp. 1643-1650.
[5] L. Babun, A. I. Yurekli, and I. Guvenc, “Multi-hop and D2D commu -
nications for extending coverage in public safety scenarios,” in 2015
IEEE 40th L ocal Computer Ne tworks Conference Workshops (LCN
Workshops), Oct 2015, pp. 912-919.
[6] V. Bhardwaj and C. R. Murthy, “On optimal routing and power allocat ion
for D2 D comm unicatio ns,” in 2015 IEEE International Conference on
Acoustics, Speech and Signal Processing (ICASSP), April 2015, pp.
3063-3067.
[7] J. Li, W. Xia, S. X ing, and L. Shen, “Transmission scheduling and
cong estion control for multi-ho p D2D underlaying cellular networks,”
in 2014 IEEE 25th Annual International Symposium on Personal, Indoor,
and Mobile R adio Com munication (P IMRC), Sept 2014, pp. 996-1000.
[8] 3GPP, “Proximity-b ased serv ices (ProSe); S tage 2,” 3rd Generation
Partnership Project (3GPP), TS 23.303, Dec. 2016. [Online]. Available:
http://www.3gpp.org/DynaReport/23303.htm
[9]
------
, “Evolve d Universal Terrestrial Radio Acc ess ( E-UTRA);
Phys ical layer procedures (Relea se 14),” 3rd Generation Partnership
Project (3GPP), TS 36.213, Sep. 2017, v14.4.0. [Online]. Available:
http://www.3gpp.org/DynaReport/36213.htm
[10] G. F. Rile y and T. R. Hen derson, “The ns-3 Netwo rk Simulator Mod eling
and Tools for Ne twork Si mulation,” in Modeling and Tools for Network
Simulation, K. Wehrle, M. Gune§, and J. Gross, Eds. Berl in, Heidelberg:
Springer Berlin Heidelberg, 2010, ch. 2, pp. 15-3 4.
[11] Y. d. J. Bultitude and T. Rautiainen, “IS T-4-027756 WIN NER II D1.
1.2 V1. 2 W INNER II Channel Mod els,” 200 7.
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