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Device-to-Device (D2D) communication based on cognitive radio (CR) technology can significantly improve the coverage and spectral efficiency. Existing research on D2D communications mainly focus on optimizing the network Quality of Service (QoS) in single-tier networks. However, the exponential growth in data traffic has inspired the move from traditional single-tier cellular networks toward heterogeneous cellular networks (HetNets). Hence, in this paper, we consider a CR-based HetNet coexisting with cognitive D2D pairs and cellular users, where the cellular users are primary users (PUs) and D2D pairs are secondary users (SUs). Considering Quality of Experience (QoE) is an important metric to quantify and measure quality of experience from the user perspective, we focus on the QoE optimization of the D2D pairs via the BS association, the discrete power control, and the resource block (RB) assignment. To do so, we first formulate the cross-layer optimization problem to maximize the average QoE of the D2D pairs while satisfying the QoE requirements of cellular users. We then propose the centralized resource allocation, namely the genetic algorithm (GA), and semi-distributed resource allocation method, namely Stackelberg game based algorithm, to solve the non-convex optimization problem. The GA is proposed to ensure the maximum achievable QoE with known channel state information (CSI), whereas the Stackelberg game based algorithm is proposed to cope with the strong needs for distributed D2D solutions with only local CSI of each D2D link. Our proposed algorithms can achieve substantial improvement of QoE performance for D2D pairs via increasing the number of RBs.
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1
Cross-layer QoE Optimization for D2D
Communication in CR-enabled Heterogeneous
Cellular Networks
Jian Chen, Member, IEEE, Yansha Deng, Member, IEEE, Jie Jia, Member, IEEE,
Mischa Dohler, Fellow, IEEE, and Arumugam Nallanathan, Fellow, IEEE,
Abstract—Device-to-Device (D2D) communication based on
cognitive radio (CR) technology can significantly improve the
coverage and spectral efficiency. Existing research on D2D
communications mainly focus on optimizing the network Quality
of Service (QoS) in single-tier networks. However, the exponential
growth in data traffic has inspired the move from traditional
single-tier cellular networks toward heterogeneous cellular net-
works (HetNets). Hence, in this paper, we consider a CR-based
HetNet coexisting with cognitive D2D pairs and cellular users,
where the cellular users are primary users (PUs) and D2D pairs
are secondary users (SUs). Considering Quality of Experience
(QoE) is an important metric to quantify and measure quality
of experience from the user perspective, we focus on the QoE
optimization of the D2D pairs via the BS association, the discrete
power control, and the resource block (RB) assignment. To do
so, we first formulate the cross-layer optimization problem to
maximize the average QoE of the D2D pairs while satisfying
the QoE requirements of cellular users. We then propose the
centralized resource allocation, namely the genetic algorithm
(GA), and semi-distributed resource allocation method, namely
Stackelberg game based algorithm, to solve the non-convex opti-
mization problem. The GA is proposed to ensure the maximum
achievable QoE with known channel state information (CSI),
whereas the Stackelberg game based algorithm is proposed to
cope with the strong needs for distributed D2D solutions with
only local CSI of each D2D link. Our proposed algorithms can
achieve substantial improvement of QoE performance for D2D
pairs via increasing the number of RBs.
Index Terms—QoE, cross-layer optimization, user association,
resource allocation, Genetic Algorithm, Stackelberg game.
I. INTRODUCTION
The dramatic increasing usage of smart devices and applica-
tions has largely accelerated the growth of mobile data traffic.
The Cisco VNI report predicts that the global mobile users
will increase from 4.8 billion to 5.5 billion during 2015 and
2020 [1], and the monthly global mobile data traffic will reach
30.6 exabytes by 2020. It is also estimated that the sum of
all mobile videos traffic (Video-On-Demand (VOD), Internet,
and P2P) will be over 75% mobile traffic by the end of 2020.
Copyright (c) 2015 IEEE. Personal use of this material is permitted.
However, permission to use this material for any other purposes must be
obtained from the IEEE by sending a request to pubs-permissions@ieee.org.
Manuscript received January 8, 2018. Corresponding author: Yansha Deng
(Email: yansha.deng@kcl.ac.uk.)
Jian Chen and Jie Jia are with Northeastern University, Shenyang 110819,
China (email: {chenjian, jiajie}@mail.neu.edu.cn).
Y. Deng, M. Dohler are with Department of Informatics, King’s
College London, London WC2R 2LS, UK (email: {yansha.deng, mis-
cha.dohler}@kcl.ac.uk).
A. Nallanathan is with the Queen Mary University of London, London E1
4NS, U.K (email: a.nallanathan@qmul.ac.uk).
Action is being taken to deploy more inexpensive, low-power,
small-scale BSs, such as pico, femto BSs, underlaying the
conventional cellular networks to improve the spectral effi-
ciency. This is the so called heterogeneous cellular networks
(HetNets).
Another way to cope with these increasing traffic is to
enable the device-to-device (D2D) communication operating
in the licensed bands belong to the cellular user equipments
(CUEs). With this technology, D2D users in close proximity
can exchange rich content via direct connections while by-
passing the cellular base stations (BSs). D2D communication
can have dedicated spectrum (overlay) or shared spectrum
(underlay) with cellular users. In the overlay mode, however,
still the dedicated spectrum for D2D users may not be ef-
ficiently utilized. On the other hand, in the underlay mode,
the most critical part is the interference mitigation between
the D2D users and cellular users due to the shared spectrum
[2]. Therefore, cognitive radio (CR) technology is applied
in D2D communication. By sensing the spectrum conditions
and seek to send their signals by reusing the spectrum of
primary users (PUs), CR-enabled D2D communication can
improve the spectrum resource utilization more effectively, and
be viewed as a cost-efficient way to increase the transmission
rate and lower the end-to-end latency [3]. Considering these
benefits, the D2D assisted video streaming transmission has
been widely applied in social networking applications or media
sharing applications [4].
In order to support the CUEs and D2D pairs with cus-
tomized and personalized services in accordance with their
preference in a CR-enabled HetNets, it is crucial for the
network operators to guarantee a high Quality of Experience
(QoE) for each service user, especially for those using the
video streaming services [5]. The negative effects due to the
interference caused by the frequency reuse in D2D-enabled
HetNets may affect the quality and fluency of streaming
videos, and thus affect the user experience. More importantly,
from the commercial aspect, the user perception and satisfac-
tion are the dominators for the success of a application and
service in the marketplace.
According to International Telecommunication Union
Telecommunication Standardization Sector Study Group 12
(ITU-T, SG 12), QoE is the overall perception and satisfaction
of an application or service subjectively by the end-user [6].
Different from network-oriented Quality of Service (QoS),
which is only determined by the technology-centric metrics,
such as the packet loss rate, the delay, and the available
2
bandwidth, user-oriented QoE is basically an assessment of
the service from the user’s point of view. Although a better
network QoS in many cases will result in better QoE, fulfilling
all traffic QoS parameters alone may not guarantee satisfied
service users. For example, throughput maximization can not
lead to optimal user perceived quality for multimedia appli-
cations, such as video and voice, due to that they are highly
sensitive to fluctuations in data rate, packet loss, and delay [7].
This is mainly due to the fact that QoE is also affected by other
factors, such as the service type, the viewer demography, the
video length and the CUE. Such non-network-related factors
may not have a direct impact on the QoS but do influence
the QoE. The relationship between QoS and QoE becomes an
important research topic for the purpose of QoE assessment.
There is mainly two types of QoE assessment methods,
either subjectively or objectively . The subjective assessment
method measures the human’s subjective satisfaction and
interest via questionnaires and rating scales [8]. Although
this subjective method may be the only method to assess
the actual QoE closest to the “ground truth”, it is extremely
expensive and time-consuming [9]. The objective assessment
method measures QoE using different models of human per-
ceptions, and approximate the QoE automatically without the
need of human’s participation. In this way, the QoE can be
mapped from the the QoS parameters and other media-related
parameters using a certain function. Specially, the QoE is
characterized by the application-oriented mean opinion score
(MOS), which reflects the degree of user satisfaction from
a scale of 1 (bad) to 4.5 for audio and video applications
(excellent) [10], or 5 for other applications (excellent) [11].
Of course, this objective assessment method is more efficient
and feasible for the service provider. Hence, some well-known
objective models that allow the mathematical evaluation of the
MOS have been proposed, such as the Weber-Fechner law
based QoE assessment [12], and these application-oriented
QoE models for web browsing [13], voice application [14],
[15], video streaming [16], and file download application [7].
The new generation of CR-enabled cellular networks (Het-
Nets) have to support the CUEs and D2D pairs using heteroge-
neous applications with diverse QoE models and requirements,
which suffer from the interference due to the resource reuse
between D2D pairs and CUEs in each tier. Meanwhile, the
MOS-based QoE models for different applications [7], [13]–
[16] are usually determined by various factors in different
network layers. To make sure the key parameters of different
layers are exchangeable, the cross-layer QoE optimization is
the key to realize the efficient resource allocation between
different layers in CR-enabled HetNets with diverse QoE
requirements.
A. Related works
The cross-layer optimization for video streaming video
application have been proposed in MIMO systems [17], single
cell cellular networks [18], heterogeneous wireless networks
[19], single cell LTE networks [20], multiuser OFDMA system
[21] and wireless sensor networks [22]. In [21], the centralized
QoE-aware resource allocation of multiuser OFDM systems
with users operating in audio, video and best-effort appli-
cations was studied. In [23], QoE-aware resource allocation
was studied for D2D video streaming, where the scheduling
algorithm was proposed for multiple D2D users sharing a
single channel.
In the underlay D2D-enabled cellular networks, the D2D
pairs and CUEs suffer from the mutual interference be-
tween each other, thus, the centralized resource allocation
can coordinate between the performance of D2D pairs and
that of CUEs to achieve the optimal for the objective. The
centralized resource allocation has been studied in D2D-
enabled single cell cellular networks via the power allocation
[24], and the joint RB assignment and power allocation [25].
The centralized resource allocation can provide the maximum
achievable performance of the proposed problem, but large
signalling overhead can be induced via collecting the global
channel state information (CSI), which may be difficult to
obtain in some practical scenarios [26]. As such, in [26],
a distributed resource allocation based on stackelberg game
was proposed. Furthermore, in [27], an hybrid centralized-
distributed resource allocation for single cell D2D-enabled
cellular networks was proposed, where the channel allocation
was realized via the centralized graph-theoretical approach,
and the power control was realized via the distributed game
theory approach. However, existing resource allocation for
D2D-enabled systems considered continuous transmit power
allocation, which can not be directly applied to in systems
supporting discrete transmit power allocation. For instance,
only discrete power allocation is supported in the 3GPP LTE
cellular networks with a use-specific data-to-pilot-power offset
parameters [28]. Compared with the continuous power control,
the discrete power control offers two main benefits [29]:
(i) the transmitter is simplified, and more importantly, (ii)
the overhead of information exchange among networks is
significantly reduced. Nevertheless, using simple discretization
on the solution obtained by existed continuous power control
is not an effective approach. Discrete power allocation for
cellular networks has been proposed in [29], [30]. In [29], two
discrete power control algorithms were proposed to maximize
the weighted system capacity. In [30], a discrete power control
was proposed for multi-cell networks aiming at improving its
energy efficiency. In [31], the joint discrete power control and
RB assignment was proposed to improve the availability of
HetNets based on spectrum aggregation. However, to the best
of our knowledge, there is no work dealing with the discrete
power control for D2D-enabled systems.
With the increasing interests in HetNets, research has been
extended to the resource allocation of D2D-enabled HetNets
from the aspect of QoS [32]–[35], [35], [36]. In [35], the social
interactions among UEs in a HetNet was designed, and a UE
association algorithm based on recommendation system was
proposed.In [36], a UE association scheme aiming at load bal-
ancing was proposed, and a low-complexity distributed algo-
rithm was proposed to converge to a near-optimal solution. In
[32], an intelligent RB selection and power adaption algorithm
in D2D-enabled HetNets was proposed by first determining
the maximum and minimum transmission powers, and then
selecting the RB. In [33], the centralized resource allocation
3
was proposed to solve the quasi-convex optimization problem
in D2D-enabled small cell networks, with an objective to
achieve the maximum overall throughput of the D2D pairs and
CUEs. In [34], an auction-based distributed resource allocation
was proposed to achieve the maximum overall data rate of
D2D pairs and small cell UEs in D2D-enabled multi-tier
cellular networks with single macrocell BS. They assumed
that the UE association was determined and known prior
to the resource allocation, thus the UE association was not
taken into account in the process of resource allocation, and
the resource allocation for the single macrocell BS was also
ignored. Observing from the existing literature, we notice that
the joint QoE cross-layer optimization taking into account the
UE association, the power allocation at both BSs and D2D
transmitters, and the RB assignment in a CR-enabled HetNets
has never been well treated.
B. Contribution
Unlike existing works, the aim of this work is to design
a QoE-oriented resource allocation optimization framework
in CR-enabled HetNets with discrete power control. At the
application layer, the network can accommodate heteroge-
neous services with different QoE models and requirements.
Different from their QoE model applied for web-browsing
application in [21], we employ a more practical web-browsing
application QoE model, in which the Web page size, the
service response time, and the transmission rate are the three
main factors in determining the MOS value ranged from 1
to 5. At the bottom layers, the user association for CUEs,
RB assignment and power allocation at both BS and D2D
transmitters are joint optimized. To the best of our knowledge,
this is the first study on the QoE optimization for D2D
communication in CR-enabled HetNets. Besides that, this is
also the first work taking into account the cell association,
the discrete power control and the RB assignment for both
D2D pairs and CUEs. The main contributions of this paper
are summarized as follows:
We present a novel cross-layer optimization model to
maximize the MOS of D2D pairs in HetNets, which
is regarded as an user-oriented QoE metric, rather than
typical network oriented QoS metric.
We propose a GA-based discrete power allocation jointly
with the RB assignment and the UE association to opti-
mize the QoE of the D2D pairs while still satisfying the
QoE requirement of each CUE. We design an efficient
individual encoding scheme and effective constraints han-
dling mechanisms to achieve quick convergence. This
algorithm is executed in a centralized manner and serves
as a benchmark for the system performance, and can be
achieved with polynomial time complexity.
We then propose the semi-distributed algorithm based
on Stackelberg game with low overhead, where the BS
is the leader to decide the price of each RB, and the
D2D pairs is the followers that compete selfishly in a
non-cooperative Nash game to maximize their own QoE
values based on the prices set by BS. We also prove the
existence of Nash equilibrium and designed the algorithm
to converge to the NE.
Our simulation results shown that our proposed central-
ized algorithm and semi-centralized algorithm achieve
substantial improvement compared with random alloca-
tion. With heavy loaded CUEs, increasing the number of
RBs can substantially improve the average MOS of D2D
pairs while satisfying the minimum MOS requirement at
each CUEs.
The remainder of this paper is organized as follows. In Sec-
tion II, we present the system model and problem formulation.
Section III proposes GA-based algorithm and analyzes their
computational complexities. Section IV proposes the semi-
distributed algorithm based on Stackelberg Game. Section
V presents numerical results and Section VI highlights our
conclusions.
II. SY ST EM MO DE L AN D PROB LE M FOR MU LATI ON
A. System Model
We consider the downlink transmission in a CR-enabled K-
tier HetNets with K={1, ..., K}consists of macro BSs, pico-
cell BSs, femtocell BSs, and further radiating elements. The
set of BSs are denoted as B=B1∪B2...∪BK={1,2, ..., S },
where Bkrepresents the set of BSs in tier k. We also denote
the set of active CUEs as N={1,2, ..., N}and the set of
active D2D pairs as D={1,2, ..., D}. Similar as that in [2],
[3], we consider CUEs as PUs and D2D pairs as SUs. We
consider the open access strategy where a CUE is allowed to
connect to any tier without any restriction. The dth D2D pair
(d∈ D) consists of the D2D transmitter dT∈ DTand D2D
receiver dR∈ DR, where DT={1T,2T, ..., DT}and DR=
{1R,2R, ..., DR}. The set of all UEs of the network is denoted
as U=N ∪ DT∪ DR. We denote the set of UEs associated
with the sth BS as Ns, and assume each CUE can associate at
most one BS, thus N=N1N2... NSand NiNj= Φ
for i6=j. For simplicity, we ignore shadowing and consider
Rayleigh fading only. The frequency band available for CR
transmission is divided into M={1,2, ..., M}RBs and each
RB occupies a bandwidth of BHz.
The resource allocation in the proposed CR-enabled Het-
Nets includes the RB assignment, the UE association, and the
transmit power allocation as follows:
1) RB Assignment and UE Association: :We assume each
BS has the same Morthogonal RBs.
CUE: Each RB can be allocated to at most one CUE
to avoid co-tier interference from other CUEs, and each
CUE can associated with a single BS. Similar as the in
[31], [36], we assume a CUE can be associated to an
arbitrary BS despite its tier. To specify the RB assignment
and the UE association of CUE, we define vm
s,n as its
RB assignment and UE association indicator, which is a
binary variable. If vm
s,n = 1, it indicates that nth CUE
(n∈ N)is associated with the mth RB of sth BS (s
B), and vm
s,n = 0 (m∈ M)if otherwise. This is different
from [34] where the UE association with the BS in each
tier has already been fixed.
D2D Pair: Multiple different D2D pairs can reuse the
same RB with CUE during a transmission interval in
underlay mode to improve the spectrum utilization. To
4
specify the RB assignment for D2D pairs, we define the
binary variable vm
das its RB assignment indicator. If
vm
d= 1, it indicates that the mth RB is allocated to dth
D2D pair (d∈ D), and vm
d= 0 (m∈ M)if otherwise.
2) Transmit Power Allocation: We consider the discrete
power allocation, where the transmitters can select the transmit
power from the power level sets L={0,1,2,··· , L}, and L
is the maximum integral level.
CUE: The CUE occupied at the mthe RB of the sth BS
can select a random power level ls,m, where
ls,m ([1, L],If mth RB of sth BS serves one UE,
= 0,If mth RB of sth BS serves no UE,
(1)
To be more specific, the transmit power allocated to
the CUE at the mth RB of the sth BS belongs to
the set [0,1
LPmax
sRB ,2
LPmax
sRB ,·· · ,ls,m
LPmax
sRB ,·· · , P max
sRB ],
where Pmax
sRB is the maximum transmit power at each RB
of sth BS.
D2D Pair: The dth D2D pair can select a power level
ηd, with ηd∈ L and L={0,1,2,· ·· , L}while satisfy-
ing the minimum transmit power requirement ηmin
d. To
ensure that the D2D receiver is located within the D2D
proximity of D2D transmitter rdT,dR< Rmax
d, we use the
channel inversion power control to compensate the large
scale fading, and enable that the average received power
at the D2D receiver is larger than the minimum sensitivity
ρmin [37]. Hence, we have the D2D proximity as
Rd=ηdPmax
d
min α
,(2)
and the minimum transmit power level of the dth D2D
transmitter as
ηmin
d=min
Pmax
d
Rα
dT,dR.(3)
B. Downlink Data Rate of CUE
It is noted that each CUE is assigned with single RB of
a single BS, thus the downlink data rate of the nth CUE is
defined as
rn=X
s∈B X
m∈M
vm
s,nrm
s,n,(4)
where
rs,m
n=Wlog(1 + SI N Rm
s,n),(5)
is the downlink data rate of the nth CUE associating sth
BS over the mth RB, Wis the RB bandwidth (i.e. W=180
kHz), SI N Rm
s,n is the signal-to-interference-plus-noise ratio
(SINR) of the nth CUE at the mth RB of the sth BS, and
P
s∈B P
m∈M
vm
s,n = 1.
Let us define Hi,j as the channel power gain between node
iand jand Ri,j as the distance between iand j, where i, j
{n, s, dT, dR}, we then formulate the SINR of the nth CUE
at the mth RB of the sth BS as
SI N Rm
s,n =
ls,m
LPmax
sRB Rα
s,n Hs,n
Im
D,n +Im
B,n +N0
,(6)
where Im
D,n is the aggregate interference at the nth CUE from
all D2D transmitters over the RB m, and Im
B,n is the aggregate
interference at the nth CUE from all the BSs over the mth RB,
and N0is the noise power. In (6), Im
D,n and Im
B,n are given by
Im
D,n =X
dT∈DT
ηd
LPmax
dRα
dT,nHdT,n vm
d,(7)
and
Im
B,n =X
j∈B\s
lj,mPmax
j,m
LRα
j,n Hj,n,(8)
respectively.
C. Data Rate of D2D Pairs
Each D2D pair can only be allocated with single RB with
a certain transmit power level, thus the data rate of the dth
D2D pairs is represented as
rd=X
mMX
ηdL
vm
drm,ηd
d,(9)
where
rm,ηd
d=Wlog(1 + SI N Rm,ηd
d),(10)
is the data rate of the dth D2D pair, which is allocated at the
mth R with the power level ηd,SIN Rm,ηd
dis the SINR of
the dth D2D pair at the mth RB with the power level ηd, and
P
s∈B P
m∈M
vm
d= 1.
We then formulate the SINR of the dth D2D pair over mth
RB with power level ηdas
SI N Rm,ηd
d=
ηd
LPmax
dTRα
dHdT,dR
Im
D,d +Im
B,d +N0
,(11)
where Im
D,d is the aggregate interference at dth D2D pair from
other D2D transmitters over RB m, and Im
B,d is the aggregate
interference at dth D2D pair from all BSs over RB m. In (11),
Im
D,d and Im
B,d are given as
Im
D,d =XiDT\dT
ηi
LPmax
iRα
i,dRHi,dRvm
i,(12)
and
Im
B,d =X
sB
lj,mPmax
j,m
LHs,dRRα
s,dR,(13)
respectively.
D. Application-driven Cross-Layer Optimization
To focus on optimizing the user’s perceived quality for
interactive and real-time services, and increases the customs’
satisfaction from the service provider perspective, the QoE
model is required to measure the human perception of quality.
The QoE models vary depends on different types of applica-
tion, in this work, we limit our study to three most typical
applications, which are the web browsing, the audio and the
video applications. Different from existing QoE model mainly
focus on data rate [12], application parameters such as daly,
5
050 100 150 200
0
20
40
60
80
100
1
1.5
2
2.5
3
3.5
4
4.5
5
Rate(kbps)
PG(kB)
MOS
(a)
050 100 150 200
0
5
10
15
20
1
1.5
2
2.5
3
3.5
4
4.5
5
Rate(kbps)
PEP(%)
MOS
(b)
0 500 1000 1500 2000
1
1.5
2
2.5
3
3.5
4
4.5
Data rate (kbps)
MOS
Mother&Daughter
Foreman
(c)
Fig. 1: (a) MOS model of web browsing application, (b) MOS model of audio application, (c) MOS model of video application
page size, packet error probability (PEP) is also employed in
the design of the QoE models.
The traditional network metrics, such as throughput or
delay, are not sufficiently reliable for the QoE evaluation
[38]. Alternatively, the application-oriented mean option score
(MOS) methodology is a widely used QoE evaluation metric
capable of transferring the technical objective parameters to
the subjective user perceived quality. The UE’s QoE is clas-
sified into five levels with corresponding MOS values (ITU-T
P.800): “Excellent” =5, “Good” =4, “Fair” =3, “Poor” =
2, “Bad” =1, and the acceptable QoE quality is above the
MOS value of 3.5 [11].
Considering that the video application is more bandwidth
intensive than the web browsing and audio application, we
assume that the D2D pairs are limited to video application,
and the CUEs are limited to the web browsing and the
audio applications in this work. However, the cross-layer
optimization method proposed in the next section of this work
can be applied to more general scenario, where the CUEs
and the D2D pairs delivers any type of applications. In the
following, to evaluate the QoE of the CUEs and D2D pairs
in HetNets, we present the QoE models of the web browsing,
the audio and the video applications, respectively.
1) Web Browsing Application: The MOS value of the web
browsing application is mainly determined by the Web page
size, the service response time, and the transmission rate.
The QoE model of the web browing application proposed in
[13] has been tested and verified using a web page download
scenario in a 3G LTE network. This QoE model is given as
MOS1=max (5578
1 + 11.77 + 22.61
t2,1),(14)
where tis the service response time measured in seconds.
This service response time is defined as the delay between
the time a request for a web page was sent and the time
of reception of the entire web page contents. Note that the
QoE value of a web user ranges from 1 to 5 (i.e., the score
1 denotes “extremely low quality” whereas score 5 denotes
“excellent quality”). The constants 578, 1, 11.77 and 22.61
are obtained from by analyzing the experimental results for
the web browsing application.
We assume TCP and HTTP protocols are applied to set the
HTTP request message. If the transmission rate of CUE nN
is rn,tcan be given by,
t3RTT +PS
rn
+L(MSS
rn
+RTT)2MSS(2L1)
rn
(15)
where RTT is the round trip time, PS is the web page size,
MSS is the maximum segment size, and L is the number of
slow start cycles with idle periods. Define L1as the number of
cycles the congestion window takes to reach the bandwidth-
delay product and L2as the number of slow start cycles before
the web page size is completely transferred. Since L1and L2
should be larger than L, it therefore can be defined as
L=min(L1,L2)(16)
where L1=dlog2(rnRTT
MSS + 1)e − 1, and L2=dlog2(PS
2MSS +
1)e − 1. To give an example, Fig .1 (a) plots the MOS value
versus various actual transmission rate and web page size with
RTT 0.
2) Audio Application: In the audio application, the per-
ceived voice quality mainly depends on the data rate rn, and
the packet error probability (PEP). According to the QoE
model in [14], [15], the MOS of the the audio application
at the nth CUE is definde as
MOS2=alog (brn(1 PEP)) (17)
where constants aand bare calculated by fixing the MOS at
a given rate rnand PEP= 0. For example, if the BS provides
a specific service with rate rn, and the CUE experiences
the service with rate rn, then the MOS value of the user
satisfaction achieves the maximum (i.e., 4.5) when there is
no packet loss.
To obtain the constants aand b, we define a minimum
transmission rate and the maximum PEP (e.g., 20%), which
corresponds to the minimum MOS value 1, and define a
maximum transmission rate and the minimum PEP (e.g.,
0%), which corresponds to the maximum MOS value 4.5. By
fitting a logarithmic curve for the estimated MOS under the
predetermined PEP with obtained aand b, we plot Fig. 1(b) to
showcase the relationship between the MOS value and various
actual transmission rate.
6
3) Video Application: We apply the QoE model of the video
application given in [16], which has been tested and verified
using H.264/AVC encoded video test sequences (”Foreman”
and ”Mother & Daughter”). In this model, the MOS value is
mainly determined by the peak signal to noise ratio (PSNR).
The PSNR of the dth D2D pair is calculated using
PSNRd=a+brrd
c1c
rd,(18)
where the parameters a,b, and cis determined by the
rate-distortion characteristics of a specific video stream or
sequence. In this paper, we apply three MOS-Rate pairs to
obtain the parameters a,band cof a video. Fig. 1(c) plots
the QoE curves for different video sequences that correspond
to the discrete MOS values of the actual dynamic adaptive
streaming over HTTP protocol for mobile LTE users.
The MOS of the video application is defined as
MOS3=
4.5PSNRiPSNR4.5
dlog(PSNRk) + ξPSNR1.0<PSNRi<PSNR4.5
1PSNRiPSNR1.0,
(19)
where PSNRdis the peak signal-to-noise ratio achieved at the
D2D receiver. For the known rate-distortion characteristics of
a specific video stream or sequence, we define a minimum
transmission rate, which corresponds to the minimum MOS
value 1, and define a maximum transmission rate, which
corresponds to the maximum MOS value 4.5, in order to derive
the parameters PSNR1.0and PSNR4.5. With the threshold
values of PSNR1.0and PSNR4.5, the constants dand ξcan be
derived using
(d=3.5
log(PSNR4.5)log(PSNR1.0)
ξ=log(PSNR4.5)4.5 log(PSNR1.0)
log(PSNR4.5)log(PSNR1.0).(20)
To give an example, Fig .1 (c) plots the MOS value versus
various actual date rate. Here for the video titled ”Mother &
Daughter”, the PSNR4.5and PSNR1.0are set as 45 db and 35
db. For the video titled ”Foreman”, the PSNR4.5and PSNR1.0
are set as 42 db and 30 db respectively.
E. Cross-layer QoE Optimization
In this section, we formulate the optimization problem with
the objective to achieve the maximum average QoE over all
D2D pairs while satisfying the minimum QoE requirement of
each CUEs in HetNets. This can be achieved by searching the
optimal RB assignment, UE association and power allocation
for each CUE n∈ N and finding the optimal RB assignment,
and power allocation for each D2D pair d∈ D.
We define the binary variable xq
nas the application service
indicator, where xq
n= 1 represents that the application service
of the nth CUE is the qth application, and otherwise xq
n= 0.
Note that q= 1 corresponds to the web browsing application,
and q= 2 corresponds to the voice application. We also define
the minimum QoE requirement of the qth application as τq.
Similar as that in [21], we assume this QoE requirement is
defined according to the application type and is given in priori.
For instance, for CUEs with audio application, its minimum
QoE should be at least 3.5 [11]. We formulate this optimization
problem as
max Pd∈D MOS3(rd)
D(21)
s.t. Xq∈{1,2}xq
nMOSq(rn)τq,n∈ N,(21a)
Xq∈{1,2}xq
n= 1,n∈ N,(21b)
XmMvm
d= 1,d∈ D,(21c)
ηdηmin
d,d∈ D,(21d)
XsSXmMvm
s,n = 1,n∈ N (21e)
XnNs
vm
s,n = 1,s∈ B, m ∈ M,(21f)
XnNXmMvm
s,n M, sS, (21g)
ls,m [0,·· · , L],s∈ B, m ∈ M,(21h)
The constraints in (21a)-(21g) are named as the CUE QoE
requirement in (21a), the application service constraint in
(21b), the D2D per-RB assignment constraint in (21c), the
D2D pair power allocation constraint in (21d), the per-CUE
association constraint in (21e), the CUE per-RB assignment
constraint in (21f), and per-BS association constraint in (21g).
The CUE QoE requirement in (21a) implies that the minimum
QoE requirement τqfor the qth application of the CUE
should be satisfied, which is different from previous work only
concerning QoS threshold. The application service constraint
in (21b) implies that each CUE should select one type of
application. The D2D per-RB assignment constraint in (21c)
represents that each RB can be allocated to at most one
D2D pair. The D2D pair power allocation constraint in (21d)
represents that the minimum discrete transmit power level
of ith D2D pair should be larger than ηmin
d. The per-CUE
association constraint in (21e) represents each RB of each
BS can allocated to at most one CUE. The CUE per-RB
assignment constraint in (21f) represents that different UEs
associated with the same BS should be allocated different RBs.
The per-BS association constraint in (21g) represents that each
BS can serve at most MCUEs.
III. GENETIC ALGORITHM APPROACH
In this section, we assume the macro BS has global CSI, and
propose a centralized algorithm based on genetic algorithm
(GA). GA is one of the most popular bio-inspired algorithms
and is widely used to tackle real world NP-hard problems,
such as BS placement optimization for LTE heterogeneous
networks [39] or D2D communication for video streaming [4]
and clustering for wireless sensor networks [40]. In general,
bio-inspired algorithms imitate the natural evolution of bio-
logical organisms to provide a robust, near optimal solution
for various problems [41]. GA is inherently an evolutionary
process that involves individual encoding, selection, crossover,
mutation, and replacement operations [42].
7
A. Individual encoding
GA cannot deal with the solutions of the optimization
problem directly. The solutions needs to be represented as
chromosomes in terms of data structure. In our optimization
problems, an integer-based encoding scheme containing the
joint UE association RB allocation and power allocation for
the CUEs, as well as the RB allocation and power allocation
for the D2D pairs, is proposed to represent the potential
solution.
We generate the initial population R={1, ..., R}consisting
of Rdifferent individuals, and each individual consists of four
integer-based vectors, which are the potential solutions of the
considered optimization problem. These vectors are generated
according to Algorithm 1 in order to satisfy the D2D per-RB
assignment constraint, the D2D pair power allocation con-
straint, the per-CUE association constraint, the CUE per-RB
assignment constraint, and the per-BS association constraint
during initialization to accelerate the convergence process.
Also note that all the individuals in the initial population
are randomly generated, thus to preserve the diversity of the
population and avoid converging to a local optima [42]. We
represent four integer-based vectors in the rth individual as
the following.
1) Joint UE association and RB allocation vector Γr
Nis
Γr
N= [γr
1,·· · , γ r
n,·· · , γ r
N],(22)
where the matrix elements γr
n(1 nN, 1γr
nSM )
indicates the nth UE associated with the γr
nM(dγr
n/Me
1)th RB of the dγr
n/Meth BS. For instance, if S= 4,M= 10,
and γr
n= 36, it corresponds to v6
4,n = 1, which means nth
CUE is occupying the 6th RB of 4th BS.
To initialize the joint UE association and RB allocation
vector Γr
Nof population R, we first generate PSM
Npermu-
tation vectors Ki
1×N(1iPSM
N) based on the vector
[1,2,3, ..., SM ]. Note that PSM
N=(SM )!
(SM N)! . Then Γr
Nat
each individual of Rare given from first R vectors in K. Thus,
we have to limit the total number of inidividuals RPSM
N,
the number of active CUEs NSM in this algorithm, which
is enough and possible to obtain the optimal after evolution.
2) Power allocation vector at the BS for its associated CUE
Lr
Nis
Lr
N= [lr
1,·· · , lr
n,·· · , lr
N],(23)
where the matrix elements lr
n(1 nN, 1lr
nL)
indicates allocated power at the BS to CUE n. The matrix
element lr
nis initialized in correspondence to the initializa-
tion of γr
n, and its transmit level is randomly selected from
[1,2, ..., L]. According to (22), UE nis associated with the
γr
nM(dγr
n/Me − 1)th RB of the dγr
n/Meth BS, therefore,
the actual allocated power of nth UE is lr
n
LPmax
dγr
n/Me,RB .
3) D2D pair RB allocation vector Γr
Dis
Γr
D= [βr
1,·· · , β r
d,·· · , β r
D],(24)
where the matrix elements βr
d(1 dD, 1βr
dM)
indicates the dth D2D pair is allocated with the βr
dth RB. For
instance, if M= 10, and βr
d= 3, the dth D2D pair is allocated
the 3th RB, i.e. v3
d= 1.
S1: Macro-BS
S3: Pico-BS2
UE1
UE2UE3
UE4
UE5
UE6
S2: Pico-BS1S4: Pico-BS3
r
N
L
6
r
5
r
4
r
3
r
2
r
1
r
r
N
d1d2
d3
d4
6
r
l
5
r
l
4
r
l
3
r
l
2
r
l
1
r
l
4517210
789110 5
1 2 3 3
N
D
2
r
3
r
4
r
1
r
12 14 4 7
4
r
3
r
2
r
1
r
N
D
L
Fig. 2: Individual encoding scheme
4) D2D pair power allocation vector Lr
D
Lr
D= [ηr
1,·· · , ηr
d,·· · , ηr
D](25)
where the matrix elements ηr
d(1 dD, ηmin
dηr
dL)
indicates the dth D2D pair is allocated with the ηr
dth power
level. For instance, if L= 16,ηmin
d= 3 and ηr
d= 5,
it indicates that the dth D2D pair is allocated with power
5
16 Pmax
d.
Algorithm 1: Population initialization
set r= 1
while rRdo
randomly generate a permutation vector
Kr
1×N=PSM
N
for CU E n = 1 to Ndo
initialize lr
nas a random integer from [1,2, ..., L]
end
for D2D pair d = 1 to Ddo
initialize vr
das a random integer from [1,2, ..., M ]
initialize lr
das a random integer from
[ηmin
d, ηmin
d+ 1, ..., L]
end
r=r+ 1
end
One example of this encoding scheme is illustrated in Fig.
2 with 4 BSs, 6 CUEs and 4 D2D pairs deployed in HetNets,
where each BS has 3 RBs, and the maximum integral power
levels as 16. Assume one obtained joint UE association and RB
allocation vector Γr
Nas [4,5,1,7,2,10] and the corresponding
allocation vector Lr
Nas [7,8,9,1,10,5], from which we
observe that the 2nd BS communicates 1th CUE over the 1st
RB and the 7th power level, and the 2nd BS communicates 2nd
CUE over the 2nd RB and the 8th power level. Similarly, with
RB allocation vector Γr
Das [1,2,3,3] and power allocation
vector Lr
Das [12,14,4,7], we can observe that the 1th D2D
pair occupy the 1st RB with the 12th power level, and the
2nd D2D pair occupy the 2nd RB with the 14th power level.
These encoding vectors can be mapped as a feasible resource
allocation to all CUEs and D2D pairs. It also can be observed
8
that this encoding scheme meet all the constraints except CUE
QoE requirement, which will be satisfied in the following
selection process.
B. Fitness functions and natural selection
In GA, selection operation is applied to choose individuals
to participate in reproduction, which has a significant impact
on driving the search towards a promising trend and finding
optimal solutions in a short time. We adopt the famous roulette
wheel selection method to select the individual based on
its selection probability, which is proportional to its fitness
function. The selection probability of the rth individual is
defined as
qr=f(r)
Pr∈R f(r),(26)
where f(r)is the fitness function of individual r. The quality
of the individual is judged by this fitness function.
For the design of fitness function, in order to further satisfy
the CUE QoE requirement, we define the fitness function as
the objective value of (21). It should be noted that, with the
given RB assignment and power allocation for each CUE or
D2D pair, the data rate rn(n∈ N) or rd(d∈ D) can be
obtained with (4) or (9). Therefore, combined with the priori
given application parameters, their MOS value can be obtained
according to the MOS model (14), (18) or (20). However,
due to the fact the obtained MOS value may violate the the
application service constraint in (21b), the penalty method [43]
is adopted. Thus to provide an efficient search and ensure
that the final best solution is feasible. The fitness function is
expressed as
f(r) =PdDMOS3(rd)
D+
PnNµnmin Pq∈{1,2}xq
n(MOSq(rn)τq),0
Nv
,
(27)
where µnrepresents the penalty coefficient determined by the
CUE QoE requirement, and Nvis the total number of CUEs
can not satisfy their QoE requirements.
C. Crossover and mutation
The crossover operation is used to mix between the indi-
viduals to increase their fitness. The conventional two-points
crossover [42] is performed to produce new child individuals
for power allocation vector of CUEs Lr
N, D2D pair RB
allocation vector Vr
Dand D2D pair power allocation vector
Lr
D. However, the conventional crossover operation can not
be directly applied to the joint user association and RB
allocation vector Γr
N, due to the fact that some genes in
Γr
Nmay be the same after operation, and violate the per-RB
assignment constraint. Thus, we propose an enhanced two-
points crossover method to produce new child individuals for
Γr
N.
1) Conventional two-points crossover: For Lr
N,Γr
Dand
Lr
D, every genes between the two crossover points are
switched between two parent individuals to produce two child
individuals, where this two crossover points are generated
randomly. To give an example for parent A La
Dand parent B
Lb
Din Fig. 3 (a), with the randomly generated two crossover
points c1= 1 and c2= 4, the 1st and 56th genes of LP a
Dare
swapped with the 1st and 56th genes of LP b
D, while the 2nd
4th genes remain as the same as their parents. Here, those
elements in LP b
Dare shown in dark to make the results after
crossover more obvious. Note that this crossover operation
always satisfy the D2D per-RB assignment constraint, the D2D
pair power allocation constraint constraint.
2) Enhanced two-points crossover: The enhanced two-
points crossover is performed to satisfy the per-RB assignment
constraint for arbitrary parent A ΓP a
Nand parent B ΓP b
N, as
shown in Fig. 3 (b). First, the genes between the randomly
generated points c1and c2in parents are inherited to child
individuals ΓCa
Nand ΓCb
N. Second, all the genes in parent B
ΓP b
Nare filled into the child individual ΓCa
N, and all the genes
in parent A ΓP a
Nare filled into the child individual ΓCb
N. Third,
the repetitive values in the genes of ΓCa
Nand ΓCb
Nare removed,
and the genes out of the original length of ΓP a
Nand ΓP b
N
are also removed, which become the final child individuals
ΓCa
Nand ΓCb
Nafter the enhanced two-points crossover. By
doing so, different feasible individuals can be produced and
the population diversity can be maintained.
In the mutation operation, the genes in both vectors of each
individual are randomly altered to diversify the population
after the crossover operation, which will pave the way towards
global optima. 1) For the mutation occurring at the arbitrary
element γr
n, repair operation may be required to satisfy the
CUE per-RB assignment constraint to speed up the conver-
gence; 2) For the mutation occurring at the arbitrary element
lr
n,vr
dand ηr
d, mutation operation will be performed using the
random integer generated from its valid range, and no repair
execution is needed.
D. Replacement
After generating a new population through the crossover
and mutation operators, an elitist model based replacement
is employed to update a certain number of individuals in
the old population with the new generated individuals. The
low quality individuals with the low fitness values in the
parental population are replaced by their children in the next
generation.
E. Joint optimization algorithm
In this section, we present the joint optimization algo-
rithm based on GA, which consists of individual encoding,
population initialization, selection, crossover, mutation, and
replacement operations. The joint optimization of UE asso-
ciation, RB assignment and power allocation based on GA
is depicted in Algorithm 2, where Gis the given number
of generations, Ris the population size, qcis the crossover
probability, and qmis the mutation probability. According to
[44], we can derive the time complexity of our algorithm is
9
4 5 1 7 2 9 2 4 5 6 8 3
2 5 1 7 4 6 1 4 5 6 7 2
Pa
N
Pb
N
Ca
N
Cb
N
12 14 4 7 2 9 11 9 8 9 8 3
11 14 4 7 8 3 12 9 8 9 2 9
Pa
N
LPb
N
L
Ca
N
LCb
N
L
6
Pa
l
5
Pa
l
4
Pa
l
3
Pa
l
2
Pa
l
1
Pa
l
1
Ca
l2
Ca
l3
Ca
l4
Ca
l5
Ca
l6
Ca
l
1
Pb
l2
Pb
l3
Pb
l4
Pb
l5
Pb
l6
b
l
1
Cb
l2
Cb
l3
Cb
l4
Cb
l5
Cb
l6
Cb
l
1
Pa
2
Pa
3
Pa
4
Pa
5
Pa
6
Pa
1
Ca
2
Ca
3
Ca
4
Ca
5
Ca
6
Ca
1
Pb
2
Pb
3
Pb
4
Pb
5
Pb
6
Pb
1
Cb
2
Cb
3
Cb
4
Cb
5
Cb
6
Cb
(a)
4 5 1 7 2 9 2 4 5 6 8 3
2 5 1 7 4 6 1 4 5 6 7 2
Pa
N
Pb
N
Ca
N
Cb
N
12 14 4 7 2 9 11 9 8 9 8 3
11 14 4 7 8 3 12 9 8 9 2 9
Pa
N
LPb
N
L
Ca
N
LCb
N
L
6
Pa
l
5
Pa
l
4
Pa
l
3
Pa
l
2
Pa
l
1
Pa
l
1
Ca
l2
Ca
l3
Ca
l4
Ca
l5
Ca
l6
Ca
l
1
Pb
l2
Pb
l3
Pb
l4
Pb
l5
Pb
l6
P
b
l
1
Cb
l2
Cb
l3
Cb
l4
Cb
l5
Cb
l6
Cb
l
1
Pa
2
Pa
3
Pa
4
Pa
5
Pa
6
Pa
1
Ca
2
Ca
3
Ca
4
Ca
5
Ca
6
Ca
1
Pb
2
Pb
3
Pb
4
Pb
5
Pb
6
Pb
1
Cb
2
Cb
3
Cb
4
Cb
5
Cb
6
Cb
(b)
Fig. 3: (a) conventional crossover for vector Lr
N, (b) enhanced crossover for vector Γr
N
Application: QoE
requirement
RRC: Radio Resource
control
PDCP
RLC
MAC
L1
QoE
mapping RRC
PDCP
RLC
MAC
L1
UE
S1-AP
SCTP
IP
L2
L1
S1-AP
SCTP
IP
L2
L1
NAS: Central resource
allocation
eNodeB
MME
1. D2D RRC connection
request 3. D2D Bearer connection
request
1.D2D QoE mapping
from Application
layer to RRC layer
4. Dedicated CUE Bearer
connection request
5.Centralized Resource
allocation for both
CUEs and D2Ds
6. CUE Bearer setup request
7. D2D Bearer setup request
8. D2D RRC connection
configuration
9. D2D RRC connection
complete 10. D2D Bearer setup
response 11. CUE Bearer setup
response
12.D2D data
transmission 13. CUE data
transmission
eNodeB MMED2D SGW
Fig. 4: Signaling procedure of the centralized algorithm
o(GR((N+D) + R)). Since this algorithm is executed in
a centralized manner, we assume there exists a centralized
resource manager (RM) located at the Macro BS, which
are responsible for determining the UE association, the RB
allocation and power level allocation for each CUE, and to
determine the RB allocation and power level allocation for
D2D pair.
For clarification, , Fig. 4 plots the signaling procedure of
this centralized algorithm. Here, we assume a Long Term
Evolution (LTE) system of release 8 is applied, which is
comprised of a core network and a access network. In our
paper, we assume the core network consists two logical nodes,
the Mobility Management Entity (MME) and the Serving
Gateway (SGW). Here, MME is responsible for the resource
management, and SGW is responsible for transferring all
downlink data to CUEs. The access network is made up of
the evolved NodeB (eNodeB), where all D2D pairs connecting
via LTE-Uu interfaces. Due to the fact the application layer is
above the Radio Resource Control (RRC) layer, the D2D QoE
mapping is first executed to transform a QoE request as a RRC
connection request, as shown in the message 1 and 2. And
then, the eNodeB transforms it to a bearer connection request
message on the S1 Application Protocol (S1-AP) to the MME
node, as shown in message 3. Except from message 3, the
MME node also receives the downlink resource request of all
CUEs from the SGW node, as shown in message 4. When the
MME node successfully receives all these resource requests,
the centralized resource allocation algorithm is executed to
determine the UE association, RB assignment and power
Algorithm 2: Joint optimization based on GA
set g= 1
Generate initiation population Rusing Algorithm 1
Calculate fitness value for each individual in R
while gGdo
Set R0= Φ
for i= 1 to R/2 do
Select two parents Aand Bfrom Rusing
roulette wheel selection method
Cross the vector ΓA
Nof Awith ΓB
Nof Busing
enhanced two-point crossover with probability
qc, and produce two children vectors ΓA
Nand
ΓB
N
Cross vectors LA
N,ΓA
D, and LA
Dof Awith LB
N,
ΓB
D, and LB
Dof Busing conventional two-point
crossover with probability qc, and produce
children vectors LA
N,ΓA
D,LA
Dand LB
N,ΓB
D, and
LB
D
Combine the vectors ΓA
N,LA
N,ΓA
D,LA
Dto
produce child A, and combine the vectors ΓB
N,
LB
N,ΓB
D,LB
Dto produce child B
Mutate Aand Busing mutation strategy with
probability qm
Repair elements in ΓA
Nin Aand ΓB
Nin Bif
needed
R0=R0∪ {A, B}
Calculate fitness value for each individual in R0
end
Replace the individuals with low fitness values in
population Rwith the children in offspring R0
g=g+ 1
end
Return the fittest individual in R
allocation for CUEs, and determine the RB assignment and
power allocation for all D2D pairs. If the resource allocation
configuration is finished by these CUEs and D2D pairs, a
response message is sent back to the RM module. After
that, the requested data will be transmitted via this allocated
resources.
IV. SEM I-DISTRIBUTED ALGORITHM
In this section, we present a semi-distributed algorithm,
where the D2D pairs independently determine their power
allocation and RB assignment with the minimum assistance
10
of BSs based on the Stackelberg game, considering its large
signalling overhead, and the lack of reliable channel state
information (CSI). The Stackelberg game is a strategic game,
which includes a leader and some followers competing with
each other on certain resources. The leader sets the price of
the resource first, and then the followers compete with each
other for better price.
A. Stackelberg Game Formulation
In our model, the BS plays the role as the leader in this
Stackelberg game, it owns all the RB resources and has the
right to set the “price” per RB per unit power. The BSs can
gain profit according to the set price by allowing the D2D pairs
to use RB with certain transmit power, this will encourage the
BS to share more resources, which belongs to CUEs, with the
D2D pairs. From the perspective of D2D pairs, they are always
intend to transmit with optimal power and RB, but it will cost
a lot of money, thus, each D2D pair interacts with each other
in a non-cooperative manner to maximize its revenue. While
from the perspective of BSs, they wants to maximize their
revenue, under the condition that the QoE requirements of all
CUEs are fulfilled. As such, we maximize the utility function
of BS as
max UBS (RD,RN,FM) = XdDXmMfmvm
dηd
pmax
d
L
(28)
s.t. Xq∈{1,2}xq
nMOSq(rn)τq,n∈ N,(28a)
Xq∈{1,2}xq
n= 1,n∈ N,(28b)
XsSXmMvm
s,n = 1,n∈ N (28c)
XnNs
vm
s,n = 1,s∈ B, m ∈ M,(28d)
XnNXmMvm
s,n M, sS, (28e)
ls,m [0,·· · , L],s∈ B, m ∈ M,(28f)
where FM={f1, f2,·· · , fM}is the charging price for all
RBs per unit power, RD=Γ1
D
L1
Dand RN=Γ1
N
L1
Nare
the RB assignment and power allocation of all the D2D pairs
and all the CUEs, respectively.
As a follower, with the predefined price FM, we maximize
the utility function of the dth D2D pair at the mth RB with
power level ηdas
max Ud(RD,RN,FM) = MOS3(rd)fmηd
pmax
d
L,dD.
(29)
s.t. XmMvm
d= 1,d∈ D,(29a)
ηdηmin
d,d∈ D.(29b)
B. Stackelberg Equilibrium
Equilibrium is a stable state of the Stackelberg game, where
the BSs and D2D pairs interact through self-optimization
and reach a point where no player wishes to deviate. The
Stackelberg equilibrium (SE) of the the proposed game is
defined in the following.
Definition 1: Assuming RN,FMbe a solution for (28) and
RDbe the solutions for (29) of all the D2D pairs with RD=
Γ1
D
L1
D. The optimal point R
D,R
N,F
Mis the Stackelberg
equilibrium of the proposed game if the following conditions
are satisfied:
UBS (R
D,R
N,F
M)UBS (RD,RN,FM)
Ud(R
D,R
N,F
M)Ud(RD,RN,FM),d∈ D,(30)
To achieve the SE, a two-stage iterative algorithm is ex-
ecuted in a consecutive manner, which includes the optimal
resource allocation among all the D2D pairs, the resource
allocation among all the CUEs and the update of prices
at the BSs to avoid violating CUE QoE requirement. More
specifically, the BS sets a price for each RB and broadcasts it
in the system, then each follower compete in a non-cooperative
fashion to select its best RB and power level. The leader will
update the price for all RBs and allocate the optimal RBs for
all CUEs based on RD. These steps will be repeated until the
two conditions in Definition 1 are satisfied to arrive at SE.
C. Non-cooperative Game for D2D pairs
With the given price FMdecided by the BS, RB allocation
and power level selection can be modeled as a non-cooperative
game G= [D,RD,{Ud}], the existence of Nash equilibrium
(NE) at D2D pairs is proved in the following theorem when
the RB predetermined.
Theorem 1. With the predetermined FM, the non-cooperative
game G= [D,RD,{Ud}]admits at least one NE, only when
the utility function {Ud}of the dth D2D pair occupying the
mth RB is concave on ηd.
Proof. Let A0=PSNRd, and substituting (19) into (29), we
have
Ud=
4.5fmηdpmax
d
LA0PSNR4.5
dlog(A0) + ξfmηdpmax
d
LPSNR1.0< A0<PSNR4.5
1fmηdpmax
d
LA0PSNR1.0,
(31)
Taking the first-order derivative of (31), we have
∂Ud
∂ηd
=
(fmpmax
d
LA0PSNR4.5or A0PSNR1.0
d
ln 2
1
A0A0
0fmpmax
d
LPSNR1.0< A0<PSNR4.5,
(32)
11
where A0
0=∂A0
∂ηd. Further, the second-order derivative is given
by
2Ud
∂ηd2=
(0A0PSNR4.5or A0PSNR1.0
d(A2
0)(A0
0)2
ln 2 +dA00
0
ln 2A0PSNR1.0< A0<PSNR4.5,
(33)
where A00
0=2A0
∂ηd2. Based on (18), it can be calculated by
A00
0=b1
4cr3
2
d+3c
4r5
2
d∂rd
∂ηd2
+b1
2cr1
2
d+c
2r3
2
d2rd
∂ηd2
(34)
According to (10), the second-order derivative of 2rd
∂ηd2can
be calculated by
2rd
∂ηd2=W
ln 2 (SINRm,ηd
d)2Pmax
dTRα
dHdT,dR
L(Im
D,d +Im
B,d +N0)(35)
Combining (35) and (34) into (33), we have 2Ud
∂ηd20.
Therefore, the utility function of utility function Udof dth
D2D pair selecting mth RB is concave with respect to ηd.
In the non-cooperative game among D2D pairs, there may
exists multiple NEs, and each NE varies dramatically. Hence,
we apply the smoothed better response (SBR) learning scheme
to enable the convergence to the optimal SE with high
probability [45]. For the dth D2D pair, the probability that
it updates with the randomly generated resource allocation
strategy Rnew
dis
p=1
1 + exp (Uold
dUnew
d)χ,(36)
where χis the smoothing factor (χ > 0),Uold
dand Unew
d
are the utility values before and after Rnew
dis adopted. As
seen from (36), if Unew
d> Uold
d, the dth D2D pair will
change to use the new strategy Rnew
dwith high probability;
otherwise, it will keep the same strategy with high probability.
If a small difference occurs, the player will use the same
strategy or change to new strategy almost randomly. In this
case, the player may select a “worse” strategy or not to select a
marginally “better” strategy, this uncertainty allows this player
to move from a local optimum state and start the negotiation
towards a new SE. In (36), smoothing factor is responsible for
controlling the tradeoff between the algorithmic performance
and convergence speed. With larger smoothing factor, the more
extensive strategy search and slower convergence speed will
be needed. In our simulations, we employ the concept of
temperature in simulated annealing [45] with χcalculated
as 10/t2, where tdenotes the negotiation iterations. It is
advisable that χkeeps deceasing as the negotiation iterates.
We present the distributed algorithm for the non-cooperative
game in the following Algorithm 3, where each player updates
its resource allocation strategy according to SBR.
Algorithm 3: Distributed resource allocation based on
non-cooperative game
Given the the price FMand resource allocation of all the
CUEs RN
Randomly generate a resource allocation strategy Rnew
d
Calculate the utility function {Unew
d}D
d=1 with Rnew
d
repeat
Randomly select d∈ D with probability of 1/D
Uold
d=Unew
dand Rold
d=Rnew
d
Randomly choose a strategy Rrand
d
Calculate Urand
dwith (29)
Calculate the updating probability pwith (36)
if prand(0,1) then
Update its current strategy Rnew
das Rrand
d
else
reserve its current strategy Rnew
das Rold
d
end
Broadcast negotiation ending message with Rnew
d
for j∈ D\ddo
Calculate utility function Unew
jwith Rnew
d
end
until convergence;
D. Price mechanism at the BS
In this subsection, we present the price optimization algo-
rithm at the BSs to achieve (28) via the CUE association,
the CUE RB assignment, and the power allocation at the
CUE. The centralized resource allocation algorithm based
on GA is applied to ensure the CUE QoE requirement is
not violated, which follows from Algorithm 2 with fixed
resource allocation of the D2D pairs obtained from the Nash
Equilibrium.
For the case where there still exists the QoE of CUE
violating the CUE QoE requirement after GA optimization,
we adopt the uni-direction update algorithm [46] to increase
the price FM. For the mth RB, this algorithm starts at fm= 0
and updates price according to
fnew
m=fold
m+ ∆ if vm
s,n = 1 and MOSq(rm
s,n)τq,
fold
motherwise
(37)
where is a leader defined parameter using to converge to
the optimal price. A larger leads to a faster convergence.
However, should not be set excessively high so as to prevent
other D2D players from accessing the RB, a proper should
be set to balance between CUE protection and maximum profit
gained by selling this RB to D2D pairs.
E. Semi-distributed optimization algorithm
At last, we present our proposed semi-distributed optimiza-
tion algorithm in Algorithm 4, which includes the inner
loop and the outer loop. In the inner loop, each D2D pair
competes for the RB via a non-cooperative game, which is
executed in a distributed manner. In the outer loop, the BSs
allocate the optimal RBs for CUEs and updates the price
12
Application: QoE
requirement
RRC: Radio Resource
control
PDCP
RLC
MAC
L1
QoE
mapping RRC
PDCP
RLC
MAC
L1
UE
S1-AP
SCTP
IP
L2
L1
S1-AP
SCTP
IP
L2
L1
NAS: Central resource
allocation
eNodeB
MME
1. Dedicated CUE Bearer
connection request
2.Centralized Resource
allocation for all CUEs
3. CUE Bearer setup request
4. CUE RRC broadcast
5. CUE RRC configuration
8. D2D Bearer setup
response 9. CUE Bearer setup
response
11. CUE data
transmission
eNodeB MMED2D SGW
6.Distributed
Resource allocation
for all D2D pairs 7. D2D RRC connection
complete
10.D2D data
transmission
Fig. 5: Signaling procedure of the semi-distributed algorithm
for each RB to maximize its profit, which is executed in a
centralized manner. Denote Goas the number of iterations
required for convergence in the outer loop, and Gias the
number of iterations required for convergence of Algorithm
3, we can derive the time complexity of this algorithm as
o(Go((GiN)+GR(N+R))).Fig. 5 plots the signaling proce-
dure of this semi-distributed algorithm. Unlike the centralized
algorithm, the MME node module is only responsible for
the resource allocation of all CUEs, and only the resource
allocation of all CUEs are broadcast to all D2D pairs. With the
received price FM, the resource allocation for all D2D pairs
is executed in a distributed manner, thus to save the signaling
overhead.
Algorithm 4: Semi-distributed optimization
Initialize t= 1 and FM=0
Initialize random RNfor all the CUEs
repeat
Run Algorithm 3 to with RNand FMto generate
RD
fold
m=fnew
mm∈ M
Run GA with RDto generate RN
for n=1 to Ndo
if QoEqwith the allocated RB m< τqthen
fnew
m=fold
m+ ∆
else
fnew
m=fold
m
end
end
until convergence;
V. NUMERICAL RESULTS
In this section, we provide numerical results to illustrate
the performance of our proposed algorithm. We consider
HetNets consisting of 2 tiers (Macro and Pioc) with no more
than 10 RBs. The set-up is a circle area with size (π5002)
m2, where the macro BS is located at the center, the pico
BSs and UEs are randomly distributed in this circle area.
The details of parameters are summarized in Table I unless
TABLE I: SIMULATION PARAMETERS
Parameter Value
The number of macro BS 1
The number of pico BS 410
The number of CUEs 10 20
The number of D2D pairs 10 20
Maximum transmit power of macro BS 46dBm (40W)
Maximum transmit power of pico BS 30dBm (1W)
Maximum transmit power at D2D Transmitter 10dBm (0.01W)
D2D link length 100m
The number of RBs M310
Bandwidth of each RB W180KHz
Web Page Size PS 50KB
BER 104
RTT 30ms
MSS 1460bytes
PSNR1.030dB
PSNR4.542dB
path loss exponent α4
Maximum integer power level 16
Noise PSD -174dBm/Hz
SINR threshold τ1
Population size 40
Crossover probability 0.95
Mutation probability 0.005
0 100 200 300 400 500
1
1.5
2
2.5
3
3.5
4
4.5
Number of Generations
Average MOS value
D = 20
D = 15
D = 10
Fig. 6: Convergence behavior with 10 CUEs
otherwise specified. All the results are obtained by Monte
Carlo simulations.
A. Convergence behavior
In this subsection, we present the convergence behavior of
the GA algorithm, and the Stackelberg game. Fig. 6 10 are
plotted with the number of BSs S= 7 (1 Macro BS and 6
Pico BSs), the number of CUEs N= 10, and the number of
RBs M= 4.
Fig. 6 plots the convergence behavior of the average MOS
of D2D pairs with increasing the number of generations using
GA algorithm. It is shown that the GA algorithm converges
after 250 generations for various number of D2D pairs, and
decreasing the number of D2D pairs improves the converge
speed. Importantly, it is shown that the GA algorithm achieves
at least 65% increase of QoE value compared with that of the
random resource allocation at the initialization, which testify
the effectiveness of algorithm. Fig. 7 plots the CDF of the
13
1 1.5 2 2.5 3 3.5 4 4.5
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
MOS value
CDF
Empirical CDF
D=10
D=15
D=20
Fig. 7: CDF of the MOS value of D2D pair
MOS value of D2D pair during the evolution of GA algorithm.
For D= 10, we notice that almost 35% individuals has a MOS
value of 4.5, and increasing the number of D2D pairs reduces
the maximum MOS value can be achieved at the D2D pair.
Fig. 8 plots the MOS value for each D2D pair versus the
number of iterations using Stackelberg game. We observe the
interactions between all the D2D pairs before converge, and at
last converge to a SE with less than 20 iterations. Fig. 9 plots
the price of each RB versus the number of iterations, which
also showcase the convergence after 17th iterations. Due to
the fact that the 1st RB is occupied by many D2D pairs, the
CUE with the 1st RB has a lower QoE value than required.
Thus, the price of 1th RB is increasing until the CUE QoE
requirement constraint is not violated.
Fig 10 compares the MOS value of each D2D pair using GA
algorithm with that using the Stackelberg game after conver-
gence. We also calculate the optimal solutions by brute force
approach, and present the obtained MOS value that maximize
date rate for each D2D pair. In this simulation, the first 8 D2D
pairs are set to be audio application, and the other 12 D2D
pairs are set to be video application. We observe that the MOS
value of some D2D pairs obtained through Stackelberg game is
almost the same as that using centralized GA algorithm, but
with less computational complexity and signaling overhead.
We also observe that the MOS values obtained by these two
algorithms are very close to the optima, which showcase
the benefits of our proposed algorithms. Additionally, we
observe that for audio applications, the MOS value obtained
by MaxDate aglortihm is larger than that achieved by GA
and Stackelberg Game. However, for video applications, the
MOS value obtained by MaxDate aglortihm is much smaller
than that achieved by GA and Stackelberg Game. This can
be explained by the fact that small capacity is required for
audio applications to achieve a high QoE, whereas a higher
capacity is required to achieve the QoE threshold for video
applications. As the MaxData algorithm aims at maximizing
the date rate for all D2D pairs while not considering users’
application type, network resource allocation is not effective.
B. Impact of the number of D2D pairs and CUEs
To further compare and showcase the impact of the GA
algorithm and the Stackelberg game, we plot the average MOS
per D2D pair versus the number of CUEs with D= 15, and
the number of D2D pairs with N= 15 in Fig. 11, and Fig.
12, respectively. We set S= 7 and M= 5 in both figures.
It is revealed that the GA algorithm outperforms the semi-
distributed algorithm, which is mainly because the price in the
semi-distributed algorithm updated with a defined parameter
, and resulting in a lower performance than the centralized
algorithm. We also observe that both algorithms achieve sub-
stantial improvement in terms of the average MOS compared
with random allocation, which showcases the benefits of our
proposed algorithm. We observe that the average MOS value
decreases with increasing the number of CUEs and D2D pairs.
This can be explained by the fact that the interference from
the CUEs and the D2D pairs using the same RB increases
with increasing Nand D. We also noticed that the decreasing
speed with increasing Nis faster than that with increasing D,
which can be contributed to the higher interference from BSs
with more underlay transmission with D2D pair.
C. Impact of the number of Pico BSs and RBs
Fig. 13 (a) and (b) plot the average MOS versus the
number of Pico BSs Swith M= 5. It is shown that
substantial improvement of average MOS can be achieved with
increasing the number of Pico BSs, which is due to the reduced
interference from less underlay transmissions between CUEs
and D2Ds. Fig. 14 (a) and (b) plot the average MOS versus
the number of RBs Mwith S= 5. We also see the substantial
improvement of average MOS when increasing M.
Another important observations is that the increasing trend
of average MOS with increasing the number of RBs is much
faster than that with increasing the number of Pico BSs, which
can be explained by the fact that increasing the number of Pico
BSs can only relieve the pressure of hot spots, but the network
interference still exists. However, when the number of RBs
are slightly large, network interference can be eliminated by
assigning different subcarriers to all active communications.
With heavy loaded CUEs in Fig. 13 (b) and Fig. 14 (b), the
maximum average MOS for D2D pairs can not be achieved
by increasing the number of Pico BSs, which indicates that
increasing the number of RBs can be a better option to achieve
maximum MOS compared with increasing the number of Pico
BSs.
VI. CONCLUSIONS
In this paper, we have formulated the cross-layer QoE
optimization problem mathematically to maximize the aver-
age QoE value of D2D pairs in CR-enabled HetNets. The
joint optimization taking into account the UE association,
the power allocation at both BSs and D2D pairs, and the
RB assignment in a CR-enabled HetNet were performed via
our proposed centralized algorithm based on GA and semi-
distributed algorithm based on Stackelberg Game. Our results
shown that the centralized algorithm based on GA outperforms
the semi-distributed algorithm based on Stackelberg Game,
14
0 5 10 15 20 25 30
2
4
D2D pair 1
0 5 10 15 20 25 30
2
4
D2D pair 2
0 5 10 15 20 25 30
2
4
MOS value
D2D pair 3
0 5 10 15 20 25 30
2
4
D2D pair 4
0 5 10 15 20 25 30
Number of Iterations
2
4
D2D pair 5
(a)
0 5 10 15 20 25 30
2
4
D2D pair 6
0 5 10 15 20 25 30
2
4
D2D pair 7
0 5 10 15 20 25 30
2
4
MOS value
D2D pair 8
0 5 10 15 20 25 30
2
4
D2D pair 9
0 5 10 15 20 25 30
Number of Iterations
2
4
D2D pair 10
(b)
Fig. 8: (a) MOS value of 15D2D pairs in different iterations, (b) MOS value of 610 D2D pairs in different iterations
0 5 10 15 20 25 30
0
0.5
1
1.5
2
2.5
3
3.5
4
Number Of Iterations
Price
RB 1
RB 2
RB 3
RB 4
Fig. 9: Convergence behavior of the price of each RB
0 5 10 15 20
D2D pair No.
1.5
2
2.5
3
3.5
4
4.5
MOS Value
GA
Stackelberg Game
Optimal
MaxData
Fig. 10: MOS comparision with 20 D2D pairs
and both of them achieves substantial improvement compared
with the random allocation and very close to the optima,
which showcase the effectiveness of our proposed algorithms
in optimizing the QoE of D2D pairs in CR-enabled HetNets.
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... Recently, several QoE-driven resource allocation solutions have been proposed for different scenarios that include multi-antenna base stations (BSs) [9], device-to-device communications [10], cognitive radio networks [11], and MC-NOMA-enabled HetNet [12]. Most of these algorithms rely on tools from standard optimization, which makes them unscalable and computationally expensive, thereby not suitable for real-time multimedia applications. ...
... We assume that channel state information (CSI) is fully available at the BSs. The SUEs are served for the web surfing, video streaming and audio application as multimedia services [10] 1. Note that we separate the user association phase (denoted by θ) from the subcarrier allocation phase (denoted by ε) as in [25] and [26]. ...
... In order to perform a QoE-aware wireless resource allocation, as done in [9], [10], [12], we adopt the MOS as the main QoE criterion for the web surfing, HTTP live video streaming, and voice over LTE (VoLTE) audio-services. We define the set J = {1, 2, 3}, in which the index 1 refers to web surfing, the index 2 refers to HTTP live video streaming, and the index 3 refers to VoLTE. ...
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... The authors in [9] proposed a resource allocation scheme for web and video multimedia services using multi-antenna BSs. In [10], a resource allocation for satisfying web, video and audio multimedia services is carried out in Device-to-Device (D2D) networks. The authors in [11] employed MC-NOMA and performed a QoE-driven resource allocation, where user association and subcarrier allocation operations were treated over different phases and each user was served by only one BS. ...
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... (11) After achieving successful SIC and signal decoding operation in SUTs, the QoE requirement is conceivable if [10] MOS j g l ∈L n∈N θ l,g ε n l,g log 2 1 + γ n l,g (θ, ε, p, q) ≥ MOS min, j g . ...
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... The authors in [9] proposed a resource allocation scheme for web and video multimedia services using multi-antenna BSs. In [10], a resource allocation for satisfying web, video and audio multimedia services is carried out in Device-to-Device (D2D) networks. The authors in [11] employed MC-NOMA and performed a QoE-driven resource allocation, where user association and subcarrier allocation operations were treated over different phases and each user was served by only one BS. ...
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... (11) After achieving successful SIC and signal decoding operation in SUTs, the QoE requirement is conceivable if [10] MOS j g l ∈L n∈N θ l,g ε n l,g log 2 1 + γ n l,g (θ, ε, p, q) ≥ MOS min, j g . ...
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... Evolutionary [61][62][63] • By applying Evolutionary Algorithms (EA), the most suitable solution is found out in iterations and after many iterations it eventually converges the solution to the closest sub-optimal solution. • Evolutionary algorithms are usually an effective technique to solve NP hard problems. ...
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