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Abstract

The exponential growth in data traffic and dramatic capacity demand in fifth generation (5G) have inspired the move from traditional single-tier cellular networks towards heterogeneous cellular networks (HCNs). To face the coming trend in 5G, the high availability requirement in new applications, needs to be satisfied to achieve low latency service. Usually, these applications require an availability of six nines or even higher. In this work, we present a tractable multi-tier multi-band availability model for spectrum aggregation-based HCNs. We first derive a closed-form expression for the availability of spectrum aggregation-based HCNs using the signal-to-interference-plus-noise (SINR) model. By doing so, we formulate two optimization problems, one is to maximize the average availability, and the other one is to minimize the average power consumption. These two optimization problems are both non-convex problems, which are challenging to solve. To cope with them, we propose to apply genetic algorithm (GA) for the joint user equipment (UE) association, subcarrier assignment and power allocation problem. Our results show that the average availability in spectrum aggregation-based HCNs improves with decreasing the number of UEs, as well as increasing the power budget ratio. We also show that increasing the maximum number of aggregated subcarriers decreases the average power consumption, but can not guarantee the substantial improvement of average availability.
10156 IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. 66, NO. 11, NOVEMBER 2017
Achieving High Availability in Heterogeneous
Cellular Networks via Spectrum Aggregation
Jie Jia , Member, IEEE, Yansha Deng , Member, IEEE,JianChen, Member, IEEE,
Abdol Hamid Aghvami, Fellow, IEEE, and Arumugam Nallanathan , Fellow, IEEE
Abstract—The exponential growth in data traffic and dramatic
capacity demand in fifth generation (5G) have inspired the move
from traditional single-tier cellular networks toward heteroge-
neous cellular networks (HCNs). To face the coming trend in 5G,
the high availability requirement in new applications needs to be
satisfied to achieve low latency service. Usually, these applications
require an availability of six nines or even higher. In this paper, we
present a tractable multitier multiband availability model for spec-
trum aggregation-based HCNs. We first derive a closed-form ex-
pression for the availability of spectrum aggregation-based HCNs
using the signal-to-interference-plus-noise model. By doing so, we
formulate two optimization problems, one is to maximize the av-
erage availability, and the other one is to minimize the average
power consumption. These two optimization problems are both
nonconvex problems, which are challenging to solve. To cope with
them, we propose to apply genetic algorithm for the joint user
equipment (UE) association, subcarrier assignment, and power al-
location problem. Our results show that the average availability in
spectrum aggregation-based HCNs improves with decreasing num-
ber of UEs, as well as increasing power budget ratio. We also show
that increasing the maximum number of aggregated subcarriers
decreases the average power consumption, but cannot guarantee
the substantial improvement of average availability.
Index Terms—Genetic algorithm, heterogeneous cellular net-
work, high availability, power consumption, spectrum aggregation.
Manuscript received January 10, 2017; revised May 16, 2017 and July 24,
2017; accepted September 12, 2017. Date of publication September 26, 2017;
date of current version November 10, 2017. This work was supported in part
by the National Natural Science Foundation of China under Grants 61772126,
61402096, 61173153, and 61572123, in part by the Fundamental Research
Funds for the Central Universities under Grant N150404006, in part by the
National Science Foundation for Distinguished Young Scholars of China under
Grants 61225012 and 71325002, in part by the Specialized Research Fund of
the Doctoral Program of Higher Education for the Priority Development Areas
under Grant 20120042130003. The review of this paper was coordinated by
Prof. Y.-B. Lin. This paper was presented at the IEEE Global Communications
Conference, Washington, DC, USA, December 2016. (Corresponding author:
Yansha Deng.)
J. Jia and J. Chen are with the Key Laboratory of Medical Image Computing,
Northeastern University, Ministry of Education, Shenyang 110819, China, and
with the School of Computer Science and Engineering, Northeastern University,
Shenyang 110819, China, and also with the Department of Informatics, King’s
College London, London WC2R 2LS, U.K. (e-mail: jiajie@mail.neu.edu.cn;
chenjian@mail.neu.edu.cn).
Y. Deng and A. H. Aghvami are with the Department of Informatics, King’s
College London, London WC2R 2LS, U.K. (e-mail: yansha.deng@kcl.ac.uk;
hamid.aghvami@kcl.ac.uk).
A. Nallanathan is with the Department of Informatics, King’s College Lon-
don, London WC2R 2LS, U.K., and also with the Queen Mary University of
London, London E1 4NS, U.K. (e-mail: a.nallanathan@qmul.ac.uk).
Color versions of one or more of the figures in this paper are available online
at http://ieeexplore.ieee.org.
Digital Object Identifier 10.1109/TVT.2017.2755504
I. INTRODUCTION
IN THE past, the target of wireless technologies has mainly
focused on achieving higher data rates and data volumes.
However, high average rate and high total data are not the only
performance indicators that guarantee the ubiquitous connectiv-
ity in next generation wireless networks. According to ABI Re-
search (Allied Business Intelligence Inc.), more than 30 billion
devices will be wirelessly connected to the Internet by 2020 [2].
The target of next generation wireless networks has extended
to realize high availability and low latency, in order to support
the upcoming new applications under the context of Internet of
Things (IoT), such as haptic communication [3], cloud comput-
ing [4], smart energy grids [5], vehicular communication [6], or
industrial automation [7]. The availability requirement of these
applications is six nines or higher. A detailed analysis on future
application as well as high availability requirement can be found
in [8].
The rapid growth of wireless data traffic, fueled by an ever
increasing availability requirement of smart mobile computing
devices, imposes a huge challenge on current cellular networks.
Deploying more macro base stations (BSs) is no longer a sus-
tainable solution to handle the traffic load. Whereas, deploy-
ing inexpensive, small-scale, low-power nodes in conventional
macrocells becomes a cost-effective solution, which is the so
called heterogeneous cellular networks (HCNs) [9]. These low
power nodes could be pico or femto BSs. However, due to the
heterogeneous deployments of those low power nodes, the in-
terference management among tiers becomes very challenging
and extremely important. In [10], [11], the ambient interfer-
ence from BSs have been ultized for energy transfer to improve
the energy efficiency of HetNets. With the irresistible demand
to support the aforementioned new applications in HCNs, the
modeling, characterization and optimization of availability in
HCNs becomes extremely important.
According to the reliability theory [12], generally, there are
two feasible methods to achieve high availability in a system.
The first method is to substitute or improve some unreliable
sub-components to make the system more reliable. The other
method is to incorporate redundancy in order to improve the
system reliability, through utilizing multiple sub-components
in parallel. With multiple less reliable links connected to BSs
in parallel boost equivalent availability as that a single more
reliable link with higher transmit power or more robust coding.
Data transmission availability can be bootstrapped from
physical layer technology. For instance, Spectrum aggregation
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JIA et al.: ACHIEVING HIGH AVAILABILITY IN HETEROGENEOUS CELLULAR NETWORKS VIA SPECTRUM AGGREGATION 10157
(carrier aggregation) [13] is a well-known technique that enables
multiple less reliable links in parallel to boost availability. As
specified by 3GPP in [14], spectrum aggregation, which enables
the concurrent utilization of multiple component carriers (CCs)
in the physical layer, was originally proposed to increase bit
rates and capacity. With spectrum aggregation, the aggregated
bandwidth as large as 100 MHz can be obtained by aggregating
5 20 MHz CCs, and the propagation characteristics of differ-
ent component carriers may also vary significantly. e.g., a CC
in the 800 MHz has very different propagation characteristic
from a CC in the 2.4 GHz. Recently, spectrum aggregation has
been regarded as the primary feature deployed by operators with
commercial LTE-Advanced service [15]. In [16], the spectrum
aggregation was proposed to improve peak data rate in multi-
band HCNs.
The spectrum aggregation has recently been applied to en-
hance the availability. In [17], the spectrum aggregation was
applied to guarantee high availability by a joint transmission
over multiple links over different carrier frequencies. However,
their work was limited to Rayleigh-fading channel. The work
in [17] was extended to [18] by including selection combin-
ing and maximal ratio combining over Nakagami-m fading. It
is revealed in [17] and [18] that it is more beneficial in terms
of power to utilize multiple links in parallel rather than boost-
ing the power of a single link. In [19], combined macro- and
microdiverse uplink connections and composite correlated dis-
tributions of Nakagami fading and log-normal shadowing was
investigated. More recently, an analytical model for availability
in multi-connectivity systems utilizing macro- and microdiver-
sity was studied in [20]. Nevertheless, all of the aforementioned
works have neglected path loss in the availability model or in-
terference in each carrier.
In order to provide the availability for emergency calls, the
priority based schemes has been designed, where network re-
sources are occupied only by these emergency services [21].
Different from emergency services, IoT applications coexist
with traditional data-centric applications, and share the network
resources with each other. Due to the different achievable ca-
pacity of each link and cumulative interference caused by all
the simultaneously transmitting nodes, nearby or faraway, sim-
ply considering the received power from the desired transmitter
may not accurately capture the availability characteristics. A
more appropriate model taking into account the interference
statistics is the signal-to-interference-plus-noise ratio (SINR)
model, which is also the main element determining the shannon
capacity. The SINR model can be widely found in solving the
optimization problem in spectrum allocation [22], power control
[23], load balancing [24] and UE association [25]. Assuming the
shadowing fading as a random variable, [26] studied the high
availability in wireless networks with different transmit power
at the BS based on SINR model. However, modeling and ana-
lyzing the availability in HCNs based on SINR model can be
computationally and analytically challenging.
Resource allocation has been proposed to solve power con-
sumption problem in [27]–[30]. In [27], a power optimization
scheme was proposed for interference-limited wireless commu-
nications. In [28], the energy-efficient spectrum sharing problem
was studied in cognitive radio femtocell networks. In [29], the
BS sleep-mode strategies in HCNs with the small cell deploy-
ment were proposed to minimize the power consumption. In
[30], the resource allocation and UE association was jointly in-
vestigated to find the near optimal solution for the minimum
total energy consumption of the cellular system using iterative
algorithm. However, most of existed resource allocation algo-
rithms consider continuous transmit power allocation, which
can not be directly applied to in systems supporting discrete
transmit power allocation. For instance, the 3GPP LTE cellular
networks only support discrete power allocation in the down-
link with a use-specific data-to-pilot-power offset parameters
[31]. Compared with the continuous power control, the discrete
power control offers two main benefits [32]: (i) the transmitter
is simplified, and more importantly, (ii) the overhead of in-
formation exchange among networks is significantly reduced.
Nevertheless, using simple discretization on the solution ob-
tained by existed continuous power control is not an effective
approach. Discrete power allocation for cellular networks has
been proposed in [32], [33]. In [32], two discrete power control
algorithms were proposed to maximize the weighted system
capacity. In [33], a discrete power control was proposed for
multi-cell networks aiming at energy efficiency. However, to
the best of our knowledge, there is no work dealing with the
discrete power control for availability optimization.
Unlike existing works, the aim of this work is to propose a
joint UE association, subcarrier assignment and discrete power
allocation technique to optimize the availability and power con-
sumption via genetic algorithms (GAs) [34] in HCNs. Due to the
advantages in versatility, scalability, and computational simplic-
ity, GAs have become increasingly popular method of solving
combinatorial optimization problems in wireless networks [35]–
[43]. GAs are proposed to solve the problem of antenna selection
for MIMO networks [35], subcarrier pairing and power alloca-
tion for cognitive relay networks [36], channel assignment for
wireless mesh networks [37], [43], channel and bandwidth allo-
cation for mobile cellular networks [38], [39], energy saving for
LTE networks [40], cell deployment for 5G networks [41], and
routing and traffic scheduling for multi-hop cellular networks
[42]. The main contributions of this paper are summarized as
follows:
1) We present an analytical model for availability in HCNs
based on SINR model. Unlike [44] and [45], where a
UE connects to one BS offering the highest instantaneous
SINR, we assume each UE connects to multiple BSs with
arbitrary SINR values simultaneously. This results is a
novel approach to model and analyze availability with
multiple connections.
2) We derive an exact closed-form expression for the avail-
ability of a random UE in HCNs, which is verified by
Monte Carlo simulation. Its numerical results reveal the
importance of the UE association, the subcarrier as-
signment and the power allocation in achieving high
availability.
3) We formulate two optimization problems with the aims
of maximizing the average availability under the power
budget constraint, and minimizing the average power
10158 IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. 66, NO. 11, NOVEMBER 2017
TAB LE I
NOTATIONS
Symbol Definition
KSet of BS tiers
NSet of all the UEs in the network
BSet of all the BSs in the network
BkSet of BSs in tier k
NsSet of UEs associated with the sth BS
MSet of subcarriers at each BS
ρMaximum number of subcarriers that can be aggregated
for each UE due to the hardware constraints
vm
s,n Binary variable indicates if the mth subcarrier of the sth
BS is allocated to the nth UE or not
Pmax
sMaximum transmit power of the sth BS
Pmax
s,m Maximum transmit power at the mth subcarrier of the
sth BS
LMaximum integer level of transmit power
ls,m Power allocation level at the mth subcarrier of the sth
BS
δPower budget ratio at any BS
Hs,n Channel power gain between the sth BS and the nth UE
ds,n Distance between the sth BS and the nth UE
N0Noise power
αqPath loss exponent of the qth band
CqPath loss constant of the qth band
μqWavelength of the qth band
τPredefined SINR threshold
consumption while satisfying the availability requirement.
Due to the complex topology of HCNs, these two opti-
mization problems are NP-hard in nature.
4) We propose to apply GA for the joint UE association,
subcarrier assignment and power allocation problem. The
average availability in spectrum aggregation-based HCNs
improves with decreasing the number of UEs, and in-
creasing the maximum number of aggregated subcarriers
allowed for each UE. The average power consumption
decreases with increasing the maximum number of ag-
gregated subcarriers, and decreasing the number of UEs.
To the best of our knowledge, this is the first work of the
availability optimization in spectrum aggregation-based
HCNs using GA.
The remainder of this paper is organized as follows. In
Section II, we present the multi-tier multi-band availability
model. Next, in Section III, we formulate the availability max-
imization problem and the power consumption minimization
problem. Section IV applies GA for the joint UE association,
subcarrier assignment and power allocation problem. Section
V presents the numerical results and Section VI highlights our
conclusions.
II. SYSTEM MODEL AND AVAILABILITY CHARACTERIZATION
A. System Model
We consider HCNs with K={1,...,K}denoting the set
of Ktiers which may include macrocells, picocells, femtocells,
and further radiating elements. In this paper, we focus on the
downlink transmission and assume open access for all the small
cells. We list all the notations in Table I.
We denote the set of UEs as N={1,2,...,N}and the set
of BSs as B=B1∪B
2...∪B
K={1,2,...,S}, where Bk
represents the set of BSs in tier k. To achieve high availability via
multiple link connections, each UE is allowed to be connected
with multiple BSs simultaneously. We assume the massive non-
continuous carrier aggregation [46] is applied, where UEs can
aggregate a large number of (up to 32) continuous and non-
continuous subcarriers from heterogeneous spectrum bands. We
denote the set of UEs associated with the sth BS as Ns, and
thus N=N1∪N
2...∪N
S. We assume that each BS has
maximum Qavailable bands (e.g., 800 MHz, 2.5 GHz, . . . ),
and each band contains Fsubcarriers. We denote the set of bands
in each BS as Q={1,2,...,Q}, and the set of subcarriers at
each BS as M={1,...,F

band1
,...,(Q1)F+1,...,QF

bandQ
}.
We assume that the maximum subcarrier transmit power at
the mth subcarrier of the sth BS is Pmax
s,m , and the maximum
transmit power of the sth BS is Pmax
s. We consider the discrete
power allocation at the mth subcarrier of the sth BS with integer
level ls,m, where
ls,m [1,L]If UE occupied mth subcarrier of sth BS
=0 If no UE occupied mth subcarrier of sth BS,
(1)
and Lis the maximum integer level. Thus, the transmit power
allocated to each subcarrier of a BS belongs to the set [0,1
LPmax
s,m ,
2
LPmax
s,m ,··· ,ls,m
LPmax
s,m ,··· ,Pmax
s,m ].
To specify the UE association and the subcarrier assignment,
we denote vm
s,n as the resource-allocation indicator, which is a
binary variable. If vm
s,n =1, it indicates that the mth subcarrier
of the sth BS (s∈B)is allocated to the nth UE (n∈N), and
vm
s,n =0(m∈M)if otherwise.
We assume the following resource assignment constraint, sub-
carrier aggregation constraint, and per-BS power constraint need
to be satisfied:
1) The variable vm
s,n must satisfy that each subcarrier for a
BS can only be occupied by at most one UE.
2) The total number of aggregated subcarriers for each UE
should be at most ρdue to hardware constraints.
3) The total power consumption at each BS over all its sub-
carriers m∈M
ls,m
LPmax
s,m should not exceed a power bud-
get δPmax
swith the power budget ratio δ.
We use different path loss exponents for different bands to
capture the possible large differences in propagation characteris-
tics associated with each band’s carrier frequency. We formulate
the SINR of the nth UE associated with the mth subcarrier of
the sth BS as
SINRm
s,n =
ls,m
LPmax
s,m Hs,nCqdαq
s,n vm
s,n
i∈B\s
li,m
LPmax
i,m Hi,nCqdαq
i,n

Im
s,n
+N0
,(2)
where q=m/F , and · is the ceiling function. For instance,
if m=15, F=10, we have q=2. In (2), Im
s,n is the aggregate
interference at the nth UE from all the other BSs over the mth
subcarrier, Hs,n is the channel power gain between the sth BS
and the nth UE, ds,n is the distance between the sth BS and the
nth UE, N0is the noise power, αqis the path loss exponent of the
JIA et al.: ACHIEVING HIGH AVAILABILITY IN HETEROGENEOUS CELLULAR NETWORKS VIA SPECTRUM AGGREGATION 10159
qth band, and Cqis the path loss constant depending strongly on
carrier frequency with Cq=(
μq
4π)2for the wavelength μq.Sim-
ilar as [16], [47]–[49], we ignore shadowing and only consider
independent quasistatic Rayleigh fading with Hi,n exp(1)
for simplicity. The extension to take the shadowing into account
or Rician fading can be incorporated in the availability analysis
in Section II via some mathematical manipulations, remind that
the GAs proposed in this work will be still valid.
B. Availability Analysis
The signal cannot be successfully received if the SINR value
SINRm
s,n is below a certain threshold τ. Therefore, the outage
probability of the nth UE associated with the mth subcarrier of
the sth BS is characterized as
Om
s,n =PSINRm
s,n τ.(3)
Thus the availability of the nth UE associated with the mth
subcarrier of the sth BS can be derived as
Am
s,n =1Om
s,n =1−PSINRm
s,n τ
=PSINRm
s,n
.(4)
Generally, Am
s,n denotes the availability of a single connection
between UE nwith an arbitrary BS sover subcarrier m, and
Am
s,n is given in the form of 1 10x, where xindicates the
number of nines. Considering that UE nmay connect multiple
BSs over multiple connections, its availability is defined by
the combination of multiple connection availabilities, which is
derived in the following theorem.
Theorem 1: The availability of the nth UE connected to mul-
tiple BSs in HCNs is derived as
An=1
s∈B,m∈M 1Am
s,n,n∈N,(5)
where the availability of the nth UE associated with the mth
subcarrier of the sth BS is given by
Am
s,n
=
0if vm
s,n =0
exp (ΘsτN0)ifvm
s,n =1,Im
s,n =0
S
i=1ΘiS
j=1,j=s
exp(ΘsτN0)
Θsjsτ)S
k=1,k=s,j kΘj)
if vm
s,n =1,Im
s,n =0,
(6)
where
Θξ=L/(lξ,mPmax
ξ,m Cqdαq
ξ,n ),(7)
and ξcan be s,i,j, and k.
Proof: For vm
s,n =0, we can directly obtain Am
s,n =0.
For vm
s,n =1 with no interference (Im
s,n =0), we present
Am
s,n as
Am
s,n =PSINRm
s,n
=1−Pls,m
LPmax
s,m Hs,nCqdαq
s,n τN0
(a)
=exp(ΘsτN0),(8)
where Θsis given by (7), and (a)is performed based on Hs,n
exp(1).
For vm
s,n =1 and Im
s,n =0, we employ the change of variables
X=Im
s,n +N0,Y=ls,m
LPmax
s,m Hs,nCqdαq
s,n , and Z=Y/X to
obtain
Am
s,n =P(Z>τ)
=
τ
fZ(z)dz
=
τ
0
xfX(x)fY(xz)dxdz. (9)
We have
fY(xz)=Θ
sexp (Θsxz),(10)
where Θsis given by (7).
Next, we focus on computing fX(x)with X=Im
s,n +N0
and
Im
s,n =
i∈B\s
Ωi,(11)
where
Ωi=li,m
LPmax
i,m Hi,nCqdαq
i,n .(12)
According to the distribution of channel power gain, we derive
fΩi(x)=Θ
iexp (Θix),(13)
where Θiis given by (7).
In order to obtain the probability density function (PDF) of the
sum of independent exponential random variables i∈B\sΩi,
we apply the following lemma [50].
Lemma 1: Let (Wi)i=1...n ,n2, be the independent expo-
nential random variables with pairwise distinct respective pa-
rameters Θi, the PDF of their sum is given as
fW1+W2+...+Wn(w)=
n
i=1
Θin
j=1
eΘjw
n
k=1,k=jkΘj).
(14)
Based on Lemma 1, we derive the PDF of Xas
fX(x)=fIm
s,n (xN0)
=
S
i=1,i=s
Θi
S
j=1,j=s
eΘjN0
S
k=1,k=s,j kΘj)eΘjx,
(15)
where Θi,Θj, and Θkcan be obtained by using (7).
10160 IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. 66, NO. 11, NOVEMBER 2017
Substituting (10) and (15) into (9), we obtain
Am
s,n
=
τ
N0
x
S
i=1,i=s
Θi
S
j=1,j=s
eΘjN0eΘjxΘseΘsxz
S
k=1,k=s,j kΘj)dxdz
=
S
i=1
Θi
S
j=1,j=s
eΘjN0
S
k=1,k=s,j kΘj)Z(τ,N0,Θj
sz).
(16)
To solve (16), we derive Z(τ,N0,Θj
sz)as
Z(τ,N0,Θj
sz)
=
τ
N0
xejsz)xdxdz
=
τN0eN0jsz)
j
sz)+eN0jsz)
j+λsz)2dz.
(b)
=
N0jsτ)N0
Θs
eu
u+N0
Θs
eu
u2du
=eN0jsτ)
Θsj
sτ),(17)
where (b) is performed by using u=N0j
sz).
Substituting (17) into (16), we finally derive Am
s,n as
Am
s,n =
S
i=1
Θi
S
j=1,j=s
eN0Θsτ
Θsj
sτ)S
k=1,k=s,j kΘj),
(18)
where Θs,Θi,Θj, and Θkcan be obtained by using (7).
Note that the derived availability of an arbitrary UE in spec-
trum aggregation-based HCNs is a easy-to-evaluate closed-form
expression. Based on this expression, each UE connects to sev-
eral BSs, which enables the optimal solution of the proposed
availability optimization and power consumption optimization
problem. In other words, the connection between each UE and
the BSs is decided to achieve the optimal overall network per-
formance.
It should be observed that the availability defined in (5) is dif-
ferent from that of reliability. According to [51], reliability refers
to the probability to guarantee a required function/performance
under stated conditions within a given time latency, and the spe-
cific reliability requirements differ for various types of services
and applications. While availability is a transport-agnostic def-
inition from the applications point, and showcases the presence
or absence of reliability [52].
Due to the fact that wireless communication systems are typ-
ically not designed to provide a reliable level at all times and
in every reception scenario, this would harm the acceptance of
ultra reliable communication (URC) services and restrict their
usage. Our availability measurement is also different from tra-
ditional methods, where the availability can be calculated by
measuring the ping non-responses and interpolating differences
in time between down link alert and uplink alert during months
[53]. With the help of availability definition and evaluation in
Fig. 1. Single link availability.
Fig. 2. Multiple links availability.
(5), we can quickly evaluate the availability under given con-
ditions, and find those factors influencing current availability.
Thus, the URC services can be quickly deployed in a wide range
of scenarios by just considering whether the obtained availabil-
ity meets its requirement [52].
C. Availability Validation
To verify the derived analytical results for the availability,
we plot the analytical curves for the single link availability
and the multiple link availability using (18) and (5) with the
simulation curves using Monte Carlo simulation in Figs. 1 and
2, respectively. In these two figures, we assume the macro BS
with Pmax
1,m =43 dBm and all the pico BSs with Pmax
j,m =30 dBm
for any subcarrier (j=1) for two-tier HCNs, where the distance
between the UE and the sth BS is randomly generated. Both
figures showcase that the derived analytical results match well
with the simulation, which proves the accuracy of our derived
results.
JIA et al.: ACHIEVING HIGH AVAILABILITY IN HETEROGENEOUS CELLULAR NETWORKS VIA SPECTRUM AGGREGATION 10161
Fig. 1 plots the single link availability versus the power al-
location level l1,m at the macro BS in two-tier HCNs. We set
Cq=(
0.375
4π)2for all band q. The power allocation level lj,m at
the pico BSs is equal to L, which indicates the full power allo-
cation at each pico BSs. As expected, the single link availability
of UE connected to the macro BS increases with increasing the
transmit power of macro BS. Increasing the number of BSs in
HCNs increases the interference, which degrades the single link
availability. Importantly, the single link availability is very low,
and can hardly achieve the availability with six nines, which
reveals the potential of improving the availability via multiple
links.
In Fig. 2, we assume that the number of subcarriers at each BS
is M=2 with Cq1=(
0.375
4π)2, and Cq2=(
0.125
4π)2, respectively.
By comparing Figs. 2 with 1, we see that the availability of
a UE connected with multiple links substantially outperforms
that with single link, which reveals the need to apply spectrum
aggregation technique. We can also see that the multiple link
availability decreases with increasing the transmit power, and
the highest availability of a UE achieved for the lowest power
allocation level L=1 and the minimum number of BSs S=2
reveals the importance of joint optimization on power allocation,
UE association and subcarrier assignment in multi-tier multi-
band HCNs.
III. PROBLEM FORMULATION
Next, We formulate two optimization problems to achieve
the maximum average availability, and to achieve minimum
power consumption in spectrum aggregation-based HCNs, re-
spectively.
Availability Maximization Problem: Network aggregate util-
ity is conventionally regarded as a measure for evaluating
the performance of resource management protocols [54]–[56].
Based on this criterion, the objective of this problem is to maxi-
mize the average availability over all the UEs. Here, the average
availability is the sum of availability of all UEs averaging over
the total number of UEs as shown in (19). This can be achieved
by searching the optimal UE association, subcarrier assignment,
and discrete power allocation under the total power consump-
tion constraint. This availability maximization problem is for-
mulated as
max n∈N An
N(19)
s.t.
n∈N
vm
s,n 1,s∈B,m∈M,(20)
s∈B
m∈M
vm
s,n ρ, n∈N,(21)
ls,m L, s∈B,m∈M,(22)
m∈M
ls,m
Pmax
s,m
LδPmax
s,s∈B.(23)
The constraints in (20)–(23) are named as the UE association
and subcarrier assignment constraint in (20), the subcarrier ag-
gregation constraint in (21), the power level constraint in (22)
and the per-BS power constraint in (23). The subcarrier as-
signment and UE association constraint in (20) represents that
each subcarrier of each BS can be allocated to at most one UE.
The subcarrier aggregation constraint in (21) implies that the
maximum number of aggregated subcarriers must satisfy the
hardware constraints. The power level constraint in (22) repre-
sents that the maximum discrete transmit power level of each
subcarrier is L.Theper-BS power constraint in (23) represents
that the maximum transmit power at each BS is limited by its
total power budget.
Power Consumption Minimization Problem: The objective
of the problem is to minimize the average power consumption
while satisfying each UE’s availability requirement, which is
formulated as
min s∈B m∈M
ls,m
LPmax
s,m
N(24)
s.t.
n∈N
vm
s,n 1,s∈B,m∈M,(25)
s∈B
m∈M
vm
s,n ρ, n∈N,(26)
ls,m L, s∈B,m∈M,(27)
m∈M
ls,m
Pmax
s,m
LδPmax
s,s∈B,(28)
1
s∈B,m∈M 1Am
s,nAth ,n∈N.(29)
Note that the constraints of (25)–(28) are the same as (20)–
(23) in the availability maximization problem, while the per-UE
availability requirement in (29) represents that the availability
requirement for each UE should be satisfied.
Instinctively, both of these two optimization problems are in
the form of mixed integer non-linear programming (MINLP)
problem, which are generally NP-hard and cannot be solved by
traditional optimization methods [30]. In the next section, we
will develop the bio-inspired GA to solve these two optimization
problems.
IV. GENETIC ALGORITHM APPROACH
For these above MINLP problems, a straightforward solu-
tion is to conduct an exhaustive search by testing all feasible
channel and power allocation vectors vm
s,n and ls,m . This ap-
proach, however, is infeasible for networks with larger number
of BSs and UEs. Some other algorithms, such as those in [30],
[57], are based on decomposition. In their algorithm, the near-
optimal subcarrier assignment and UE association is determined
first via heuristic algorithm under fixed power allocation, and
the optimal or near-optimal power allocation is obtained via
Lagrangian dual based method or iterative heuristic approach
with the predetermined optimal subcarrier assignment. How-
ever, their approach may be suboptimal due to the fact that the
subcarrier assignment and power allocation are interacting with
each other, and the subcarrier assignment and power allocation
should be optimized in a compact form [58]. Therefore, we
10162 IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. 66, NO. 11, NOVEMBER 2017
apply GA to integrate these two steps to achieve the interaction
between the subcarrier assignment and power allocation.
By simulating the process of evolution in the natural system,
GA can be considered as an adaptive heuristic search algorithms,
and is very suitable to provide a robust, near optimal solution
for many real world NP-hard problems, such as BS placement
optimization for LTE heterogeneous networks [59], channel as-
signment for wireless mesh networks [43]. GA is inherently an
evolutionary process that involves individual encoding, selec-
tion, crossover, mutation, and replacement operations [34].
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 reflecting the UE association,
the subcarrier assignment, and the power allocation, is proposed
to represent the potential solutions.
We first generate an initial population Rwith Rindividu-
als, and each individual consists of two integer-based matri-
ces, which are the potential solutions of the considered opti-
mization problem. These matrices are generated according to
Algorithm 1 in order to satisfy the UE association and subcar-
rier assignment constraint, the subcarrier aggregation constraint,
the power level constraint, and the per-BS power constraint dur-
ing initialization to accelerate the convergence process. We rep-
resent the two integer-based matrices in the rth individual as
follows (1rR):
1) UE association and subcarrier assignment matrix Γris
Γr=
γr
1,1,···
r
1,M
γr
2,1,···
r
2,M
.
.
..
.
..
.
.
γr
S,1,···
r
S,M
,(30)
where the matrix element γr
s,m (1sS, 1mM)indi-
cates the γr
s,m th UE associated with the mth subcarrier of the
sth BS. For instance, γr
s,m =nindicates the nth UE associated
with the mth subcarrier of the sth BS, thus vm
s,n =1; γr
s,m =0
indicates no UE associated with the mth subcarrier of the sth
BS, thus n∈N vm
s,n =0.
Note that this matrix always satisfies the subcarrier assign-
ment and UE association constraint. According to the population
initialization in Algorithm 1, we count the number of subcarri-
ers assigned to the nth UE cnto ensure that cnis no larger than
the subcarrier aggregation constraint ρ.Ifcn,thenth UE
will become infeasible and be excluded from the set of feasible
UEs Nfeasible .
2) Power allocation matrix Lris
Lr=
lr
1,1,··· ,l
r
1,M
lr
2,1,··· ,l
r
2,M
.
.
..
.
..
.
.
lr
S,1,··· ,l
r
S,M
,(31)
where lr
s,m represents the power level allocated to the mth sub-
carrier of the sth BS.
To satisfy the per-BS power constraint, the matrix element
lr
s,m is initialized in sequence with increasing m. According
to Algorithm 1, we compare the maximum subcarrier trans-
mit power Pmax
s,m with the remaining power premain
sat each BS,
where premain
s=δPmax
spassign
s, with passign
srepresenting the
power allocated for the sth BS. If premain
sPmax
s,m , the trans-
mit power allocated to the mth subcarrier can be randomly
selected from [1,L], thus lr
s,m =randi(L). Otherwise we set
lr
s,m =randi(L
Pmax
s,m premain
s), to guarantee that the assigned
power cannot be larger than the maximum transmit power at
each BS, where · is the ceiling function.
One example of encoding scheme is illustrated in Fig. 3 with
4 BSs and 6 UEs deployed in HCNs, where each BS has 3 sub-
carriers and each UE can associate at most 2 subcarriers. We
set the maximum transmit power at each BS Pmax
s=40 W,
the maximum transmit power at each subcarrier Pmax
s,m =16 W,
and the maximum power level L=16. For instance, γ3,1=5
and l3,1=9 indicates that the power level allocated by the 1st
BS at the 3rd subcarrier to the 5th UE is 9. It can be also ob-
served that this encoding scheme meets all the constraints except
JIA et al.: ACHIEVING HIGH AVAILABILITY IN HETEROGENEOUS CELLULAR NETWORKS VIA SPECTRUM AGGREGATION 10163
Fig. 3. Individual encoding scheme.
the per-UE availability requirement of the power consumption
minimization, 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)
r∈R f(r),(32)
where f(r)is the fitness function of individual r. The quality of
the individual is judged by this fitness function.
For the availability maximization problem, since all the con-
straints are satisfied during initialization, we directly take the
objective function as the fitness function, which is given by
fI(r)=n∈N An
N.(33)
For the power consumption minimization problem, the fit-
ness function is defined by taking the average network power
consumption and a penalty function determined by the relative
degree of infeasibility. To provide an efficient search and ensure
that the final best solution is feasible, the penalty method [60]
is adopted to deal with the availability constraint. The fitness
Fig. 4. Two-point crossover and individual repair.
function is expressed as
fII(r)=s∈B m∈M
ls,m
LPmax
s,m
N
+
n∈N
αnmax (Ath An,0),(34)
where αnrepresents the penalty coefficient determined by the
per-UE availability requirement. This transforms the power con-
sumption minimization problem to a maximization problem.
C. Crossover and Mutation
The crossover operation is used to mix between the individu-
als to increase their fitness. In this paper, two-point crossover is
performed to produce new solutions. In order to avoid violating
the per-BS power constraint, we limit the crossover operation
between arbitrary row of the matrices of one individual and that
of another individual. Every elements between the two points
are switched between two parent individuals to produce two
child individuals. The subcarrier aggregation constraint may be
violated after crossover operation, thus some elements of UE as-
sociation and subcarrier assignment matrix need to be repaired
by allocating to other UEs.
We illustrate an example of two-point crossover and individ-
ual repair operation in Fig. 4, the parameters setting of which
is the same as that of Fig. 3, and the randomly generated two
crossover points are c1=1 and c2=3. The crossover between
parent Aand parent Bis performed by switching the rows of
the 1th BS and the 4th BS in both matrices of parent Awith
10164 IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. 66, NO. 11, NOVEMBER 2017
that of parent B. After crossover, the assigned subcarriers for
the 2th UE and the 4th UE violate the subcarrier aggregation
constraint ρ=2 in child A. As such, we repair γ1,3and γ2,2in
child Ausing randomly generated number 5 and 1 to obtain a
repaired child A.
In the mutation operation, the elements in both matrices 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 of the UE association and subcarrier assignment ma-
trix, repair operation may be required to satisfy the subcarrier
aggregation constraint to speed up the convergence; 2) For the
mutation occurring at the arbitrary element lr
s,m of the power
allocation matrix, mutation operation will be performed using
lr
s,m = randi
min
Pmax
s
M
i=1,i=m
ls,i
Pmax
s,i
L,Pmax
s,m
L
Pmax
s,m
,
(35)
where · is the ceiling function.
D. Replacement
After generating a new population through the crossover and
mutation operators, an elitist model based replacement is em-
ployed 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.
Now, we have designed the key components of the GA oper-
ation, which are the individual encoding, population initializa-
tion, selection, crossover, mutation, and replacement operation.
The joint optimization of UE association, subcarrier assignment
and power allocation based on GA is depicted in Algorithm 2,
where Gis the given number of generations, Ris the popula-
tion size, qcis the crossover probability, and qmis the mutation
probability.
In the proposed GA-based optimization, the computational
complexity is dominated by the complexity in evaluating the
objective function in (33) or (34), which has to be evaluated
Rtimes in each iteration. For the availability maximization
problem, with the number of subcarriers as Mand the number of
UEs as N, the time complexity in calculating the fitness function
of the average availability in (33) is O(MNR)within a iteration.
For the power consumption minimization problem, with the
number of subcarriers as M, the number of UEs as N, and
the number of BSs as S, the time complexity in calculating the
fitness function of the power consumption in (34) is O(R(MS +
MN)) within a iteration.
Apart from this, a GA-based approach also depends on other
factors, which are difficult to clearly enumerate, such as strate-
gies to generate new population, and the tolerance allowable
for cumulative changes in fitness values [61]. Excluding these
parameters, the total complexity of our algorithm in solving the
availability maximization problem and the power consumption
TAB LE I I
SIMULATION PARAMETERS
Parameter Value
The number of macro BS 1
The number of pico BS 9
The number of UEs N220
Maximum transmit power of macro BS 46 dBm (40 W)
Maximum transmit power of pico BS 30 dBm (1 W)
Maximum aggregated subcarriers per UE 1 10
The availability threshold Ath 1106(six nines)
800MHz band’s wavelength μ10.375 m
2.5GHz band’s wavelength μ20.125 m
800MHz band’s path loss exponent α13
2.5GHz band’s path loss exponent α24
The number of subcarriers in each band 10
Maximum integer power level L132
Maximum subcarrier transmit power of macro BS (40/10)W
Maximum subcarrier transmit power of pico BS (1/10)W
Noise PSD 174 dBm
SINR threshold τ1
Population size 20
Crossover probability 0.95
Mutation probability 0.005
Maximum generation 2000
minimization problem are O(G(MNR+R2)) and O(G
(MSR+MNR +R2)), respectively.
V. N UMERICAL RESULTS
In this section, we provide numerical results to illustrate the
performance of our proposed algorithm. We consider spectrum
JIA et al.: ACHIEVING HIGH AVAILABILITY IN HETEROGENEOUS CELLULAR NETWORKS VIA SPECTRUM AGGREGATION 10165
Fig. 5. (a) Convergence behavior of the availability maximization problem. (b) Convergence behavior of the power consumption minimization problem.
aggregation-based HCNs consisting of 2 tiers (macro and pico)
with 2 bands (800 MHZ and 2.5 GHZ). The set-up is a circle
area with size (π5002)m
2, 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 II
unless otherwise specified. The corresponding simulations are
implemented in Matlab 7 in a laptop with Intel (i5-4300) CPU.
All the results are obtained by averaging 100 simulations.
A. Convergence Behavior
In GA, the convergence behavior is affected by many control
parameters, such as the initial population, mutation probability,
crossover mechanism, etc.. To the best of our knowledge, the
conditions for GAs to converge have been proved only for the
binary encoding with Markov chain models [62]. However, for
the GA algorithm with integer or real encoding, the convergence
is still an open problem [39]. In this paper, instead of using
an analytical approach, extensive simulations are employed to
look at the convergence issue. In our simulations, we set the
maximum number of generation as 2000. Actually, the number
of generations depends on the number of size of individuals.
For instance, more generations are needed for a larger number
of UEs or number of subcarriers.
Fig. 5(a) plots the convergence behavior of the availabil-
ity maximization problem with the maximum number of ag-
gregated subcarriers ρ=5, and the power budget ratio δ=1.
Fig. 5(b) plots the convergence behavior of the power consump-
tion minimization problem with the availability threshold of
6 nines (Ath =1106), and ρ=5. From Fig. 5(a) and (b),
we can observe that the algorithm converge after approximately
500 number of generations for various number of UEs. It takes
20 seconds to converge for N=10 HCNs. This is sufficient for
many applications. If we use a more powerful computer, it is
expected that it can converge much faster.
For the availability maximization problem, the average avail-
ability with random allocation at the initialization is 0.564944,
while the final average availability after optimization with GA
is 0.999859, which showcase that the GA achieves nearly 50%
more average availability compared with that of the random
TABLE III
OPTIMIZED AVERAGE AVAILABILITY VALUE
N4 8 12 16 20
Availability by GA 10 nines 7 nines 5 nines 3 nines 3 nines
Optima 11 nines 7 nines 5 nines 3 nines 3 nines
TAB LE I V
OPTIMIZED POWER CONSUMPTION VALUE
N4 8 12 16 20
Fitness 0.009 0.023 0.138 0.771 3.448
Availability 6 nines 6 nines 5 nines 3 nines 3 nines
APC (W) 0.009 0.023 0.042 0.087 0.214
OPC (W) 0.009 0.021 0.038 0.079 0.193
resource allocation. For the power consumption minimization
problem, the GA achieves a huge decrease of fitness value dur-
ing evolution, this can be explained by the fact that the random
resource allocation cannot satisfy the per-UE availability re-
quirement, thus a large penalty value is introduced in the fitness
function in (34). Additionally, it is revealed that the converge
speed can be substantially increased with reduced number of
UEs in HCNs.
We then present the optimized average availability, and the
optimized power consumption with corresponding achieved av-
erage availability for various number of UEs in Tables III and
IV, where APC means the average power consumption. Ad-
ditionally, we present the optimal availability and power con-
sumption that based on brute force approach, where OPC means
the optimal power consumption. In both Tables, we see that the
availability of 6 nines can be achieved when the number of UEs
is less than 8. In Table IV, due to the availability of 6 nines
requirement is satisfied for N=4 and N=8, no penalty value
is introduced to the fitness value, and results in equal value
as the power consumption. However, the violation of per-UE
availability requirement (6 nines) for N=12, 16, and 20 re-
sults in the added penalty values as shown in the fitness values.
10166 IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. 66, NO. 11, NOVEMBER 2017
Fig. 6. (a) Average availability versus the number of UEs. (b) Average power consumption versus the number of UEs.
Fig. 7. (a) Average availability versus different power levels. (b) Average power consumption versus different power levels.
We also observe that the optimized value based on GA closely
approaches the optima obtained by brute force approach, which
showcases the effective of GA for availability maximization or
power consumption minimization.
B. Impact of the Number of UEs and the Subcarrier
Aggregation Constraint
Fig. 6(a) plots the average availability versus the number of
UEs for various subcarrier aggregation constraint ρ. We ob-
serve that the average availability decreases with increasing the
number of UEs. This can be explained by the fact that the trans-
mit power allocated to the UE decreases and the interference
from the same subcarrier at other BSs increases with increasing
the number of UEs. More importantly, the average availability
can be improved by relaxing the maximum number of aggre-
gated subcarriers. For the availability maximization problem, we
can observe that the substantial improvement of average avail-
ability is achieved from single subcarrier constraint to three
aggregated subcarriers constraint, however further increasing
the maximum number of aggregated subcarriers can not achieve
much improvement. This indicates that increasing the maximum
number of aggregated subcarriers may not guarantee substantial
improvement of average availability.
Fig. 6(b) plots the optimized average power consumption ver-
sus the number of UEs for various subcarrier aggregation con-
straint ρ. Due to the increased per-subcarrier interference with
increasing the number of UEs, the average power consumption
increases with increasing the number of UEs. Another important
observation is that utilizing multiple connections can be an effi-
cient way to save power and improve availability. For instance,
for HCNs with 9 UEs fulfilling the availability requirement,
the average power consumption with ρ=4 is around 0.059 W,
whereas that with ρ=9 is around 0.023 W.
C. Impact of the Maximum Power Levels and Power Budget
Ratio
Fig. 7(a) plots the average availability versus the maximum
power levels for various number of UEs. It is shown that the av-
erage availability increases with increasing the maximum power
levels for the same number of UEs. And the achieved availability
is much larger than that with on power control (L=1), which
showcases the importance of discrete power control. However,
JIA et al.: ACHIEVING HIGH AVAILABILITY IN HETEROGENEOUS CELLULAR NETWORKS VIA SPECTRUM AGGREGATION 10167
Fig. 8. (a) Average availability of 10 UEs versus different power budget ratios. (b) Average availability of 20 UEs versus different power budget ratios.
Fig. 9. Average power consumption of 4 UEs.
the average availability of 6 nines is not achievable in HCNs
with N=16 or 20 UEs even with L=32, which means that
increasing Lcan not guarantee substantial improvement in the
average availability. Fig 7(b) plots the power consumption ver-
sus different Lfor different number of users N. We see that
average power consumption decreases with increasing L, espe-
cially for Nis larger. However, when Nis small, increasing
Lcan not guarantee substantial improvement in minimizing
average power consumption.
Fig. 8(a) and (b) plot the average availability versus different
power budget ratio δfor different ρ. It is shown that the average
availability increases with increasing δfor the same ρ, which
results from the increased received power. The six nines of
average availability can be achieved for HCNs with 10 UEs for
ρ=59 and δ=1, these availability values are sufficient for
the requirement of many real-time applications. However, the
average availability of 6 nines is not achievable in HCNs with
20 UEs even with δ=1 and ρ=9. Similar as the observation
in Fig. 6(b), increasing the maximum number of aggregated
subcarriers can not guarantee substantial improvement in the
average availability.
D. Impact of the Maximum Number of Aggregated Subcarriers
Fig. 9 plots the average power consumption versus different
maximum number of aggregated subcarriers ρfor various avail-
ability threshold Ath with N=4 UEs. We see that in order
to achieve higher per-UE availability requirement, more num-
ber of allowed aggregated subcarriers is needed. It is revealed
that the average power consumption decreases with increasing
the maximum number of aggregated subcarriers. The higher
per-UE availability requirement results in higher average power
consumption.
VI. CONCLUSION
In this paper, we have presented the theoretical model and
optimization algorithm to achieve high availability in spectrum
aggregation-based HCNs. We have developed a novel availabil-
ity model under the SINR model. We have also derived a closed-
form expression for the availability in spectrum aggregation-
based HCNs. We have formulated two optimization problems
to maximize the average availability and minimize the aver-
age power consumption. To solve the non-convex optimization
problems, we have proposed an efficient GA-based algorithm
for the joint optimization of the UE association, the subcar-
rier assignment, and the power allocation. The average avail-
ability in spectrum aggregation-based HCNs can be improved
by decreasing the number of UEs as well as increasing the
power budget ratio. Increasing the maximum number of ag-
gregated subcarriers decreases the average power consumption,
but can not guarantee the substantial improvement of average
availability.
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Jie Jia received the Ph.D. degree in computer sci-
ence and technology in 2009 from the Northeastern
University, Shenyang, China, where she is currently
an Associate Professor. In 2016, she was a Visiting
Research Associate at the King’s College London.
She is a member of various international societies,
such as the IEEE and China Computer Federation.
She has published more than 100 technical papers
on various aspects of wireless networks. Her current
research mainly includes HetNets, IoT, and cognitive
radio networks.
Yansha Deng (S’13–M’17) received the Ph.D. de-
gree in electrical engineering from the Queen Mary
University of London, London, U.K., in 2015. From
2015 to 2017, she was a Postdoctoral Research
Fellow in the Department of Informatics, King’s Col-
lege London, London, U.K., where she is currently
a Lecturer. Her research interests include massive
MIMO, HetNets, molecular communication, cogni-
tive radio, cooperative networks, and physical layer
security. She received the Best Paper Award in IEEE
International Conference on Communications 2016.
She is currently an Editor of the IEEE COMMUNICATIONS LETTERS. She has also
served as a TPC member for many IEEE conferences, such as IEEE GLOBE-
COM and IEEE ICC.
Jian Chen received the Ph.D. degree in computer sci-
ence and technology in 2010 from the Northeastern
University, Shenyang, China, where he is currently
an Associate Professor. He is also a Senior Soft-
ware Engineer at the Neusoft Corporation, Shenyang,
China. In 2016, he was a Visiting Research Associate
at King’s College London. His research interests in-
clude D2D communication, location technology, net-
work management, and signal and image processing.
Abdol Hamid Aghvami (M’89–SM’91–F’05) is cur-
rently a Professor of telecommunications engineer-
ing at King’s College London, London, U.K. He
joined the academic staff at King’s College London
in 1984. In 1989, he was promoted to a Reader, and
in 1993 was promoted to a Professor in telecommu-
nications engineering. He is the founder of the Centre
for Telecommunications Research at King’s College
London. He was the Director of the centre from 1994
to 2014.
He carries out consulting work on digital radio
communications systems for British and international companies. He has pub-
lished more than 560 technical journal and conference papers, filed 30 patents,
and given invited talks and courses the world over on various aspects of mobile
radio communications. He was a Visiting Professor at the NTT Radio Com-
munication Systems Laboratories in 1990, a Senior Research Fellow at the BT
Laboratories during 1998–1999, and an Executive Advisor to the Wireless Fa-
cilities Inc., USA, during 1996–2002. He is the Chairman of Advanced Wireless
Technology Group Ltd. He is also the Managing Director of the Wireless Multi-
media Communications Ltd, London, U.K., his own consultancy company. He
is also the Founder of the International Symposium on Personal Indoor and Mo-
bile Radio Communications, a major yearly conference attracting some 1000
attendees.
Prof. Aghvami received the IEEE Technical Committee on Personal Commu-
nications Recognition Award in 2005 for his outstanding technical contributions
to the communications field, and for his service to the scientific and engineering
communities. He is a Fellow of the Royal Academy of Engineering and a Fellow
of the IET. In 2009, he received a fellowship from the Wireless World Research
Forum in recognition of his personal contributions to the wireless world, and for
his research achievements as the Director of the Centre for Telecommunications
Research, King’s College London.
Arumugam Nallanathan (S’97–M’00–SM’05–
F’17) has been a Professor of wireless communi-
cations in the School of Electronic Engineering and
Computer Science, Queen Mary University of Lon-
don, London, U.K, since September 2017. From De-
cember 2007 to August 2017, he was with the Depart-
ment of Informatics, King’s College London, where
he was a Professor of wireless communications from
April 2013 to August 2017. He was an Assistant Pro-
fessor in the Department of Electrical and Computer
Engineering, National University of Singapore, from
August 2000 to December 2007. He has published more than 350 technical pa-
pers in scientific journals and international conferences. His research interests
include 5G wireless networks, Internet of Things, and molecular communi-
cations. He is a corecipient of the Best Paper Award presented at the IEEE
International Conference on Communications 2016 and the IEEE International
Conference on Ultra-Wideband 2007. He is an IEEE Distinguished Lecturer.
He has been selected as a Web of Science (ISI) Highly Cited Researcher in
2016. He is an Editor of the IEEE TRANSACTIONS ON COMMUNICATIONS and
IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY. He was an Editor of the
IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS (2006–2011), the IEEE
WIRELESS COMMUNICATIONS LETTERS, and the IEEE SIGNAL PROCESSING
LETTERS.
... The complexity of the objective function exponentially increases with the space size of x, y, and z, together with binary characteristic variables and the inequalities of constraints c1, c2, c4, and c5. The BILP problem can be reduced to either the Travel Saleman problem (TSP) or the Partition problem [29] [30], which is proved to be NP-hard. • The number of BSs and the number of files in practice make the solution space of sets x, y, and z become very large. ...
... We are motivated to develop an algorithm that is effective and can be easily implemented by network operator. The heuristic search algorithm GA is considered to be suitable for massively parallel optimization [28], [29]. GA provides a robust, nearoptimal solution for many real-world NP-hard problems such as BS placement in heterogeneous networks [30], video chunks placement in CDN [31], channel subcarrier assignment [29], [32]. ...
... The heuristic search algorithm GA is considered to be suitable for massively parallel optimization [28], [29]. GA provides a robust, nearoptimal solution for many real-world NP-hard problems such as BS placement in heterogeneous networks [30], video chunks placement in CDN [31], channel subcarrier assignment [29], [32]. On our side, we choose GA because its parallelization is just suitable to our problem. ...
Article
Small base stations (BSs) equipped with caching units are potential to provide improved quality of service (QoS) for multimedia service in ultra-dense cellular networks (UDCNs). In addition, the Coordinated MultiPoint (CoMP) transmission method, allowing multiple BSs to jointly serve users, is proposed to increase the throughput of cell-edge mobile terminals (MTs). Yet, the combination of content caching and CoMP in UDCNs is still not well explored for future networks. In this paper, we focus on the application of caching in CoMP-integrated UDCNs, where the cache-enabled BSs can collaboratively serve each MT using either joint transmission or single transmission. We propose a multidimensional cooperative caching (MDCC) scheme, supporting storage-dimension and transmission-dimension cooperations for the content placement. In particular, we analyze the delivery delay based on request patterns, transmission method, and the proposed cooperation strategy. Then the content placement problem is formulated as a problem of minimizing the overall expected delay. The problem is a mixed binary integer linear programming (BILP) problem, which is NP-hard. Therefore, we address the problem with approximation and substitution, and design a genetic algorithm (GA) based method to solve it. Simulation results demonstrate that the proposed MDCC scheme contributes performance gain in terms of content delivery delay in both cell-core and cell-edge areas.
... For instance, spectrum aggregation(SA) is a typical technology to boost the system reliability [23]. With SA, multiple component carriers (CCs) dispersed within and across different bands can be used simultaneously [19]. By establishing redundant links and duplicating packets over each parallel link, the reliability of the whole network can be bootstrapped much easier. ...
... In this paper, we use the SINR which has been proved more practical for reliability modeling [19] to model the reliability of our network. The wireless channel will certainly fade to some extent during the signal propagation process, therefore, a mathematical model is needed to simulate this fading. ...
... As mentioned before, this problem contains two processes, sub-carrier assignment and power allocation. In order to decompose and simplify the problem, we employ the solution in [19]. During the phase of sub-carrier assignment, our algorithm will decide how to establish links between UE and sub-carrier. ...
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Full-text available
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... There have been some works investigating the resource management algorithms in Heterogeneous Networks (HetNet) to coordinate multitier interference. In [16], the authors investigated the joint subcarrier assignment, user equipment (UE) association, and power allocation algorithms for the carrier aggregationbased HetNets. With the same control schemes, [17] studied the max-min UE availability problem in the coordinated multi-point (CoMP) and CA-enabled HetNets. ...
... Next, we propose a sequential convex approximation (SCA) based iterative algorithm to solve the problem in (8), which is summarized in Algorithm 1. In each iteration, we solve the approximated problem in (16), which is a concave problem (see Lemma 1) and can be tackled by some mature softwares (e.g., CVX). The optimal solutionŜ of (16) is utilized as the initial point of the next iteration. ...
... Lemma 1. T he problem in (16) is a concave optimization problem. P roof : All of the constraints C1-C5 in (16) are linear, thus the feasible region of (16) is a convex set. Then, to prove the concavity of the problem, we only need to prove that the objective function in (16) is concave. ...
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Full-text available
This paper investigates the application of non-orthogonal multiple access (NOMA) and device-to-device (D2D) into the scenario of massive Machine Type Communications (mMTC). Specifically, we first propose a new NOMA-and-D2D integrated network, where NOMA is utilized to deal with the cross-tier and co-tier interference at the base station side. To fully exploit the advantages of the network, we formulate a joint channel allocation and power control problem with the objective to maximize the performance of the D2D communications under the constraints of the rate requirements of the cellular users. For solving the formulated problem efficiently, we first adopt the sequential convex approximation method to solve the channel allocation subproblem, and then transform the power control subproblem into a convex optimization problem. To further reduce the computational complexity, we employ the convolutional neural network (CNN) to devise a resource management framework, where the relation between the system states and the control policies is established by multiple neurons. Finally, simulation results indicate that the convex approximation based algorithm outperforms the other algorithms in terms of utility, sum-rate, and user satisfaction, and the CNN based algorithm achieves orders of magnitude speedup in computational time with only slight loss of performance.
... Possible future extensions of this work can include other important LPWAN features, such as power allocation and multiple base stations. Moreover, one may consider adapting the proposed algorithms to maximize reliability given fixed network geometry and number of users, in a way similar to what [28] does, or to analyze latency and energy efficiency of the models, similarly to [29], noting that neither [28] nor [29] consider LoRaWAN networks. In the future, we also plan to validate our models using data from a multi-technology large scale IoT network at the University of Oulu. ...
... Possible future extensions of this work can include other important LPWAN features, such as power allocation and multiple base stations. Moreover, one may consider adapting the proposed algorithms to maximize reliability given fixed network geometry and number of users, in a way similar to what [28] does, or to analyze latency and energy efficiency of the models, similarly to [29], noting that neither [28] nor [29] consider LoRaWAN networks. In the future, we also plan to validate our models using data from a multi-technology large scale IoT network at the University of Oulu. ...
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Smart Utility Networks (SUN) rely on the Wireless-SUN (Wi-SUN) specification for years. Recently practitioners and researchers have considered Low-Power Wide-Area Networks (LPWAN) like LoRaWAN for SUN applications. With distinct technologies deployed in the same area and sharing unlicensed bands, one can expect these networks to interfere with one another. This paper builds over a LoRaWAN model to optimize network parameters while accounting for inter-technology interference. Our analytic model accounts for the interference LoRaWAN receives from IEEE 802.15.4g networks, which forms the bottom layers of Wi-SUN systems. We derive closed-form equations for the expected reliability of LoRaWAN in such scenarios. We set the model parameters with data from real measurements of the interplay among the technologies. Finally, we propose two optimization algorithms to determine the best LoRaWAN configurations, given a targeted minimum reliability level. The algorithms maximize either communication range or the number of users given constraints on the minimum number of users, minimum communication range, and minimum reliability. We validate the models and algorithms through numerical analysis and simulations. The proposed methods are useful tools for planning interference-limited networks with requirements of minimum reliability.
... The first equality holds because α m d and β m d are calculated based onγ m d , which means the bound is tight; the second inequality holds becauseP t+1 d is the optimal solutions of (28) for the t + 1-th iteration; the third inequality holds because z(2P t+1 d ) is the lower bounds of f (P t+1 d ). Therefore, from (30), it is known that the value of f (P t d ) increases after each iteration. Due to the fact the value of f (P t d ) is upper bounded due to limited spectrum resources, algorithm 3 can finally converge to the optimal power allocation. ...
... Note that the convergence behavior of DE is [29]. Similar as that in [30], extensive simulations are employed to look at the convergence issue. In our simulations, we set the maximum number of generation as 10000. ...
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A novel joint optimization framework for device to device (D2D) enabled non-orthogonal multiple access (NOMA) networks is proposed. Our objective is to maximize the performance of D2D communication by jointly optimizing the resource block (RB) assignment, the power allocation, by considering the SIC decoding order of NOMA based cellular user equipments (CUEs). We invoke the distributed decision making (DDM) framework to decouple the formulated problem into two sub-problems. For RB assignment sub-problem with integer variables, we propose differential evolution (DE) algorithm to obtain the optimal NOMA CUE group and RB assignment for D2D pairs. For power allocation sub-problem with continuous variables and decoding order variables, we first use a heuristic algorithm to optimize the power allocation for NOMA based CUEs with given D2D power allocation. We prove that the power allocation for NOMA based CUEs is the optimal solution. We then invoke the successive convex approximation (SCA) and DE to find the sub-optimal power allocation of the D2D pairs. Numerical results validate the feasibility, fast convergence, and flexibility of the proposed algorithm, and the performance with our algorithm outperforms conventional OMA technology in terms of energy efficiency and sum rate.
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The WiFi sensor constrains the Human activity recognition scheme to an immovable orientation when providing training samples, drastically reducing practical applications. In addition, the empirical investigation through the ubiquitous experience of participants in environments with wireless signals makes it imperatively challenging to evaluate a location-independent method to recognize human activity. In this research, a 1D CNN-LSTM model was built to comparatively analyze location-independent human activity recognition through WiFi CSI. Thus, the method reduces the impact of human activity recognition on location independent. Nevertheless, the experimental results demonstrate that our method can achieve over 94.9% coverage accuracy for location-independent human activity recognition and 90% coverage accuracy for CNNs using our proposed method. The location-independent model developed can be used possibly for practical applications in any situation, and data from each antenna is processed independently, making it applicable in any location or antenna setup. A variety of input sample lengths has been tested to overcome the measurement sensors’ sampling rate limitations. The results show that human activities can be recognized in real-time through WiFi signaling. Therefore, the CSI WiFi connectivity is potentially enhancive in building an excellent platform to locate human activities in modern age.
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This paper investigates the secrecy energy efficiency (SEE) for a two-tier heterogeneous cellular network having a macro cell and multiple small cells, where the macro cell consists of a macro base station (MBS), a macro user and an eavesdropper and meanwhile each small cell comprises of a small base station (SBS), a small user and an eavesdropper. We consider the use of artificial noise (AN) signals emitted at MBS and SBSs at the expense of transmit power to defend against eavesdroppers. For the sake of obtaining a better balance between the secrecy rate (SR) and energy efficiency of heterogeneous cellular networks, we propose an SEE maximization (SEEM) scheme in small cells through jointly optimizing the beamformers of confidential signals and AN at MBS and SBSs, called joint beamforming based SEEM (JBF-SEEM) while guaranteeing the SR requirements and the power constraints for MBS and each SBS. However, the proposed JBF-SEEM problem is a complicated optimization problem because of the non-convex fractional form. Thus, we firstly transform the original objective function in fractional form into a subtractive one through applying the Dinkelbach's method, and then the non-convex subtractive form is approximated into a convex optimization problem by combining the penalty function and the difference of two-convex functions approach. Furthermore, we propose a two-tier iterative JBF-SEEM algorithm to obtain the near-optimal beamforming solution. Numerical results show that the JBF-SEEM algorithm is convergent while achieving a better SEE performance than conventional approaches.
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