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Availability Analysis and Optimization in

CoMP and CA-enabled HetNets

Jie Jia, Member, IEEE, Yansha Deng, Member, IEEE, Jian Chen, Member, IEEE,

A. Hamid Aghvami, Fellow, IEEE, and Arumugam Nallanathan, Fellow, IEEE

Abstract—Traditional cellular networks are moving towards

heterogeneous cellular networks (HetNets) to satisfy the strin-

gent demand for data rates and capacity. To enable the new

applications in 5G, such as haptic communications, we face

new challenges of achieving high availability with low latency

in HetNets. In this paper, we introduce coordinated multi-point

(CoMP) and carrier aggregation (CA) techniques in HetNets to

guarantee the availability of all UEs, where CoMP improves

the single-path availability, and CA enhances availability via

multi carrier gain combining. To characterize the availability, we

ﬁrst derive an exact closed-form expression for the availability

of a random UE in a CoMP and CA-enabled HetNets. To

achieve the maximum UE availability, we formulate a max-

min optimization problem. To solve it, we then propose a two-

step optimization algorithm and a joint two-step optimization

algorithm. The two-step optimization algorithm (TSOA) is based

on heuristic algorithm for the optimal subcarrier assignment

and UE association, and based on Lagrangian dual method for

the power allocation. The joint two-step optimization algorithm

(JTOA) is based on genetic algorithm (GA) to achieve the

interaction between the ﬁrst step and the second step. Our results

showcase the effective of our proposed JTOA, and the effective

of CoMP in availability improvement in HetNets.

Index Terms—Heterogeneous cellular networks, high availabil-

ity, coordinated multi-point, carrier aggregation, genetic algorith-

m.

I. INTRODUCTION

In the past, cellular networks have mainly focused on

achieving higher data rates and greater user capacities for

human-centric applications, such as telephone, mobile inter-

net or video streaming. However, it is expected that future

wireless network will be complemented by a wide range

of innovative and unconventional services and applications,

such as M2M communication, IoT applications, machine-

type communications (MTCs), and haptic communications.

According to Gartner [2], about 6.4 billion connected things

Copyright (c) 2017 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 Aug. 31, 2016; revised Dec. 30, 2016; accepted Feb.

24, 2017. The associate editor coordinating the review of this manuscript and

approving it for publication was Prof. Tony Q.S. Quek. This paper has been

published in part at IEEE International Conference on Communications (ICC),

Paris, 2017 [1].

Corresponding author: Yansha Deng (Email: yansha.deng@kcl.ac.uk.)

Jie Jia and Jian Chen are with the Key Laboratory of Medical Image

Computing of 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 Department

of Informatics, King’s College London, London WC2R 2LS, UK (email:

{jiajie, chenjian}@mail.neu.edu.cn).

Y. Deng, A.H. Aghvami, A. Nallanathan are with Department of Informat-

ics, King’s College London, London WC2R 2LS, UK (email: {yansha.deng,

hamid.aghvami, arumugam.nallanathan}@kcl.ac.uk).

will be in use worldwide this year, which is nearly up to 30

percent increase from last year. And they also foretasted that

the number would keep growing, and reach nearly 21 billion

by the year 2020.

Usually, these specialized, mission-critical applications have

speciﬁc requirements, which seems too stringent for the

conventional human-centric applications, like the ultra high

availability and ultra low latency requirements. Examples of

application having these requirements include haptic com-

munication [3], cloud computing [4], smart energy grids

[5], vehicular communication [6], or factory automation [7].

The temporal availability requirement of these applications

is 99.9999% (six nines) or higher. A more detailed example

is that the factory automation application in a smart factory

needs the end-to-end latency with 1ms and the availability

requirement as 9 nines [8]. In other words, only one message

in 109data transfers can be lost or delayed in more than

1ms. A detailed analysis on future application as well as high

availability requirement can be found in [9]. How to provide

an availability of six nines or even higher for applications with

ultra-reliable requirement using the existing or future cellular

networks has become a major challenge.

The traditional cellular networks are undergoing a signiﬁ-

cant transition to handle the increasing wireless data demands,

as well as the ever increasing availability requirement. Simply

deploying more macro base stations (BSs) is no longer a

sustainable solution to cope with those stringent requirements.

Therefore, action is being taken to deploy more inexpensive,

low-power, small-scale BSs, such as pico, femto BSs, un-

derlaying the conventional cellular networks to improve the

spectral efﬁciency and reduce the communication distance

[10]. This is the so called heterogeneous cellular networks

(HetNets). However, due to the heterogeneous deployments of

those low power nodes, the interference management among

tiers becomes very challenging and extremely important.

According to the reliability theory [11], there are two

feasible methods to improve availability of a system: 1) the

serial approach, which substitutes or adds more reliable sub-

components in serial with the single sub-component system;

and 2) the parallel approach, which enables multiple sub-

components working in parallel. Multi-connection is one ex-

ample using parallel approach, where the receiver is allowed

to be served by multiple transmitters simultaneously, in or-

der to achieve the multi-link diversity gain and availability

improvement [12]–[16].

In [12], it was shown that the higher availability could be

achieved via multiple less reliable links connection than single

powerful link connection. However, this work was limited to

2

Rayleigh-fading links. The model in [12] has been extended

to [13] by including selection combining and maximal ratio

combining over Nakagami-m fading. In [14], combined macro-

and uplink connections was studied under Nakagami fading

and log-normal shadowing. In [15], multi-input multi-output

(MIMO) was proposed to achieve ultra-reliable and low-

latency communications in 5G machine-type communication

(MTC) use cases. It is noticed that [12]–[15] only considered

the single-user case, and hence the effects resulted from multi-

user and multi-cell interference are not explicitly studied [16].

Due to the different achievable capacity of each link and

cumulative interference caused by all the simultaneously trans-

mitting nodes, nearby or faraway [17], simply considering the

received power from the desired transmitter may not accurately

capture the availability characteristics. A more appropriate

model is to measure the signal quality in terms of the signal-

to-interference-plus-noise ratio (SINR) value. The SINR is,

however, affected by many variable factors that are intrinsic for

any wireless systems. The desired signal power can be slightly

attenuated as a result of the fading nature of the wireless

channel, whereas the received interference can be large due to

the typical aggressive reuse of the time-frequency resources

for maximizing the system capacity in the network. Assuming

the shadowing fading as a random variable, [18] studied the

high availability in wireless networks with different transmit

power at the BS based on SINR model. However, modeling

and analyzing the availability in HetNets based on SINR model

can be computationally and analytically challenging.

Another example of multi-connectivity is the carrier ag-

gregation (CA) technique [19], where the concurrent utiliza-

tion of multiple component carriers (CCs) at the physical

layer is enabled, bringing wider effective bandwidth. CA

has already been included in the 3rd Generation Partnership

Project (3GPP), which combines contiguous or non-contiguous

spectrum fragments to create a virtual wideband channel. The

aggregated bandwidth as large as 100MHz can be obtained by

aggregating 5 20MHz CCs, and the propagation characteristics

of different component carriers may also vary signiﬁcantly.

e.g., a CC in the 800MHz has very different propagation

characteristic from a CC in the 2.4 GHz. With CA, another

dimension of diversity can be achieved via carrier-selecting

fading [20].

Even though CA improves the availability of single UE in

HetNets via multi-path connectivity, the single path availability

is still low due to the full spectrum reuse in HetNets [21],

[22]. The intercell interference is the most detrimental factor

impairing the single path availability. To cope with it, coordi-

nated multi-point (CoMP) was proposed in 3GPP [23]. With

CoMP, the BSs in coordinated BS cluster are connected via

a backhaul link, and transmit data to the UE simultaneously

to improve single path availability under universal frequency

reuse [24].

Different from CA that exploiting the spectral diversity gain,

CoMP is a coordination technique between BSs to enhance

inter-cell interference coordination in the same carrier. There

are two categories of CoMP: 1) CoMP coordinated beamform-

ing (CoMP-CB) was proposed to avoid inter-cell interference

[25]; and 2) CoMP joint processing (CoMP-JP) is capable

of converting the inter-cell interference to useful signal [26],

therefore provides an external capacity gain over CoMP-CB.

More importantly, with the help of CoMP-JP, the availability

gain of each path can be achieved to bring substantial overall

availability improvement of single UE [27]. However, their

potential to provide ultra-reliable communications in HetNets

has not been treated until recently.

The resource allocation is an effective way to optimize the

system performance for cellular networks with CA/CoMP. In

[20], the joint downlink and uplink resource allocation for

energy-efﬁcient CA was studied, where the optimal power

allocation was solved using the Lagrangian dual method.

In [28], a joint clustering and resource allocation problem

for ultra dense cellular networks was solved using a two-

step algorithm, which consists of the user-centric clustering

based on load information and scheduling algorithm based on

graphic coloring. In [29], the subcarrier allocation algorithm

was proposed to satisfy both throughput and fairness. In

[30], with the aim of maximizing the energy efﬁciency, the

joint optimization on BS coordination, user scheduling, data

rate adaption, and power allocation was solved via iterative

algorithm.

Different from aforementioned works, the aim of this work

is to achieve high UE availability in HetNets with the help of

CA and CoMP. To the best of our knowledge, this is the ﬁrst

work taking into account the SINR-based availability modeling

and optimization in HetNets. The main contributions of this

paper are summarized as follows:

•We propose CoMP and CA-enabled HetNets to improve

the UE availability in HetNets, where CoMP improves

the availability of each path via interference coordination,

and CA improves the UE availability via multi-carrier

gain combining. This approach for availability improve-

ment is different from previous works only using parallel

method [12], [13].

•We present an analytical model for the UE availability in

CoMP and CA-enabled HetNets based on SINR model.

Different from the coverage model or outage model

deﬁned in [31] and [32], where a UE connects to one BS

offering the highest instantaneous SINR, we assume each

UE can be served by multiple subcarriers and multiple

BSs via muli-path connectivity.

•We derive an exact closed-form expression for the avail-

ability of a random UE in CoMP and CA-enabled

HetNets, which is veriﬁed by Monte Carlo simulation.

Its numerical results reveal the importance of the UE

association, the subcarrier assignment and the power

allocation in achieving high availability.

•We formulate an optimization problem with the aims of

maximizing the minimum UE availability for multi users

under the BS transmit power constraint in a multi-cell

HetNet. Due to the complex topology of proposed model,

the optimization problem is NP-hard in nature.

•We ﬁrst propose the two-step optimization algorithm (T-

SOA) to solve the optimization problem. In this algorith-

m, the optimal subcarrier assignment and UE association

is determined ﬁrst via heuristic algorithm under equal

power allocation, and the optimal power allocation is

3

obtained via Lagrangian dual based method with the

predetermined optimal subcarrier assignment.

•We then propose the joint two-step optimization algorith-

m (JTOA), which is an integration of the TSOA with the

GA algorithm to achieve the interaction between the ﬁrst

step and the second step. Numerical results show that our

JTOA is an effective way for availability improvement.

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

optimization problem. In section IV, we propose the TSOA and

JTOA. Section V presents the numerical results and Section

VI highlights our conclusions.

II. SYSTEM MODEL

A. Availability Analysis

We consider HetNets including macrocells, picocells, femto-

cells, and further radiating elements. In this network, there are

Nrandomly distributed UEs, denoted as N={1,2, ..., N},

and the set of BSs as B={1,2, ..., S}, where Srepresents

the number of BSs. Each BS has Qavailable bands (e.g.,

800MHz, 2.4GHz, ...), each spectrum band contains For-

thogonal subcarriers. 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

| {z }

band1

, ..., (Q−1)F+ 1, . . . , QF

| {z }

bandQ

}. We focus on

the downlink transmission with open access for all the small

cells.

With CoMP, the coordinated BS cluster can transmit data

to the UE simultaneously to eliminate the co-channel inter-

ference and improve the received signal quality. The BSs in

each coordinated BS cluster are connected via high-capacity

backhaul links on which complex signaling and user data

are exchanged [33]. To fully exploit the macro diversity of

coordinated BS cluster, we adopt the user-centric adaptive

clustering [34], where any UEs can be served by arbitrary

number of coordinated BSs, and the coordinated BS cluster

for each UE can overlap with each other. Each UE can access

to different sub-carriers in each BS simultaneously, and can

potentially aggregate data from all the available sub-carriers.

For clarify, Fig. 1 presents the illustration of our system model

with 3 BSs and 2 UEs, where each UE can aggregate 2 sub-

carriers, and each UE can also apply CoMP technique on one

sub-carrier to enhance its availability.

To specify the UE association and the resource assignment,

we denote vm

s,n as the resource-allocation indicator 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 if otherwise vm

s,n = 0 (m∈ M). To specify the power

allocation, we denote the power allocated at the mth subcarrier

of the sth BS is Ps,m, where

Ps,m (∈(0, P max

s],If UE occupied mth subcarrier of sth BS,

= 0,If no UE occupied mth subcarrier of sth BS,

(1)

and Pmax

sis the maximum transmit power of the sth BS.

s1

Carrier

Aggregation

Carrier

Aggregation

Interference

CoMP CoMP

s2s3

UE1UE2

Marco BS

Pico BS Pico BS

Fig. 1: System model with CoMP and CA

Due to the hardware limitation, the following per-subcarrier

assignment 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 transmit power at each BS over all its sub-

carriers PmPs,m should not exceed its maximum power

Pmax

s.

We deﬁne the set of coordinated BS cluster serving the

nth UE at the mth sub-carrier as Bm

n={s|vm

s,n = 1, s ∈

B, m ∈ M}, the SINR of the nth UE at the mth subcarrier

with CoMP-JP is formulated as

SI N Rm

n=P

i∈Bm

n

Pi,mHi,n Cqd−αq

i,n

X

j∈B−Bm

n

Pj,mHj,n Cqd−αq

j,n

| {z }

Im

n

+N0

,

(2)

where q=dm/F e, with d·e as the ceiling function, Im

nis

the aggregate interference at the nth UE from all the other

non-coordinated BSs, αqis the path loss exponent of the qth

band, Hi,n is the random variable capturing the fading effects

of the subcarrier between the ith BS and the nth UE, di,n is

the distance between the ith BS and the nth UE, N0is the

noise power, and Cqis the constant depends strongly on carrier

frequency with Cq= (µq

4π)2for the wavelength µq. Similar as

[22], we ignore shadowing and only consider Rayleigh fading

with Hi,n ∼exp(1) for simplicity.

According to the user-centric adaptive clustering, the choic-

es and the size of coordinated BS cluster for each UE can be

adaptive. It can be seen from (2) that increasing the number of

BSs in the coordinated BS cluster for a given UE increases its

SINR value, due to that the coordinated BS cluster convert the

intercell interference between each other to the useful signal.

However, it should be also be noted that increases the number

of BSs involved in this coordinated BS cluster decreases the

probability of other UEs accessibility, due to the fact that all

sub-carriers in a cell are orthogonal and each sub-carrier can

only be occupied by at most one UE at a time.

The signal of a single path cannot be successfully received

if the SINR value SINRm

nis below a certain threshold τ, thus

4

the availability of the nth UE associated with the coordinated

BS cluster Bm

nat the mth subcarrier is expressed as

Am

n=P(SI N Rm

n> τ).(3)

And the availability nth UE in HetNets is deﬁned by

the combination of multiple single-path availabilities (parallel

model), which is derived in the following theorem.

Theorem 1. The availability of the nth UE in a HetNet with

CoMP-JP and CA is derived as

An= 1 −Y

m∈M

(1 −Am

n),∀n∈ N ,(4)

where

Am

n=

0 if Bm

n=∅

ΩBm

nP

s∈Bm

n

e−ΞsτN0

ΘBm

n/s

if Bm

n6=∅, Im

n= 0

ΩBP

s∈Bm

nP

j∈B−Bm

n

e−ΞsN0τ

(Ξj+Ξsτ)ΘB−Bm

n/j ΘBm

n/s

if Bm

n6=∅, Im

n6= 0

(5)

with

Ξs=1

Ps,mCqd−αq

s,n

.(6)

ΩBm

n=Y

i∈Bm

n/s

Ξi,(7)

ΩB=Y

i∈B/s

Ξi,(8)

ΘBm

n/s =Y

k∈Bm

n/s Ξk−Ξs,(9)

and

ΘB−Bm

n/j =Y

l∈B−Bm

n/j Ξl−Ξj.(10)

Proof. For Bm

n=∅, we can directly obtain Am

n= 0.

For the case Bm

n6=∅and with no interference Im

n= 0, we

have

Am

n=P(SI N Rm

n> τ)

=PX

s∈Bm

n

1

Ξs

Hs,n ≥τN0.(11)

In order to obtain the probability density function (PDF) of

Y=P

s∈Bm

n

1

ΞsHs,n, we apply the lemma as follows [35].

Lemma 1. Let (Xi)i=1...n,n≥2, be independent exponential

random variables with pairwise distinct respective parameters

θi. we have the PDF of their sum as

fX1+X2+...+Xn(X) = n

Y

i=1

θin

X

i=1

e−θix

n

Q

k=1,k6=i

(θk−θi)

.(12)

Based on Lemma 1, the PDF of Y=Ps∈Bm

n

1

ΞsHs,n is

derived as

fY(y) = Y

i∈Bm

n

ΞiX

s∈Bm

n

e−Ξsy

Q

k∈Bm

n/s Ξk−Ξs.(13)

Substituting (9) into (7), we obtain

Am

n=P(SI N Rm

n> τ)

=Z∞

τN0

fY(y)dy

=Y

i∈Bm

n

ΞiX

s∈Bm

n

e−ΞsτN0

ΞsQ

k∈Bm

n/s Ξk−Ξs

=Y

i∈Bm

n/s

ΞiX

s∈Bm

n

e−ΞsτN0

Q

k∈Bm

n/s Ξk−Ξs.

(14)

For Bm

n6=φand Im

n6= 0, we employ the change of

variables X=Im

n+N0and Z=Y/X to obtain

Am

n=P(z > τ )

=Z∞

τ

fZ(z)dz

=Z∞

τZ∞

0

xfX(x)fY(xz)dxdz.

(15)

By plugging y=xz into (14), we obtain

fY(xz) = Y

i∈Bm

n

ΞiX

s∈Bm

n

e−Ξsxz

Q

k∈Bm

n/s Ξk−Ξs.(16)

Next, we focus on computing fx(x). Employing ti=

li,m

LPmax

i,m Hi,nCmd−αq

i,n and t=Im

n, we can rewrite tas

t=Xi∈B−Bm

n

ti,(17)

with

fti(x)∼Ξiexp (−Ξix),(18)

where Ξi=1

Pi,mCqd−αq

i,n

.

Based on Lemma 1, the PDF of P

i∈B−Bm

n

tiis derived as

fX(x) = fIm

n(x−N0)

=Y

j∈B−Bm

n

ΞjX

j∈B−Bm

n

eΞjN0

Q

l∈B−Bm

n/j

(Ξl−Ξj)e−Ξjx.

(19)

Combining (15), (16) and (19), we obtain

5

0 2.5 5 7.5 10 12.5 15 17.5 20

0

0.05

0.1

0.15

0.2

0.25

0.3

Transmit Power of Marco BS (W)

Availability with CoMP

Ex.

Sim.

Bn

1={1,2,3,4}

Bn

1={1,2,3}

Bn

1={1,2}

Bn

1={1}

(a)

0 2.5 5 7.5 10 12.5 15 17.5 20

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

Transmit Power of Macro BS (W)

Availability with CoMP and SA

Ex.

Sim.

Bn

m={1,2,3,4}

Bn

m={1,2,3}

Bn

m={1,2}

Bn

m={1}

(b)

Fig. 2: (a) Single UE Availability with CoMP, (b) Single UE Availability with CoMP and CA.

Am

n=

Y

i∈B

ΞiX

s∈Bm

nX

j∈B−Bm

n

eΞjN0

Q

k∈Bm

n/s

(Ξk−Ξs)

Z(τ, N0, θj+θsz)

Q

l∈B−Bm

n/j

(Ξl−Ξj),

(20)

where

Z(τ, N0,Ξj+ Ξsz)

=Z∞

τZ∞

N0

xe−(Ξj+Ξsz)xdxdz

=Z∞

τN0e−N0(Ξj+Ξsz)

(Ξj+ Ξsz)+e−N0(Ξj+Ξsz)

(Ξj+ Ξsz)2dz.

(21)

Employing a change of variable of u=N0(Ξj+ Ξsz), we

obtain

Z(τ, N0,Ξj+ Ξsz)

=Z∞

N0(Ξj+Ξsτ)N0

Ξs

e−u

u+N0

Ξs

e−u

u2du

=e−N0Ξj+Ξsτ

ΞsΞj+ Ξsτ.

(22)

Combining (20) and (22), we obtain Am

nwith Bm

n6=φand

Im

n6= 0 as

Am

n=Y

i∈B/s

ΞiX

s∈Bm

nX

j∈B−Bm

n

1

Q

k∈Bm

n/s Ξk−Ξs

e−ΞsN0τ

(Ξj+ Ξsτ)Q

l∈B−Bm

n/j Ξl−Ξj.

(23)

B. Availability Validation

To verify the derived analytical results, we plot the an-

alytical curves for the availability with CoMP-JP and the

availability with CoMP-JP and CA using (23) and (4) with

the simulation points using Monte Carlo simulation in Fig.

2a and Fig. 2b, where Ex. denotes the Exact results from (4)

and Sim. denotes the results from Monte Carlo Simulation.

In these two ﬁgures, we consider two-tier HetNets, including

single macro BS with Pj,m =46 dBm, 4 pico BSs with Pj,m =

30 dBm, and single UE. The single UE and all these BSs are

randomly deployed in a circle area with radius of 500m, and

the path loss exponent is set as 4. Both ﬁgures demonstrate

the well match between the derived analytical results and the

simulation, which proves the accuracy of our derived results.

In Fig. 2a, we plot the availability of the single UE versus

the transmit power at the macro BS with different number

of BSs in the coordinated BS cluster B1

n, with the single

subcarrier in each BS (M= 1). In Fig. 2b, we plot the

availability of the single UE with CA, where the number of

subcarriers at each BS is M= 2 with Cq1= ( 0.375

4π)2, and

Cq2= (0.125

4π)2, respectively. The equal power allocation is

applied in each subcarrier, Note that the CoMP-JP technique

is not used when Bm

n={1}in both ﬁgures.

We ﬁrst observe that the availability of the single UE

increases with increasing the transmit power at the macro

BS and the number of coordinated BSs. However, due to

the uneven distribution of these BSs, the distance between

the UE and BSs are not equal, and the improvement gap

between Bm

n={1,2}and Bm

n={1}is larger than that

between with Bm

n={1,2,3}and Bm

n={1,2}, which

also reveals the importance of UE association for availability

improvement. Comparing Fig. 2a with Fig. 2b, we see that

the availability of the single UE occupying two subcarriers

substantially outperforms that occupying single subcarrier,

which reveals the beneﬁts of CA technique. However, due to

the interference from the non-coordinated BSs, the availability

in Fig. 2b is still far from the availability goal of six nines,

which reveals the importance of using resource allocation to

6

optimize the availability.

III. PROB LE M FORMULATION

The target of this paper is to maximize the minimum

availability among all UEs, which is referred to the Max-

Min Availability optimization problem. To achieve this, an

optimization algorithm is required to perform the optimal UE

association, resource assignment, and power allocation under

the transmit power constraint of each BS. We ﬁrst present the

optimization problem as

max

v,P min

nAn(24)

s.t. XmPs,m ≤Pmax

s,∀s∈ B,(24a)

Xn∈N vm

s,n ≤1,∀s∈ B,∀m∈ M,(24b)

Ps,m ≥0,∀s∈ B,∀m∈ M,(24c)

vm

s,n ∈ {0,1},∀n∈ N ,∀m∈ M,∀s∈ B.(24d)

In (24), Anis given by (4). The constraint in (24a) indicates

that the maximum power constraint of each BS, and the

constraints (24b) indicates that each BS can be allocated to at

most one UE. Relying on the strictly increasing characteristic

of logarithmic function [36], we thus convert the optimization

problem of (24) into the following equivalent problem

min

v,P max

nXmln 1−Am

n(25)

s.t. XmPs,m ≤Pmax

s,∀s∈ B,(25a)

Xn∈N vm

s,n ≤1,∀s∈ B,∀m∈ M,(25b)

Ps,m ≥0,∀s∈ B,∀m∈ M,(25c)

vm

s,n ∈ {0,1},∀n∈ N ,∀m∈ M,∀s∈ B.(25d)

Optimizing vm

s,n and Ps,m in (25) is a mixed integer

programming problem, which is generally NP-hard, so the op-

timality for any polynomial time solutions is hard to guarantee.

However, if we relax the integer constraint (vm

s,n ∈ {0,1})by

treating vm

s,n as a sharing factor (0 ≤vm

s,n ≤1), or determine

vm

s,n by some other method, the optimization problem becomes

a convex optimization problem, because the objective function

is concave and all constraints are linear [37]. Remind that

simply relaxing vm

s,n may results in non-integer solutions of

subcarrier assignment. To avoid that, we propose the two-

step optimization algorithm, where the optimal subcarrier

assignment and UE association achieving (24) with equal

power allocation is determined and ﬁxed ﬁrst, and then the

optimal power allocation is obtained using Lagrangian dual

based method.

IV. OPTIMIZATION ALGORITHMS

In this section, we propose two optimization algorithms to

solve the max-min optimization problem: the TSOA and the

JTOA. In both algorithms, we divide the resource allocation

into the power allocation, and the subcarrier assignment and

UE association. In TSOA, the optimal subcarrier assignment

and UE association is determined ﬁrst via heuristic algorithm

under equal power allocation, and the optimal power alloca-

tion is obtained via Lagrangian dual based method with the

predetermined optimal subcarrier assignment. The JTOA is an

integration of the two-step optimization algorithm with the

GA algorithm to achieve the interaction between the ﬁrst step

and the second step. In this algorithm, the optimal subcarrier

assignment and UE association is obtained by GA, and the

Lagrangian based power allocation is used to evaluate the

ﬁtness of each individual in GA and guide the evolution

process.

A. Two-Step Optimization Algorithm

In this subsection, we present the ﬁrst step and the second

step of TSOA in the following subsections.

1) Subcarrier assignment and UE association: In this

section, we propose the heuristic algorithm for sub-carrier

assignment to decide {vm

s,n}. The description of Algorithm

1for the subcarrier assignment and UE association is given

in the following.

In the initialization step of Algorithm 1, we assume the

equal power allocation among all BSs and thus the power

allocation vector at any subcarrier of each BS is given as

Ps,m =Pmax

s

M. We denote Fs={1,2,· · · , M }as the avail-

able subcarrier set of the sth BS, and F={F1,F2,· · · ,FS}

as all the available subcarriers of all BSs with the total number

of the available subcarriers as |F| =S×Mduring the

initialization.

After the initialization, the heuristic algorithm performs

three steps: the UE selection,the potential gain calculation

and the subcarrier assignment. At the UE selection step, the

UE with the lowest availability n∗is selected as the ﬁrst to be

given access to subcarrier, with the objective of maximizing

the minimum availability among UEs as in (24). If there are

more than one UEs with the same minimum availability, a

random UE among them is selected.

At the potential gain calculation step, we calculate the

potential availability gain before and after single subcarrier m

is allocated to UE n∗. For an available subcarrier m∈ Fs, we

denote P re(Am

n∗)and Cur(Am

n∗)as the availability of UE n∗

before and after m∈ Fsis allocated to UE n∗, respectively.

Thus, the potential gain Gm

s,n∗for allocating mth subcarrier

of sth BS to n∗UE is given by

Gm

s,n∗=Cur(Am

n∗)−P re(Am

n∗).(26)

Using (26), we calculate and record the potential gains

Gm

s,n∗for all the available subcarriers and all the available

BSs. At the subcarrier assignment step, the optimal subcarrier

m∗of the BS s∗with the maximum potential gain Gm∗

s∗,n∗

is assigned to the n∗th UE. Note that only single subcarrier

of a BS is allocated to the n∗th UE to reduce the possible

impact on the availability of the other UEs. These three steps

are iteratively executed until the available subcarrier set F

becomes empty.

7

Algorithm 1: Heuristic algorithm for subcarrier assign-

ment and UE association

Initialization

Set Am

n= 0,vm

s,n = 0, and Ps,m =Pmax

s

Mfor

∀n∈ N ,∀s∈ B,∀m∈ M

Set F={F1,F2,· · · ,FS}, and Fs={1,2,· · · , M }

while F 6=∅do

Step1: UE selection

Find UE n∗satisﬁes An∗< Ak∀k∈ N

Step2: potential gain calculation

for s= 1 to Bdo

for m∈ Fsdo

Calculate and record

Gm

s,n∗=Cur(Am

n∗)−P re(Am

n∗)

end

end

Step3: subcarrier assignment

Find a subcarrier m∗in BS s∗satisﬁes

Gm∗

s∗,n∗> Gm

s,n∗∀m∈ Fs,∀s∈ B

Update vm∗

s∗,n∗= 1,Fs∗=Fs∗/m∗, and F=F/m∗

end

2) Power allocation with ﬁxed subcarrier assignment and

UE association: Fixing the optimized subcarrier assignment

and UE association in the ﬁrst step, we limit vm

s,n to integer

with ﬁxed value. Thus, we can represent the optimization

problem in (25) as

min

Pmax

nXmln 1−Am

n(27)

s.t. XmPs,m ≤Pmax

s,∀s∈ B,(27a)

Ps,m ≥0,∀s∈ B,∀m∈ M.(27b)

Following [38], we further convert this problem into the

following optimization problem

min

v,p ζ(28)

s.t. XmPs,m ≤Pmax

s,∀s∈ B,(28a)

Ps,m ≥0,∀s∈ B,∀m∈ M,(28b)

Xmln (1 −Am

n)≤ζ, ∀n∈ N .(28c)

The above optimization problem can be solved by the

Lagrangian dual method, where the corresponding Lagrangian

is written as

L(P;α,β) = ζ+X

s

αsX

m

Ps,m −Pmax

s

+X

n

βnX

m

ln(1 −Am

n)−ζ,

(29)

where α(α≥0) is the Lagrange multiplier vector associated

with constraint in (28a) and β(β≥0) is the Lagrange

multiplier vector associated with constraint in (28c). As such,

the dual problem is given by

max

α≥0,β≥0min

PL(P;α,β).(30)

The above dual problem can be solved iteratively by decom-

posing it into two nested loops: the inner loop that minimizes

over Pwith the given αand β, and the outer loop that is the

master dual problem maximizing over αand β.

A. Solution to the inner loop: With the given αand β,

minPL(P;α,β)is a standard concave form, and hence we

apply the Karush-Kuhn-Tucker conditions to ﬁnd the optimal

solution. To solve the inner loop, we ﬁrst derive the ﬁrst-order

derivatives as

∂L

∂Ps,m

=αs−X

n

βn

1

1−Am

n

∂Am

n

∂Ps,m

,(31)

Note that Am

ndepends on Bm

nand Im

n. If Bm

n=∅, we can

directly obtain ∂Am

n

∂Ps,m = 0.

If Bm

n6=∅and Im

n= 0, we derive

∂Am

n

∂Ps,m

=ΩBm

nX

s∈Bm

n

e−ΞsτN0−τN0Θ−∂Θ

∂Ξs

Θ2

∂Ξs

∂Ps,m

=ΩBm

n

P2

s,mCqd−αq

s,n X

s∈Bm

n

e−ΞsτN0

Θ2τN0Θ−fk,s,

(32)

where

fk,s =X

k∈Bm

n/k,s Y

k∈Bm

n/s Ξk−Ξs.(33)

If Bm

n6=∅and Im

n6= 0, we have

∂Am

n

∂Ps,m

=∂ΞsΩB

∂Ps,m X

s∈Bm

nX

j∈B−Bm

n−Υ

Θ2

Bm

n/s

∂ΘBm

n/s

∂Ξs

+∂Υ

∂Ξs

1

ΘBm

n/s

=ΩB

P2

s,mCqd−αq

s,n X

s∈Bm

nX

j∈B−Bm

n

Υfk,s

Θ2

Bm

n/s

−

T0(−N0−1)τe−θsN0τ

ΘB−Bm

n/j Ξj+ Ξsτ2ΘBm

n/s

,

(34)

where

Υ = e−ΞsN0τ

Ξj+ ΞsτQ

l∈B−Bm

nΞl−Ξj.(35)

By substituting (32) and (34) into (31) and setting ∂L

∂Ps,m =

0, we derive the optimal power allocation P∗

s,m as

8

P∗

s,m =

0 if |Bm

n|= 0

r=ΩBm

nP

s∈Bm

n

e−ΞsτN0

Θ2

Bm

n/s τN0ΘBm

n/s −fk,s

if Bm

n6=∅, Im

n= 0

s=ΩBP

s∈Bm

nP

j∈B−Bm

nΥfk,s

Θ2

Bm

n/s

+(1+N0)τe−θsN0τ

ΘB−Bm

n/j (θj+θsτ)2ΘBm

n/s

if Bm

n6=∅, Im

n6= 0

(36)

where

==1

αsCqd−αq

s,n X

n

βn

1−Am

n

.(37)

and ΩBm

n,ΩB,ΘBm

n/j ,ΘB−Bm

n/j ,fk,s and Υare given in (7)

∼(10), (33) and (35).

Note that the local optimal solution ζ∗and local optimal

availability (Am

n)∗can be obtained using P∗

s,m in (36).

B. Solution to the outer loop: To ﬁnd αand βwith the

obtained P∗and ζ∗in the inner loop, we apply the subgradient

method. By doing so, αand βcan be updated iteratively using

αg+1

s="αg

s−κPmax

s−X

m

P∗

s,m#+

∀s∈ B,(38)

βg+1

n="βg

n−κζ∗−X

m

ln(1 −(Am

n)∗)#+

∀n∈ N ,

(39)

where κ=0.1

√gis a diminishing step size, gis the iterative time,

[·]+denotes the updated αand βneeds to be non-negative.

The calculation process of the optimal power allocation

P∗and the update process of αand βare repeated until

convergence, where the dual optimal is reached. Knowing that

the inner loop is a convex problem, the duality gap is zero.

The detailed procedures for solving the dual problem in (28)

are illustrated in Algorithm 2.

Algorithm 2: Power allocation based on Lagrangian dual

approach

Set g= 0, and initialize αg,βg, and P

repeat

In prim domain, solve min

PL(P;α,β)to obtain P∗,

ζ∗and (Am

n)∗

In dual domain, update the dual variable vector αg+1

according to (38)

In dual domain, update the dual variable vector βg+1

according to (39)

g=g+ 1

until convergence;

In TSOA, Algorithm 2 is executed after Algorithm 1, we

thus calculate the complexity of TSOA as O(M2S2) + O(L),

where Sis the total number of BSs in B, and O(L)is the time

complexity of Algorithm 2, which depends on the complexity

of outer and inner loops. Due to the fact that Algorithm 2

is a standard convex optimization, a fast convergence speed

can be guaranteed for the subgradient method and power

optimization based on KKT condition [20]. We thus can

qualitatively conclude that O(L)is low and acceptable. It also

should be observed that algorithm 2 can only be executed after

determining the subcarrier assignment and UE association,

which means Algorithm 1 and Algorithm 2 can not be

iteratively operated in TSOA. In the next section, we will

design a GA based approach to iteratively update the subcarrier

assignment and UE association, which will ﬁnally converge to

the optimal solution. However, much more time complexity is

required.

B. Joint Two-step Optimization based on Genetic Algorithm

In this section, we propose JTOA based on GA to achieve

the interaction between the ﬁrst step and the second step of

TSOA. GA has already been widely used to tackle many real

world NP-hard problems, such as BS placement optimization

for LTE heterogeneous networks [39] or joint channel and

power allocation for HetNets [40]. This bio-inspired algorith-

m imitates the natural evolution of biological organisms to

provide a robust, near optimal solution for various problems.

In Fig. 3, the JTOA based on GA is illustrated in detail. The

ﬁrst operation is initialization. Initially, the GA generate Rma-

trices to form the initial population set R={Γr}R

r=1, where

each matrix Γr=γr

s,mS×Mcorresponds to a potential

solution of the UE association and the subcarrier assignment.

Each matrix element γr

s,m ∈Γr(1 ≤r≤R)denotes that the

γr

s,mth UE is associated with the mth subcarrier of the sth BS

(0 ≤γr

s,m ≤N). Generally, the γr

s,m in the initial population

should be randomly generated to preserve the diversity of the

population. However, considering that the solution obtained

by our proposed heuristic algorithm in Algorithm 1 is also

a sub-optimal solution of the subcarrier assignment and UE

association, we take the sub-optimal solution in Algorithm 1

as a potential individual in the initial population. Thus, the

initial population in our algorithm contains R−1randomly

generated individuals and one existing sub-optimal solution.

By doing so, this initialization can converge much faster than

that without using the sub-optimal solution in Algorithm 1,

as validated by the simulation in Fig. 4b.

The initialized Rindividuals only describes the subcarrier

assignment and UE association using R={Γr}R

r=1. We then

perform the power allocation for these Rindividuals using

Algorithm 2 based on the Lagrangian dual method in the

second operation of Fig. 3.

The third operation is the ﬁtness value calculation and the

natural selection. We calculate the ﬁtness values (minimum

UE availability) of all the individuals {Γr}R

r=1 in population

Ras

f(r) = min

nAn,∀n∈ N (40)

where Anis calculated using (4). Each two individuals are

selected using roulette wheel selection method [41], where

9

3. Fitness calculation with (4) and natural selection to

produce offspring

6. Replace low fitness individuals in R with children in offspring

2

3

R

……

'

1

'2

'

3

'R

1

1. Initialize population R with R-1 random individuals and one

sub-optimal individual with Algorithm 1

2

3

R

……

1

2. Power allocation for these R individuals using Algorithm 2

……

P1P2P3P4

……

4. Crossover and mutation individuals in offspring

'

1

'2

'

3

'R

……

'

1

'2

'

3

'R

……

'

1

'2

'

3

'R

……

2

3

R

……

1

5. Power allocation with Algorithm 2 and fitness calculation

with (4)

'

1

'2

'

3

'R

……

……

P’1P’2P’3P’4

Fig. 3: Flowchart describing one iteration of the GA in solving

the optimization problem

the selection probability of each individual is given as

qr=f(r)

Pr∈R f(r).(41)

This selection is repeated until Rindividual are selected.

These selected individuals are used to generate new popula-

tions with crossover and mutation operators.

The fourth operation is the crossover and the mutation. The

conventional two-point crossover is performed to produce new

solutions for two parent individuals in R={Γr}R

r=1. We ﬁrst

randomly generate two crossover points, then each element

between the two points are switched between two parent

individuals to produce two child individuals. In the mutation

operation, some elements in these two child individuals are

randomly altered to diversify the population and pave the

way towards optima. More speciﬁcally, each element of the

matrix in R={Γr}R

r=1 can be mutated or not decided by

the predetermined mutation probability pm. If a element γr

s,m

performs the mutation, a random integer value xbetween 1

and Nwill be chosen to replace the original value (γr

s,m =x).

The sixth operation is the replacement based on an elitist

model, which is used to update a certain number of individuals

in the old population with the new generated individuals. Since

the UE association and subcarrier assignment described by

individuals have been altered during third and fourth operation,

we need to calculate the ﬁtness value of the new generated

individuals using (40) in the ﬁfth operation, then the parent

individuals with the low ﬁtness value will be replaced by

the new generated individuals with higher ﬁtness value in

the next generation in the sixth operation. This population

evolution operations will repeat until convergence, where

the convergence is deﬁned when the maximum ﬁtness value

remains constant for a ﬁxed number of successive iterations

[42].

The JTOA of the UE association and subcarrier assign-

ment, and the power allocation based on GA is described in

Algorithm 3, where Gis the given number of generations,

Ris the population size, pcis the crossover probability,

and pmis the mutation probability. Due to the fact the

Lagrangian dual method is applied to evaluate each individual

in each population, the time complexity of solving this JTOA

is O(GR(O(L) + R)), which showcases the higher imple-

mentation complexity is required to obtain a better solution

compared with that of TSOA.

Algorithm 3: JTOA

set g= 1

Generate initiation population with R−1randomly

generated individuals and 1individual by Algorithm 1

Calculate ﬁtness value for each individual in Rusing

Algorithm 2

repeat

for i= 1 to R/2 do

Select two parents p1and p2from Rusing

roulette wheel selection method

r2∗i−1=p1and r2∗i=p2

Cross r2∗i−1and r2∗iusing two-point crossover

strategy with probability pc, and produce two

children r0

2∗i−1and r0

2∗i

Mutate r0

2∗i−1and r0

2∗iusing mutation strategy

with probability pm

R0=R0∪r0

2∗i−1, r0

2∗i

Calculate ﬁtness value for each individual in R0

using Algorithm 2

end

Replace the individuals with low ﬁtness values in

population Rwith the children in offspring R0

until convergence;

Return the ﬁttest individual in R

V. NUMERICAL RESULTS

In this section, we provide numerical results to illustrate the

performance of our proposed algorithm. We consider CoMP

and CA-enabled HetNets consisting of 2 tiers (marco and pico)

with 2 bands (800MHz and 2.5GHz), where each band has a

bandwidth of 10MHz. 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

otherwise speciﬁed. All the results are obtained by averaging

100 random simulations, and the obtained availability is the

minimum availability among all UEs.

Fig. 4a plots the convergence behavior of our proposed

JTOA with different number of UEs with M= 20, 9 Pico

BSs and 1 Marco BS, where the initial population is a solution

generated by proposed heuristic algorithm in Algorithm 1.

10

0 200 400 600 800 1000 1200 1400 1600 1800 2000

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Number of Generations

Availability

N=4

N=8

N=12

N=16

N=20

0 200 400

0.9

1

(a)

0 300 600 900 1200 1500 1800 2100 2400 2700 3000

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Number of Generations

Availability

N=15 without heuristic

N=15 with heuristic

N=20 without heuristic

N=20 with heuristic

0 300 600

0.8

0.9

1

(b)

Fig. 4: (a) Convergence behavior with different number of UEs, (b) Convergence comparison with and without heuristic

algorithm.

TABLE I: SIMULATION PARAMETERS

Parameter Value

The number of macro BS 1

The number of pico BS 1∼9

The number of UEs 2∼20

Maximum transmit power of macro BS 46dBm (40W)

Maximum transmit power of pico BS 30dBm (1W)

800MHz band’s wavelength µ10.375m

2.5GHz band’s wavelength µ20.125m

800MHz band’s path loss exponent α13

2.5GHz band’s path loss exponent α24

The number of subcarriers in each band 10

Noise PSD -174dBm

SINR threshold τ1

Population size 20

Crossover probability 0.95

Mutation probability 0.005

Maximum generation 3000

TABLE II: Optimized Availability Value

Tech.

N4 8 12 16 20

CA 10 nines 7 nines 5 nines 3 nines 3 nines

CA & CoMP 15 nines 15 nines 10 nines 6 nines 4 nines

Fig. 4b plots the convergence behavior of JTOA, where the

initial population is a solution generated by proposed heuristic

algorithm in Algorithm 1 or random generated population. In

Fig. 4a, we see that our proposed algorithm converges after

approximately 1000 number of generations for various number

of UEs. However, in Fig. 4b, we notice that our proposed

algorithm converges approximately after 1500 generations if

the initial population is not generated by the sub-optimal

solution in Algorithm 1. This reveals that applying Algorithm

1for initial population generation can speed up convergence.

In both ﬁgures, we observe that the converge speed can be

substantially increased with decreasing number of UEs in

HetNets.

In Table II, we also present the optimized availability based

on JTOA for various number of UEs with and without CoMP

in HetNets. We see that with the interference coordination

at each path, the optimized availability is always higher than

that without CoMP, which can be contributed to the single

path gain obtained via CoMP. More importantly, with higher

number of UEs, the beneﬁts of CoMP in achieving high

availability in HetNets become less obvious, which is due to

the reduced number of paths for each UE.

Fig. 5 compares the optimized UE availability based on

our proposed JTOA with that based on TSOA, and the non-

optimized UE availability, and the optima with M= 20,

9 Pico BSs and 1 Marco BS. Here, the optima is obtained

by searching all feasible subcarrier allocations with brute

force approach. Note that Fig. 5a plots the actual availability,

and Fig. 5b plots the corresponding number of nines. We

ﬁrst observe that the availability decreases with increasing

the number of UEs. This can be explained by the fact that

the transmit 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

optimized UE availability based on JTOA outperforms that

based on TSOA, and the non-optimized UE availability, and

closely approaches the performance of the optima obtained

by brute force approach, which showcases the effective of our

proposed JTOA.

Fig. 6 plots the availability versus the number of subcarriers

per BS Mwith 9 Pico BSs and 1 Marco BS, where Fig. 6a

plots the actual availability and Fig. 6b plots the corresponding

number of nines. We can see that the availability increases

with increasing the number of available subcarriers. This can

be explained by the fact that interference decreases with the

increasing the number of subcarriers, thus the single path

availability is improved. This can also be contributed to the

fact that increasing the number subcarriers also increases the

potential gain from the spectral diversity. We ﬁnd that more

subcarriers are needed to achieve the same availability with

more UEs. In order to achieve a minimum availability of 6

nines, we need at least 15 subcarriers per BS for 15 random

11

2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

N

Availability

Non−Optimized

TSOA

JTOA

Optimal

(a)

2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

0

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

N

Number Of Nine(s)

Non−Optimized

TSOA

JTOA

Optimal

(b)

Fig. 5: Performance comparison with different number of UEs, (a) actual availability, (b) number of nines.

2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

M

Availability

N=5

N=10

N=15

N=20

(a)

2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

0

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

M

Number Of Nine(s)

N=5

N=10

N=15

N=20

(b)

Fig. 6: Availability with different number of subcarriers, (a) actual availability, (b) number of nines

123456789

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

Number of Pico(s)

Number Of Nine(s)

N=5

N=10

N=15

N=20

Fig. 7: Availability with different number of Pico BSs

deployed UEs.

Fig. 7 plots the availability versus the number of Pico BSs

with M= 20. We can see that the availability increases with

increasing the number of Pico BSs. This is because increasing

the number of Pico BSs increases the number of paths can

be connected for each UE, and decreases the co-channel

interference in the same subcarrier. However, we observe that

availability can not be further increased when the number

of Pico BSs is larger than 8. This indicates that increasing

the number of Pico BSs can not constantly increase the UE

availability.

Fig. 8 plots the availability versus the BS allocated power

ratio ρwith M= 20, 9 Pico BSs and 1 Marco BS, where ρis

the maximum BS allocated power divided by the maximum BS

transmit power. It is shown that the availability increases with

increasing ρ. For the number of UEs is small N=5, 10, or 15,

6 nines availability can be achieved with very low allocated

power ratio ρ= 1/16, whereas for large number of UEs N=

20, 6 nines availability can not be achieved even with full

power allowance ρ= 1. This indicates that increasing the BS

power allocation ratio can not always guarantee substantial

improvement in the availability of HetNets.

12

0 1/8 2/8 3/8 4/8 5/8 6/8 7/8 1

0

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

ρ

Number Of Nine(s)

N=5

N=10

N=15

N=20

Fig. 8: Availability with diferent allocated power ratio

VI. CONCLUSIONS

In this paper, we have presented the theoretical model and

optimization algorithms to achieve high availability in CoMP

and CA-enabled HetNets. We have derived a closed-form

expression for the availability of random UEs in a CoMP

and CA-enabled HetNets. We have formulated an optimization

problems to maximize the minimum availability under the BS

transmit power constraint. To solve the optimization problem,

we have proposed the TSOA, where the subcarrier assignment

and UE association solution is obtained via heuristic algorithm,

and power allocation solution is obtained via Lagrangian dual

based method. Moreover, we have proposed JTOA based on

GA to achieve the interaction between the ﬁrst step and

the second step. Numerical results show that our proposed

JTOA is effective in achieving ultra-high availability. The high

availability requirement in 5G applications, such as haptic

communications, can be achieved via multiple connectivity

with CA and CoMP. However, when the number of UEs

is small, increasing the number of Pico BSs and the power

allocation ratio can not constantly increase the UE availability.

ACK NOW LE DG ME NT S

This work is supported by the National Natural Sci-

ence Foundation of China under Grant No. 61402096,

No. 61173153 and No. 61572123; the Fundamental Re-

search Funds for the Central Universities under Grant No.

N150404006; the National Science Foundation for Distin-

guished Young Scholars of China under Grant No. 61225012

and No. 71325002; the Specialized Research Fund of the

Doctoral Program of Higher Education for the Priority De-

velopment Areas under Grant No. 20120042130003.

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Jie Jia received her PhD degree in Computer sci-

ence and technology from Northeastern University in

2009. She currently works as an associate professor

in Northeastern University, China. In 2016, she

worked as a visiting research associate in King’s

College London (KCL). She is a member of various

international societies such as the IEEE and China

Computer Federation (CCF). She has published over

100 technical papers on various aspects of wireless

networks. Her current research mainly focuses on

HetNets, IoT, and cognitive radio networks.

Yansha Deng (S’13-M’16) received the Ph.D. de-

gree in Electrical Engineering from Queen Mary

University of London, UK, 2015. She is currently

the postdoctoral research fellow in the Department

of Informatics, at King’s College London, UK. Her

research interests include massive MIMO, HetNets,

molecular communication, cognitive radio, coopera-

tive networks, and physical layer security. She has

received the Best Paper Award in ICC 2016. She

is currently an Editor of of IEEE Communications

Letters. She has also served as TPC member for

many IEEE conferences, such as IEEE GLOBECOM and ICC.

Jian Chen received his PhD degree in Computer

science and technology from Northeastern Univer-

sity in 2010. He currently works as an associate

professor in Northeastern University, and as a Senior

Software Engineer in Neusoft Corporation. In 2016,

he worked as a visiting research associate in K-

ing’s College London (KCL). His research interests

include D2D communication, location technology,

network management, signal and image processing.

Abdol-Hamid Aghvami (M’89–SM’91–F’05) is a

Professor of telecommunications engineering at K-

ing’s College London. He joined the academic staff

at King’s College London in 1984. In 1989 he was

promoted to Reader, and in 1993 was promoted

Professor in Telecommunications Engineering. He is

the founder of the Centre for Telecommunications

Research at King’s. He was the Director of the

Centre from 1994 to 2014.

He carries out consulting work on Digital Radio

Communications Systems for British and Interna-

tional companies; he has published over 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 Visiting Professor

at NTT Radio Communication Systems Laboratories in 1990, Senior Research

Fellow at BT Laboratories in 1998-1999, and was an Executive Advisor to

Wireless Facilities Inc., USA, in 1996-2002. He is the Chairman of Advanced

Wireless Technology Group Ltd. He is also the Managing Director of Wireless

Multimedia Communications Ltd, his own consultancy company.

He leads an active research team working on numerous mobile and personal

communications projects for Fourth and ﬁfth generation networks; these

projects are supported both by government and industry. He was a member

of the Board of Governors of the IEEE Communications Society in 2001-

2003, was a Distinguished Lecturer of the IEEE Communications Society

in 2004-2007, and has been member, Chairman, and Vice-Chairman of

the technical programme and organising committees of a large number of

international conferences. He is also founder of the International Symposium

on Personal Indoor and Mobile Radio Communications (PIMRC), a major

yearly conference attracting some 1,000 attendees.

He was awarded the IEEE Technical Committee on Personal Communi-

cations (TCPC) Recognition Award in 2005 for his outstanding technical

contributions to the communications ﬁeld, and for his service to the scientiﬁc

and engineering communities. Professor Aghvami is a Fellow of the Royal

Academy of Engineering, Fellow of the IET, Fellow of the IEEE, and in

2009 was awarded a Fellowship of the Wireless World Research Forum

in recognition of his personal contributions to the wireless world, and for

his research achievements as Director at the Centre for Telecommunications

Research at King’s.

14

Arumugam Nallanathan (S’97-M’00-SM’05-F’17)

is Professor of Wireless Communications in the

Department of Informatics at Kings College London

(University of London). He served as the Head

of Graduate Studies in the School of Natural and

Mathematical Sciences at Kings College London,

2011/12. He was an Assistant Professor in the De-

partment of Electrical and Computer Engineering,

National University of Singapore from August 2000

to December 2007. His research interests include

5G Wireless Networks, Internet of Things (IoT) and

Molecular Communications. He published more than 300 technical papers

in scientiﬁc journals and international conferences. He is a co-recipient of

the Best Paper Award presented at the IEEE International Conference on

Communications 2016 (ICC2016) and IEEE International Conference on

Ultra-Wideband 2007 (ICUWB 2007). He is an IEEE Distinguished Lecturer.

He has been selected as a Web of Science Highly Cited Researcher in 2016.

He is an Editor for IEEE Transactions on Communications and IEEE Trans-

actions on Vehicular Technology. He was an Editor for IEEE Transactions

on Wireless Communications (2006-2011), IEEE Wireless Communications

Letters and IEEE Signal Processing Letters. He served as the Chair for the

Signal Processing and Communication Electronics Technical Committee of

IEEE Communications Society and Technical Program Chair and member of

Technical Program Committees in numerous IEEE conferences. He received

the IEEE Communications Society SPCE outstanding service award 2012 and

IEEE Communications Society RCC outstanding service award 2014.