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Analysis of the cell association for decoupled wireless access in a two tier network

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A practical blockage model where a human body is a blockage to millimeter wave (mmW) is considered and an in-depth simulation study is done to explore the effectiveness of decoupled wireless access in a crowded environment.
Abstract
In this paper, we analyze the association of a user terminal in a two-tier network (ie, macrocells and millimeter wave small cells) We assumed a decoupled wireless access where a user terminal has the liberty to choose different base stations (BSs) in uplink and downlink based on the received power and the channel quality A practical blockage model where a human body is a blockage to millimeter wave (mmW) is considered An in-depth simulation study is done to explore the effectiveness of decoupled wireless access in a crowded environment In addition to that, a detailed analysis on the intuitiveness and the mathematical tractability of the blockage model used is also provided In the end, few research questions on the efficacy of decoupled wireless access are raised in this paper

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Analysis of the Cell Association for Decoupled
Wireless Access in a Two Tier Network
Zeeshan Sattar, Joao V. C. Evangelista, Georges Kaddoum, and Na
¨
ım Batani
Department of Electrical Engineering
Ecole de technologie superieure, Montreal, Canada
Email: {zeeshan.sattar.1, joao-victor.de-carvalho-evangelista.1}@ens.etsmtl.ca
{georges.kaddoum, naim.batani}@etsmtl.ca
Abstract—In
this paper, we analyze the association of a user
terminal in a two-tier network (i.e., macrocells and millimeter
wave small cells). We assumed a decoupled wireless access where
a user terminal has the liberty to choose different base stations
(BSs) in uplink and downlink based on the received power and
the channel quality. A practical blockage model where a human
body is a blockage to millimeter wave (mmW) is considered. An
in-depth simulation study is done to explore the effectiveness
of decoupled wireless access in a crowded environment. In
addition to that, a detailed analysis on the intuitiveness and
the mathematical tractability of the blockage model used is also
provided. In the end, few research questions on the efficacy of
decoupled wireless access are raised in this paper.
Index Terms—Millimeter wave, fifth-generation networks, het-
erogeneous network, cell association, urban environment, human-
body blockage.
I. INTRODUCTION AND MOTIVATION
The network densification and the use of extremely high
frequencies
(EHF) which commonly known as millimeter
wave (mmW) band are the two most promising candidates for
the future wireless access to fulfill the ever increasing demand
of capacity. It is the small wavelength of mmW which made it
practical to increase the density of BSs significantly without
any increase in the absurdly large footprint of conventional
BSs [1]. Though, intuitively the network densification in a
heterogeneous network sounds a straight forward way to
increase the capacity of an overall system but it also forces us
to revisit some of the conventional techniques in cell planning
and deployment of a communication system [2], [3].
Recently an idea to decouple the downlink (DL) and uplink
(UL) BSs has been proposed [4], [5]. This idea not only flips
the convention of coupled BSs (since the inception of mobile
technology) but indirectly it also questions the way we do
channel estimation as it breaks the channel reciprocity by its
very design. In [4], Boccardi et al. argues on the efficacy
of decoupled wireless access in hyper-dense heterogeneous
networks. Though they also pointed out that without chan-
nel reciprocity in decoupled wireless access, the problem of
channel estimation would become a bit more challenging,
especially in case of mmW.
It is the susceptibility to blockage of mmW, which makes
it significantly different from all other standard wireless tech-
nologies. Since, electromagnetic waves can not travel around
any obstacle which exceeds their wavelength, therefore various
objects which had never been considered as a blockage for
microwave cause significant propagation losses for mmW [6].
Therefore to analyze the heterogeneous network with mmW
BSs, it is necessary to assume a blockage model which emu-
lates the practical scenario mmW faces. In the past couple of
years, there has been some progress in blockage modeling for
mmW wireless access [7], [8], [9].In this paper, we are using
a very recently proposed blockage model which quantifies the
effect of th human body on mmW [10] to analyze the cell
association in a decoupled wireless access.
The proposal of decoupled wireless access is getting con-
siderable attention since its inception [11] and authors in
[4], [5] made quite reasonable arguments in its favor. In this
paper, we explore the efficacy of decoupled wireless access
in an environment where the human body is considered as
a blockage to mmW wireless link. Since, highly populated
areas would be the one which will attract the deployment of
mmW network to fulfill the ever increasing demand of wireless
traffic, therefore, it is very important to study the effects of
the human body on the decoupled wireless access.
The rest of the paper is organized as follows. In Section
II, we describe the system model in detail, which includes
the propagation assumptions and a precise description of the
blockage model used. In Section III, a commentary on the
mathematical feasibility of the considered blockage model is
provided. In Section IV, discussion on the obtained simulation
results is provided and Section V concludes the paper.
II. S
YSTEM MODEL
The system model consists of a two-tier heterogeneous cel-
lular
network, where sub-6GHz (i.e., conventional microwave
or mcell) BSs and mmW (i.e., scell) BSs are modeled using
independent homogeneous Poisson point process (PPP) as
shown in Fig.1 . All the BSs are uniformly distributed in an
area of concern (a circular area with radius µ ). We use Φ
k
to denote the set of points obtained through PPP with density
λ
k
, that can be explicitly written as
Φ
k
= {x
k,i
R
2
: i N
+
},
k K,
where set K
= {s
cell, mcell}. In addition to that all the user
equipments (UEs) are assumed to form an independent PPP
with density λ
u
and they are denoted by a set Φ
u
given as
Paper presented at IEEE 28th Annual International Symposium on Personal, Indoor, and Mobile Radio Communications (PIMRC)
Montreal, Canada, Oct. 8-13, 2017
© 2017 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current
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mmW BS Sub-6GHz BS Human blockers
! "
#$%&&
! "
'$%&&
! "
(
Fig. 1: System Model
Φ
u
= {u
j
R
2
: j N
+
}.
Since
the distribution of a point process is completely
indifferent to the addition of a node at the origin, thanks to
Slivnyak’s theorem [12], the analysis is done for a typical UE
located at origin u
j
= (0, 0).
The summary of parameters and notations used in the rest
of this paper is presented in Table I
TABLE I: System parameters and their definitions
Notation Description
P
uk
UE transmit power to BS in k
th
tier, where k
{scell, mcell}
P
k
Transmit power of BS in k
th
tier, where k
{scell, mcell}
T
k
, T
k
DL and UL association bias for k {scell, mcell}
ψ
k
The combination of antenna gain and near-field pathloss
for k {scell, mcell}
L
min,k
The minimum pathloss ||x||
α
k
of the typical UE from
the k
th
tier
α
k
The pathloss exponent, for macrocell i.e., when k =
mcell its value remains constant. On the other hand for
k = scell, pathloss exponent becomes a function of the
distance between the transmitter and the receiver, and its
value switches between line of sight (LOS) and non line
of sight (NLOS) exponent values with the probability
P
LOS
and P
NLOS
, respectively
A. Propagation assumptions and cell association criteria
In our system model it is assumed that all the UEs and sub-
6GHz BSs have omni directional antennas and antenna gains
from a massive array of antenna elements are only accounted
for the mmW BSs. It is a realistic assumption in a sense that in
such hybrid BSs’ deployment, the sub-6GHz BSs will provide
an umbrella coverage to all the UEs to guarantee a consistent
service, whereas the mmW BSs will mainly focus on high
capacity link with individual UEs. Therefore the antenna gain
is only considered with mmW BS.
It is assumed that in both UL and DL, a typical UE
associates with a BS based on the received power. The
typical UE associates with a BS in UL at x Φ
l
, where
l
{scell, mcell} if and only if
P
ul
T
l
ψ
l
L
l
(x)
1
P
uk
T
k
ψ
k
L
1
m
in,k
,
k
{scell, mcell}. (1)
h
R
h
T
r
x
h
m
A
B
K
O
C
Blocker
Fig. 2: Blockage Scenario
Similarly, a typical UE associates with a BS in DL at x
Φ
l
if and only if
P
l
T
l
ψ
l
L
l
(x)
1
P
k
T
k
ψ
k
L
1
min,k
,
k {scell, mcell}. (2)
B. Blockage Model
In this paper, we use a very intuitive blockage model [10],
where a human body is considered as blockage to mmW.
The potential blockers are generated using a independent
homogeneous PPP Φ
I
over the area of concern with intensity
λ
I
as shown in Fig. 1. Each blocker is modeled as a cylinder
with a certain height H and a width W . Here, both the
height and the width are generated randomly using the well
researched statistical data [13].
Moreover, it is obvious from Fig. 2 that not all blockers
can affect the LOS link between transmitter and receiver.
Therefore, we can model the PPP of blockers whose height
can cause the LOS link to break by thinning the Φ
I
with
probability P
r(H > h
m
(x)). The thinned PPP is denoted as
Φ
IB
with density λ
IB
,
λ
IB
(x) = λ
I
P r(H > h
m
(x)), x (0, r), (3)
where h
m
(x) is a function describing the distance between the
LOS link and the ground at x
h
m
(x) =
h
T
h
R
r
x + h
T
.
And as shown in Fig. 2, h
T
and h
R
are the Tx and Rx
heights, respectively. The aforementioned process Φ
IB
is non-
homogeneous but still remains Poisson with thinned density
λ
IB
(x), which increases non-linearly as x grows [12]. The
probability P r(H > h
m
(x)) is a complementary cumulative
distribution function (CCDF) of H. Since, H follows Normal
distribution [13], The probability P r(H > h
m
(x)
) takes the
following form
P r (H > h
m
(x)
) = 1
1
2
1 + erf
h
m
(x) µ
H
σ
H
2

, (4)

Tx Rx
r
d
max
d
max
d
min
Fig. 3: Top view of the blockage scenario
where erf(.) is the error function, µ
H
,σ
H
are mean and
variance of H, respectively.
For the mathematical formulation of probability of LOS
(P
LOS
) we have to determine the probability of few events
described in Table II. Having defined all the events and
TABLE II: Probabilistic events and their definitions
Events Description
A
i
There are i blockers in the area of interest
B
0
Diameter of the blocker is not large enough to cross the
LOS link
B
1
Complementary to B
0
C
0
Blocker’s height is not large enough to block the LOS
link
C1
Complementary to C
0
probabilities the expression for P
LOS
can be formulated as
follows:
P
LOS
= P r{A
0
} +
X
i=1
P r{A
i
}
· [P r{B
0
} + P r{B
1
}P r{C
0
}]
i
, (5)
where the first part of the equation P r{A
0
} is the probability
that there are no blockers in the area of interest and the second
part of the equation sums the probability in the event that there
are i blockers in the area of interest, but their width and height
are not enough to block the LOS link. A rectangular area
shown in Fig. 3 is considered where the widths of all blockers
are uniformly distributed between d
min
and d
max
, therefore,
the width of this area is bounded by d
max
. As mentioned
in the start of this section, the number of blockers follow a
Poisson distribution, hence, the number of blockers in the area
of concern follows a Poisson distribution with the intensity
λ
I
rd
max
. Having defined all the necessary assumptions, the
mathematical expressions of aforementioned events can be
easily formulated as in [10].
Even though this blockage model is intuitive in nature and
it can accurately emulates a crowded environment [10], so far,
there is no closed-form expression for this model. To the best
of our knowledge, it is mathematically intractable to provide
a closed-form expression of P
LOS
, as its expression contains
double integral of erf function. Since, it is a well known fact
that, mathematically, it is extremely difficult to approximate
an integral of erf function over a wide range of values (which
is the case here). Hence, further discussion on the efficacy,
intuitiveness, and mathematical intractability of this blockage
model in calculating the association probabilities is provided
in the following section.
III. A
NALYTICAL ANALYSIS
In this section expressions for the association probability
for a typical user in the human blockage model scenario are
derived. On the association scenario under analysis there are
two random variables to be considered; they are the associated
tier for uplink A
UL
and the associated tier for downlink A
DL
.
Considering the model proposed in Section II with two tiers
there are four possible outcomes:
A
UL
= mcell, A
DL
= mcell
A
UL
= mcell, A
DL
= scell
A
UL
= scell, A
DL
= mcell
A
UL
= scell, A
DL
= scell
As the events A
UL
and A
DL
are independent, the derivation
of the probabilities P r(A
UL
= mcell), P r(A
UL
= scell),
P r(A
DL
= mcell) and P r(A
DL
= scell) are enough to
calculate the probabilities of the four possible outcomes.
Furthermore, the user only associates to one base station for
uplink and one for downlink, therefore
P r(A
UL
= mcell) = 1 P r(A
UL
= scell), (6)
and
P r(A
DL
= mcell) = 1 P r(A
DL
= scell). (7)
As seen in equations (1) and (2) the base station to which
the user associates depends on the minimum path loss of
the typical UE from the k
th
tier, so, in order to derive the
probabilities of association, the point process obtained from
the path loss between the typical user and each base station
must be characterized. Following a similar approach to [5],
the path loss point process is defined as
P
k
: {L
k
(x) = kxk
α
k
(kxk)
}
xΦ
k
, for k {scell, mcell}. (8)
From the displacement theorem [14], P
k
is a Poisson point
process with intensity measure Λ
k
(·) and CCDF
¯
F
L
k
(t) = P r(L
k
(x) t) = exp(Λ
k
([0, t]). (9)
Lemma 1. The intensity measure of the path loss process of
the tagged BS for tiers 1 and 2 are given by
Λ
m
([0, t]) = πλ
m
t
2
α
m
, (10)
Λ
s
([0, t]) = 2πλ
s
"
Z
t
1
α
LOS
0
rP
LOS
(r)dr
+
Z
t
1
α
NLOS
0
r(1 P
LOS
(r))dr
#
. (11)

Proof. The proof for the macro cell case (10) is available on
[5]. For the scell (mmWave) we have that the intensity of the
path loss process P
s
: {L
s
(x) = kxk
α
s
(kxk)
}
xΦ
s
is given by
Λ
s
([0, t]) = λ
s
Z
R
2
P r(L
s
(x) < t)dx.
Switching to polar coordinates leads to
Λ
s
([0, t]) = 2πλ
s
Z
0
P r(r
α
2
(r)
< t)rdr.
As described in Section II α
s
(r) is equal to α
LOS
with
probability P
LOS
and α
NLOS
with probability 1 P
LOS
. Thus,
we have
Λ
s
([0, t]) = 2πλ
s
"
Z
0
rP
LOS
(r)1(r < t
1
α
LOS
)dr
+
Z
0
r(1 P
LOS
(r))1(r < t
1
α
NLOS
)dr
#
,(12)
which leads to (11).
From (10) and (9) it is possible to obtain the probability
density function (PDF) as
f
L
m
(t) =
d
¯
F
m
(t)
dt
=
2πλ
m
t
2
α
m
1
α
m
exp(πλ
m
t
2
α
m
). (13)
For the millimeter wave scell tier the CCDF is given by
¯
F
L
s
(t) = exp
"
2πλ
s
Z
t
1
α
LOS
0
rP
LOS
(r)dr
+
Z
t
1
α
NLOS
0
r(1 P
LOS
(r))dr
!#
. (14)
By manipulating (1) and (2) it is possible to obtain an
expression for the probability of associating to the macro cell
in the uplink and in the downlink as
P r(A
UL
= mcell) = P r(L
min,scell
> a
UL
L
min,mcell
)
=
1
a
UL
Z
0
¯
F
L
s
(l)f
L
m
l
a
UL
dl,
(15)
and
P r(A
DL
= mcell) = P r(L
min,scell
> a
DL
L
min,mcell
)
=
1
a
DL
Z
0
¯
F
L
s
(l)f
L
m
l
a
DL
dl,
(16)
where
a
UL
=
P
u,scell
T
scell
ψ
scell
P
u,mcell
T
mcell
ψ
mcell
,
and
a
DL
=
P
scell
T
scell
ψ
scell
P
mcell
T
mcell
ψ
mcell
.
As the calculation of P
LOS
(r) is not obtained in closed-
form and involves the numerical evaluation of three integrals,
it is not feasible to obtain a closed-form expression for
¯
F
L
s
(t) as well. Considering the intractability of calculating
¯
F
L
s
(l) due to the blockage model, a simulation approach is
taken to characterize the probabilities of association under this
blockage model.
IV. S
IMULATION RESULTS
A. Simulation setup
A system-level simulation model is developed to mimic the
real scenario of association between a UE and its tagged BS(s)
in a decoupled wireless access environment. The simulation
model not only provides the association probabilities of a
particular UE with its tagged BS(s) but it also gives an insight
on the portability of having a decoupled wireless access.
We generated the blockers, the mmW BSs, and the sub-
6GHz BSs in a circular area of radius µ as described in
Section II. In case of mmW wireless access, for the sake of
consistency with previous published work [10] the height of
the transmitter and the receiver are assumed to be 4m and
1.3m, respectively. And as described in section II-B, each
generated blocker has a random height and width, following
[10], the height and width of the blockers are generated using
normal N(µ
H
, σ
H
) and uniform U(d
min
, d
max
) distributions,
respectively. Here, µ
H
, σ
H
, d
min
, and d
max
are assumed to
be 1.7m, 0.1m, 0.2m, and 0.8m, respectively. The rest of the
parameters used in the simulation are same as listed in [5].
5 10 15 20 25 30 35 40 45 50
Height of Tx of small cell BS [m]
20
30
40
50
60
70
80
Average Pathloss [dB]
r=10m
r=30m
r=50m
r=70m
Fig. 4: Average pathloss vs optimal Tx height for different r
B. Discussion
As already mentioned in III that the blockage model under
consideration has no closed-form expression and this fact made
it mathematically intractable for further analytical analysis.
Nevertheless, its practical nature is still very useful. For

5 10 15 20 25 30 35 40
λ
s
/λ
m
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Probability of Association
Sim-DL (Mcell)
Sim-DL (Scell)
Sim-UL (Mcell)
Sim-UL (Scell)
Fig. 5: Association probability for antenna gain = 30dBi, and
blockers intensity λ
I
= 0.3 blockers/m
2
5 10 15 20 25 30 35 40
λ
s
/λ
m
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Joint probability of association
DL (Mcell), UL (Scell)
DL (Scell), UL (Mcell)
DL (Scell), UL (Scell)
DL (Mcell) UL (Mcell)
Fig. 6: Joint association probabilities for antenna gain = 30dBi,
and blockers intensity λ
I
= 0.3 blockers/m
2
example, it is obvious that the average distance between the
transmitter and the receiver is a function of the intensity of
blockers λ
I
. It implies that the optimal height of the Tx of
scell BS to minimize the average pathloss is also a function
of λ
I
, as the optimal height of the Tx depends on the average
distance between Tx and Rx. Using this blockage model we
can easily predict the optimal height of the Tx of scell BSs for
different urban environments as shown in Fig. 4. The dashed
curve in Fig. 4, which is intersecting all the other curves
shows the optimal height of the Tx for different values of
distance r. Here, we want to emphasize on the fact that to
choose the optimal height of the Tx in scell is extremely
important, because it makes a huge difference in average
pathloss. Therefore, any arbitrary height of the Tx can make
or break the connection completely. Hence, in our opinion Txs
for next generation of wireless access should be designed to
adjust their heights in real-time according to the density of
blockers λ
I
.
5 10 15 20 25 30 35 40
λ
s
/λ
m
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Probability of Association
Sim-DL (Mcell)
Sim-DL (Scell)
Sim-UL (Mcell)
Sim-UL (Scell)
Fig. 7: Association probability for antenna gain = 18dBi, and
blockers intensity λ
I
= 0.3 blockers/m
2
5 10 15 20 25 30 35 40
λ
s
/λ
m
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
Joint probability of association
DL (Mcell), UL (Scell)
DL (Scell), UL (Mcell)
DL (Scell), UL (Scell)
DL (Mcell), UL (Mcell)
Fig. 8: Joint association probabilities for antenna gain = 18dBi,
and blockers intensity λ
I
= 0.3 blockers/m
2
The association probabilities of a UE with two tiers of BSs
are shown in Fig. 5 and Fig. 7. Whereas Fig. 6 and Fig. 8 show
the joint probabilities of four possible association scenarios
of a particular UE as mentioned in Section III. It is obvious
from the simulation results in Fig. 5, Fig. 6, Fig. 7, and Fig.
8 that antenna gain plays a significant role on the efficacy
of decoupled wireless access. A higher antenna gain (which
would be the case in future mmW BSs) significantly reduces
the decoupling gain (i.e., when a UE chooses to select two
different types of BSs in DL and UL).
Moreover, an interesting observation which we can be made
from Fig. 6 and Fig. 8 is that the joint association probability
of an event when a particular UE connects to scell in DL
and mcell in UL is zero. This contradicts with the argument
made in [4] in support of decoupled wireless access; that
is for future generation of wireless network, more UEs will
connect with scell in DL for higher data rate and mcell will
provide an umbrella coverage as well as UL connection to

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Q1. What are the contributions in "Analysis of the cell association for decoupled wireless access in a two tier network" ?

In this paper, the authors analyze the association of a user terminal in a two-tier network ( i. e., macrocells and millimeter wave small cells ). In addition to that, a detailed analysis on the intuitiveness and the mathematical tractability of the blockage model used is also provided. In the end, few research questions on the efficacy of decoupled wireless access are raised in this paper. 

Lastly, if TDD becomes a standard for next generation of wireless network, then the future of decoupled wireless access is certainly very bleak. 

The thinned PPP is denoted as ΦIB with density λIB ,λIB(x) = λIPr(H > hm(x)), x ∈ (0, r), (3) where hm(x) is a function describing the distance between the LOS link and the ground at xhm(x) = − hT − hRr x+ hT . 

It implies that the optimal height of the Tx of scell BS to minimize the average pathloss is also a function of λI , as the optimal height of the Tx depends on the average distance between Tx and Rx. 

The authors use Φk to denote the set of points obtained through PPP with density λk, that can be explicitly written asΦk ∆ = {xk,i ∈ R2 : i ∈ N+}, k ∈ K,where set K ∆= {scell,mcell}. 

It is obvious from the simulation results in Fig. 5, Fig. 6, Fig. 7, and Fig. 8 that antenna gain plays a significant role on the efficacy of decoupled wireless access. 

The intensity measure of the path loss process of the tagged BS for tiers 1 and 2 are given byΛm([0, t]) = πλmt 2 αm , (10)Λs([0, t]) = 2πλs[ ∫ t 1 αLOS0rPLOS(r)dr+∫ t 1 αNLOS0r(1− PLOS(r))dr ] . 

The summary of parameters and notations used in the rest of this paper is presented in Table IIn their system model it is assumed that all the UEs and sub6GHz BSs have omni directional antennas and antenna gains from a massive array of antenna elements are only accounted for the mmW BSs. 

From (10) and (9) it is possible to obtain the probabilitydensity function (PDF) asfLm(t) = − dF̄m(t)dt =2πλmt 2 αm −1αm exp(−πλmt2αm ). (13)For the millimeter wave scell tier the CCDF is given byF̄Ls(t) = exp[ −2πλs (∫ t 1 αLOS0rPLOS(r)dr+∫ t 1 αNLOS0r(1− PLOS(r))dr )] . (14)By manipulating (1) and (2) it is possible to obtain an expression for the probability of associating to the macro cell in the uplink and in the downlink asPr(AUL = mcell) = Pr(Lmin,scell > aULLmin,mcell) = 1aUL∫ ∞0F̄Ls(l)fLm(laUL)dl,(15)andPr(ADL = mcell) = Pr(Lmin,scell > aDLLmin,mcell) = 1aDL∫ ∞0F̄Ls(l)fLm(laDL)dl,(16)whereaUL = Pu,scellT′ scellψscellPu,mcellT ′mcellψmcell ,andaDL = PscellTscellψscell PmcellTmcellψmcell . 

This contradicts with the argument made in [4] in support of decoupled wireless access; that is for future generation of wireless network, more UEs will connect with scell in DL for higher data rate and mcell will provide an umbrella coverage as well as UL connection toThe authors derive following conclusions from this study. 

if TDD becomes a standard for next generation of wireless network, then the future of decoupled wireless access is certainly very bleak.