Promises and Caveats of Uplink
IoT Ultra-Dense Networks
Ming Ding‡ , David López Pérez†
‡

arXiv:1801.06623v1 [cs.NI] 20 Jan 2018

†

Data61, Australia {Ming.Ding@data61.csiro.au}
Nokia Bell Labs, Ireland {david.lopez-perez@nokia.com}

Abstract—In this paper, by means of simulations, we evaluate
the uplink (UL) performance of an Internet of Things (IoT)
capable ultra-dense network (UDN) in terms of the coverage
probability and the density of reliably working user equipments
(UEs). From our study, we show the benefits and challenges
that UL IoT UDNs will bring about in the future. In more
detail, for a low-reliability criterion, such as achieving a UL
signal-to-interference-plus-noise ratio (SINR) above 0 dB, the
density of reliably working UEs grows quickly with the network
densification, showing the potential of UL IoT UDNs. In contrast,
for a high-reliability criterion, such as achieving a UL SINR
above 10 dB, the density of reliably working UEs remains to
be low in UDNs due to excessive inter-cell interference, which
should be considered when operating UL IoT UDNs. Moreover,
considering the existence of a non-zero antenna height difference
between base stations (BSs) and UEs, the density of reliably
working UEs could even decrease as we deploy more BSs. This
calls for the usage of sophisticated interference management
schemes and/or beam steering/shaping technologies in UL IoT
UDNs.

I. I NTRODUCTION
Recent years have seen rapid advancement in the development and deployment of Internet of Things (IoT) networks,
which can be attributed to the increasing communication and
sensing capabilities combined with the falling prices of IoT
devices [1]. For example, base stations (BSs) can be equipped
with the latest IoT technologies, such as the new generation
of machine type communications [2], to collect data from gas,
water, and power meters via uplink (UL) transmissions. In
practice, such BSs can take the form of both terrestrial and
aerial ones [3].
This poses, however, a challenge to the wireless industry,
which must offer an increasing volume of reliable traffic in a
profitable and energy efficient manner, especially for the UL
communications. In this context, the orthogonal deployment
of ultra-dense (UD) small cell networks (SCNs), or simply
ultra-dense networks (UDNs), have been selected as one of the
workhorse for network enhancement in the fourth-generation
(4G) and fifth-generation (5G) networks developed by the 3rd
Generation Partnership Project (3GPP) [2]. Here, orthogonal
deployment means that UDNs and macrocell networks operate
on different frequency spectrum, which simplifies network
management due to no inter-tier interference.
The performance analysis of IoT UDNs is, however, particularly challenging for the UL because i) UDNs are fundamentally different from the current sparse/dense networks [4]
and ii) the UL power control mechanism operates according

to the random user equipment (UE) positions in the network,
which is quite different from the constant power setting in the
downlink (DL) [5].
In this paper, by means of simulations, we evaluate the
network performance of UL IoT UDNs in terms of the
coverage probability and the density of reliably working UEs.
The main findings of this paper are as follows:
• We find that for a low-reliability criterion, such as achieving a UL signal-to-interference-plus-noise ratio (SINR)
above γ = 0 dB, the density of reliably working UEs
quickly grows with the network densification, showing
the benefits of UL IoT UDNs. In contrast, for a highreliability criterion, such as achieving a UL SINR above
γ = 10 dB, the density of reliably working UEs remains
low in UDNs due to excessive inter-cell interference,
which should be considered when operating UL IoT
UDNs.
• We find that due to the existence of a non-zero antenna
height difference between BSs and UEs, the density of
reliably working UEs could even decrease as we deploy
more BSs in a UL IoT UDN. This calls for the usage
of sophisticated interference management schemes and/or
beam steering/shaping technologies in UL IoT UDNs.
• We find that the correlated shadow fading allows a BS
with a lower environmental fading factor to provide connection to a larger number of UEs. Thus, its theoretical
analysis is an open problem for further study.
• We find that the optimized hexagonal-like BS deployment
can improve network performance for relatively sparse
networks, but not for UDNs. Thus, its theoretical study
is not urgent.
II. D ISCUSSION

ON THE

A SSUMPTIONS

OF

UL I OT UDN S

In this section, we discuss several important assumptions in
UL IoT UDNs.
A. BS Deployments
In general, to study the performance of a UL IoT network,
two types of BS deployments can be found in the literature,
i.e., the hexagonal and the random deployments as shown in
Fig. 1.
In Fig. 1, BSs are represented by markers “x” and cell
coverage areas are outlined by solid lines. Note that the hexagonal BS deployment leads to an upper-bound performance
because BSs are evenly distributed in the network scenario,

(a) The hexagonal BS deployment.

(b) The random BS deployment.

Fig. 1: Illustration of two widely accepted types of BS deployments. Here, BSs are represented by markers “x” and cell
coverage areas for user equipment (UE) distribution are outlined by solid lines.
and thus very strong interference due to close BS proximity is
precluded [6]. In contrast, the random BS deployment reflects
a more realistic network deployment with more challenging
interference conditions [2, 7]. For completeness, in our following performance evaluation, we will consider both BS
deployments.
B. Antenna Heights
In the performance analysis of the conventional sparse or
dense cellular networks, the antenna height difference between
BSs and UEs is usually ignored due to the dominance of
the horizontal distance. However, with a much shorter distance between a BS and its served UEs in an UDN, such
antenna height difference becomes non-negligible [7]. The
performance impact of such antenna height difference between
BSs and UEs on the DL UDNs has been investigated in [8].
More specifically, the existence of a non-zero antenna height
difference between BSs and UEs gives rise to a non-zero
cap on the minimum distance between a BS and its served
UEs, and thus a cap on the received signal power strength.
Thus, and although each inter-cell interference power strength
is subject to the same cap, the aggregate inter-cell interference
power will overwhelm the signal power in an UDN due to the
sheer number of strong interferers. Consequently, the antenna
height difference between BSs and UEs should be considered
in the performance evaluation of UL IoT UDNs.
C. Line-of-Sight Transmissions
A much shorter distance between a BS and its served
UEs in an UDN implies a higher probability of line-of-sight
(LoS) transmissions. The performance impact of such LoS
transmissions on the DL of UDNs has been shown to be
significant in [9, 10]. Generally speaking, LoS transmissions
are more helpful to enhance the received signal strength
than non-line-of-sight (NLoS) transmissions. However, after
a certain level of BS densification, not only the signal power,
but also the inter-cell interference power will significantly
grow due to the emergence of LoS interfering paths. Thus,
the transition of a large number of interfering paths from

NLoS to LoS will overwhelm the signal power in an UDN.
Consequently, the probabilistic LoS transmissions should also
be considered in the performance evaluation of UL IoT UDNs.
D. BS Idle Mode
Considering the surplus of BSs in UDNs, a BS can be put
to sleep when there is no active UE connected to it, which is
referred as the BS idle mode capability (IMC) [11, 12]. As a
result, the active UEs’ SINR can benefit from i) a BS selection
diversity gain, i.e., each UE has a plurality of BSs to select its
server from, and ii) a tight control of inter-cell interference,
as effective UL inter-cell interference only comes from active
UEs served by active neighboring BSs. The surplus of BSs
together with the IMC can be seen as a powerful tool that can
mitigate the interference problems presented in the previous
subsections. However, it should be noted that switching off
BSs has a negative impact on the number of IoT UEs that can
concurrently transmit.
III. S YSTEM M ODEL
For a certain time-frequency resource block (RB), we consider a UL IoT network with BSs deployed on a plane according to the hexagonal deployment or the random deployment,
as shown in Fig. 1. For both BS deployments, the density of
BSs is denoted by λ BSs/km2 . Furthermore, we consider a
homogeneous Poisson point process (HPPP) Φ to characterize
the random deployment.
Active UEs are assumed to be distributed following an
HPPP with a density of ρ UEs/km2 . Here, we only consider
active UEs in the network because non-active UEs do not
trigger data transmission. Note that the total number of UEs,
e.g., phones, gateways, sensors, tags, etc., in a UL IoT network
should be much higher than the number of the active UEs.
However, we believe that in a certain time-frequency RB, the
active UEs with non-zero data traffic demands should still be
not many. For example, a typical density of active UEs is
around 300 UEs/km2 in 5G [2].

NL

A. Channel Model
The two-dimensional (2D) distance between a BS and a
UE is denoted by r. Moreover, the absolute antenna height
difference between a BS and a UE is denoted by L. Thus, the
3D distance between a BS and a UE can be expressed as
p
w = r 2 + L2 .
(1)

Note that the value of L is in the order of several meters [13].
Following [10], we adopt a general path loss model, where
the path loss ζ (w) is a multi-piece function of w written as

ζ1 (w) , when L ≤ w ≤ d1




ζ2 (w) , when d1 < w ≤ d2
ζ (w) = .
,
(2)
..
..


.



ζN (w) , when w > dN −1

where each piece ζn (w) , n ∈ {1, 2, . . . , N } is modeled as
(
L
ζ L (w) = ALn w−αn ,
LoS: PrLn (w)
ζn (w)= nNL
, (3)
NL
−αn
ζn (w) = ANL
, NLoS: 1 − PrLn (w)
n w

where
L
NL
• ζn (w) and ζn (w) , n ∈ {1, 2, . . . , N } are the n-th piece
path loss functions for the LoS and the NLoS cases,
respectively,
L
NL
• An and An are the path losses at a reference 3D distance
w = 1 for the LoS and the NLoS cases, respectively,
L
NL
• αn and αn are the path loss exponents for the LoS and
the NLoS cases, respectively, and
L
• Prn (w) is the n-th piece LoS probability function that a
transmitter and a receiver separated by a 3D distance w
has an LoS path, which is assumed to be a monotonically
decreasing function with respect to w. Existing measurement studies have confirmed this assumption [13].
Moreover, we assume that each BS/UE is equipped with an
isotropic antenna, and that the multi-path fading between a BS
and a UE is independently identical distributed (i.i.d.) Rayleigh
distributed [9, 10, 14].
B. User Association Strategy
We assume a practical user association strategy (UAS), in
which each UE is connected to the BS giving the maximum
average received signal strength [10, 14]. Such UAS can be
formulated by

bo = arg max R̄b (w) ,
(4)
b

where R̄b (w) denotes the average received signal strength
from BS b and the UE of interest, separated by a distance
of w. Assuming a constant BS transmission power, R̄b (w)
can be equivalently evaluated by ζ (w) defined in (2).
As a special case to show our numerical results in the
simulation section, we consider a practical two-piece path
loss function and a two-piece exponential LoS probability
function, defined by the 3GPP [13]. More specifically, in (2)
L
we use N = 2, ζ1L (w) = ζ2L (w) = AL w−α , ζ1NL (w) =

ζ2NL (w) = ANL w−α , PrL1 (w) = 1 − 5 exp (−R1 /w), and
PrL2 (w) = 5 exp (−w/R2 ), where R1 = 156 m, R2 = 30 m,
1
= 67.75 m [13]. For clarity, this path loss case
and d1 = lnR10
is referred to as the 3GPP Case hereafter.
C. BS Activation Model
As discussed in Subsection II-D, a BS will enter an idle
mode if there is no UE connected to it. Thus, the set of active
BSs is determined by the UAS. Since UEs are randomly and
uniformly distributed in the network and given the adopted
UAS strategy, we can assume that the active BSs also follow
an HPPP distribution Φ̃ [11], the density of which is denoted
by λ̃ BSs/km2 , where λ̃ ≤ λ and λ̃ ≤ ρ. Note that λ̃ also
characterizes the density of active UEs because no collision
exists in the centralized cellular IoT UDNs.
For illustration purposes, considering a single-slope path
loss model and a nearest-BS UAS, λ̃ can be calculated as [11]


1
q  ,
λ̃ = λ 1 − 
(5)
ρ
1 + qλ

where an empirical value of 3.5 was suggested for q in [11]1 .
D. UL Power Control Model

The UE power, denoted by P UE , is subject to semi-static
power control (PC) in practice. In this paper, we adopt the
fractional path loss compensation (FPC) scheme standardized
in 4G [13], which can be modeled as
P0

P UE = 10 10 [ζ (w)]

−η

N RB ,

(6)

where P0 is the target received power in dBm on each RB at
the BS, η ∈ (0, 1] is the FPC compensation factor, and N RB
is the number of RBs in the frequency domain.
E. The Coverage Probability
Based on this system model, we can define the coverage
probability that the typical UE’s UL SINR is above a designated threshold γ as


pcov (λ, γ) = Pr SINRU > γ ,
(7)
where the UL SINR is calculated by
SINRU =

PbUE
ζ (wbo ) h
o
,
U + PU
Iagg
N

(8)

where bo denotes the serving BS of the typical UE, PbUE
is
o
the UE transmission power given by (6), wbo is the distance
from the typical UE to its serving BS bo , h is the Rayleigh
channel gain modeled as an exponentially distributed random
variable (RV) with a mean of one as mentioned above, PNU
is the additive white Gaussian noise (AWGN) power at the
U
serving BS bo , and Iagg
is the UL aggregate interference.
1 Note that according to [12], q should also depend on the path loss model
with LoS/NLoS transmissions. Having said that, [12] also showed that (5) is
generally very accurate to characterize λ̃ for the 3GPP Case with LoS/NLoS
transmissions.

F. The Density of Reliably Working UEs
Based on the definitions of the active BS density in Subsection III-C and the coverage probability in Subsection III-E,
we can further define a density of reliably working UEs that
can operate above a target UL SINR threshold γ as
ρ̃ = λ̃pcov (λ, γ) ,

(9)

where the active BS density λ̃ measures the maximum density
of UEs that can simultaneously transmit, and the coverage
probability pcov (λ, γ) scales down λ̃, giving the density of
reliably working UEs. The larger the UL SINR threshold γ, the
higher the reliability of the IoT communications, and thus the
less the UEs that can simultaneously achieve such reliability.
G. More Refined Assumptions
In performance analysis, the multi-path fading is usually
modeled as Rayleigh fading for simplicity. However, in the
3GPP, a more practical model based on generalized Rician
fading is widely adopted for LoS transmissions [15]. In such
model, the K factor in dB scale (the ratio between the power
in the direct path and the power in the other scattered paths)
is modeled as K[dB] = 13 − 0.03w, where w is defined in (1).
More specifically, let hL denote the multi-path fading power
for LoS transmissions. Then, for the 3GPP model of Rician
fading, hL follows a non-central chi-squared distribution with
its PDF given by [16]


= (K + 1) exp −K − (K + 1) hL
f hL
 q

L
×I0 2 K (K + 1) h ,
(10)

where K is the distance-dependent value discussed above and
I0 (·) is the 0-th order modified Bessel function of the first
kind [16].
Moreover, the shadow fading is also usually not considered
or simply modeled as i.i.d. RVs in performance analysis.
However, in the 3GPP, a more practical correlated shadow
fading is often used [13, 15, 17], where the shadow fading in
dB unit is modeled as zero-mean Gaussian RV [13]. More
specifically, the shadow fading coefficient in dB unit between
BS b and UE u is formulated as [13]
√
√
(11)
Sbu = τ SuUE + 1 − τ SbBS ,
where τ is the correlation coefficient of shadow fading, SuUE
and SbBS are i.i.d. zero-mean Gaussian RVs attributable to UE
u and BS b, respectively. The variance of SuUE and SbBS is
2
denoted by σShad
. In [13], it is suggested that τ = 0.5 and
σShad = 10 dB.
Considering the distance-dependent Rician fading for LoS
transmissions and the correlated shadow fading, we can upgrade the 3GPP Case to an advanced 3GPP Case. In the next
section, we will present simulation results of UL IoT UDNs
for both the 3GPP Case and the Advanced 3GPP Case. It
should be noted that for the Advanced 3GPP Case, shadow
fading should be considered in the computation of R̄b (w),
Sbu
i.e., R̄b (w) should be evaluated by ζ (w) × 10 10 in (4).

IV. S IMULATION AND D ISCUSSION
In this section, we present numerical results to validate the
accuracy of our analysis. According to Tables A.1-3~A.1-7
of [13], we adopt the following parameters for the 3GPP Case:
αL = 2.09, αNL = 3.75, AL = 10−10.38 , ANL = 10−14.54 ,
P0 = −76 dBm, η = 0.8, N RB = 55, PN = −91 dBm (with
a noise figure of 13 dB), τ = 0.5 and σShad = 10 dB.
A. Performance Results of the 3GPP Case
In Figs. 2 and 3, we plot the performance results of the
3GPP Case for γ = 0 dB and γ = 10 dB, respectively.
Here, we only consider realistic networks with the random
deployment of BSs. From these two figures, we can draw
the following observations:
• Figs. 2a and 3a show that the active BS density λ̃
monotonically increases with the network densification,
and it is bounded by ρ = 300 UEs/km2 . Such results are
in line with the analytical results in (5) [11, 12]. However,
the density of reliably working UEs ρ̃, i.e., λ̃pcov (λ, γ)
defined in (9), does not necessarily grow as the BS density
λ increases. This is because pcov (λ, γ) is a non-monotone
function with respect to λ, which will be explained in the
following.
• When
BS density λ is around λ
∈
 −1 the

10 , 70 BSs/km2 , the network is noise-limited,
and thus pcov (λ, γ) increases with λ as the network is
lightened up with coverage and the signal power strength
benefits form LoS transmissions.
2
• When the BS density λ is around λ ∈ [70, 400] BSs/km ,
cov
p (λ, γ) decreases with λ. This is due to the transition
of a large number of interfering paths from NLoS to
LoS, which accelerates the growth of the aggregate intercell interference. Such performance behavior has been
reported in [10] for the
[18] for the UL.
 DL and
4
• When λ ∈ 400, 10
BSs/km2 , pcov (λ, γ) continuously
increases thanks to the BS IMC [12], i.e., the signal power
continues increasing with the network densification due
to the BS diversity gain, while the aggregate interference
power becomes constant, as λ̃ is bounded by ρ. However,
as shown in Figs. 2b and 3b, the antenna height difference
L between BSs and UEs has a large impact on pcov (λ, γ)
because a non-zero L places a bound on the signal power
strength, which degrades the coverage performance. In
more detail, when λ = 104 BSs/km2 and γ = 0 dB,
the coverage probability with L = 8.5 m loses 13 %
compared to that with L = 0 m. Such performance degradation further enlarges to 32 % when λ = 104 BSs/km2
and γ = 10 dB, showing a much less chance of UE
working reliably above 10 dB.
• Due to the complicated performance behavior of
pcov (λ, γ), the density of reliably working UEs ρ̃ displayed in Figs. 2c and 3c depends on the following
factors:
– For a low-reliability criterion, such as surpassing a
UL SINR threshold of γ = 0 dB, the density of reliably working UEs ρ̃ grows quickly with the network

(a) The active BS density λ̃.

(b) The coverage probability pcov (λ, γ).

(c) The density of reliably working UEs ρ̃.

Fig. 2: Performance results of the 3GPP Case (Rayleigh fading, no shadow fading) with γ = 0 dB.

(a) The active BS density λ̃.

(b) The coverage probability pcov (λ, γ).

(c) The density of reliably working UEs ρ̃.

Fig. 3: Performance results of the 3GPP Case (Rayleigh fading, no shadow fading) with γ = 10 dB.

(a) The active BS density λ̃.

(b) The coverage probability pcov (λ, γ).

(c) The density of reliably working UEs ρ̃.

Fig. 4: Performance results of the Advanced 3GPP Case (Rician fading for LoS, correlated shadow fading) with γ = 0 dB.

(a) The active BS density λ̃.

(b) The coverage probability pcov (λ, γ).

(c) The density of reliably working UEs ρ̃.

Fig. 5: Performance results of the Advanced 3GPP Case (Rician fading for LoS, correlated shadow fading) with γ = 10 dB.

densification, showing the benefits of UL IoT UDNs.
In contrast, for a high-reliability criterion, such as
surpassing a UL SINR threshold of γ = 10 dB, the
density of reliably working UEs ρ̃ does not exhibit
a satisfactory performance even in UDNs, e.g., we
merely get ρ̃ < 50 UEs/km2 when λ = 103 BSs/km2 .
The situation only improves when the BS IMC fully
kicks in, e.g., λ > 103 BSs/km2 .
– Considering the existence of a non-zero L, the
density of reliably working UEs ρ̃ could even decrease as we deploy more BSs (see Fig. 3c, λ ∈
[200, 600] BSs/km2 ). This calls for the usage of
sophisticated interference management schemes [19]
in UL IoT UDNs. Another solution to mitigate
such strong inter-cell interference is beam steering/shaping using multi-antenna technologies [2].
B. Performance Results of the Advanced 3GPP Case
In Figs. 4 and 5, we plot the performance results of the
Advanced 3GPP Case for γ = 0 dB and γ = 10 dB, respectively. To make our study more complete, here we consider
both the random and the hexagonal deployments of BSs. From
these two figures, we can see that the previous conclusions are
qualitatively correct, which indicates that it is not urgent to
investigate Rician fading and/or correlated shadow fading in
the context of UDNs. However, there are two new observations
that are worth mentioning:
• From Figs. 2a/3a and Figs 4a/5a, we can see that the
active BS density λ̃ of the Advanced 3GPP Case is
smaller than that of the 3GPP Case. This means that (5)
is no longer accurate to characterize λ̃ for the Advanced
3GPP Case. This is because the correlated shadow fading
allows a BS with a lower environmental fading factor,
i.e., SbBS , to attract more UEs than other BSs with higher
values of SbBS . Its theoretical analysis is an open problem
for further study.
• The hexagonal deployment of BSs can improve network performance for relatively sparse networks (e.g.,
λ < 102 BSs/km2 ), but not for UDNs (e.g., λ >
103 BSs/km2 ). Such conclusion indicates that it is not
urgent to investigate the performance of UDNs with the
hexagonal deployment of BSs, which has been a longstanding open problem for decades [5].
V. C ONCLUSION
We presented simulation results to evaluate the network
performance of UL IoT UDNs. From our study, we can see that
for a low-reliability criterion, the density of reliably working
UEs grows quickly with the network densification. However,
in our journey to realize a more reliable UL IoT UDNs, we
should be aware of several caveats:
• First, for a high-reliability criterion, the density of reliably
working UEs remains low in UDNs due to excessive
inter-cell interference, which should be considered when
operating UL IoT UDNs.

•

•

Second, due to the existence of a non-zero antenna height
difference between BSs and UEs, the density of reliably
working UEs could even decrease as we deploy more
BSs. This calls for further study of UL IoT UDNs.
Third, well-planned hexagonal-like BS deployments can
improve network performance for relatively sparse networks, but not for UDNs, showing that alternative solutions other than BS position optimization should be
considered in the future UL IoT UDNs.
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