BER based Assessment of Spectral and Energy Efficiency in a

Two-tier Heterogeneous Network

Jasmin Musovic

, Adriana Lipovac

and Vlatko Lipovac

Communications Regulatory Agency, Sarajevo, Bosnia and Herzegovina

Dept. of Electrical Engineering and Computing, Univ. of Dubrovnik, Dubrovnik, Croatia

Keywords: BER, Heterogeneous Network, Spectral Efficiency, Energy Efficiency.

Abstract: In this paper, we analyze an arbitrary heterogeneous cellular network applying stochastic geometry, and

propose a modified model for assessing network spectral and energy efficiency. With this regard, we

recognize that, in practice, determining Signal-to-Noise-and-Interference Ratio (SINR) as the key

performance indicator, requires complex field test equipment, which might not be available or affordable.

Therefore, we propose here a simple model that is based on the relatively easy measurable Bit-Error Rate

(BER), whose degradation caused by various impairments is considered here as if it was due to the according

additive white Gaussian noise (AWGN), thus abstracting any specific non-AWGN distortion. The proposed

analytical model is verified by ns3 software network simulator, whose test results are found to match the

corresponding estimated values. This indicates that both spectral and energy efficiencies of small-cell

networks are higher than in larger-cell networks, even more for heterogeneous two-tier networks.

1 INTRODUCTION

It has been quite a while since it has become evident

that homogeneous cellular network architecture

cannot adequately fulfil the fast growing users’

demand for capacity and Quality- of Service (QoS)

(Parkvall, 2008), as well as efficient spectrum and

energy consumption.

Starting with the fourth generation (4G) mobile

networks, it has become evident that smaller cells

enhance the network performance, and off-loads the

macro network from excessive traffic. So, for

example, simple plug-and-play installed femto cells

are more profitable than macrocells, due to reduced

backhaul costs and less transmitted power required in

small cells.

Specifically, state-of-the-art Radio Access

Systems (RAS) encompass cells of different classes

to make up a Heterogeneous Cellular Network

(HetNet), which includes at least two same-class

groups – tiers (Slamnik, 2016; Slamnik, 2017).

The actual explosive growth of data traffic implies

severe demand on energy efficiency (EE), so with the

4G Long-Term Evolution (LTE) and its extension

LTE Advanced (LTE-A), as well as with the

incoming 5G HetNets, transmission performance

enhancements include reduction of the distance

between the transmitting and the receiving antennas.

With respect to EE of wireless access networks,

the metrics is focused (Bousia, 2014 – ETSI TS

2011)) on the energy per information [J/b], enriched

by some QoS-related features (ETSI TR 2021) to

improve HetNet’s capacity and coverage, which both

depend on Signal-to-Interference-plus-Noise Ratio

(SINR).

Therefore, we investigate various HetNet

performance scenarios, but using Bit-Error Rate

(BER) rather than SINR at each User Equipment

(UE) (Mukherjee, 2014) within the serving tier area

of a single BS, and a single candidate-serving BS.

We will pursue BER analysis towards network

spectral efficiency (SE) and EE. Concretely, instead

of the classic hexagonal-grid based cellular network

composition with a BS-cantered each cell (Baccelli,

1997 – Baccelli, 2001); we used stochastic geometry

to capture randomness in network topology (Baccelli,

1997 – Brown 2000).

With this regard, the Herne topology is modelled

through Poisson Point Process (PPP) (Mukherjee,

2014), which describes irregular placements of BSs

within a real network, better than the classic

hexagonal-grid model (Baccelli, 1997).

116

Musovic, J., Lipovac, A. and Lipovac, V.

BER based Assessment of Spectral and Energy Efﬁciency in a Two-tier Heterogeneous Network.

DOI: 10.5220/0010852600003121

In Proceedings of the 10th International Conference on Photonics, Optics and Laser Technology (PHOTOPTICS 2022), pages 116-122

ISBN: 978-989-758-554-8; ISSN: 2184-4364

Although the PPP-based topology analysis is not

new (Baccelli, 1997; ElSawy, 2013; Dhillon, 2012),

it was not long ago when the PPP-distributed BSs

were introduced in various Herne (Brown, 2000),

(Dhillon, 2012 – Heath, 2013) and MIMO inclusive

network scenarios.

In Section II, we firstly provide a short basic

theoretical review, specifically considering

performance limits and related trade-off between SE

and EE. The short-term BER, SE and EE based

analytical model is presented as applicable for large

Honest who’s serving and candidate-serving BSs

have random distribution in the actual serving tier

area. Finally, the analytical model is verified in

Section III by presenting the test results obtained by

means of ns3 simulation tool that provided the short-

term BER values for all UEs of the network under

test. Conclusions are summarized in Section IV.

2 ANALYSIS

Complex relationship between SE and EE of

multiuser radio networks is determined by

compromises involving throughput, overall system

energy, frequency resources distribution, traffic flow

patterns, acceptable erroneous protocol data unit

rates, and achieved vs. target QoS level.

Generally, SE of wireless communication

networks is the ratio of the transmission rate R [b/s]

to the bandwidth B [Hz] that is needed to achieve R

(Musovic, 2021).

Moreover, the radio channel EE [b/J] is the ratio

between the energy per bit Eb and the noise spectral

density N0, i.e. EE expresses the count of information

bits per energy unit.

So, the Shannon formula for radio channel

capacity C [b/s] originally depending on channel

bandwidth B and mean power P

, can be expressed by

SE and EE as it follows (Musovic, 2021):

𝐶=𝐵𝑙𝑜𝑔





1











=𝐵𝑙𝑜𝑔





1

















= 𝐵  𝑙𝑜𝑔





1𝑆𝐸𝐸𝐸



(1)

Specifically, for transmission over the Additive-

White-Gaussian-Noise (AWGN) channel, having

given P

and B, where we consider EE as the ratio

C/B, (1) implies that:

𝑆𝐸 = log





1𝑆𝐸∙𝐸𝐸



(2)

Thus, we can explicitly express EE as a function

of SE:

𝐸𝐸 =



1

𝑆𝐸

(3)

In the utmost simple case of a single-BS and a

single-UE wireless network, (3) enables the analysis

of SE vs. EE relationship in linear and non-linear

power and energy regions, Figure 1, thus aiming to

enable considerably enlargements of throughput and

data rate (Musovic, 2021).

Figure 1: EE vs E

relationship.

From these considerations, it is obvious that

increasing data rate requires significantly larger

received signal power (Musovic, 2021).

This implies the BS-to-UE distances of the order

of tens of meters, whereas still in the linear-region

tolerating considerably larger values (but with

considerably smaller SE, due to EE reduction by

propagation impairments.)

In the non-linear-region, however, considerably

larger EE can be achieved, as stronger received

signals enable reduction of cell dimensions as low as

tens of meters, with the variety of cell classes

comprising: micro, nano, pico and femto cells. These

enable close-to-uniform EE distribution,

considerably larger SE and thus the throughput and

rational coverage with still good enough EE,

especially in areas crowded with active users, and

considerably lower electromagnetic radiation

(Musovic, 2021).

So far, the HetNet overall efficiency was analyzed

by considering both SE and EE, and determining

SINR for each UE within the k-tier of HetNet having

tiers overall (Musovic, 2021).

Each tier (e.g. k-th) is modeled by a homogeneous

PPP Φ

, with the transmit power P

, BSs density λ

and the SINR threshold τ

(often referenced as “bias”)

at UE, respectively.

BER based Assessment of Spectral and Energy Efﬁciency in a Two-tier Heterogeneous Network

117

2.1 BER based Analytical Model

Degraded SINR usually implies constellation symbol

errors, and thereby SINR is often tested, which

requires complex equipment to measure the noise and

inter-symbol interference (ISI) (Lipovac, 2021).

Instead, estimating BER, can be an alternative, i.e. an

easy-to-measure performance trade – off “currency”,

rather than SINR (where by “easiness”, we consider

the possibility to estimate BER in-service, simply by

counting the retransmissions at the physical/MAC

layer whose count determines the Block-Error ratio

(BLER). Then an appropriate model can be applied to

estimate BER from BLER.

This could be useful in practice encompassing

various phases of a product related research,

development, manufacturing, and finally its

exploitation of a product in LTE and 5G New Radio

environment.

Let us review the classical BER expression as a

function of Signal-to-Noise Ratio (SNR), for the M-

QAM signal transmission over AWGN channel

(Rumnay, 2013):













−

⋅

⋅=

log

SNR

BER

(4)

where Q stands for the Gaussian tail function,

represented by the “waterfall” - steep curves in Fig.

2, which visualize the threshold effect that is

immanent to digital radio receivers.

Figure 2: Waterfall BER vs SNR curves (for Nyquist BW).

Furthermore, it is quite often that in various

propagation environments, specifically in very small

cells, presuming strong received signals (i.e. high

SNR) is realistic, which implies successful

elimination of the time-dispersion-caused inter-

symbol interference (ISI) by long-enough cyclic

prefix (CP) (Lipovac, 2021).

This practically reduces SINR to SNR, so (4)

implies that:

log

























⋅−

=≈

−

MBER

SNRSINR

(5)

where

1−

denotes the inverse function of the

Gaussian tail.

In addition, it is quite justifiable to consider the

radio interference to be a dominant impairment,

which (as a sum of enough many mutually

independent RF interfering signals, and according to

the Central Limit Theorem), is a Gaussian random

variable.

Moreover, applying link abstraction, any

distortion, be it additive or not, or non-Gaussian, can

be considered equivalent to that much additive

Gaussian noise which would produce the same BER

degradation, i.e. shift the BER(SNR) curves from Fig.

2 to the right for the adequate SNR degradation, which

is in Fig. 3 expressed as the ratio of E

to N

Figure 3: AWGN abstraction of non-AWGN impairments.

With this regard, we can justifiably assume

successful CP-aided mitigation of channel time

dispersion, i.e. that the standard CP is long enough

(e.g. as the “normal” one in LTE) to eliminate the vast

majority of error bursts mostly arising from multipath

propagation, and retain only sporadic bit errors that

mostly occur sporadically in residual bursts (to be

scattered by interleaving, anyway) (Lipovac, 2021).

Finally, as the simple and common BER tests

have been “ex-communicated” from the LTE (and 5G

as well) transmission performance specifications for

network operators, in favor of BLER (Rumnay,

2013), therefore, in order to estimate BER in-service,

we need to adopt a certain relationship between

BLER and BER.

PHOTOPTICS 2022 - 10th International Conference on Photonics, Optics and Laser Technology

118

However, although the common binomial

distribution well statistically describes mutually

independent bit error occurrences within a data block

(e.g. the LTE code-block), in this case, we could

consider that the appropriate error generating model

should still preserve (moderate) mutual dependability

among the individual bit-error occurrences. This

conforms to the statistical model of sampling

without replacement, well described by the hyper-

geometric distribution of errors within an errored data

block (containing one or more erroneous bits)

(Lipovac, 2021):

2.2 Spectral and Energy Efficiency

Model

The tiers are ranked in ascending order according to

the density of access points: λ

≤ λ

...λ

k−1

≤ λ

. For

any specific λ

, the count of access points of tier k

(i=1,2,…,N

) within the covered area 𝒜 [m

] is a

Poisson random variable with mean 𝒜∙𝜆



independent of other tiers. Moreover, all k-tier access

points transmit with power P

Each downlink is modeled as Rayleigh fading

channel, with the BS-transmitted power 𝑃





and the

UE-received power 𝑃





at R

distance from BS.

In this model, we have chosen the path-loss

exponent to be equal to 4 (Slamnik, 2016), and that

macro BSs do not transmit during the Almost Blank

Subframes (ABS) (Slamnik, 2017).

For each tier, we consider the frequency reuse

factor of unity, and the RF band of one channel

skipped between the two same-standard tiers, which

implies that for a particular UE connected to tier k, all

interfering BSs are within that tier (k), with the

exception of the serving one.

In the considered scenario, each UE is allowed to

access only the BSs in tiers 1,2,...,K

open

from Open

Access (OA) macro/femto cells, whereas the Closed

Subscriber Group (CSG) femto cells are mostly not

allowed to serve those users under consideration [8].

So, a certain HetNet would be represented by the

count of tiers: N

= 3 and the count of OA tiers: N

open

= 2, with tier 1 representing the macro cells, tier 2

standing for the OA femto cells, and tier 3 for the

CSG femto-cells.

Furthermore, we assume maximal allowed BS-

transmitted power (for the actual tier).

Now, let us analyze the above explored

relationship between the network SE and the total

power so that the distribution of BSs within the tiers

is in the form of PPP.

In addition, we suppose that a particular BS b

any serving tier k

transmits only to a subset of users

served by b

∈Φ

Let us consider the SINR 𝛤



𝑢





for the specific

user u

∊U

, expressed by BER, according to (5).

Then the spectral efficiency SE

of the link from

to any target u

is:

[]

{}















































⋅

−

+⋅≈

=+⋅=

−

log

1logE

)(1logE

MBER

uΓSE

𝑏∈Φ,𝑃



𝑈



=𝑢





𝑈



,𝑢



∈𝑈



(6)

The proposed analytical model provides the

spectral efficiency SE

for each tier (k=1…N

), as

well as the one - SE

TOT

for the whole HetNet.

Furthermore, the selection of serving or

candidate-serving cells according to the LTE-A

standard is mostly based on the pico-cell BSs range

extension to enable traffic load balancing, and

prevent inter-cell RF interference in the areas with

evident or expected signal overlapping coverage

(Musovic, 2021).

The mean levels of the UE-received pilot

originating by the candidate-serving macro and pico

BSs, were used for selecting the optimal small-cell

tier to serve a particular UE, according to two

schemes:

Firstly, we consider the macro tier i to be the

serving tier, and the pico tier j to be the candidate-

serving tier, otherwise it is the pico tier j to serve the

UE, whereas the macro tier i is the candidate-serving

tier (Mukherjee, 2014).

In the following, with R

and R

, we denoted the

distances between the UE and the candidate-serving

(i.e. the nearest) macro BS, and femto BS,

respectively.

As we plan to simply model the HetNet SE we

adopt that the instantaneous transmitted signal power

of any macro BS is considered a random variable

ranging from zero during ABS state, or to 𝑃





otherwise. Furthermore, we denote the instantaneous

transmit power of the serving BS by 𝑃





Firstly, we adopt that a certain UE of an arbitrary

location is being served by the micro tier i, whose

SINR Γ

is greater than the threshold γ with the

probability 𝒫



Secondly, we consider that a certain UE is being

served by the micro tier i, whereas the probability of

the UE being served by the pico tier with appropriate

SINR, is denoted as 𝒫



BER based Assessment of Spectral and Energy Efﬁciency in a Two-tier Heterogeneous Network

119

Thereby, from (1) and (2), SE

and SE

can be

expressed as:

𝒫



=𝒫𝛤



𝛾∥ℛ



=𝑟



,ℛ



=𝑟





(7)

𝒫



=𝒫𝛤



𝛾∥ℛ



=𝑟



,ℛ



=𝑟





(8)

Integrating the (exponential) probability density

functions of distances between the UE and the serving

tier i, as well as from the candidate-serving tier j,

provides 𝑆𝐸



and 𝑆𝐸



, as well as the overall HetNet

spectral efficiency as it follows:

𝑆𝐸



=𝑆𝐸



𝑆𝐸



(9)

3 TEST RESULTS

The above presented analytical model is software

implemented using ns3 network simulator.

Our preliminary test results are aimed to just

verify the proposed concept, whereas the follow-up

tests of this kind can be repeated as many times as

needed.

Five rounds of according simulations were made,

with the BER results in particular, enhanced by

statistical data averaging. Finally, the three

considered scenarios were tested:

- single-tier, 5 macro BSs, BS power: 40 W,

- single-tier 250 pico BSs, BS power: 0.25W,

- two-tier 5 macro + 250 pico BSs.

The set up data for the simulation are presented in

Table 1.

Table 1: Parameters used in ns3 simulations.

Parameter Value

LTE code-block maximal size (L) 6144 Bytes

Count of macro cell BSs 5

Maximal output transmit power of the

macro-cell BS

40W

Maximal output transmit power of the

small-cell BS

250mW

Count of small-cell BSs 250

Population density per m

3.8·10

-4

Maximal distance between BSs in the

macro cell

500m

Maximal distance between BSs in the

small cell

50m

Count of resource blocks with

the LTE 5MHz channel bandwidth

Center of the frequency operating band: 2.1GHz

LTE channel bandwidth 5MHz

Furthermore, based on the set up values given in

Table 1, in Table 2, are the obtained simulation

results.

Table 2: Simulation results (after averaging).

BER SINR SE[b/s/Hz] EE[b/J]

0.0378 11.98 17.28 0.53

0.0550 11.06 15.96 1.04

0.0659 10.55 15.22 1.65

0.0813 9.86 14.22 3.09

0.0921 9.45 13.63 4.45

0.0996 9.16 13.22 5.75

Accordingly, the proposed analytical model is

graphically represented in Fig. 4, reflecting various

exemplar scenarios that we considered. Coming out

of the presented curves, it is evident that SE of the

entire HetNet of interest grows exponentially with

transmit power ratio, when small cells are

implemented surrounding a typical macro cell.

However, it is quite different with only a single macro

tier, where SE does not change with transmit power

ratio.

Figure 4: Spectral efficiency vs. relative transmit power and

cell range expansion bias (theta).

Therefore, more pico cells in the network

inevitably imply higher spectral efficiency, which

complies to the expected values obtained by the

proposed analytical model.

Accordingly, the diagrams in Fig. 5(a) and (b)

represent SE and EE, respectively, resulting from

simulations of the three above reviewed scenarios and

parameters’ values in Table 1:

PHOTOPTICS 2022 - 10th International Conference on Photonics, Optics and Laser Technology

120

(a) (b)

Figure 5: Simulation results for: a) SE, b) EE.

In both above diagrams, it can be seen that the

two-tier scenario exhibited the most efficient network

performance.

Furthermore, the small-cell scenario (250 pico

BSs) came out to be more efficient than what was

achieved with macro cells (5 BSs), while still

preserving the same count and layout of users.

Finally, considering various transmit power in the

pico tier with the macro-tier transmit power

remaining constant, SE shows growing trend with

respect to the ratio of transmit powers.

4 CONCLUSIONS

Instead of SINR, we proposed the simpler-to-measure

BER as the key performance indicator, by abstracting

the performance degradation due to various

(generally non-AWGN) impairments, by the

according AWGN ones which have the same effect

on BER as any specific distortion.

It came out that inserting small cells into HetNets

of any distribution of BSs, significantly improved

both the energy and spectral efficiency.

So, with smaller distances in between BSs and

UEs of contemporary networks – e.g. LTE and LTE-

A, the trend is rationalization and optimization of

signal coverage by reinforcing it in the areas of

increased traffic.

Such a strategy seems to be appropriate in the

tested exemplar environments, but needs to be

enhanced and fine-tuned with other sophisticated

tests taking into account other impairments e.g.: RF

interference, traffic patterns, bandwidth and channel

allocation etc., whose management is aimed enable

the projected QoS level, complexity reduction, and

fair distribution.

REFERENCES

Parkvall, S., Dahlman, E., Furuskar, A., Jading, Y., Olsson,

M., Wanstedt, S. and Zangi, K., LTE-advanced-

evolving LTE towards IMT-advanced, In IEEE 68th

VTC, 2008, pp. 1–5.

Slamnik, N., Okic, A. and Musovic, J., Conceptual radio

resource management approach in LTE heterogeneous

networks using small cells number variation. In IEEE

XI International Symposium (BIHTEL) 2016; pp. 1-5.

Slamnik, N., Musovic, J., Okic, A., et al., An approach to

analysis of heterogeneous networks’ efficiency, In

XXVI IEEE International Conference ICAT, 2017, pp.

1–5.

Bousia, A., Kartsakli, E., Antonopoulos, A., Alonso, L. and

Verikoukis, C., Energy efficient schemes for base

station management in 4G broadband systems. In

Broadband Wireless Access Networks for 4G: Theory,

Application, and Experimentation, 2014, pp. 100-120,

IGI Global.

Imran, MA., Alonso-Rubio, J., Auer, G., et al., Most

suitable efficiency metrics and utility functions. In

EARTH Project Report, 2011, pp. 1-89.

ETSI TS 102 706 Standard, Environmental engineering

(EE) measurement method for energy efficiency of

wireless access network equipment, V1.2.1, 2011.

Available online: https://etsi.org (Accessed on 30th

January 2021).

ETSI TR 103 117, Environmental engineering (EE);

principles for mobile network level energy efficiency,

v1.1.1, 2012. Available online: https://etsi.org

(Accessed on 30th January 2021).

Mukherjee, S., Analytical modeling of heterogeneous

cellular networks. Cambridge University Press; 2014.

ISBN 978-1-107-05094-5.

Andrews, J.G., Baccelli, F. and Ganti, R.K., A tractable

approach to coverage and rate in cellular networks. In

IEEE Transactions on communications, 59(11), 2011,

pp.3122-3134.

Baccelli, F., Klein, M., Lebourges, M. and Zuyev, S.,

Stochastic geometry and architecture of communication

networks. In Telecommunication Systems, 7(1), 1997,

pp. 209-227.

Baccelli, F. and Błaszczyszyn, B., On a coverage process

yaranging from the Boolean model to the Poisson-

Voronoi tessellation with applications to wireless

communications. In Advances in Applied Probability,

2001, pp. 293-323.

ElSawy, H., Hossain, E. and Haenggi, M., Stochastic

geometry for modeling, analysis, and design of multi-

tier and cognitive cellular wireless networks: A survey.

In IEEE Communications Surveys & Tutorials, 2013,

15(3), pp. 996-1019.

Brown, T.X., Cellular performance bounds via shotgun

cellular systems. In IEEE J. Sel. Areas Commun., 2000,

18(11), pp.2443-2455.

Dhillon, H.S., Ganti, R.K., Baccelli, F. and Andrews, J.G.,

Modeling and analysis of K-tier downlink

heterogeneous cellular networks. In IEEE J. Sel. Areas

Commun., 2012, 30(3), pp.550-560.

BER based Assessment of Spectral and Energy Efﬁciency in a Two-tier Heterogeneous Network

121

Dhillon, H.S., Ganti, R.K. and Andrews, J.G., Load-aware

modeling and analysis of heterogeneous cellular

networks. In IEEE Trans. Wirel. Commun., 2013,

12(4), pp.1666-1677.

Mukherjee, S., Distribution of downlink SINR in

heterogeneous cellular networks. In IEEE J. Sel. Areas

Commun., 2012, 30(3), pp.575-585.

Madhusudhanan, P., Restrepo, J.G., Liu, Y., et al., Multi-

tier network performance analysis using a shotgun

cellular system. In IEEE GLOBECOM, 2011, pp. 1-6.

Heath, R.W., Kountouris, M. and Bai, T., Modeling

heterogeneous network interference using Poisson

point processes. In IEEE Trans. Signal Process., 2013,

61(16), pp.4114-4126.

Musovic, J., Lipovac, V. and Lipovac, A., Stochastic

Geometry-Based Analysis of Heterogeneous Wireless

Network Spectral, Energy and Deployment Efficiency,

Electronics, vol. 10, no. 7, p. 786, Mar. 2021.

Lipovac, V., Lipovac, A. and Modlic, B., PHY, MAC, and

RLC Layer Based Estimation of Optimal Cyclic Prefix

Length, Sensors, vol. 21, no. 14, p. 4796, Jul. 2021

[Online]. Available: http://dx.doi.org/10.3390/s2114

4796

Rumnay, M., LTE and the Evolution of 4G Wireless;

Design and Measurements Challenges, 2nd edition,

John Wiley & Sons, UK, 2013.

PHOTOPTICS 2022 - 10th International Conference on Photonics, Optics and Laser Technology

122