ADDIS ABABA UNIVERSITY

ADDIS ABABA INSTITUTE OF TECHNOLOGY

SCHOOL OF ELECTRICAL AND COMPUTER ENGINEERING

COMMUNICATION ENGINEERING STREAM

PERFORMANC ANALYSIS OF ENERGY EFFICIENCY ENSURING

TECHNIQUES IN MASSIVE MIMO FOR 5G COMMUNICATION
NETWORKS

By: Haile Araya

Advisor: - Dr.-Eng. Yihenew Wondie

A research Thesis Submitted to Addis Ababa University Institute of Technology in

Partial Fulfillments of the Requirements for the Degree of Master of Science in
Electrical and Computer Engineering (Communication Engineering Stream)

September 2023

Addis Ababa, Ethiopia

 Addis Ababa University

Addis Ababa Institute of Technology

School of Electrical and Computer Engineering

Performance Analysis of Energy Efficiency Ensuring Techniques in Massive

MIMO for 5G Communication Networks

By: Haile Araya

Approval by Board of Examiners

_____________________________ ____________ ________

Chairman, Dept. Graduate Signature Date

Committee

Dr-Eng. Yihenew Wondie ______________ _______

Advisor Signature Date

_______________ __________ _____

Internal Examiner Signature Date

____________________ __________ ________

External Examiner Signature Date

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Abstract
Wireless communication technology is increasing to satisfy the needs of customers. With the
emergence of new technologies, energy consumption is one of the most important performance
metrics. According to the requirements of the 5th generation wireless communication system,
energy consumption should not increase from the level of the current networks (4G), even
though the amount of data is expected to be significantly higher. Therefore, energy efficiency has
been set as one of the major objectives for recent cellular networks. Massive multiple-input-
multiple-output (M-MIMO) is the key technology to providing higher energy efficiency (EE) and
data throughput in 5G wireless communication systems.

This thesis focuses on the performance analysis of energy efficiency higher than energy
consumption for 5G networks using massive multiple-input multiple-output (M-MIMO).
Minimizing the power consumption per user’s equipment (UE) with increasing throughput. The
main design parameters used are the power consumption per user’s equipment (PC), the data rate
of the system (R), and the massive number of antennas (M) and users’ equipment (K). Energy
efficiency is defined as the system throughput per unit of power consumption as a function of a
massive number of antennas and users. The performance analysis and comparison used are pre-
coding schemes such as multi-cell minimum means square error (M-MMSE), zero-forcing
(ZF/RZF), and maximum ratio combination (MRC). MATLAB tools are used to analyze and
demonstrate numerical results.

The analyzed results show that energy efficiency (EE) is higher than energy consumption in a
massive MIMO for 5G wireless communication systems. The overall simulated result of multi-
cell minimum mean square error (M-MMSE) is the best pre-coding technique to maximize
energy efficiency (EE) rather than total energy consumption in massive MIMO for 5G wireless
networks. However, MRC achieves the lowest performance and energy efficiency as the massive
number of antennas increases in massive MIMO for 5G cellular communication networks.

Keywords: fifth-generation (5thG), massive multiple-input-multiple-output (MIMO), energy

efficiency, power consumption, data rate and Precoding.

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Declaration

I declare that this thesis, which I submit to Addis Ababa Institute of Technology for examination
in partial fulfillment of the award of a master degree in Electrical and Computer Engineering, is
my original effort. It has not been presented for fulfillment of a degree in this or any other
University and all sources and materials used for the thesis are duly acknowledged.

Haile Araya _______________

Name Signature

Place: Addis Ababa

Date of Submission: ____________________________

This thesis has been submitted for examination with my approval as university advisor

Dr-Eng. Yihenew Wondie _____________ _______

Advisor’s name Signature Date

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Acknowledgment
First, I would like to give special thanks and glory to Almighty God for giving me strength,
wisdom, courage, and grace and for guiding me in all the ways of my life.

I would like to acknowledge and extend my deepest gratitude to my adviser, Dr-Eng. Yihenew
Wondie. His valuable and essential guidance, hints, motivation, ideas, support, continued to
follow up and constructive comments were so much beneficial. Moreover, my thesis would not
be possible without my advisor. He has always been available and willing to help me any time
anywhere.

I would also like to thank my family for their support in finalizing this thesis paper. Finally; I
would like to say thanks to the school of Electrical and Computer Engineering and all my friends
who helped me in accomplishing this research thesis.

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Table of Contents
Abstract ............................................................................................................................................ i

Declaration ...................................................................................................................................... ii

Acknowledgment ........................................................................................................................... iii

Table of content…………………………………………………………………………………..iv

List of table……………………………………………………………………………………….vi

List of figure……………………………………………………………………………………...vi

List of abbrevation……………………………………………………………………………….vii

List of symbols…………………………………………………………………………………….x

Chapter 1…………………………………………………………………………………...…….1

1.1 Introduction ............................................................................................................................... 1

1.2 Statement of the problem .......................................................................................................... 2

1.3 Objectives ................................................................................................................................. 4

1.3.1 General objective…………………………………………………………………..…….4

1.3.2 Specific Objective……………………………………………………….……………….4
1.4 Literature review ....................................................................................................................... 5

1.5 Methodology ............................................................................................................................. 8

1.6 Main thesis contributions .......................................................................................................... 8

1.7 Limitation of the thesis ............................................................................................................. 8

1.8 Thesis structure……………………………………………………………………………..…9

Chapter 2………………………………………………………………………………………..10

2.1 Introduction ............................................................................................................................. 10

2.2 Definition of spectral efficiency (SE) ..................................................................................... 11

2.3 Massive-MIMO....................................................................................................................... 12

2.4 Analysis of Pre-coding design: up-link-down-link duality..................................................... 13

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2.5 Time division duplex system protocol (TDD) ........................................................................ 16

2.6 Performance analysis of energy and spectral efficiency ......................................................... 17

2.6.1Definitionof energy efficiency with spectral efficiency……………………………………18

2.6.2 Mathematical equations…………………………………………………………………... 19

2.6.3 Minimum mean square error (MMSE). ............................................................................... 21

2.7 Performance analysis of antenna schemes .............................................................................. 22

2.8 Multi-cell minimum mean square errors (M-MMSE) ………………………………………24

2.9Single-cell minimum mean square error (S-MMSE)…………………………………………26

2.9.1 Down-link multi-cell minimum mean square error (M-MMSE) ......................................... 27

2.9.2 Improving energy efficiency and decreasing loss in Massive-MIMO................................. 28

2.9.3 Multiuser MIMO……………………………………………………………………..…….30

2.9.4 The wireless channel ............................................................................................................ 32

Chapter 3 ..................................................................................................................................... 33

System model of energy efficiency in massive MIMO systems................................................... 33

3.1 Introduction ............................................................................................................................. 33

3.2. Comparison of circuit power (CP) with different Precoding techniques. .............................. 35

3.3 Maximization of energy efficiency (EE) ................................................................................ 36

3.4 Tradeoff energy and spectral efficiency ................................................................................. 36

3.5 Impact of Multiple BS Antennas ............................................................................................ 37

Chapter 4…………………………………………………………………………………..……39

Simulation and numerical results .................................................................................................. 39

4.1 Introduction…………………………………………………………………………………..39

4.2Simulation parameters………………………………………………………………………..39

4.3 Simulation and result discussions ........................................................................................... 41

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4.3.1 The impact of bandwidth on energy efficiency in massive MIMO ..................................... 41

4.3.2 Analysis of multi-users and circuit power in massive MIMO system……………….…….42

4.3.3 Analysis of throughput on energy efficiency in massive MIMO system………………….42
4.3.4 Design and analysis of maximum energy efficiency in massive MIMO …………….……44

4.3.5 Maximization of energy efficiency than power consumption in massive MIMO…………46

Chapter 5 ……………………………………………………………………………………….48

Conclusion and recommendations ……………………………………………………..………..48

5.1 Conclusions ............................................................................................................................. 50

5.2 Recommendations for future work ......................................................................................... 50

Reference ...................................................................................................................................... 52

List of Tables

Table 4.1 Simulation parameters used…………………………………………….….…………39

Table 4.2 Simulation result energy efficiency vs energy consumptions…………….……….….47

List of figures

Figure2.1 cell organization, every base station (BS) covers a distinct geographical area [5] ...10

Figure2.2 Multi user MIMO [38] ………………………………………………….………...….12

Figure 2.3 (a) UL: UE k in cell j is affected by high interference from UEi in cell l [5] ……….14

Figure 2.4 (b) DL: UEi in cell l, receives high interference from base station (BSj) [5] ……….15

Figure 2.5 Proposed system models for massive MIMO [10]………………………………. ….17

Figure2.6 Comparison of Precoding, techniques and reducing interference in massive MIMO

[12] ................................................................................................................................................20

Figure2.7 Block diagram MMSE……………………………………………………………….21

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Figure 2.8 Max EE coverage area in a single-antenna system depends on the channel gainβ [3]
…………………………………………………………………………………………….……...23

Figure 2.9 pilot contamination limit performance [27] ………………………….……...………24

Figure 2.10 Multiusers MIMO [35] …………………………………...………………...………31

Figure2.11Radio signal propagation [38] …………………………………….…………………32
Figure 3.1 System model L number of cells [9]…………………………………………………33
Figure 3.2 Work flow diagram of energy efficiency in massive MIMO systems……….……....34
Figure3.3 Circuit power consumption breakdowns per cell Precoding, techniques (M-MMSE,
RZF and MRC), With K = 20 user equipment’s, and M = 200 number of antennas in the base
stations (Bs) [5] ………………………………………………………………………………….35
Figure3.4 circuit power consumption, breakdowns per cell Precoding, techniques such as: (M-
MMSE, RZF and MRC). With K = 20 user equipment’s, and M = 200 number of antennas in the
base stations (Bs) [5] ………………………………………………………….…………...…….36
Figure 4.1 Simulation result energy efficiency with bandwidth in massive MIMO..............…...41
Figure 4.2 Total circuit power (CP) with user equipment’s (K) in massive MIMO……….……42
Figure 4.3 Simulation result energy efficiency with throughput in massive MIMO…………….43
Figure 4.4 Simulation result EE with number of antennas (M) and active user equipment’s (UE)
using M-MMSE Precoding techniques in massive MIMO…………………………...………….44
Figure 4.5 Simulation result EE with number of antennas (M) and active user equipment’s (UE)
using RZF Precoding techniques in massive MIMO…………………………………………….45
Figure 4.6 Simulation result EE with number of antennas (M) and active user equipment’s (UE)
using MRC Precoding techniques in massive MIMO………………………….……………….45
Figure 4.7 Simulation result EE vs power consumptions in massive MIMO…………….…….46

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List of Abbreviations
AAEE Average Area Energy Efficiency
AATP Average Area Transmit Power
ASD Angular Standard Deviation
AWGN Additive white Gaussian Noise
BC Coherence Bandwidth
BER Bit Error Rate
BNO Noise power spectral density
BS Base Station
CDL Downlink Capacity
CN Noise channel
CP Circuit Power
CSI Channel State Information
CUL Uplink Capacity
DL Downlink
EE Energy Efficiency
EEDL Energy Efficiency Downlink
EEUL Energy Efficiency Uplink
EM Electro Magnetic
ETP Effective Transmit Power
FAIR Fixed Asset Inventory Revenue
FDMRC Frequency Division Maximum Ration Combination
GE Gain Expectation
GIS Geographical Information System
LBS Complex Operational value at the BS
LOS Line of Site
LUE Complex Operational value at the UE
MIMO Multiple Input Multiple Output
MMSE Minimum Mean Square Error
MRC Maximum Ratio Combination
MU Multi-User
OFDM Orthogonal Frequency Division Multiplexing
PA Power Amplifier
PB Power Bandwidth
PC Power Consumption
PH Power Matrix
RF Radio Frequency
RZF Regularized Zero Forcing

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SC Single Career
SDMA Space Division Multiple Access
SE Spectral Efficiency
SINR Signal Interference Noise Ratio
SNR Signal Noise Ratio
SU Single User
TC Coherence Time
TDD Time Division Duplex
TRMRC Time Reversal Maximum Ratio Combination
UE User Equipment
ULA Uniform Linear Array
ZF Zero Forcing

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List of symbols

Τρ Pilot coherence
P Power
H Matrix H
‘ɸo Phase angle
C Set of complex numbers
(.)T Transpose of matrix
tr(.) Trace of square matrix
(.)-1 Inverse matrix
E[.] Mean of the random variable/expectation
||. || Norm of vector
|. | Absolute value
(0, σ2) A gaussian random variable with zero mean and variance σ2
β Path loss
B Bandwidth
W Precoding

Transmitted power of the payload data

Covariance matrix

̂ Estimated signal
ei Identity matrix IB
gjk Arbitrarily user

Diagonal matrix

gHjk ́ jjk True channel in the decoding

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Chapter 1

1.1 Introduction
To bring faster data rates with a growing ‘N’ number of active users, the new wireless systems
generation will rely on a much denser deployment of infrastructure to provide seamless
connectivity. The spatial beam of a directive signal is being actively studied as a way to reduce
both interference and increase the data rate throughput. The massive multiple-input-multiple-
output (MIMO) wireless technology takes advantage of spatial degrees of freedom through the
use of multiple antennas on both the transmitter and the receiver sides [1]. The spatial degrees of
freedom (DoF) are used to reduce the outage probability and increase the peak achievable data
rate in single-user (SU) systems. Adding more numbers of antennas gained in multi-user (Mu)
systems is more significant to improve the data rate since large MIMO antenna arrays can be
communicating simultaneously with many numbers of active users in a given cell area.

Multiple-input multiple-output (MIMO) has advanced rapidly over the last 20 years. One reason
for this is that the fundamental technologies were developed well before they were fully
exploited. In earlier years in the 1960s, antenna arrays would make spatial filtering and separate
signals simultaneously arriving from different directions and references through an extensive
review. The processing capabilities and manufacturing progressed array gain process received a
surge of attention in the 1990s with the promise of energy-effective implementation in the area
of wireless communications [1, 2]. The LANs have been successful in sending multiple data
streams to a single-user device (‘‘single-user MIMO,’’ or SU-MIMO), due in part to the fact that
laptops and tablets are big enough to accommodate multiple antennas. In wide-area wireless
communication networks, where phone-sized devices predominate, SU-MIMO has limited
benefits. However, since the dimensions of the base station aren't as tightly constrained, it's
possible to extend the number of antennas there and utilize them for space-division multiplexing
(forming geographic beams) or MU-MIMO) [3]. Even with more antennas at each base station,
achieving high capacity within the wide-area wireless network remains a frightening task. Space
division multiplexing is conceptually straightforward and relatively easy to implement with
geographical information systems. Massive MIMO can greatly improve capacity without the
devastating complexity of inter-cell coordination. The number of value antennas in the base
station (Bs) becomes much larger than the number of user terminals (UE) M>K, it is possible to

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generalize beams such that, there is always a single active user (UE) in each beam, thus giving
each user their interference-free and high-capacity link to the base station (Bs). The probability
of a beam pointing toward a neighboring base station (Bs) becomes small as well and inter-cell
interference approaches zero without coordination between the numbers of cell coverage. Small
cell deployment is one of the foremost attractive aspects of massive MIMO [1, 2]. Massive
MIMO is considered one of the keys enabling technologies for 5G networks. The classification
capacity and benefits from deploying massive MIMO, coupled with the reservations of channel
propagation characteristics and practical hardware design issues, have led to several
demonstration projects ranging from large-scale simulations to actual hardware. The result has
studied channel estimation and beam-forming. The mm-wave frequencies and system
simulations have generally attempted to measure the performance of energy efficiency in
massive MIMO in outdoor environments with the mobility of active users. In 2011, the green
touch consortium demonstrated a 16-element array [1]. Effective antennas gain increase linearly
with the number of antennas was the main result of the study. It allows the radiated transmit
power per element to be reduced proportionally to the number of antennas in BS.

Massive-MIMO is a progressive version of the space-division multiple-access (S-DMA) which is

pushing spatial multiplexing to an external level. The main assists of massive MIMO can be
summarized as massive spectral efficiency, communication reliability, high energy efficiency,
low complexity signal processing, favorable propagation, and channel hardening [2]. The
massive MIMO receives all gains from conservative multi-user MIMO (MU-MIMO) i.e., with M
(number of antennas) in the base station (Bs) and K (single-antenna) in active number of the user
(UE), can achieve a diversity of order M (number of antennas) and a multiplexing gain of (M,
K). Increasing both the number of antennas (M) in a base station (Bs) and K (single antenna) in
an active user (UE), can obtain maximum energy efficiency (EE), spectral efficiency (SE), and
very high communication reliability with simple linear processing schemes such as maximum
ratio combination (MRC), zero forcing (ZF), and minimum-mean square error (MMSE) [2].

This thesis is dealing with the performance of energy efficiency ensuring techniques in massive
MIMO, to improve energy efficiency (EE) by minimizing the power consumption per user
equipment (UE), and the energy efficiency will be greater than the energy consumption, using

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techniques such as multi-cell-minimum means square error (M-MMSE), zero-forcing (ZF),

regularized zero-forcing (RZF) and maximum ratio combination (MRC).

1.2 Statement of the problem

In wireless communication system there are a lot of challenges and problems. The major
challenges include spectral efficiency, energy efficiency, and link reliability at anytime and
anywhere. Those challenges are created due to the scarce availability of band width, propagation
channel fading and wireless node mobility. To increases the data rate (R) reliability, a simple
method is to increase the allocation bandwidth but, energy consumption is becoming one of the
key performance indicators for network operators. Energy itself has no problem but its
production is mainly non-renewable, as environmental and economic concerns problems due to,
unbalanced energy consumption, and traffic load in wireless communication networks [5].
According to past literature, base stations alone were representing 5GW of power and 20 Mt of
carbon dioxide per year [15], [16], [17]. Since then, the figures have been constantly increasing
and becoming a problem for telecom industries. Therefore, in terms of operational expenses, and
environmental impact, energy efficiency has been targeted at the international level as one of the
key capabilities of 5G networks. As a result, this remained an engineering challenge ensuring
efficient and optimized energy-wise usage.

Massive MIMO technology is one of the key optimizations of energy consumption and serving
multiple users and antennas simultaneously with an increased data rate of the system. This work
mainly aimed at the proper usage of energy and serving multiple users by using, Pre-coding
techniques channel state information (CSI) such as (M-MMSE, ZF, and MRC) in massive
MIMO systems. To minimize the energy consumption at the base station, users equipment and
maximize the energy efficiency in massive MIMO for 5G wireless communication networks.

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1.3 Objectives
1.3.1 General objective
The general objective of this thesis is to improve energy efficiency by minimizing energy
consumption per user equipment, and base stations in massive MIMO for 5G wireless
communication networks.
1.3.2 Specific Objective
The specific objective is the performance analysis of EE ensuring technique in massive MIMO
for 5G wireless communication networks which satisfy the main requirements, these included

 Analysis of the bandwidth on energy efficiency in massive MIMO networks

 Analyse the effect of power consumption on energy efficiency in massive MIMO

 Maximize throughput/data rate in massive MIMO by analysing total power consumption

 Analyse of the effect of the number of users and reliable data rate throughput on energy
efficiency

 Analyse and simulate the effect of a massive number of antennas on energy efficiency.

 Analyse and calculate energy efficiency (EE), and area throughput in a massive MIMO
system.

 Identify the best Precoding techniques and simulation results for the performance of
maximum energy efficiency in massive MIMO

 Design optimal networks which serve massive users have a massive number of antennas,
and a reliable data rate.

 Analyse of maximum energy efficiency than power consumption, using the Precoding
techniques in massive MIMO.

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1.4 Literature review

Various studies have been made in massive MIMO technologies, to investigate the performance
analysis of energy efficiency for 5G communication network systems. From those various
researches, the following are reviewed based on proposed results and existing challenges.

The first breakthrough to massive MU-MIMO downlink TDD systems with linear Precoding and
downlink pilots was made by Thomas Marzetta, et al [8]. This reference considers an efficient
channel estimation scheme to acquire channel state information (CSI) at each user, called beam
forming training scheme. With the beam forming training schemes the base station precoders, the
pilot sequences are forward to all users. Then, based on the received pilots, each user uses
minimum mean square error channel estimation to estimate the effective channel gains. Then
they drive a lower bound on the capacity for maximum ratio transmission and zero forcing
precoding techniques to evaluate the spectral efficiency taking into account the spectral
efficiency loss associated with the transmission of the downlink pilots. They also hinted for the
potential benefit of massive MIMO for 5G wireless communication systems but not considering
the maximum data rate (R).
Because of its advantage over convectional point-to-point communications as discussed, the
massive MIMO concept has gained great attention in recent research. E. Bjornson and E. G.
Larsson [3] investigate the optimal energy efficiency, achieved for a particular ratio of transmit
power (Pt) and bandwidth (B), which typically corresponds to a low SNR. It depends strongly on
which parameter value can be selected in practice and the energy consumption modeling. If it is
modeled to capture the most essential hardware characteristics, then any data rate can be
achieved by jointly increasing transmit power and bandwidth while keeping the optimal ratio.
However, this work is concerned only with bandwidth and transmits power to maximize energy
efficiency in massive MIMO systems.
In [4], Jose Carlos Marinello, Cristiano Ponzio, Taufik Abrao, Stefano Tomasin, compare
the performance of energy efficiency of massive MIMO systems under time-reversal maximum
ratio combination (TR-MRC) and frequency-domain maximum ratio combination (FD-MRC)
receiver’s up-link. have evaluated the total energy efficiency of massive MIMO systems under
frequency-selective fading channels in the presence of pilot contamination. Compared the
conventional FD-MRC receiver operating under OFDM versus the TR-MRC receiver operating
under single carrier (SC) wave-form. The total energy efficiency metric on the basis of its

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comprehensiveness and the ability to incorporate several different aspects in a unified analysis.
The results demonstrated the superiority of the FD-MRC receiver under OFDM waveform in
terms of total energy efficiency. Despite the higher sum rates achieved by the TR-MRC/SC, and
the lower power expenditures related to the transmitted signal and power amplifier (PA), the
higher computational complexity required to run the TR-MRC processing makes the total energy
efficiency of this scheme lower than that achieved by the FD-MRC under OFDM. However, this
complexity is highly dependent on the length of the channel impulse response (CIR) such that if
a shorter cell size is considered, the TR-MRC/SC becomes a better alternative in terms of total
energy efficiency. Besides, the power required to run the detection algorithms decrease if the
computational efficiency of the available pieces of equipment increases. The analysis has
indicated that a 30% increase in the computational efficiency makes the TR-MRC/SC scheme
more efficient than the FD-MRC/OFDM but not considering maximum throughput with energy
consumptions.
In [5] the authors show the performance massive MIMO can potentially achieve a higher area
throughput than current networks while providing substantial average transmit power (ATP)
savings. The transmit power can be gradually reduced with the number of antennas while
approaching a non-zero asymptotic spectral efficiency (SE).Therefore, massive MIMO networks
reduce the transmit power required to achieve a given spectral efficiency (SE).While increasing
the number of antennas has always a positive effect on the spectral efficiency, the energy
efficiency (EE) first increases with M number of antennas, due to the improved spectral
efficiency (SE), and then decreases with M number of antennas, due to the additional hardware
that increases the circuit power (CP).The energy efficiency (EE) of a cellular network, defined as
the number of bits that can be reliably transmitted per unit of energy (measured in bit/Joule), is a
good performance metric to balance the throughput and consumed power. Substantial spectral
efficiency (SE) gains are achieved by multiplexing K number of user equipment’s (UEs) per cell,
if a proportional number of antennas M are used to counteract the increased interference. A
similar result cannot be achieved for the energy efficiency since adding more antennas increases
the spectral efficiency but also the circuit power (CP) of the network. This means that the energy
efficiency (EE) attains its maximum at a finite value of the antenna user equipment’s (UE) ratio
M/K. Multi cell minimum mean square error (M-MMSE) Precoding technique provides higher
energy efficiency for any throughput value, only when more energy efficient hardware is used.

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However, this work is concerned with improving the energy efficiency optimal value
44Mbit/Joule by reducing the total power consumption (PC) per base station (BS).
The work in [6] shows optimal design of energy-efficient multi-user MIMO systems. The
results show that energy-efficient systems are, therefore, not operating in the low SNR regime,
but in a regime where proper interference-suppressing processing (ZF or MMSE) is highly
preferable over interference ignoring MRC/MRT processing. The radiated power per antenna is,
however, decreasing with more value number of antennas (M), and the numerical results show
that it in the range of 10-100mW. This specifies that massive MIMO can be built using low
power consumption concerning transceiver equipment at the base station instead of conventional
industry-grade high power equipment.
The authors in [7] the impact of nonlinear amplifiers is investigated on the energy efficiency of
massive MIMO along with calculation of optimal parameters by using the proposed alternative
algorithm under both the perfect and imperfect channel conditions at different circuit power
consumptions. Contrary to the existing work, a realistic circuit power consumption model that
shows the dependence of circuit power consumption on the number of transmitters and users.
They have seen that when the channel conditions are not perfectly known, then the system needs
to transmit more power in order to overcome the negative effects of imperfect channel situations,
and, owing to more transmitted power amplifier (PA), the energy efficiency gets reduced as
compared to the situation when the channel is perfectly known. Numerical results do not change
much for a small change in the circuit power consumption but can otherwise change drastically.
The alternative algorithm that they have used for joint calculation of optimal parameters works
efficiently and converges quickly. The result shows that when the power amplifiers are working
at higher efficiency, then the energy efficiency of massive MIMO also is increased, while it is
better to have large cell coverage in the case of massive MIMO along with less circuit power
consumptions. In future, circuit power consumptions will be reduced, resulting in further
improved energy efficiency with less transmitted power, together with improved and simpler
signal processing. The combination of energy efficient massive MIMO along with nonlinear
amplifiers can be a fascinating option for low-cost future wireless communication systems.

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1.5 Methodology
In the first stage of the research, a literature review of past and current works on the range of 5G
MIMO, and massive MIMO networks will properly be conducted to extend awareness of such
areas of study. Following the review, the execution starts by focusing on the energy efficiency
performance and, on parameters compromising the performance of wireless networks.
System modelling and simulation: this includes system modelling of massive MIMO
performance, specifying design parameters, analysis of mathematical circuit power consumption
per user, defining total energy efficiency, and simulation of the main performance parameters to
understand their effect on energy efficiency maximization of the system using MATLAB.
Result comparison: This includes performance analysis of energy efficiency used, precoding
techniques, in the compromise analysis, linear Precoding and the effect of choosing a number of
design parameters in total performance energy efficiency (EE).
Result and recommendation: the result obtained and analysed from the simulation analysis is
studied and final conclusion and recommendation is drown.
1.6 Main thesis contributions
Due to technological development as well as the increasing network coverage area arising from
wireless telecommunication service demand, energy consumption is one of the most challenging
tasks in the telecommunication industry. Therefore, unique attention is given to reducing energy
consumption and improving energy efficiency with data rate (throughput) in massive MIMO for
5G wireless communication networks. Maximizing the energy efficiency and throughput in
massive MIMO using a knowledge of channel state information (CSI) linear Precoding
techniques such as: (M-MMSE, ZF/RZF, and, MRC), In the final study simulation, energy
efficiency was greater than the energy consumption, in massive MIMO for 5G wireless
communication networks.
All the literature reviewed [3], [4] [5], [6], and [7], suggest that, to energy efficiency
improvement through pre-coding techniques is achieved by reducing the total power
consumption per base station (Bs), in massive MIMO systems. These not concerned with
improving energy efficiency by reducing the power consumption per active user equipment.
Design and analysis of energy efficiency with an increase in the number of antennas (M) in the
base station and active user equipment (K) considered. It also, compares the best pre-coding

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techniques, less power consumption to maximum energy efficiency (EE) in massive MIMO 5G
wireless communication systems.
1.7 Limitation of the thesis
The research would present the performance analysis of energy efficiency ensuring techniques to
keep quality of service (QoS) by using different Precoding techniques in massive MIMO. There
will be a costly expense in the design and deployment of the base station array antennas. Massive
MIMO antenna designs are more complex and require more effort and time during the assembly
line compared to traditional antenna designs. The energy efficiency can be increased, with
increasing data rate but decreasing power consumption. Also, can be improved the energy
efficiency through decreasing the data rate and reducing total power consumption (Pc).
In massive MIMO, the base station is equipped with a large number of antennas, which require a
significant amount of power to operate. This can lead to higher energy consumption, which can
be a concern for network operators looking to reduce their carbon footprint. Finally, the
deployment of massive MIMO for 5G requires careful planning and optimization to maximize its
benefits. For example, the optimal number of antennas and their configuration must be carefully
selected to ensure that the network operates efficiently. Another method for future improved
energy efficiency may be through adding more hardware in base stations (Bs) this will be a
resource tradeoff that remains in conflict. If not deployed properly, the energy efficiency benefits
of massive MIMO may not be fully realized.
1.8 Thesis structure
Chapter-1 Introduction: This Chapter starts with an introduction and is then followed by
literature reviews, research objective, main contribution, and methodology of the thesis.
Chapters 2 and 3 present the theoretical fundamentals of massive MIMO, and energy efficiency
to get the required general knowledge and presents the massive MIMO throughputs,
configuration, supporting standards of energy efficiency (EE) coverage area analysis,
Chapter 4 presents the performance of energy efficiency and details simulation analysis results
with discussion studies.
In Chapter-5 this work is finalized by drawing the main conclusions and recommendations for
future works and references.

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Chapter 2

The theoretical background of energy efficiency in massive MIMO for 5G

cellular communication networks

2.1 Introduction

Wireless communication depends on the radio spectrum, implying that electromagnetic waves
(EM) are intended to convey data from a transmitter to one or numerous receivers. Since the EM
waves propagate in all potential ways from the transmitter, the signal energy spreads out and less
energy arrives at an ideal recipient as the distance increases. To convey remote administrations
with sufficiently high signal energy over wide inclusion regions, an analysis at Bell Labs
proposed in 1947 that phone network geography is required [5]. As indicated by this thought, the
inclusion zone is partitioned into cells that work independently utilizing a fixed-area base station
(BS); that is, a bit of organization equipment that encourages remote correspondence between a
device and the organization. A cell network comprises a bunch of base stations (BSs) and a
bunch of user equipment (UEs). A piece of user equipment (UE) is associated with one of the
base stations (BSs), which offers support to it. The downlink (DL) indicates signals sent from the
BSs to their individual active user (AUs), while the up-link (UL) indicates transmissions from
the user equipment (UEs) to their particular base station (BS).

Figure2.1 cell organization, every base station (BS) covers a distinct geographical area [5].

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It provides service to all active user equipment (UE) in it [5]. The region is known as a "cell" and
it is outlined with a distinctive shade. The phone may comprise all geographic areas where this
base station (BS) gives the most grounded downlink (DL) signal region.

Throughput [bit/s/km2] = B [Hz]*D [cells/km2] * SE [bit/s/Hz/cell] where B is the data transfer

capacity or bandwidth, D is the normal cell density, and SE is the spectral efficiency per cell.
2.2 Definition of spectral efficiency (SE)

Presently a definition of spectral efficiency (SE) to a correspondence channel with a transmission

capacity of megahertz (MHz) Nyquist-Shannon examining hypothesis implies that the band-
restricted correspondence signal that is sent over this channel is controlled by 2B(bandwidth)
real-valued esteemed equivalent divided samples every Second. While considering the complex-
baseband description of the signal, B complex-esteemed examples every second is the more
normal amount. These B tests are the levels of opportunity accessible for planning the
correspondence signal. Spectral efficiency (SE) is the measure of data that can be transmitted
dependably per complex-esteemed instance [5].

Channel
Noise n
response
Input Output
h
X +
y
A discrete memory-less channel with input x and output y = hx + n,
Where h is the channel response and n are an independent Gaussian noise.
If h, is deterministic, then the channel capacity is given:

C= ] …………………………………………... (2-1)
and it is achieved by the input distribution x ∼ NC (0, p). If h is a realization of a random
variable h that is independent of the desired signal and noise. The data streams function as
independent single input single output (SISO) links as under favorable channel conditions are
shown in figure 2.2, and can linearly increase the spectral efficiency with the number of
terminals served [38]. However, the benefit of spatial multiplexing regarding spectral efficiency
critically depends on the array size and accuracy of channel states at the base station (BS).

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Figure2.2 Multi user MIMO [38]

2.3Massive-MIMO

A massive multiple-input-multiple-output (MIMO) network is a multi-carrier cell network with

L cells that work standing to a simultaneous time division duplex (TDD) convention. An
equipped base station (BSj) with several antennas (Mj) receiving to accomplish channel
hardening. The base station (BSj) communicates with Kj (user) single-reception antennas user
equipment’s (UEs) all while on each time/frequency sample, with receiving antenna per user
equipment (UE), proportion to several antennas to the number of a user (Mj/Kj) > 1. Every base
station (BS) works exclusively and measures its signal utilizing direct get consolidating and
straight communicates pre-coding. A given channel response includes, a coherence block
channel with various active sub-carriers and time tests can be approximated as steady and flat-
fading. If the coherence bandwidth is defined as: BC and the coherence time is Tc, at that point,
every rationality block contains τc = BcTc complex-esteemed examples [5].

Frequency
Coherence block TC
UL data and
pilot DL data Bc

Time

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The time division duplex (TDD) multi-carrier modulation system of a canonical massive-MIMO network.
Each channel time-invariant and frequency flat is divided into coherence blocks in time-frequency
processing.
2.4Analysis Pre-coding design: up-link-down-link duality
The pre-coding vectors were because each user equipment (UE) is affected by the pre-coding
vectors in the wireless networks and network-wide pre-coding optimization is highly impractical.
Through this, the pre-coding procedure technique could balance self-directing and signals
towards the active user (AU) and altruistically avoid causing interference to other user
equipment (UEs) [5, 7]. The trouble is to find the right balance between these two goals,
particularly when many active users are involved. It is accordingly, desirable to have a sensible
controllable, design principle for pre-coding. Many heuristic pre-coding design principles can be
found in the literature, but the well-designed ones are usually rather similar and strongly
connected to a fundamental property called uplink-downlink (UL-DL) duality. Duality describes
simplicity and how it can guide the pre-coding processing [5], there is a strong connection and an
expression between the spectral efficiency (SE) for the uplink-downlink (UL-DL), except for the
diverse system for the transmit powers, the signal terms are similar and the interference terms are
comparable but the indices (j, k) and (i) are interchanged for every user equipment: the power(P)
Precoding P E {| } in the uplink (UL) is replaced by power (P) E{ } in the
downlink (DL). This signifies the fact that the uplink (UL) interference from cell l is received
over user (Kl) different user equipment channels (processed using a single combining vector),
while all the downlink (DL) interference from the cell l is received over the channel from the
base station (Bs) and depends on Kl (user1) pre-coding vectors. From the perspective of user
equipment in the network, the base station cell (BSL) can separate the user equipment well
spatially, while the base station (BSj) cannot (illustrated here as having a small angular
difference between the user equipment’s (UEs). The significance is that the users in cell j are
affected by high interference from the other cell user equipment in the uplink (UL). While the
user equipment in cell l receives high interference from the base station (BSj) in the downlink
(DL). The active (UE) shows very different interference levels in the uplink and downlink. There
is a symmetry that creates a fundamental, connection between the achievable spectral efficiency
(SEs) in uplink (UL) and downlink (DL) despite the differences in how the interference is
generated, which is called the uplink-downlink (UL-DL) duality [5],[18].

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Formula: Let P = [Pt1 . . . Ptl] T with pj = [Pj1 . . . PjKj] T, -------------------------------------- (2-2)

The Ktot × 1 vector with all the up-link given transmitting powers (Ptr) where

Ktot = denotes the total number of user equipment in the network. Consider the uplink (UL)
signal interference noise ratio uplink from the user to the base station ( ) and the

downlink (DL) signal interference noise ratio from the base station to the user ( ) for any
given set of receive combining vectors {v, i} and given power (p) can achieve:

= j = 1. . . L, k = 1. . . Kj --------------------------------------- (2-3)

The Pre-coding vectors will be selected to be:

W jk = where, combine vector ------------------------------------- (2-4)

√

Projected transmission Interfering transmission

Figure 2.3 (a) UL: UE k in cell j is affected by high interference from UEi in cell l [5].

Projected transmission , Interfering transmission

Figure 2.4 (b) DL: UEi in cell l, receives high interference from base station (BSj) [5]

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The above figure illustrates how the interference situation can change between the uplink (UL)
and downlink (DL) [5]. The uplink interference comes from the user equipment, while the
downlink interference is caused by the base station that serves the interfering user equipment
(UE). In this setup, a base station (BSj) cannot separate the two-user equipment (UEs) due to the
similar spatial channel correlation (as a small angular difference), thus its own user equipment is
affected by high uplink. The interference and the other-cell user equipment will get high
downlink interference. In contrast, a base station (BSL) can separate the user equipment well,
which leads to little interference in both uplink and downlink [5], [7]. The simple two-cell
Wyner network model shows that a power consumption (PC) model accounting for the transmit
power as well as for the circuit power consumed by the transceiver hardware at the base station
(BSj) and user equipment’s (UEs) is essential to avoid misleading conclusions about energy
efficiency (EE). This is not the only involvement that must be taken into account to properly
evaluate the circuit power (CP) of the uplink and downlink of massive multiple input multiple
outputs (MIMO). Also, it will be considering the power consumed by digital signal processing,
back-haul signaling, encoding, and decoding of a circuit power (CP) model for a generic base
station (BSj) in massive MIMO wireless networks.

CPj = + + + + ------------------------------------------------------ (2-5)

And, = + + ---------------------------------------------------------------- (2-6)

Where CP accounts for the power consumption of the transceiver chain is the power of the
BS components attached to each antenna, is the power of all receiver components of each
antenna user equipment (UE), and a signal oscillator with power is used for all BS
antennas. is fix power in the base station, is power transceiver chain, is channel
estimated power, is coding decoding power and is power for linear processing.

PCE = ---------------------------------------------------------------------------- (2-7)

Denotes power for the channel estimation process which is performed once per coherence block.
Where PFIX = Fixed power,

PCD = BN ( + ) ----------------------------------------------------------------- (2-8)

It is the power required for codding and decoding per symbol.

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PLP = B ( ) + + ------------------------------------------------------- (2-9)

Represents the power for linear processing (PLP). Where and are the computational
complexity that measures the arithmetic complex-valued operation at the base station (BS) and
user equipment’s (UE) respectively [5], [8].

2.5 Time division duplex system protocol (TDD)

User-centric cluster and uniform user distribution where the coherence blocks and the channel is
under uncorrelated Rayleigh flat fading network areas are considered to have a greater number of
active users (AU). Perfect channel state information at the receiver side and the model
parameters are M, K, R, A, and D. Where M is the number of antennas, K is the number of users,
R is data rate, A is coverage area and D is cell density of the system. The main persistence of this
paper is to analyze the physical area coverage energy efficiency and limits in a few different
cases, particularly, to give simulation results in relevant techniques on the maximum possible
energy efficiency. The ultimate limit of energy efficiency (EE) in the channels is deterministic
and the consequence of this assumption is that perfect channel state information (CSI) is
available everywhere (it is estimated to any accuracy with a negligible overhead). The capacity
of a fading channel can be upper bounded by a deterministic channel having the channel
realization from the fading distribution that maximizes the mutual information will be considered
[9]

Base station Mobile station

Figure 2.5 Proposed system models for massive MIMO [10]

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A large number of antennas in the panel base station would be connected to the active number of
users of both downlink (DL) and up-link (UL) information exchanges. Consider the up-link
Rayleigh fading channel:

hk = [hk1, hk2….hkm]T ~ CN(0,Im) --------------------------------------------------------(2-10)

Noise: n~ CN (0, Im), received signal y = + 𝑆 +n ------------------------------ (2-11)

Maximum ratio filters linear detection:

v = ∗ ----------------------------------------------------------------------------- (2-12)

v = ∗ n]. ------------------------------------------------ (2-13)

As the number of antennas (M) tends to infinity (∞) then the received signal is

S1 + 0 + 0 ------------------------------------------------------------ (2-14)
Where s S1 the required received signal and converges to zero at the number of
antennas (M) tend to infinity (∞) in the identity matrix principle for interference-free
communication with many numbers of antennas in massive MIMO systems.

2.6 Performance analysis of energy and spectral efficiency

2.6.1 Definition of energy efficiency with spectral efficiency

Energy efficiency refers to the ability of a device or system to perform its functions using the
least amount of energy possible. Spectral efficiency, on the other hand, refers to the ability of a
communication system to transmit the maximum amount of data using the least amount of
bandwidth possible. Combing energy efficiency with spectral efficiency means designing
communication systems that are optimized to transmit data using the least amount of energy and
bandwidth possible, thus reducing the overall, energy consumption the system.
This section can analyze the energy efficiency (EE) of massive MIMO based on realistic power
consumption (PC). Power consumption is a major concern for future cellular networks. Also,
massive MIMO can potentially improve the area throughput while providing substantial power
savings [5].

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EE = -----------------------------------(2-15)

Where M is the number of antennas, K is the number of users, R is throughput and A is cell area

For conventional academic approaches analysis

Maximize throughput with fixed power and minimize transmit power for fixed throughput.

Data throughput = ∗ 𝑆 ------------------------------ (2-16)

n
K-Multi-Users ( ) Data rate per user

Where, SINR is (signal interference noise ratio) given below equations:

SINR = -------------------------- (2-17)

( ) ( ) ( )

Power consumption = Fixed circuit power Signal processing

⁄
K ) + C0, 0 +C0, 1M +C1, 0K+C1, 1MK+A*Data throughput------- (2-18)

Transmit power per amplifier power per transceiver chain Coding/decoding/back-haul [7].

Select Pre-coding technique analysis in massive MIMO system

The same rate = _𝑘 for all users

“Optimal” Pre-coding: extensive computations not efficient then:

Matrix form: 𝐕 = [𝐯1…,], 𝐇 = [𝐡1…,] ----------------------------------------------------- (2-19)

Power allocation: P1…, from the heuristic closed-form pre-coding analysis

the maximum ratio combination (MRC): "v𝑘=√ (𝑃𝑘 h 𝑘) ---------------------------------------- (2-20)

For maximizing signal at the receiving side user equipment’s (UE).

Zero-forcing (ZF) pre-coding: 𝐕=𝐇 (𝐇𝐻 𝐇)-1 diag (𝑃1…, 𝑃 ) for minimizing interference---- (2-21)

Regularized ZF (RZF) pre-coding: 𝐕=𝐇 (𝜎2 𝐈+𝐇𝐻 𝐇) −1) diag (𝑃1… 𝑃 ) -------------------- (2-22)

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For balance signal and interference in massive MIMO systems [7].

2.6.2 Mathematical equations

E = 0 ---------------------------------------------------------------------------------------- (2-23)

Where; e = ̃ -x = Gy-x

E = 0 -------------------------------------------------------------------------------- (2-24)

E = 0 --------------------------------------------------------------------------------- (2-25)

E = 0 ------------------------------------------------------------------------------ (2-26)

GE = 0 ------------------------------------------------------------------------------ (2-27)

G=E -------------------------------------------------------------------------------- (2-28)

by expand the expectation E {} value to get power transmitted signal scalar.
E =E n n ------------------------------------------------------------------- (2-29)
E n n ----------------------------------------------------------------------(2-30)
E n n nn ----------------------------------------------------------------(2-31)
E nn ------------------------------------------------------------------------------------(2-32)
HE nn ---------------------------------------------------------------------------- (2-33)

Power transmitted signal (a scalar) can determine the transmission power but would not be able
to know the exact noise value added to each received signal data, but it can in long-term
statistical properties of the noise.

= n ----------------------------------------------------------------- (2-34)

n = n }, n = 0 ------------------------------- (2-35)

= which is the Power of transmitted signal

Finally, the operator matrix [G] of gain of energy consumption follows:

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And H

G=E -------------------------------------------------------------------- (2-36)

= ----------------------------------------------------------- (2-37)

= ------------------------------------------------------------------ (2-38)

Mathematically divide the energy power consumption (PC) to get the gain matrix [G].

G= --------------------------------------------------------------------- (2-39)

Where H, indicates a matrix that includes the property of pre-coding and amplification
mathematically the H is expressed as ‘Amp*H*P’, Amp amplification, H is the channel matrix
over the air and P is power of the pre-coding matrix [11], [31].

Figure2.6 comparison of Precoding techniques and reducing interference in massive MIMO [12]

Precoding technique for Uplink with L cells in massive MIMO system for 5G networks.

=[ ] channels to base station (BSj) from the user equipment’s (UE) in cell

coverage area L.

Matched filter: Vj = ---------------------------------------------------------------------------- (2-40)

Regularized zero forcing: Vj = -------------------------------------------- (2-41)

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MMSE processing: Vj = ]( ] H + I)-1 ---------------------- (2-42) [12].

2.6.3 Minimum mean square error (MMSE) in massive MIMO

A system model that minimizes the MSE (mean square error) of the received data with the
channel model [27].

y = Hx+n ------------------------------------------------------------------------------------------ (2-43)

The pre-coding technique of multi-cell-minimum-mean square error (MMSE) as an equalizer is a

kind of post-processing algorithm, the received data that is as close to the original data
(transmitted data) with matrix G (operator matrix) as the inverse of channel matrix ( ̂ )
assume that no noise.

n Gy E 𝑆

X y ̃ e
H + G e
y = Hx+n e = ̃ -x = Gy-x

Figure2.7 Block diagram MMSE

Where x is the desired received signal, H is the channel matrix, n is noise, G is the operator
matrix which is to minimize mean square error (MSE) and e is the error. The above block
diagram indicates a specific condition where there is no correlation between the received data
vector and the error vector.

N x N Matrix

Nx1 1xN

E =0 or E =0

The received signal the estimated error

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Overall, MMSE in massive MIMO for 5G network is a powerful technique for improving the
quality of received signals by reducing interference and noise, which enables more efficient use
of the available spectrum and higher data rates.

2.7 Performance analysis of antenna schemes

I. Multiple antennas value: In the system cases both, through that the communication takes
place over a given bandwidth of B in Hz, the total transmit power (Pt) is denoted by P in W, and

the noise power spectral density BNo in . Treat B and P as design variables [3].

II. Single-antenna systems without interference

Begin by considering a single-antenna system; the channel is represented by a scalar coefficient

of h ᶓ C. The receiving desired signal y ᶓ C is given by y = hx + n where x ᶓ C is the transmit
signal with power P and n = NC (0, BNo) is AWGN. Perfect CSI is available, the capacity value
of the channel is:

C = B log2 1 + [bit/s] -------------------------------------------------------- (2-44)

Where = |h|2 denotes the channel gain. The capacity value is achieved by x~ NC (0, P). When
the transmit power is the only factor contributing to the energy consumption, an upper bound on
the area coverage energy efficiency (EE) is:

B log2 --------------------------------------------------------------------(2-45)

It increases a monotonically function concerning Hence, the energy efficiency (EE) is

maximum as → 0, which can be achieved by taking the transmit power P→ 0, taking the
bandwidth B →∞ or combination theorem. The limit is easy to compute by considering a Taylor
expansion of the logarithm around = 0,
Blog2 (1+ )= ( ) -∑ n n ------------------------------ (2-46)

→ Log2 (e) as →0 ---------------------------------------------------------- (2-47)

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Where e means Euler's, number recognizes this as the proportional of the traditional least energy-

per-chomped = Noln2 for an AWGN channel [3], [4], with the only difference that a

deterministic channel gain bandwidth (B) has been included. To quantify the energy efficiency
(EE) coverage area that can be achieved in this case, use the typical noise power spectral density
BNo = -174 dBm/Hz at room temperature and consider a range of channel gains B from -110 dB
to -60 dB. The subsequent energy efficiency inclusion zone has appeared.

.
Figure 2.8 Max EE coverage area in a single-antenna system depends on the channel gainβ [3].
The propagation distances which computed for free-space propagation at 3 GHz, with lossless
isotropic antennas, while the distances are often much shorter in the practice analysis in massive
MIMO systems [3].

III. Constant circuit power performance analysis

For practical analysis of the energy consumption model P + μ where μ ≥ 0 is the circuit power
the power dissipated in the analog and digital circuitry of the transceivers. When the
communications a given long-distance, it is common to have P + μ ≈ P, but in future smalls cells
it is possible that μ > P In the case of a single-antenna value without interference, the energy
efficiency (EE) with cell coverage area can be generalized, and upper bounded given as

EE = ≤(a) ≤(b) --------------------------(2-48)

The energy efficiency coverage area is an increasing function with bandwidth (B) and letting B
→ 1, it indicates that from letting transmit power (P) →1. With additional way to view that
transmit power and bandwidth are going jointly to infinity, but the bandwidth has a significantly

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higher convergence speed such that →0. Where the upper bound, is the same as in the presence

of the circuit power value μ did not change the coverage cell area energy efficiency limit, but
only made the conditions for achieving it stricter and more applied analysis. The value of μ was
not purposely removed in the bounding but, it can be made negligible by taking the transmit
power (P) →∞. The large MIMO: Some Known Facts (Notation: M antennas, K terminals,
power per terminal (P) linear processing (MRC/MRT, ZF ...) nearly optimal as M ≫K ≫1, P
and M “large enough” ⇒ pilot contamination limits performance [27].

Figure 2.9 pilot contamination limit performance [27]

Scaling down P with M ⇒ noise will limit performance. Perfect CSI and optimal processing ⇒ P

can be scaled as . Given linear processing and imperfect CSI, in a multi user (MU) system, P
√

can be scaled as .

2.8 multi-cell minimum mean square errors (M-MMSE)

Multi-cell minimum mean square error(M-MMSE) is a signal processing technique used in
massive MIMO to improve the performance of energy efficiency in wireless communication
networks. Multi-cell minimum mean square error in massive MIMO is that it can mitigate the
inter – cell - interference (ICS) caused by the transmission of signals from multiple cells to the
same users. Multi cell minimum mean square error works by estimating the channel between the
transmitter and the receiver for each user and then using this information to cancel out the
interference caused by signals from other cell.

Each received signal at the BSj during the up-link payload data transmission phase is each
received signal at the base station (BSj) [13].

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During the up-link payload, data transmission phase is given

Yj = ∑ ∑ √ n ---------------------------------------------------- (2-49)

Where the symbol, xlk ~ CN (0, 1) is the value transmitted signal from a Gaussian code book and
2
nj ~ CN (0, IM) is additive white Gaussian noise (AWGN). is a transmitted power of the
payload data from user (K) in cell L. The linear decoder used by base station (BSj) for arbitrarily
user K in its cell as gjk then the estimate ̂ k of the signal xjk is given:

̂ k = gHjk yj = gHjk∑ ∑ √ gHjkn ----------------------------------- (2-50)

With the following up-link ergodic spectral efficiency (SE) can be achieved

= (1- E { ̇ ( j )} {log2 (1+ )}, --------------------------------------------(2-51)

Where the SINR is given below

̂
= ̂ ∑
------------------ (2-52)
| |̂

( ̂ ̂ )
= ̂ ̂
---------------------- (2-53)
[ ∑ ]

and { ̇ ( j )} is the expectation with respect to the channel estimates known at base station (BSj).

gHjk ́ jjk as the true channel in the decoding and treating interference and channel uncertainty as
worst-case uncorrelated Gaussian noise [13].

= the lower bound on the up-link ergodic capacity. Consequently, a new multi-cell-MMSE
detector that is signal interference noise ratio (SINR) in [13] for a given channel estimate can
derived as:

= ∑ ∑ ̂́ j k ̂ H j k +Cj k) + 2IM)-1 ̂́ jjk ---------------------- (2-54)

This detector minimizes the mean square error in the estimating xjk.

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E{|̂ |2| ̂ (j)}. ---------------------------------------------- (2-55)

The estimation error covariance matrix can be expressed as followed:

= ( ) ------------------------------------------- (2-56)

It allows the channel estimated is formulated as:

̂ j k= √ dj (Z ) ̂ ́ ----------------------------------------- (2-57)

Where the symbol, ei is denotes the ith column of the identity matrix IB.

By substituting the above equation, the M-MMSE detector can be expressed as:

= ̂ ̂ ( 2
+ IM)-1 ́ jjk -------------------------------------- (2-58)

Where =∑ ∑ is a diagonal matrix

and ith diagonal element depends on the large-scale fading, the pilot power and payload power
of the users that use the ith pilot sequence in The scalar is given:

=∑ ∑ --------------------- ------ (2-59)

Where is defined as estimation error [13].

= ------------------------------------ (2-60)
∑ ∑

α ικ
And is the covariance matrix

Overall, multi cell minimum mean square error is an effective technique for improving the
performance energy efficiency of massive MIMO for 5G systems by mitigating the effects of
inters cell interference and improving the system capacity

2.9 Single-cell minimum mean square error (S-MMSE)

A single-cell minimum mean square error can be defined [13].

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= ∑ ̂ ̂ 2
IM)-1 ̂ ----------------------------------------- (2-61)

The inter-cell interference is either ignored by setting Zj = 0 or only considered statistically with:

Zj = E { ∑ ̂ ̂ ∑ ∑ ----------------------- (2-62)

A single cell minimum mean square error (S-MMSE) pre-coding detector only utilizes the user
(K) estimated channel directions from within the serving cell and treats directions from other
cells as uncorrelated noise. The minimum means square error (M-MMSE) detector, however,
utilizes all the bandwidth (B) available estimated directions in the channel estimation Precoding (
̂ ) so that base station can be (BSj) actively suppress all parts of inter-cell interference where
bandwidth (B) user (K). Therefore, this can maximize the signal interference noise ratio
(SINR) while a single cell minimum mean square error can be in single-cell cases [13].

2.9.1 Down-link multi-cell minimum mean square error (M-MMSE)

During the down-link payload data transmission, the received desired signal at the user (K) in the
cell j is given:

=∑ ∑ √ s +n ---------------------------------- (2-63)

Where is the pre-coder used by base station (Bs ) for user m in its cell, 𝑆 ~
is the payload data symbol for user m in cell , is the corresponding down-link
transmit power and ~ 𝜎 is AWGN. The multi cell minimum mean square error
(M-MMSE) is the state-of-the-art up-link scheme the down-link [5], multi-cell minimum mean
square error (M-MMSE) pre-coder is constructed equation given as:

= ---------------------------------------------------------------------- (2-64)
√

Where = ‖ ‖ 2} is normalizes the average transmit power for the user (k) in cell j

to {||√ s ||2} = .Thus, the users do not know their instantaneous channel
realization. However, they can learn their average equivalent channels are given, √

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{ }, and the total interference variance. Then the desired received signal ( is written
as:

=√ { }s + ∑ ∑ √ s -√ { }s + n .
------------- (2-65)

Then a down-link spectral efficiency (SE) is given that:

= = (1- ) ) ------------------------------------------------------------------ (2-66).

2.9.2 Improving energy efficiency and decreasing loss in Massive-MIMO

The cell coverage area energy efficiency can be optimized in massive MIMO systems with
common energy efficiency (EE) definition is the ratio of the spectral efficiency (bit/channel use)
to the emitted power (Joule/channel use) [14]. It has been recently shown that the array gain
value in massive MIMO systems can be utilized to reduce the emitted energy for systems with
ideal design analysis for systems phase noise from free-running oscillators. Further specifically,
this prior work shows that one, it can reduce the transmit power consumption (Pt) as , for 0 < t

< , and still achieve non-zero spectral efficiencies (SE) as N →∞1. By following this power

scaling law, as N → 1 because the numerator has a non-zero limit and the denominator goes to
zero as 1/Nt.
Though the property specifies that massive MIMO systems can be very energy efficient, the un-
boundless also shows that the conventional energy efficiency (EE) metric desires to be revised
that applied to massive MIMO systems. Consider a refined metric of overall energy efficiency
based on prior work and use it to analyze the overall energy efficiency analysis technique of
massive MIMO systems [14]. Under the Time division duplex (TDD) protocol, the energy
consumption in the amplifiers of the transmitters (per coherence period) is given by:

Eamp = + [Joule], ---------------------------------------- (2-67)

Where the parameters ώBS, ώUE ε [0, 1] are the efficiencies of the power amplifiers at the BS, and
user equipment’s (UE), respectively. The average power (Joule/channel use) can be separated as:

= βDL ( * +( * )+ * ) --------------------------------------(2-68)

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For down-link power

+ βUL (TDLpilot/Tcoh *PBS /ωBS + TULpilot/Tcoh*PUE/ωBs) + TULdata/Tcoh* PUE /ωUE ---------------------(2-69)
For Up-link power
Where, the ratio of downlink (DL) and uplink (UL) transmission respectively follow as:

βDL= --------------------------------------------- ----------- (2-70)

βUL = --------------------------------------------------------- (2-71)

In addition to the power consumption by the amplifiers, generally a baseband circuit power
consumption which modeled as Nρ + ᶘ. Where the parameter value ρ ≥0 [Joule/channel use]
describes the circuit power (cp) that scales with the number of antennas(M), design components
that are needed at each antenna branch (converters, mixers, and filters) computational complexity
that is relative to the N (channel estimation and computing maximum ratio transceiver/maximum
ratio combination (MRT/MRC).In contrast, parameter ᶘ > 0 [Joule/channel use] is a static circuit
power term that is independent of N (but might scale with the number of active users (UEs)), the
model's baseband processing at the base station (BS), and circuit power (Pc) at the active user
equipment’s (UE). Based on the power consumption (Pc) model defined above, and inspired by
the seminal work in [14], define the overall energy efficiency (bit/Joule/cell area) as follows.
Down-link energy efficiency (EE) coverage area:
EEDL Area = CDL (2-72)
βDL (TDLpilot/Tcoh*PBS/ωBS + TULpilot/Tcoh*PUE/ωBs +Np+∫) + TDLpilot/Tcoh *PBS /ωBS
Up-link link energy efficiency (EE) coverage area:
EEUL Area = CUL (2-73)
βUL (TDLpilot/Tcoh*PBS/ωBS + TULpilot/Tcoh*PUE/ωBs +Np+∫) + TULpilot/Tcoh *PUE /ωUE
The energy efficiency (EE), the coverage cell area of the transmission power system is found by
replacing the capacities CDL and CUL with the achievable value spectral efficiency (SE). Which
define by considering a single link, which can be any of the links in a massive-MIMO system the
parameters ᶘ and ρ should then be taken as the energy per channel use per user. Extend the
power scaling laws to general system models with non-ideal design analysis. The down-link
(DL) transmit power base station (PBS) and up-link (UL) pilot power user equipment’s(pUE) are
reduced with N equivalently to:

LimN →∞ CDL ≥ log2 1+ ----------------------------------------- (2-74)

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Similarly, suppose the up-links transmit/pilot power (pUE) is reduced with N proportionally to
1/NtUE. If 0 < tUE < ½.

LimN →∞ CUL ≥ log2 1+ --------------------------------------------------- (2-75)

Then it decreases the down-link and up-link transmit powers as N grows large (roughly
proportionally to ( ) and converges cell area to non-zero spectral efficiencies (SE). The
√

asymptotic downlink (DL) capacity is lower bounded by the uplink (UL) capacity. These lower
bounds only depend on the levels of impairments analysis at the user equipment’s (UE).
Therefore, the interfering transmissions might have to reduce their transmit powers as well if
their impact should disappear asymptotically [14].
The lower bounds are achieved through the minimum mean square error (MMSE) estimator for
channel estimation and simple linear processing at the base station (BS), approximate maximum
ratio transmission (MRT) in the downlink (DL), and maximum ratio combination (MRC) in the
(UL). The upper capacity defines how to maximize the energy efficiency (EE) coverage area. To
maximize the energy efficiency of coverage metrics concerning the transmit power (Pt) and the
number of antennas [14].
Let E {IHUE} = 0 and E {||QH||} 2= 0. If ρ = 0, ------------------------------------------------------ (2-76)
The maximal energy efficiency can be bounded as:
Where the lower limits are accomplished as N → 1, utilizing the energy scaling law hypothesis.
On the off chance that ρ> 0, the upper limits are as yet legitimate, yet the asymptotic energy
efficiency:
Lim max EEDL = LimN →∞ max EEUL = 0 -------------------------------------------------------- (2-77)
Where, N →∞ PBS, PUE ≥ 0, N →∞ PUE ≥ 0
The lower limits for ρ = 0, are accomplished as depicted; the upper limits follow from dismissing
the sent power term in the denominator and applying the upper limits. On account of ρ > 0, the
energy efficiency is non-zero for N =1 for any non-zero sent power, while the energy efficiency
goes to zero as N →1, Since the denominators of the energy efficiency measurements, develop
and the numerators are limited. This result uncovered that the maximum generally energy
efficiency (EE) is limited, in the massive MIMO system framework [14].

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2.9.3 Multiuser MIMO

The MU-MIMO system where multi-antenna BS serves multiple UE is more practical than
point-to-point MIMO. The main principle of multiuser MIMO is that each BS with multiple
antennas can use the same frequency-time resources to serve a multiplicity of single antenna
terminals that share the multiplexing gain [35]. One can intuitively understand the multiuser
MIMO scenario as if the K-antennas terminal in the point-to-point MIMO was broken up into
multiple autonomous terminals [35]. Cooperation between the antennas of the UE is possible in
the case of the point-to-point MIMO, however, UEs in MU-MIMO cannot communicate with
each other. Although the poor-quality channels can sometimes severely influence the throughput
achieved by individual users, the break up actually improves the sum throughput of the system
[38]. Hence, the impact of the propagation environment on the MU-MIMO system is less than
the case of point-to-point MIMO due to the multi-user diversity. As a result, many
communication standards such as 802.16 (WiMAX), 802.11 (WiFI), and LTE have included
MU-MIMO. The BS usually is equipped with only a few numbers of antennas (i.e., 10 antennas
or less) for most MIMO applications. Thus, only modest improvement is brought to the spectral
efficacy using the MIMO technology so far.

Figure 2.10 Multiusers MIMO [35]

The performance of the MU-MIMO system if the terminals in Figure 2.5 with a single antenna
each, K is served by the BS is better than the case of point-to-point MIMO. Knowing that G is

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the M*K matrix that represents the frequency response between the BS antennas and the K, the
sum capacities of the UL and DL are given by:
CUL = | ----------------------------------------------------- (2-78)

CDL = ------------------------------------------------- (2-79)

∑ 𝑘
Where v = [v1,………. vk]T , is the DL SNR, and is the UL SNR for every terminal. The
total UL transmits the power of multiuser MIMO is greater than the transmit power of the point-
to-point MIMO by a factor of K [35]. Computing the capacity of the DL depends on solving a
convex optimization problem. CSI knowledge is important for both 2-78 and 2-79 in the above
equations. On the UL only the BS is required to know the channel while every terminal must be
separately informed about their permissible transmit rate. On the DL, however, CSI knowledge is
required in the BS and the terminals [35].

2.9.4 The wireless channel

A wireless channel is the air medium through which wireless transmission is performed via
electromagnetic waves [38]. Since there is not restricted to taking a single path, it suffers
reflection, deflection, and scattering, by buildings, hills, bodies, and other objects when traveling
from the transmitter to receiver, hence multiple copies of the signal arrive at the receivers as
shown in the figure below.

Figure 2.11Radio signal propagation [38]

Path loss refers to signal power dissipation in propagation to the distance between transmitter,
and receiver. In the free space, path loss is given be:
L= --------------------------------------------------------------------- (2.80)

Where is the wavelength, is the transmitter antenna gain, Gr is the receiver antenna gain, d is
the distance between the transmitter and receiver.

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Chapter 3

System model of energy efficiency in massive MIMO systems

3.1 Introduction

A massive multiple input multiple outputs (M-MIMO) refers to a system where the base station
communicates with several users simultaneously. The base station and the user can be equipped
with multiple numbers of antennas. The massive MIMO system enables many parallel
communications in the same time and frequency resource known as space division multiple
accesses (SDMA).

Figure 3.1 System model L number of cells [9]

Area energy efficiency (AEE) is the optimization of power consumption of a system, and to be
covered as shown in the system model the multi-cell multi-user in a massive MIMO system is
composed of L hexagonal cells with radius r. Each BS has an ‘M’ number of antennas, and each
cell has a ‘K’ number of users with a single antenna. The full frequency reuse factor of the L,
cells are considered. The reference cell is denoted as a base station (BS1) and the other L − 1 cell
are the interfering cells. The distance between a base station (BS1) and the base station (BS) in
an adjacent cell with the same area, each hexagonal cell is approximated as an equal area circle
with radius R, where R is defined as:

√ √
= n =√ ------------------------------------------------------------ (3-1)

Where R0 denotes the nearby distance from the mobile to BS, and R0 ≪ R. The random user

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location model is used, where the users are assumed to be independently and uniformly
distributed in all of the cells [9].

The system considers a massive MIMO network consisting of cellular cells and each cell is
equipped with base station antennas of M and active users K. the network cells and active users
are assumed uniformly distributed. The work starts with the definition of energy efficiency in
wireless communication, which is defined as the ratio of average data rate(R) to total energy
consumption (PC). In mathematics, it is defined as [5], [7], [9], [11], [18], [20].

The network system is assumed to be circular and uniformly identical multi-user distribution
uncorrelated Rayleigh flat fading. The overall workflow diagram is as follows below.

Start

Literature review EE

Spectral Data rate Power EE max using Precoding

UL/DL amplifier
Ptx +Pcircuit techniques (M-MMSE,
efficiency
ZF/RZF, MRC) and
EE>Pc in massive MIMO
SE=Capacity x Total power
consumption
Bandwidth

EE=Blog2 1+Ptxβ
End
Throughput/Area BNO
Throughput / Ptx+Pcircuit

R
EE =

Figure 3.2 Work flow diagram of energy efficiency in massive MIMO systems

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3.2. Comparison of circuit power (CP) with different Precoding techniques.

At each base station (BS) and K number of user equipment in each number of cells and there is
M number of antennas. The Precoding techniques (multi-cell minimum mean square error,
maximum ratio combination, and regularized zero forcing) as shown in the figure below. The
Transceiver chain requires more power consumption (46.25 dBm). The signal processing needed
for uplink (UL) reception and downlink (DL) data transmission consumes approximately
28.8dBm, while the smallest component is approximately7.27dBm of pre-coding vector
computation [5, 38]. The value circuit power (CP) breakdown is desired by the schemes
processing that is recorded for the channel estimate, computation of receive combining vectors,
back-haul, and encoding/decoding. The power consumption (CP) consumed by intra-cell channel
assessment is approximately 26 dBm) and the handling plan is autonomous. The value circuit
power depends on the framework for the computation of receiving combining vectors and the
highest circuit power (CP) is needed by multi-cell minimum mean square error (M-MMSE), for
which it is approximately 40 dBm (10W). It accounts for the circuit power (CP) needed
according to the power consumption by channel estimation [5].

Figure3.3 Circuit power consumption breakdowns per cell Precoding techniques (M-MMSE,
RZF, and MRC). With K = 20 user equipment, and M = 200 antennas in the base stations (Bs)
[5].

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Figure3.4 circuit power consumption, breakdowns per cell Precoding, techniques such as: (M-
MMSE, RZF, and MRC). With K = 20 user equipment, and M = 200 antennas in the base
stations (Bs) [5].

3.3 Maximization of energy efficiency (EE)

The energy efficiency of a cellular network is the number of bits that can be reliability
transmitted per unit of energy according to the definition of energy efficiency [5], [9], [35]
defined as

⁄ {R } {R }
= =∑ -------------------------------- (3-3)

Which is measured in bit/Joule, and can be seen as, the benefit-cost ratio, where the service
quality (throughput) is, compared with associated costs (power consumption). Hence, it is an
indicator of the network bit-delivery efficiency [5], [9], [35], [38]. The throughput can be,
computed using any of the UL and DL spectral efficiency expressions provided. Which
characterizes the performance of massive MIMO networks operating over large communication
bandwidth unlike the ATP, the EE metric is affected by changes in the numerator and
denominator since both are variable. This, means that some caution is required to avoid
incomplete and potentially misleading conclusions from EE analysis. Particular attention should

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be paid to, accurately model the PC of the network. Assume for example, that the PC only
comprises the transmit power. Lemma showed that the transmit power can be reduced, towards
zero as when M →∞ while approaching a non-zero asymptotic DL SE limit. This implies the EE
would grow without being bound as M →∞. Clearly, this is misleading and comes from the fact
that the transmit power only captures a part of the overall PC. Moreover, we notice that the
transmit power does not represent the effective transmit power (ETP) needed for transmission
since it does not account for the efficiency of the PA. The efficiency of a PA is defined as the
ratio of output power to input power [5], [9], [27], and [35]. Antenna array configuration: the
number of antennas and their arrangement in the array can have a significant impact on the
energy efficiency of massive MIMO system. Power allocation technique: can be used to optimize
the power consumption of the system by allocating the power to the users in an efficient manner.
User scheduling: can be used to select the users that should be served in each time slot, thus
improving the performance of energy efficiency in massive MIMO for 5G network.

3.4 Tradeoff energy and spectral efficiency

The SE of a cell can be increased by, using more transmits power, deploying multiple BS
antennas, or serving multiple UEs per cell. All these approaches inevitably increase the PC of the
network, either directly (by increasing the transmit power) or indirectly (by using more
hardware), and therefore may potentially reduce the EE. However, this is not necessarily the
case. There exist operating conditions under which it is possible to use these techniques to jointly
increase SE and EE. To explore this in more detail, the EE-SE trade-off is studied next and the
impact of different network parameters and operating conditions are investigated [5], [10], and
[39].
For simplicity, we focus on the UL of the two-cell Wyner model (i.e., L = 2) consider only
uncorrelated Rayleigh fading channels over a bandwidth B, under the assumption that the BSs
are equipped with M antennas, have perfect channel knowledge, and use MR combining.

3.5 Impact of Multiple BS Antennas

Assume that there is only one active UE (i.e., K = 1) in cell 0 and that no interfering signals
come from cell1 [5], [21]. An achievable SE of the UE in cell 0 is

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SE0 = = SNR0) ------------------------- (3-4)

where p is the transmit power, 𝜎 is the noise power, and denotes the average channel gain of
the active UE. We have omitted the superscript non line of sight (NLoS), since we do not
consider the LoS case here. To evaluate the impact of M on the EE, we distinguish between two
different cases in the computation of the PC: i) the CP increase due to multiple BS antennas is
neglected; ii) the CP increase is accounted for. Assume, for the moment, that the CP of cell0
consists only of the fixed power PFIX; that is, CP0 = PFIX. Hence, the corresponding EE of cell 0 is:

EE = -------------------------------------------------------------- (3-5)

Where B is the bandwidth and 𝑃 accounts for the ETP with 0 < μ ≤ 1 being the PA efficiency
[5], [21]. For a given SE, denoted as SE0, from (3-4) we obtain the required transmit power as

P= ------------------------------------------------------------------------- (3-6)

This inserted into (3-4) yields

EE0 = ---------------------------------------------------------------------- (3-7)

The throughput is obtained as the uplink and downlink spectral efficiency expressions as the
energy efficiency of cell j is computed as

R
EEj = --------------------------------------------------------------------------------- (3-8)

Where ETPj effective transmission power of pilot of sequence of cell j as well as of UL and DL

signals: ETPj = ∑ 𝑃𝑘 ∑ 𝑘 ∑ 𝑘 ----------------- (3-9)

Where ∑ 𝑃 𝑘 = ETP for pilot, ∑ 𝑘= 𝑃

Then (0< ) is the power amplifier (PA) efficiency at UEk in cell j

and is that of BSj. The energy efficiency and throughput tradeoff of
different schemes were compared [5], [21], and [38].

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Chapter 4

Simulation and numerical results

4.1 Introduction

MATLAB-based simulations are applied to confirm the numerical analysis given in the system
provided in this chapter. This chapter simulation of the main design parameters on the impact of
the performance of energy efficiency in massive MIMO for 5G wireless communication
networks. The maximum and desired design parameters for performance energy efficiency are
simulated using M-MMSE Precoding schemes at the end of the simulation result.

The simulation uses a sample of a massive MIMO scenario, number of antennas (M= up to 500),
number of active users (K = up to 140), and transmission bandwidth of 20MHZ. and more
simulation parameters are listed in the table below.

4.2 Simulation parameters

From the MATLAB demonstration, the following list of parameters is used. The parameters are
taken from the telecommunication union standard reports (TUSR) and standard values mainly
[3],[5],[9],[15],[20],[23],[25],[32],[35],[39].

Table 4.1 Simulation parameters used

Symbol System Parameter value

α Path loss exponent 3.7

S Length of coherence block 500

Power amplifier efficiency 0.35

Ϯ Symbol time 1/ 2.107[s/symbol]

A Coding, decoding, and back-haul 1.15.10-9[J/bit]
C0 Static power consumption 10w.T[J/Symbol]
C1 Circuit power per active UE 0.01w.T[J/Symbol]
D0 Circuit power per active BS 0.2w.T[J/Symbol]
D1 Signal processing coefficient 1.56.10-10[J/Symbol]
Ϭ2 Noise variance 10-20[J/Symbol]
M Maximum number of antennas 1 to 500

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K Maximum number of User 1 to 140

ω Propagation loss ≤1 km 130dB

ᶓ Hardware losses 0.03

pfix Fixed power 10w

PLO Power for BS 0.2w

PBS Power per BS antennas 0.4w
PUE Power per UE 0.01w
A Cell area 0.0625km2
Power for data encoding decoding 0.1W/(Gbit/s)

U Coherence block (symbols) 500

𝑆 Computational efficiency at BSs 12.8GW
Computational efficiency at UEs 5W
Fraction of uplink and downlink 1/3 and 2/3
transmission sample
Transmission 20MHz
bandwidth:
𝑓c Carrier frequency: 2GHz
C Channel coherence time: 10ms

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4.3 Simulation and result discussions

4.3.1 The impact of bandwidth on energy efficiency in massive MIMO for 5G networks
Here, the impact of bandwidth on the total energy efficiency of the system is analysed and
evaluated. In this simulation, the energy efficiency of the system increases as the bandwidth with
a gain of a number of antennas (M) increases. as shown in figure 4.1 below.

Figure 4.1 Simulation result energy efficiency with bandwidth in massive MIMO

Since the perfect channel state information (CSI) is available the capacity of the channel is [3]

C= ] ----------------------------------------------------------(4-1)

Where β = |h|2 denotes the channel gain(massive MIMO input). The capacity is achieved by x ∼
NC (0, P). When the transmit power is the only factor contributing to the energy consumption, an
upper bound on the energy efficiency in [3] is

----------------------------------------------------------------------------------------(4-2)

The energy efficiency approaches its limit as B → ∞ when P = 20 dBm and N0 = −174 dBm/Hz.
Different values of β are considered and these are determining how quickly we approach the
energy efficiency limit. For the cell-edge case of β = −110 dB, the limit is reached already at B =
1 GHz, while we need 100× more bandwidth every time β is increased by 20 dB the energy
efficiency increases with the bandwidth. The limit and the convergence depend strongly on the
channel gain β [3],[6].

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The impact of bandwidth on energy efficiency in massive MIMO depends on several factors,
including the number of antenna, the modulation scheme, and the signal-to-noise ratio (SNR) of
the system. In general, increasing the bandwidth in massive MIMO can lead to an increase in
energy consumption due to the need for more powerful signal processing hardware and
increasing data transmission. The transmit power required to achieve a given level of
performance, which can lead to an overall improvement in energy efficiency. Specifically,
increasing the bandwidth in massive MIMO for 5G can lead to the following benefits:

1. Increased spectral efficiency: with more bandwidth available, more user can be served
simultaneously, which increases the system’s overall spectral efficiency (SE).

2. Higher data rates: with more bandwidth available, the system can be transmitting data at
higher rates, which can lead to better user experience.

3. Reduced transmit power: with more bandwidth available, the required transmit power can be
reduced, which can lead to an overall improvement in energy efficiency.

However, increasing the bandwidth in massive MIMO can also lead to the following challenges:

1. Increased complexity: with more bandwidth available, the signal processing hardware required
to support the increased data rates can become more complex and expensive.

2. Increased interference: with more user being served simultaneously, the potential for
interference between uses can increase, which can reduce the system’s overall performance.

3. Reduced coverage: with more bandwidth being used, the coverage area of the system can be
reduced, which limit the systems overall can reach.

In conclusion, the impact of bandwidth on energy efficiency in massive MIMO depends on

several factors, and there is no one size fits all answer. However, increasing the bandwidth in
massive MIMO can lead to both benefits and challenges, and careful consideration should be
given to the specific requirements of the system before making any changes to the systems
bandwidth.

4.3.2 Analysis of multi-users and circuit power in a massive MIMO system

The total circuit power (CP) per cell for the combined uplink (UL) and downlink (DL) scenario
with different linear Precoding schemes, the circuit power required by M-MMSE is higher than
with the RZF. This is mainly due to the increased consumption efficiency. ZF, MRC, and RZF
consume less circuit power, since both invert matrices of dimensions K*K rather than M*M.

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MRC only provides a substantial complex reduction compared to RZF and ZF when the number
of the user equipment is very large in massive MIMO. Consider M = 500 and let the number of
users (K) vary from 10 to 100. The circuit power increases with the number of users.

Figure 4.2 Total circuit power (CP) with user equipment (K) in massive MIMO
In this simulation result, the circuit power required by the different linear Precoding schemes is
marginally different. For more comparison, this result is made for given configurations of (M, K)
which do not necessarily present the optimal ones for maximum energy efficiency in massive
MIMO for 5G wireless communication networks.
4.3.3 Analysis of throughput on energy efficiency in a massive MIMO system
The energy efficiency (EE) and throughput concentrate on the massive-MIMO network to
emphasize without defining the bandwidth. Energy efficiency (EE) analysis cannot be performed
for each base station (BS) and K number of users in each number of cells and number of
antennas (M). The values of the number of antennas (M) and the number of users (K) can be
defined. The cell coverage area energy efficiency (EE) is given in figure 4.3 below:
R
EE = ------------------------------------------------------------------------- (4-3)

Where ETPj is effective to transmit power, and CPj circuit power respectively. Average area
transmission power (AATP), which is defined as the average network power consumption for
data transmission per unit area is used, to calculate the transmission power consumed by a

wireless network. The measurement unit of this metric is given

AATP = Transmission power [ ] *Cell density number [ ] ---------------------------------(4-4)

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Area throughput = ------------------------------------------------------------------------- (4-5)

Area throughput = = s for M-MMSE

Figure 4.3 Simulation result energy efficiency with throughput in massive MIMO

The number of users (K) = 30 with the values number of antennas (M) = 500, in the above
simulation result shows that the multi-cell minimum mean square error (M-MMSE) Precoding
techniques allow the maximum energy efficiency (76.06Mbit/Joule) and maximum throughput
but, maximum ratio combination (MRC) having the minimum energy efficiency
(33.23Mbit/Joule) and throughput(1148Mbit/s/cell). As the number of the antenna (M), in the
base station increases, and the cell coverage area is 0.25km x 0.25km with the power
consumption per user equipment (PUE = 0.01w) in massive MIMO networks.

4.3.4 Design and analysis of maximum energy efficiency in massive MIMO

To achieve maximum energy efficiency values with multi-cell minimum mean square error (M-MMSE),
regularized zero force (RZF/ZF), and maximum ratio combination (MRC) for various value number of
antennas (M) and some users (K) combinations, consider K ᶓ {10, 20..., 140} and M ᶓ {20, 30… 500}. With
trade-off circuit power (CP) and transmit power value. M-MMSE is the best Precoding technique for a given
maximum value (M, K) from a throughput perspective. Marginally M-MMSE has higher throughput than RZF
and has disproportionately larger power consumption.

Hence, at a lower throughput value, the higher power consumptions per cell are the price to pay
with RZF; energy efficiency offers the optimum with MRC, which is smaller than with M-

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MMSE and RZF for an area throughput of 49.808Gb/s/km2, throughput 3113.032. (Mb/s/cell)
and total power consumption (PC) of 64.72W per cell.

With M-MMSE, RZF/ZF, and MRC as a function of a massive number of antennas (M) and
multi number of the active user (K). Maximum energy efficiency with fixed power 5w, power
per base station (Bs) antenna = 0.2w, power per an active number of active users (PUE =
0.01W), power data encoding 0.01w/Gb/s and power data decoding 0.08w/Gb/s which, is
maximum energy efficiency (EE) is 54.95 Mbit/Joule simulated in figure 4.4 below.

Figure 4.4 Simulation result EE with number of antennas (M) and active user equipment (UE)
using M-MMSE precoding techniques in massive MIMO

R
EEmax = then R = EE*Pc = 54.95Mbit/Joule*41.55w = 2283.1725bit/s

= = 54.95Mbit/Joule --------------------------------------------------------------- (4-6)

= this formula used to calculate the energy efficiency for each user in massive MIMO

system. Designing an optimal massive MIMO system that supports a massive number of users

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with high energy efficiency requires careful consideration of several factors, Including the
antenna configuration, signal processing techniques, and resource allocation strategies.

1. Antenna configuration: the use of large number of antennas in a fundamental future of

massive MIMO systems, and the antenna configuration plays a crucial role in the systems
performance. The optimal antenna configuration depends on several factors, such as propagation
environment, the number of users, and the available frequency bands. However, a common
approach is to use a uniform linear array of antennas or a uniform planar array of antennas.
Resource allocation: resource allocation strategies play a crucial role in determining the energy
efficiency of the system. In summary, designing an optimal massive MIMO system that
supports a massive number of users with higher energy efficiency requires careful consideration
of several factors, including the antenna configuration, signal processing techniques, resource
allocation, and hardware design. By optimizing these factors, it is possible to design a massive
MIMO system that can support a large number of users while minimizing power consumption
and maximizing energy efficiency.

Figure 4.5 Simulation result EE with number of antennas (M) and active user equipment (UE)
using RZF Precoding techniques in massive MIMO

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Figure 4.6 Simulation result EE with a number of antennas (M) and active user equipment (UE)
using MRC Precoding techniques in massive MIMO.
Compared to the result in, Figures 4.4, 4.5, and 4.6, M-MMSE becomes a potential solution for
higher energy efficiency and low power consumption (PC) when more energy-efficient hardware
is used in massive MIMO for 5G wireless communication networks.

4.3.5 Maximization of energy efficiency than energy consumption in massive

MIMO

The simulation analysis result showed that the reduction of energy consumption is the way to
maximize energy efficiency and the circuit power consumption (Pc) dominates, the transmit
power because adding more antennas in the base station (BS) in each cell to spatially multiplex
active users equipment (UEs). The corresponding energy efficiency gains come from overturning
many antennas' intra-cell interference and sharing the costs of CP per cell among multiple active
users (MUEs). In summary, the maximum energy efficiency than power consumption in massive
MIMO that can be achieved using M-MMSE Precoding techniques depends on various factors
such as the channel condition, the power constraints, and the modulation scheme used.
Analyzing the achievable rate region and optimizing the energy per bit metric are two ways to
assess the energy efficiency of Precoding techniques in wireless communication systems.

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80
Sum of Max EE
Mb/Joule
70

60 Sum of No.
Antennas
50
Unit Value

Sum of Number of
40 UE

30
Sum of Area
throughput
20 Gb/s/km2

10 Sum of power pc in
Watt
0
M-MMSE MRC RZF

Figure 4.7 Simulation result EE vs power consumptions in massive MIMO for 5G wireless
communication networks.

Table 4.2 Simulation result energy efficiency vs energy consumptions from figure 4.7 above:

Schema Maximum Values Power

Technique EE [K, M] Area throughput consumption Throughput
[Pc]
M-MMSE 54.95Mb/J [30,60] 36.53076 Gb/s/km2 41.55w 2283.173[Mb/s/cell]

RZF 48.10 Mb/J [30,80] 49.80851 Gb/s/km2 64.72w 3113.032 [Mb/s/cell]

MRC 24.25 Mb/J [30,60] 17.42896 Gb/s/km2 44.92w 1089.31[Mb/s/cell]

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The energy efficiency maximized at power consumption per active number of user equipment’s
(UE) = 0.01w of a wireless communication network defined as the number of bits that can be
transmitted reliably per unit of EE (Mb/J), is a good performance metric that balances traffic load
and power consumptions while increasing the number of antennas (M). In the simulation result,
multi-cell minimum mean square error (M-MMSE) only offers the highest EE for any
throughput value when the power consumption (Pc) lower values are used. The lower EE is
reached by the MRC; RZF represents a good tradeoff between EE and throughput in massive
MIMO for 5G communication networks.
The way to analyze the maximum energy efficiency that can be achieved using Precoding
techniques is to consider the achievable rate region of the system. The achievable rate region is
the set of all possible combinations of transmission rates that can be achieved by the system
subjected to a given power constraint. In other words, it is the region in which the system can
transmit data reliably while respecting a certain power budget. Using multi-cell minimum mean
square error Precoding techniques can increase the achievable rate region by improving the
systems channel capacity. This is because Precoding can exploit the spatial diversity of the
wireless channel, which allows for higher data rates compared to traditional modulation schemes.
By optimizing the Precoding schemes to minimize the energy per bit, it is possible to maximize
the energy efficiency of the system in massive MIMO for 5G wireless communications. In
summary, the maximum energy efficiency that can be achieved using multi-cell minimum mean
square error Precoding techniques depends on various factors such as the channel condition, the
power constraint, and the modulation schemes used.

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Chapter 5

Conclusion and Recommendations

5.1 Conclusions
In this thesis, the performance energy efficiency of a cellular network can be defined as the
number of bits that can be reliably transmitted per unit of energy measured in bits per joule,
which is a good performance metric to balance the data rate (throughput) and energy
consumption. In any case, pilot contamination gives rise to coherent impedance that develops
with M, unless this impedance is restricted by utilizing M-MMSE pre-coding techniques. The
consistency of interference is in addition to the predictable non-coherent interference that is
unaffected by a number of antennas (M). The ratio performance of energy efficiency to the
number of antennas with the number of users (M/K) in massive-MIMO is initially linearly
increased but does not continue due to some neighbouring interference effect. Massive MIMO
analysis allows for jointly increasing energy efficiency and throughput as compared to present
wireless communication MIMO networks (3G/4G). Multi-cell minimum mean square error (M-
MMSE) offers the highest energy efficiency (EE) for any output value only when more energy-
efficient hardware is used. Maximum ratio combination (MRC) accomplishes the lowest energy
efficiency result as the number of antennas increases in massive MIMO. In massive MIMO, as
the number of antennas increases twice the number of active users (M = 2K), it results in
maximum energy efficiency using Precoding techniques such as multi-cell minimum mean
square error (M-MMSE) and maximum ratio combination (MRC) in massive MIMO wireless
communication networks.

The transmitted power consumption in massive MIMO could be decreasing as the number of
antennas increases (M). M-MMSE is a less power-consuming scheme in massive MIMO
concerning MRC and RZF techniques. In this thesis, the maximum energy efficiency optimum
value simulation result is 54.95Mb/Joule at a value of M = 60, K=30, and the power
consumption per user (PUE = 0.01W). Multi-cell minimum mean square error is the best
technique for maximizing energy efficiency, but MRC simulation results have the lowest energy
efficiency in massive MIMO for 5G wireless communication networks. Finally, as compared
with the Precoding techniques and the energy consumption, M-MMSE simulated higher energy
efficiency (EE) than the energy consumption (PC) in massive MIMO wireless communication networks.

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5.2 Recommendations for future work

In this thesis, results show that energy efficiency is maximized through pre-coding techniques
such as M-MMSE by reducing the power consumption per UE, in massive MIMO wireless
communication for 5G networks. Finally, the performance analysis of energy efficiency ensuring
techniques in massive MIMO for 5G networks must take into account the dynamic nature of the
system. The channel conditions and user traffic patterns can change rapidly, which can affect the
performance of the system. Therefore, the analysis must be done in a way that captures the
dynamic behavior of the system, such as using adaptive algorithms and real-time measurements.
Then, optimize the system design parameters, such as the number of antennas and users, to
achieve the desired energy efficiency while maintaining the required performance metrics.

In future work, it is recommended to do the following studies on energy efficiency and power
consumption in massive MIMO cases:

 Design and implementation of effective energy efficiency-ensuring techniques in

massive MIMO for the next generation.
 Deployment of massive MIMO via the best power-saving techniques at a low cost
 Design and implement massive MIMO networks for energy efficiency via more traffic
load directional antennas and coverage areas using automatic switching techniques.

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