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Modem 4G LTE
Tiago Mendonça Martins Barata
Thesis to obtain the Master of Science Degree in
Electrical and Computer Engineering
Supervisors: Prof. Paulo Alexandre Crisóstomo Lopes
Prof. José António Beltran Gerald
Examination Committee
Chairperson: Prof. Fernando Duarte Nunes
Supervisor: Prof. Paulo Alexandre Crisóstomo Lopes
Member of the Committee: Prof. António José Castelo Branco Rodrigues
April 2014
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Acknowledgments I would like to express my sincere gratitude to my supervisor Prof. Paulo Alexandre Crisóstomo Lopes
for the support of my thesis.
I would like to thank also my family for the encouragement during the entire course.
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Resumo O LTE é o novo padrão de comunicações móveis que é capaz de atingir velocidades de transmissão
de dados até 100 Mbps no downlink e 50 Mbps no uplink quando se usa uma largura de banda de 20
MHz. O LTE utiliza Orthogonal Frequency Division Multiple Access (OFDMA) no downlink e Single
Carrier Frequency Division Multiple Access (SC-FDMA) no uplink.
O objectivo principal da tese passa por simular um modem LTE quer para a parte de uplink quer para
a de downlink de modo a estudar vários parâmetros importantes para avaliar o seu desempenho.No
caso do downlink os parâmetros analisados foram a taxa de erro de bit, o número de bits transmitidos
por portadora OFDM e o número de bits transmitidos por símbolo OFDM. No caso do uplink o
parâmetro analisado foi a taxa de erro de bit. Foi também analisado o Peak to Average Power Ratio
(PAPR) quer para downlink quer para uplink. O software usado para as simulações foi a aplicação
Matlab.
Palavras Chave: LTE, Modem, OFDMA, PAPR, SC-FDMA
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Abstract LTE is the new mobile telecommunications system which is capable of supporting data rates which
can go up to 50 Mbps in the uplink and 100 Mbps in the downlink when using a 20 MHz channel
bandwidth. LTE uses Orthogonal Frequency Division Multiple Access (OFDMA) for the downlink and
Single Carrier Frequency Division Multiple Access (SC-FDMA) for the uplink.
The main objective of the thesis is to simulate a LTE Modem both in downlink and uplink sides in order
to study several parameters for evaluating its performance. In the LTE downlink the parameters
analysed were the bit error rate, the number of bits transmitted per OFDM subcarrier and the number
of bits transmitted per OFDM symbol. In LTE uplink the parameter analysed was the bit error rate. It
was also analysed the Peak to Average Power Ratio (PAPR) both for uplink and downlink cases. The
software used for the simulations was Matlab.
Keywords: LTE, Modem, OFDMA, PAPR, SC-FDMA
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Table of Contents
Acknowledgments ................................................................................................................................... iii
Resumo ....................................................................................................................................................v
Abstract................................................................................................................................................... vii
List of Figures .......................................................................................................................................... xi
List of Tables ......................................................................................................................................... xiii
List of Acronyms ..................................................................................................................................... xv
Chapter 1 Introduction .......................................................................................................................... 1
1.1 LTE Overview .......................................................................................................................... 3
1.2 TDD and FDD .......................................................................................................................... 5
1.3 Channel Models ....................................................................................................................... 7
Chapter 2 Downlink .............................................................................................................................. 9
2.1 Orthogonal Frequency Division Multiple Access (OFDMA) .................................................. 11
2.2 Downlink Physical .................................................................................................................. 21
2.3 Cell Synchronization .............................................................................................................. 24
2.3.1 Zadoff-Chu Sequence ....................................................................................................... 25
2.4 Reference Signals ................................................................................................................. 29
2.5 Data and Control Downlink Physical Channels ..................................................................... 30
2.6 Adaptive Modulation and Channel Coding ............................................................................ 32
Chapter 3 Uplink ................................................................................................................................. 35
3.1 Single Carrier Frequency Division Multiple Access ............................................................... 37
3.2 Physical Uplink Channel Structure and Reference Signals .................................................. 40
Chapter 4 Modem ............................................................................................................................... 41
4.1 Introduction ............................................................................................................................ 43
4.2 Channel Estimation ............................................................................................................... 46
4.3 Bit Loading ............................................................................................................................. 47
4.4 Downlink part 1 ...................................................................................................................... 49
4.4.1 Simulation .......................................................................................................................... 49
4.4.2 Results ............................................................................................................................... 50
4.4.3 Simulation .......................................................................................................................... 52
4.4.4 Results ............................................................................................................................... 53
x
4.4.5 Simulation .......................................................................................................................... 54
4.4.6 Results ............................................................................................................................... 55
4.5 Downlink part 2 ...................................................................................................................... 57
4.5.1 Simulation .......................................................................................................................... 57
4.5.1 Results ............................................................................................................................... 58
4.6 Uplink ..................................................................................................................................... 59
4.6.1 Simulation .......................................................................................................................... 59
4.6.2 Results ............................................................................................................................... 60
4.7 Uplink vs Downlink ................................................................................................................ 61
4.7.1 Simulation .......................................................................................................................... 61
4.7.2 Results ............................................................................................................................... 61
Chapter 5 Conclusion ......................................................................................................................... 63
References ............................................................................................................................................ 65
xi
List of Figures Figure 1 – FDM and OFDM differences ................................................................................................ 12
Figure 2 – OFDM Cyclic Prefix insertion ............................................................................................... 15
Figure 3 - Example of resource allocation in a combined OFDMA/TDMA system ............................... 18
Figure 4-OFDM transmitter block diagram ............................................................................................ 18
Figure 5-OFDM receiver block diagram ................................................................................................ 20
Figure 6 – LTE frame structure.............................................................................................................. 21
Figure 7 - LTE slot structure for the extended cyclic prefix case .......................................................... 21
Figure 8 - LTE slot structure for the normal cyclic prefix case .............................................................. 22
Figure 9 – Resource Block structure when using the normal cyclic prefix ............................................ 22
Figure 10 – Zadoff-Chu Sequence in time domain with R=25 and N=63 ............................................. 26
Figure 11 – Zadoff-Chu Sequence in time domain with R=29 and N=63 ............................................. 26
Figure 12 – Zadoff-Chu Sequence in time domain with R=34 and N=63 ............................................. 27
Figure 13 – Autocorrelation of a Zadoff-Chu Sequence in time domain with R=25 and N=63 ............. 27
Figure 14 – Cross correlation between two Zadoff-Chu Sequences in time domain with R=29 and
N=63 and with R=34 and N=63 ............................................................................................................. 28
Figure 15 – SC-FDMA transmitter block diagram ................................................................................. 37
Figure 16 – SC-FDMA receiver block diagram...................................................................................... 39
Figure 17 – Communication channel model .......................................................................................... 44
Figure 18 - OFDM baseband transmitter and receiver and the communication channel block diagram
............................................................................................................................................................... 45
Figure 19 – Number of bits/symbols transmitted per subcarrier for the case of 512 subcarriers with a
Signal to Noise Ratio of 27.7 dB ........................................................................................................... 50
Figure 20 - Number of bits/symbols transmitted per subcarrier for the case of 1024 subcarriers with a
Signal to Noise Ratio of 24.8 dB ........................................................................................................... 50
Figure 21 - Number of bits/symbols transmitted per subcarrier for the case of 2048 subcarriers with a
Signal to Noise Ratio 21.7 dB ............................................................................................................... 51
Figure 22 – FIR filter frequency response ............................................................................................. 51
Figure 23 – Variation of the number of bits transmitted per OFDM symbol with the Signal to Noise
Ratio in dB for 512 subcarriers .............................................................................................................. 53
Figure 24 - Variation of the number of bits transmitted per OFDM symbol with the Signal to Noise
Ratio in dB for 1024 subcarriers ............................................................................................................ 53
Figure 25 - Variation of the number of bits transmitted per OFDM symbol with the Signal to Noise
Ratio in dB for 2048 subcarriers ............................................................................................................ 54
Figure 26 – Variation of the bit error rate with the Signal to Noise Ratio in dB for 512 subcarriers ...... 55
Figure 27 – Variation of the bit error rate with the Signal to Noise Ratio in dB for 1024 subcarriers .... 55
Figure 28 - Variation of the bit error rate with the Signal to Noise Ratio in dB for 2048 subcarriers .... 56
Figure 29 - Variation of the bit error rate with the Signal to Noise Ratio in dB ...................................... 58
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Figure 30 – Variation of the Modulation scheme (bits per moduled symbol) with the Signal to Noise
Ratio in dB ............................................................................................................................................. 58
Figure 31 – SC-FDMA baseband transmitter and receiver and the communication channel block
diagram .................................................................................................................................................. 59
Figure 32 - Variation of the bit error rate with the Signal to Noise Ratio in dB ...................................... 60
Figure 33 - Variation of the Modulation scheme (bits per moduled symbol) with the Signal to Noise
Ratio in dB ............................................................................................................................................. 60
Figure 34 - Variance of the Pick to Average Power Ration (PAPR) with the number of OFDM
subcarriers ............................................................................................................................................. 61
Figure 35 - Variation of the Pick to Average Power Ration (PAPR) with the number of SC-FDMA
subcarriers ............................................................................................................................................. 62
xiii
List of Tables Table 1 – Comparison between TDD and FDD....................................................................................... 5
Table 2 – Extended ITU channel models ................................................................................................ 7
Table 3 – LTE downlink characteristics for different bandwidths .......................................................... 14
Table 4 - Uplink-Downlink configuration possibilities ............................................................................ 23
Table 5 – All the fifteen possible CQI index defined for LTE and characteristics ................................. 32
Table 6 – Channel coding features of UMTS and LTE used for data transmission .............................. 33
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List of Acronyms Acronyms Meaning
ADSL Asymmetric Digital Subscriber Line
AMPS Analogue Mobile Phone System
AWGN Additive White Gaussian Noise
BCCH Broadcast Control Channel
CAZAC Constant Amplitude Zero Autocorrelation
Waveform
CCCH Common Control Channel
CDMA Code Division Multiple
Access
CFI Control Format Indicator
CQI Channel Quality Indicator
DCCH Dedicated Control Channel
DECT Digital Enhanced Cordless Telecommunications
DFT Discrete Fourier Transform
DVB Digital Video Broadcast
DwPTS Downlink Pilot TimeSlot
eNodeB Evolved Node B
EPA Extended Pedestrian A
ETU Extended Typical Urban
EVA Extended Vehicular A
FDD Frequency Division Duplex
FDM Frequency Division Multiplexing
FDMA Frequency Division Multiple Access
FEC Forward Error Correction
FIR Finite Impulse Response
FFT Fast Fourier Transform
GSM Global System for Mobile communications
GP Guard Period
GPRS General Packet Radio Service
HSPA High Speed Packet Access
IDFT Inverse Discrete Fourier Transform
IFFT Inverse Fast Fourier Transform
IIR Infinite Impulse Response
IMT International Mobile Telecommunications
J-TACS Japanese Total Access Communication System
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LTE Long Term Evolution
MBSFN Multimedia Broadcast Single Frequency Network
MIMO Multiple Input Multiple Output
MLS Maximum Length Sequences
MMS Multimedia Messaging Service
NMT Nordic Mobile Telephone
OFDM Orthogonal Frequency Division Multiplexing
OFDMA Orthogonal Frequency Division Multiple Access
PAPR Peak to Average Power Ratio
PBCH Physical Broadcast Channel
PCFICH Physical Control Format Indicator Channel
PDCCH Physical Downlink Control Channel
PDSCH Physical Downlink Shared Channel
PHICH Physical Hybrid ARQ Indicator Channel
PMCH Physical Multicast Channel
PRACH Physical Random Access Channel
PSS Primary Synchronization Signal
PUCCH Physical Uplink Control Channel
PUSCH Physical Uplink Shared Channel
QAM Quadrature Amplitude Modulation
QPSK Quadrature Phase Shift Keying
RB Resource Block
RE Resource Element
RFPA Radio Frequency Power Amplifier
RTT Round Trip Time
SC-FDMA Single Carrier Frequency Division Multiple
Access
SMS Short Message Service
SNIR Signal to Noise plus Interference Ratio
SNR Signal to Noise Ratio
SRS Sounding Reference Signal
SSS Secondary Synchronization Signal
TACS Total Access Communication System
TB Transport Block
TDD Time Division Duplexing
TDMA Time division multiple access
UE User Equipment
UMTS Universal Mobile Telecommunications System
UpPTS Uplink Pilot Time Slot
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WiMAX Worldwide interoperability for
Microwave Access
WCDMA Wideband Code Division Multiple
Access
ZC Zadoff-Chu
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1
Chapter 1 Introduction
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3
1.1 LTE Overview
The first generation of mobile telecommunication systems arrived in the 1980s. The first generation
used analogue technology and it had several independently developed systems worldwide: Analogue
Mobile Phone System (AMPS), Total Access Communication System (TACS), Nordic Mobile
Telephone (NMT) and Japanese Total Access Communication System (J-TACS).
The second generation of mobile telecommunication systems is based in digital technology. The most
important second generation system is GSM (formerly Groupe Spéciale Mobile and now Global
System for Mobile communications). GSM was commercially launched in Finland in 1991 and today it
is provided in 220 countries. GSM introduced mobile data services, starting with the short message
service (SMS) and later with Multimedia Messaging Service (MMS). Nowadays the usual data rates of
GSM are approximately 50 kbit/s. The cell sizes in GSM can vary between 100 m and 35 km
depending on several factors like the user density, geography, transceiver power. A GSM TDMA
frame has duration of 4.615 ms containing 8 time slots and each of these time slots has duration of
577 µs. GSM define two types of traffic channels control channels (data and voice) and three types of
control channels: Broadcast Control Channel (BCCH), Common Control Channel (CCCH) and
Dedicated Control Channel (DCCH). GSM was the first system which used global roaming. GPRS
(General Packet Radio Service) is a technology used in GSM and its main goal was to achieve higher
data rates. It is commercially introduced in 2001 and it is usually called a 2.5 generation technology.
Universal Mobile Telecommunications System (UMTS) is a third generation mobile telecommunication
system which marked the entry of Code Division Multiple Access (CDMA). Due to the UMTS 5 MHz
carrier bandwidth CDMA is called Wideband CDMA or simply WCDMA. UMTS can support both TDD
and FDD modes. Each frame UMTS has time duration of 10 ms and it contains 15 time slots. Each
time slots has time duration of 666.7 µs. Originally UMTS data rates could go up to 2 Mbps but with
some enhancement UMTS technologies like HSPA+ the data rates are much higher.
LTE was initiated in 2004 by NTT DoCoMo, became stable for commercial implementation in 2008
and the first public service started to be available in 2009 in Stockholm and Oslo. It is designed to
support high speed data transfer and high capacity voice.
LTE uplink target is to support data rates which can go up to 50 Mbps and the LTE downlink data
rates which can go up to 100 Mbps when using a 20 MHz channel bandwidth. These data rates
correspond to 2.5 bps/Hz and 5bps/Hz in the uplink and downlink respectively. LTE carrier frequencies
are in the range 400 MHz to 4 GHz and its bandwidths are 1.4 MHz, 3 MHz, 5 MHz, 10 MHz, 15 MHz
and 20MHz both for downlink and uplink. LTE has a round trip time (RTT) less than 10ms which is
especially good for real time applications like online gaming or video calls. In terms of mobility it is
optimized for speeds between 0 and 15 km/h, it has high performance between 15 km/h and 120 km/h
and it is functional between 120 km/h and 350 km/h. LTE uses Orthogonal Frequency Division Multiple
Access (OFDMA) technology in the downlink and Single Carrier Frequency Division Multiple Access
(SC-FDMA) in the uplink.
4
Multiple Input Multiple Output (MIMO) technology is used in LTE and it consists in exploring the spatial
domain using multiple antennas in the transmitter and/or in the receiver in order to improve the overall
communication efficiency. Multiple antennas can be used in several ways which can be divided into
three main sections:
Diversity gain: Robustness of the communication against multipath fading achieved with the
use of spatial diversity of the multiple antennas
Array gain: Concentration of energy in one or more given directions
Spatial multiplexing gain: A single user receives multiple signal streams from different
antennas.
MIMO technology can also contribute to a higher spectral bandwidth. Thus data rates are higher using
MIMO. For example LTE peak data rate is 172.8Mbps for 2x2 MIMO antenna configuration and
326.4Mbps for 4x4 MIMO antenna configuration. The main drawbacks of this technology are the
system complexity in terms of signal processing and the number of antennas required. MIMO
technology is also used in other wireless systems like Wi-Fi, WiMAX and HSPA+.
LTE is a packet oriented multiservice system which as the name says is based on the packet
switching principle. Packet switching is digital networking method which consists in dividing the
transmission information into small blocks called packets.
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1.2 TDD and FDD
In order to transmit data in both directions (downlink and uplink), it is necessary to use either a half-
duplex scheme or a full-duplex scheme to make it possible. LTE can use two duplex schemes:
Frequency Division Duplexing (FDD) and Time Division Duplexing (TDD).
Time Division Duplex (TDD) is a duplex scheme which consists in separating downlink from uplink by
allocating different timeslots in the same frequency band. TDD is more suitable for asymmetric traffic
due to the fact that it is possible to dynamically allocate timeslots for both downlink and uplink when
they support different data rates. TDD is also used in IEEE 802.16 WiMAX, Digital enhanced cordless
telecommunications (DECT) wireless telephony, Universal Mobile Telecommunications System 3G
supplementary air interfaces, TD-CDMA for indoor mobile telecommunications and TD-SCDMA 3G
mobile telephony air interface.
Frequency Division Duplex (FDD) is a duplex scheme which consists in separating downlink from by
using different frequency bands. Due to the fact that FDD uses different frequency bands for sending
and receiving data, the downlink and uplink signals don’t interfere with each other and so it makes
FDD more suitable for symmetric traffic. FDD is also used in Asymmetric digital subscriber line
(ADSL), very high bit rate digital subscriber line (VDSL), UMTS/WCDMA Frequency Division
Duplexing mode, CDMA2000 system and IEEE 802.16 WiMAX Frequency Division Duplexing mode.
Each of these two duplex schemes has advantages and disadvantages. The table below shows the
main characteristics of both TDD and FDD:
Table 1 – Comparison between TDD and FDD
Parameter TDD FDD
Paired Spectrum
Paired spectrum is not used because
both transmit and receive occur on the
same channel
Paired spectrum is used with a guard
band to separate in order to allow
simultaneous transmission and
reception
Hardware Cost
Lower cost because there is no need to
use a diplexer to isolate the transmitter
and receiver
Higher cost because it is necessary to
use a diplexer
Channel
Reciprocity
Channel propagation characteristics
are the same both in downlink and
uplink directions
Channel propagation characteristics
are different in downlink and uplink
directions because of the different
frequency bands used
Downlink/Uplink
Asymmetry
It is possible to dynamically change the
downlink and uplink transmission ratios
to match demand
Downlink and uplink transmission
ratios determined by frequency
allocation set out by the regulatory
authorities. It is not possible to change
dynamically in order to match demand
6
Guard
Period/Guard
Band
It is required to use guard period to
guarantee no conflicts between uplink
and downlink transmissions. Large
guard period will limit transmission
It is required to use guard band to
provide sufficient isolation between
uplink and downlink
Discontinuous
Transmission
Discontinuous transmission is required
to allow both uplink and downlink
transmissions. This can degrade the
performance of the RF power amplifier
in the transmitter
Continuous transmission is required
Cross Slot
Interference
It is necessary that neighbour base
stations are synchronised because
they could share the same channel
-
LTE FDD and LTE TDD are identical in the main features. Most operators are opting for LTE FDD
because they already have 2G and 3G networks. New operators have tendency to opt for LTE TDD
main due to the reduced costs in the technology.
Although commonly it is said that LTE belongs to 4G, it does not fulfil all requirements for IMT
advanced. It can be fit in the 3.9G because it is an enormous evolution from 3G but still it cannot fit in
4G category. LTE advanced is an enhancement of LTE which fulfil IMT requirements and so it is
considered 4G. LTE advanced has the target of having bandwidths which can up to 100MHz both for
uplink and downlink, data rates which can go up to 1Gbps in the downlink and 500 Mbps in the uplink
and spectral efficiency which can achieve 30 bps/Hz for the downlink and 15 bps/Hz in the uplink.
7
1.3 Channel Models
Channel models have a huge importance in the systems´ performance and in the networks´ planning
and they depend on the environment which is supposed to model. Different typical environment such
as rural, suburban, urban, and indoor require different system´s parameters. In the real world, it is
necessary to do several measurements in order to obtain an approximate channel model.
There are three types of factors which can affect the signal between the transmitter and the receiver:
Propagation path loss
Slow fading
Fast fading
Slow fading is caused mainly due to obstacles between the transmitter and the receiver like buildings
and trees. Fast fading corresponds to quick fluctuations in the amplitude of the signal and it occurs
due to multiple reflexions in several objects while the user is moving.
The table below shows some LTE channel models considering no use of MIMO:
Table 2 – Extended ITU channel models
Tap
Number
EPA model EVA model ETU model
Excess Tap
Delay (ns)
Relative
Power (dB)
Excess Tap
Delay (ns)
Relative
Power (dB)
Excess Tap
Delay (ns)
Relative
Power (dB)
1 0 0 0 0 0 -1
2 30 -1 30 -1.5 50 -1
3 70 -2 150 -1.4 120 -1
4 80 -3 310 -3.6 200 0
5 110 -8 370 -0.6 230 0
6 190 -17.2 710 -9.1 500 0
7 410 -20.8 1090 -7.0 1600 -3
8 1730 -12.0 2300 -5
9 2510 -16.9 5000 -7
8
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Chapter 2 Downlink
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2.1 Orthogonal Frequency Division Multiple Access
(OFDMA)
Multicarrier communication systems were first introduced in the 1960s. Bell Labs was the first
research and development institution to patent orthogonal frequency division multiplexing (OFDM) in
1966. Further complexity reductions were realized in 1980 by the application of the Fast Fourier
Transform (FFT).
Orthogonal frequency division multiplexing (OFDM) is a multicarrier modulation scheme based on the
frequency division multiplexing (FDM) concept and which consists in dividing a stream of information
into several sub streams and then each of these sub streams are transmitted in parallel carried by
different sub carriers. Each subcarrier may use a specific modulation scheme. The sub streams have
a much higher symbol time duration than the original stream (increases approximately linearly with the
number of subcarriers) because they carry less information for the same period of time. An OFDM
signal can contain thousands of subcarriers.
In a general wireless communication channel there are usually several communication paths between
the transmitter and the receiver. There are two types of transmission paths:
Line of sight path: It is a direct communication path between the transmitter and receiver
Reflection path: It is communication path which is created by reflection in buildings, cars and
other obstacles.
The higher symbol time duration of each OFDM sub stream provides more immunity to the inter
symbol interference (ISI) caused by the multipath propagation than the original stream because the
original stream is more likely that the symbol time duration is less than the channel delay spread. In
this case transmission will necessarily have errors due to the ISI.
A basic OFDM signal in complex baseband notation is given by the following expression:
( ) ∑ ( )
∑ ( )
( ) (1)
is the number of OFDM subcarriers, ( ) is the signal carried by the kth subcarrier with carrier
frequency equal to . ( )
is the modulated symbol carried by the kth subcarrier in the nth
OFDM symbol time. There are modulated symbols transmitted in parallel during each OFDM period
of time T. The number of bits transmitted per OFDM symbol depends on the modulation schemes
used for each subcarrier.
All OFDM subcarriers have the property of being orthogonal to each other which is the same as saying
that the following criterion is satisfied:
12
∫ ( ) ( )
( )
(2)
( ) and ( ) are signals in the time domain carried by different subcarriers. In traditional FDM,
different frequency channels must have a guard band to avoid errors in frequency selecting channels.
This fact decreases the spectral efficiency because each frequency channel has a substantial empty
frequency band between itself and the neighbour channel. OFDM has the importance feature that all
its subcarriers are orthogonal to each other which permit avoiding the need of having guard bands to
separate the frequency channels like in FDM and also subcarriers overlap in frequency without
introducing errors. Due to the last stated fact, the spectral efficiency is higher than in the traditional
FDM which is very important nowadays where many frequency bands are already occupied and so
there is less frequency spectrum available for new services.
The figure below illustrates the differences in the frequency domain between FDM and OFDM:
Figure 1 – FDM and OFDM differences
LTE uses fixed subcarrier spacing and its value is 15 kHz. The OFDM symbol time duration is the
inverse of the subcarrier spacing. In the following formula it is calculated the LTE OFDM symbol time
duration:
(3)
In the case of the Multimedia Broadcast Single Frequency Network (MBSFN) transmission supported
by the LTE specification, the subcarrier spacing is different and it is equal to 7.5 kHz.
Each sub stream can be modulated with a different modulation scheme. LTE specification defines that
there are three possible modulations for each OFDM sub stream:
13
QPSK modulation: This modulation scheme is the less susceptible to errors because the four
possible combinations of modulated symbols are distant from each other as it can be seen in
a typical QPSK constellation diagram. The main drawback of this modulation scheme is the
smaller spectral efficiency compared with the other two. It is capable of carrying 2 bits per
modulated symbol.
16 QAM modulation: This modulation scheme is more susceptible to errors than QPSK but
less than 64 QAM. It is also a compromise between QPSK and 64 QAM in terms of spectral
efficiency, with a higher value than QPSK and less than 64 QAM. It is capable of carrying 4
bits per modulated symbol.
64 QAM modulation: This modulation scheme has the highest error rate but it can carry more
data per frequency unit than the other two modulations. It is capable of carrying 6 bits per
modulated symbol.
The modulation scheme chosen for each sub stream depends mainly on the communication channel
quality in the frequency band correspondent to the respective subcarrier. The better the
communication channel quality for a specific subcarrier is, the higher index modulation scheme is
possible to use. In LTE case, if it is used 64 QAM modulation, it means the quality of the
communication channel is very good for a particular frequency band. Due to the fact that each
subcarrier can be modulated in a different way, the receiver must contain the information of the
modulation scheme used for each subcarrier to correctly demodulate the information transmitted.
Gray coding is a very good method of reducing the overall bit error rate without changing any
transmission parameter. It is as simple as numerical sequence where neighbour numbers differ only in
one bit. In order to obtain benefits in the bit error rate reduction, it should be assigned in the
constellation diagram numbers which differ only in one bit to neighbour symbols.
The practical implementation of OFDM uses the IFFT (Inverse Fast Fourier Transform) and FFT (Fast
Fourier Transform) in the transmitter and receiver respectively mainly due to the fact that it is very
efficient and has a low complexity implementation. The size of the FFT/IFFT can be equal or greater
than the number of modulated symbols of the OFDM subcarriers in each cycle.
The sampling rate of the time discrete the OFDM signal is obtained using the following expression:
(4)
N corresponds to the FFT/IFFT size and it should be equal or larger than the number of subcarriers.
The IFFT/FFT size N is must also be a power of 2 to be efficient.
The oversampling ratio is a relation between and N values given by the following expression:
(5)
14
Not all the sub-carriers are modulated. The DC sub carrier (centre subcarrier) is not used and some
sub-carriers on both sides of the channel band neither. Approximately 10% of sub-carriers are used as
guard carriers.
The following table shows some LTE downlink characteristics like the sampling frequencies and the
FFT/IFFT sizes for the different channel bandwidths:
Table 3 – LTE downlink characteristics for different bandwidths
Total Channel
Bandwidth
( MHz )
1.4 3 5 10 15 20
Sampling
Frequency
( MHz )
1.92 3.84 7.68 15.36 23.04 30.72
FFT/IFFT size 128 256 512 1024 1536 2048
Occupied
subcarriers 72 180 300 600 900 1200
Guard bands
(MHz) 0.32 0.30 0.50 1 1.5 2
Number of
Resource Blocks 6 12 25 50 75 100
Occupied
Channel
Bandwidth (MHz)
1.08 2.7 4.5 9 13.5 18
Downlink
Bandwidth
Efficiency (MHz)
77.1% 90% 90% 90% 90% 90%
Subcarrier
spacing (kHz) 15
Physical
Resource Block
Bandwidth (kHz)
180
OFDM symbols
per slot
(extended/normal
cyclic prefix)
7/6
The cyclic prefix consists in introducing a guard period in the beginning of each OFDM symbol. To
preserve the continuity of the signal, the content of this guard period will be a copy of the information
in the end of the symbol. If the guard period is longer than the delay spread, then there will be no inter
15
symbol interference and so the previous and the following symbols do not overlap with the current
symbol. The following figure illustrates the OFDM cyclic prefix insertion procedure:
Figure 2 – OFDM Cyclic Prefix insertion
The main drawback of the cyclic prefix insertion is the reduction of the effective transmission data rate
compared with no cyclic prefix insertion by a β factor which value is given by the following expression:
(6)
is the OFDM symbol time duration and is cyclic prefix time duration. The reduction of the
effective transmission rate is the same of saying that the energy per useful bit transmitted increases
which is a negative factor. The higher the value of the OFDM symbol time duration compared to the
cyclic prefix length, the higher the spectral efficiency is but on the other hand if the cycle prefix is too
small the transmission can suffer errors due to the ISI.
There are two types of cyclic prefixes defined for LTE:
Normal cyclic prefix - The time duration of the normal cyclic prefix is 4.7µs with an exception in
the first OFDM symbol in the timeslot which has time duration of 5.2µs. The reason in order to
have a different time duration in the cyclic prefix of the first OFDM symbol in a timeslot is due
to accommodate an integer number of symbols in a timeslot. The normal cyclic prefix is used
mainly in urban cells where the channel delay spread is relatively small. It is capable of
handling path delay variations up to about 1.4 km.
Extended cyclic prefix - The time duration of the extended cyclic prefix is 16.7μs. The
extended cyclic prefix is mainly used in rural cells or very large urban cells where the channel
delay spread is higher. It is capable of handling path delay variations up to 10km.
In the discrete domain, the number of cyclic prefix samples is obtained by multiplying the cyclic prefix
time duration with the sampling frequency:
(7)
is the sampling frequency. The delay spread is one the ways to measure the quality of a
communication channel. It can be described as the time interval between the latest and the earliest
component of the signal that arrive to the receiver. The delay spread is originated due to the different
16
paths between the transmitter and the receiver which have different time delays. In a wireless
environment the delay spread can be calculated using the following formula:
(8)
ΔL is the difference between the longest path and the shortest path and c is the speed of light value.
For macro cells the typical value of ΔL is about 300 meters which gives a delay spread of 1 µs
approximately. The worst case of delay spread is 5 µs for the Extended Typical Urban model (ETU).
The coherent bandwidth is another parameter of a communication channel. It can be defined by the
frequency scale where the amplitude and the phase are changed due to the multiple paths between
the transmitter and the receiver. The coherent bandwidth is calculated by the following expression:
(9)
is the value of the delay spread. Frequency errors typically can occur due to slightly drifts between
the frequencies in the transmitter and the receiver local oscillators. Due to these frequency errors, the
perfect orthogonally of the subcarriers is lost, causing subcarrier leakage, also known as Inter Carrier
Interference (ICI).
One of the drawbacks of OFDM is the high sensitivity to frequency offset. The Doppler shift due to the
mobility of the terminals is one of aspects that can cause problems. If we guarantee that the Doppler
shift is much smaller than the subcarrier spacing than there is no problem. For the LTE case the
maximum mobile speed in normal conditions is 350 km/h and the maximum carrier frequency is about
3.5 GHz. With these two parameters it is possible to calculate the Doppler shift due to the mobility:
(10)
It can be considered that the Doppler shift value is acceptable for a good communication if it follows
the next criteria:
(11)
.
The coherent time is a parameter which can be defined by the timescale where the amplitude and the
phase of the received signal changes due to the mobility of the terminal.
The coherent time can be calculated by the following expression:
17
(12)
In summary OFDM communication must obey some criteria to operate correctly.
In order to prevent ICI the following criterion must be satisfied:
(13)
To prevent ISI:
(14)
And to maximize the spectral efficiency:
(15)
The main drawback of the OFDM is the high pick-to-average-ratio (PAPR) which occurs because of
the constructive addition of the signals corresponding to each of the multiple subcarriers. These big
power variations due to the PAPR can cause problems in the transmitter´s amplifier because common
amplifiers are not perfectly linear (they can be almost linear but also in a limited band). This fact can
distort the signal and thus introduce errors in the transmissions. To avoid these problems, base
stations usually have high quality amplifiers which are almost linear in almost all the frequency bands
but they are very expensive.
An OFDM signal containing thousands of subcarriers in the time domain can be approximated by the
Central Limit Theorem to a Gaussian Waveform. In theory, an OFDM signal with a higher number of
subcarriers has a higher PAPR than an OFDM signal with less because it is more likely to happen that
all the signals corresponding to the OFDM subcarriers can contribute constructively to the overall
OFDM signal. In conclusion, generally more subcarriers can result in a higher PAPR in the OFDM
signal.
The PAPR of an OFDM symbol can be formally defined by the square of the peak amplitude divided
by the mean power. In the discrete time domain, considering (n is a natural number) the time
domain samples of an OFDM symbol, PAPR is equal to:
(
)
( )
(16)
OFDMA is an extension of the OFDM based on the concept of FDMA and which consists in
implementing a multi-user communication system. OFDMA assigns for different users, different
number of subcarriers for a specific period of time. Usually subcarriers are allocated in contiguous
groups for simplicity and to reduce the overhead of indicating which subcarriers have been allocated
to each user.
OFDMA can be combined with TDMA such that a specific user has a specific number of subcarriers
and time duration assigned. LTE has a basic quantity which is the smallest unit that can be assigned
to different users and it is called a resource block (RB). Each resource block has a fixed time and
frequency dimension. It is defined of 12 consecutive subcarriers for time duration of one slot of time.
18
Taking into account the value of the subcarrier spacing the occupied bandwidth of a single resource
block is given by the expression bellow:
(17)
The resource blocks can be grouped in multiple ways in the time-frequency grid to form bigger blocks
that can be assigned to specific users in order to provide the best transmission efficiency. The figure
bellow illustrates an example of resource allocation:
Figure 3 - Example of resource allocation in a combined OFDMA/TDMA system
It is possible to divide a basic OFDM transmitter into several blocks where each block has a unique
function. The following figure shows a possible OFDM transmitter block diagram:
Figure 4-OFDM transmitter block diagram
It is now explained for each of the eight blocks its main functions:
19
The first OFDM block is the serial to parallel block which converts the bit stream into several
blocks of variable number of bits and each of one will be modulated. The number of bits in
each block depends on the modulation scheme used. In LTE the number of bits for each
block can be two, four or six bits.
The second OFDM block is called the constellation mapping which converts the blocks of bits
into modulated symbols. The modulation schemes defined for LTE are QPSK, 16 QAM and
64 QAM. The criterion to choose a specific modulation scheme rather than other will depend
on communication channel quality in the frequency band of the subcarrier carrying a specific
modulated symbol.
The third OFDM block is called the subcarrier mapping which consists in assigning the
subcarriers to the modulated symbols. Each subcarrier can carry one modulated symbol each
time. It is possible that some subcarriers do not carry any modulated symbol. For example
LTE uses guard subcarriers which do not carry data bits.
The fourth OFDM block is the N-point IFFT block which applies the Inverse Fast Fourier
Transform to the modulated symbols already in the desired order. Usually the number of
subcarriers carrying data is less than N. When this happens the input of the IFFT is fulfilled
with zeroes in order to match the IFFT size.
The fifth block is the cyclic prefix block which consists in adding samples to the N
samples from the output of the IFFT. The number depends on the type of cyclic prefix
used and on the sampling frequency. LTE cyclic prefix can have two lengths namely the
normal cyclic prefix and the extended cycle prefix.
The sixth block is the parallel to serial block and consists in converting the parallel samples
from the output of the cyclic prefix clock into a discrete time sequence which represents the
OFDM time discrete baseband signal.
The seventh block is the digital to analogue (D/A) block which converts the discrete time
signal into an analogue/continuous time signal.
The fifth block is called the Radio block which basically up converts the baseband signal to a
radiofrequency signal.
20
It is possible to divide a basic OFDM receiver into several blocks where each block has a unique
function. The following figure shows a possible OFDM transmitter block diagram:
Figure 5-OFDM receiver block diagram
It is now explained for each of the eight blocks its main functions:
The first block is the Radio block. This block will realize the inverse operation of the Radio
block mentioned above in the OFDM transmitter above. It is basically down converts the radio
signal into a continuous baseband signal.
The second block is the analogue to digital (A/D) block which converts the continuous time
received by the output of the radio block into a discrete time signal.
The third block is the serial to parallel block and consists in converting the discrete time
sequence into parallel sets of samples.
The fourth block has the task of removing the cyclic prefix samples from each of the sets
of samples received from the S/P block.
The fifth block is the N-point FFT block which applies the Fast Fourier Transform. The set of
the FFT output samples are in the frequency domain signal.
The sixth block is the subcarrier de-mapping and channel equalization block which consists in
doing the inverse operation of the subcarrier mapping block and the channel equalization is
supposed to compensate the amplitude and phase distortion caused by the communication
channel to the signal.
The seventh block converts the modulated symbols (QPSK, 16 QAM or 64 QAM) symbols
into the correct.
The eighth block is the P/S block which consists in converting the parallel blocks of bits into a
single bit stream.
OFDM is also used in other systems like Asymmetric Digital Subscriber Line (ADSL), WiMAX,
some WLAN standards and Digital Video Broadcast (DVB) technology.
21
2.2 Downlink Physical
It is possible to divide LTE resources into three dimensions in the downlink transmission: time,
frequency and space.
The space dimension is measured in layers and each of these layers can be accessed by different
antenna ports.
In the time resource dimension there are defined LTE time units. The longest time unit is the LTE
frame and it has an overall 10ms of time duration. This frame is constituted by 20 time slots, each one
with time duration of 0.5ms. The LTE sub frame is a group of two consecutive time slots and so its
time duration is 1ms. The figure above shows the LTE frame structure:
Figure 6 – LTE frame structure
Each one of the LTE time slots contains seven OFDM symbols using the normal cyclic prefix or six
time slots using the extended cyclic prefix. As already mentioned the time duration of the OFDM
symbol is approximately equal to 66.67 µs. The following expressions demonstrate that in the both
cyclic prefix cases the time slot equals the established LTE time duration:
(18)
(19)
The two figures above illustrate the LTE slot structure:
Figure 7 - LTE slot structure for the extended cyclic prefix case
22
Figure 8 - LTE slot structure for the normal cyclic prefix case
The smallest unit of resource is the Resource Element (RE), which consists of one subcarrier for
duration of one OFDM symbol. One Resource Block (RB) consists of twelve consecutive subcarriers
for duration of one slot. LTE default subcarrier spacing is 15 kHz and so a resource block occupies
180 kHz of the frequency spectrum (12×15 = 180 kHz). A resource block contains 84 REs in the case
of using the normal cyclic prefix and 72 REs in the case of the using the extended cyclic prefix.
Figure 9 – Resource Block structure when using the normal cyclic prefix
Some resource blocks contain special resource elements reserved for special functions like
synchronization signals, reference signals, control signalling and critical broadcast system information.
All the time units described above are defined for LTE FDD. The LTE TDD has some slightly
differences to LTE FDD. In TDD mode the LTE frame has 10ms of time duration and can be divided
into two equal time parts called the half frames with time duration of 5ms. These half frames are thus
constituted by 5 sub frames with time duration of 1ms.
There are two types of sub frames:
Normal sub frames
Special sub frames
The special sub frame contains three fields:
23
DwPTS - Downlink Pilot Time Slot
GP - Guard Period
UpPTS - Uplink Pilot Time Slot
LTE TDD uses the same frequency bands both for uplink and downlink. The transmission directions
are separated by transmitting the UL and DL information in different subframes. LTE provides
configuration standards to achieve this goal. There are seven Uplink-Downlink configuration
possibilities and all of these configurations use either 5ms or 10ms switch point periodicity.
The table below shows all of the seven Uplink-Downlink configurations:
Table 4 - Uplink-Downlink configuration possibilities
Uplink-
Downlink
Configuration
Downlink
to Uplink
Switch
Periodicity
Sub-frame Number
0 1 2 3 4 5 6 7 8 9
0 5ms D S U U U D S U U U
1 5ms D S U U D D S U U D
2 5ms D S U D D D S U D D
3 10ms D S U U U D D D D D
4 10ms D S U U D D D D D D
5 10ms D S U D D D D D D D
6 5ms D S U U U D S S U D
D is a sub-frame for downlink transmission, S is a special sub frame used for a guard time and U is a
sub frame for uplink transmission.
24
2.3 Cell Synchronization
Any User Equipment to establish a LTE communication must undertake a cell search procedure. The
cell search procedure consists of a series of synchronization stages by which the UE determines time
and frequency parameters that are necessary to demodulate the downlink and to transmit uplink
signals with the correct timing.
The three major synchronization requirements are:
Symbol and frame timing acquisition where the correct symbol start position is determined.
Carrier frequency synchronization, which is required to reduce or eliminate the effect of
frequency errors that occur due to different frequencies in the local oscillators of transmitters
and receivers and as well as the Doppler shift caused by any UE motion.
Sampling clock synchronization.
The cell search procedure starts with two physical signals that are broadcasted in each cell:
Primary Synchronization Signal (PSS)
Secondary Synchronization Signal (SSS)
In FDD mode PSS is located in the last OFDM symbol of the first and eleventh slots of each LTE
frame. SSS is located in the previous OFDM symbol of PSS. In TDD mode PSS is located in the third
OFDM symbol of the third and thirteenth slots and SSS is located three OFDM symbols before. In the
frequency domain, PSS and SSS are transmitted in the central six resource blocks.
The Primary Synchronization Signal is constructed in the frequency domain by a Zadoff-Chu
sequence with a length equal to 63 and there are three roots 25, 29 and 34.
The Secondary Synchronization Signal is based on maximum length sequences (MLS). The maximum
length sequences are generated using maximal linear feedback shift registers with length n.
25
2.3.1 Zadoff-Chu Sequence
The Zadoff-Chu sequence is a sequence of complex numbers which has special properties.
The Zadoff-Chu sequence is given by the following equation:
( )
( )
(20)
R is the root, l is a natural number and N is the length of the sequence.
A Zadoff-Chu sequence has three major properties:
It has constant amplitude and its N-DFT has also constant amplitude. This property limits the
Peak to Average Power Ration (PAPR).
ZC sequences of any length have ideal cyclic autocorrelation which is same of saying that the
correlation with its circularly shifted version is a delta function. Delta function is zero for all
values except the origin.
The absolute value of the cyclic cross-correlation function between any two ZC sequences is
constant.
This type of sequence that has the properties shown above is called a CAZAC sequence.
The normalized cross correlation of two sequences x and y is given by the expression:
( ) ∑ (( ( ) ) ( ( ) ))
√∑ ( ( ) ) √∑ ( ( ) )
(21)
and are the means of the sequences x and y respectively. In the expression above when the index
of a sequence is out of the range, it is possible to have two approaches:
Consider that all those elements from the sequence have value zero.
Consider that the sequence is circular. Example: x(-1)=x(N+1).
In the autocorrelation and cross correlation calculated below is considered that the series are circular.
The figures below illustrate the proprieties of the Zadoff-Chu sequence for the cases used in LTE.
26
Figure 10 – Zadoff-Chu Sequence in time domain with R=25 and N=63
Figure 11 – Zadoff-Chu Sequence in time domain with R=29 and N=63
0 10 20 30 40 50 60 70-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
0 10 20 30 40 50 60 70-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
27
Figure 12 – Zadoff-Chu Sequence in time domain with R=34 and N=63
Figure 13 – Autocorrelation of a Zadoff-Chu Sequence in time domain with R=25 and N=63
0 10 20 30 40 50 60 70-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
0 20 40 60 80 100 120-0.2
0
0.2
0.4
0.6
0.8
1
1.2
28
Figure 14 – Cross correlation between two Zadoff-Chu Sequences in time domain with R=29 and N=63
and with R=34 and N=63
Zadoff–Chu sequences are used in LTE in the Primary Synchronization Signal (PSS), Physical
Random Access Channel (PRACH), Physical Uplink Control Channel (PUCCH), Physical Uplink
Shared Channel (PUSCH) and Sounding Reference Signals (SRS).
0 20 40 60 80 100 120-0.2
0
0.2
0.4
0.6
0.8
1
1.2
29
2.4 Reference Signals
Reference Signals (RS) are sent only on particular resource elements. Downlink reference symbols
are inserted in the first and the fifth OFDM symbols of each time slot if it is used the normal cyclic
prefix. In the case of the extended cyclic prefix the reference symbols are inserted in first and in the
fourth OFDM symbols of each time slot. In order to estimate the communication channel as accurately
as possible, all correlations between channel coefficients in time, frequency and space should be
taken into account.
In the LTE downlink, there are five different types of Reference Signals:
Cell Specific Reference Signals - They are available to all UEs in a cell and no specific EU
processing is applied to them.
UE specific Reference Signals - They may be embedded in the data for specific UEs (also
known as Demodulation Reference Signals (DM-RSs).
MBSFN specific Reference Signals - They are used only for Multimedia Broadcast Single
Frequency Network (MBSFN) operation.
Positioning Reference Signals - They may be embedded in certain ‘positioning subframes’ for
the purpose of UE location measurements.
Channel State Information (CSI) Reference Signals - They have specifically purpose of
estimating the downlink channel state and not for data demodulation.
30
2.5 Data and Control Downlink Physical Channels
LTE defines a number of downlink physical channels to carry data blocks received from MAC and
higher layers. There are channels for data transporting and channels for control.
There are three types of physical data transporting channels defined for the LTE downlink:
Physical Downlink Shared Channel (PDSCH)
Physical Broadcast Channel (PBCH)
Physical Multicast Channel (PMCH)
The Physical Downlink Shared Channel (PDSCH) is designed for very high transmission rates and it is
mainly used for data and multimedia transport but it can also be used for transmission of information
data which is not transmitted by the PBCH and also for paging messages. Data is transmitted on the
PDSCH in units known as Transport Blocks (TBs) which correspond to a MAC Protocol Data Unit
(PDU).All the three possible modulation schemes defined for LTE (QPSK, 16 QAM and 64 QAM) can
be used in the PDSCH. The channel coding used in this channel with the intention of protecting
against propagation channel errors is the 1/3 rate turbo coding.
The Physical Broadcast Channel (PBCH) is used to transmit system information in order to operate
and configure the other channels. Its broadcasts limited number of parameters essential for initial
access of the cell like the downlink system bandwidth, the Physical Hybrid ARQ Indicator Channel
structure, and the most significant eight bits of the System Frame Number. These parameters are
carried in Master Information Block (MIB). MIB has a data length of 14bits. The main mechanisms
employed to facilitate reliable reception of the PBCH in LTE are time diversity, Forward Error
Correction (FEC) coding and antenna diversity. The FEC coding used in PBCH is convolutional coding
with a code rate of 1/3.
The Physical Multicast Channel (PMCH) is designed to carry data for multimedia broadcast and
multimedia services (MBMS). The PMCH can only be transmitted in certain specific sub frames known
as Multimedia Broadcast Single Frequency Network (MBSFN) sub frames, indicated in the system
information carried on the PDSCH.
Control information can be located in the first 1, 2 or 3 OFDM symbols in a sub frame over the entire
bandwidth. In narrow bandwidth systems the control information can include also a fourth OFDM
symbol.
There are three types of physical control channels defined for the LTE downlink:
Physical Downlink Control Channel (PDCCH)
Physical Control Format Indicator Channel (PCFICH)
Physical Hybrid ARQ Indicator Channel (PHICH)
31
The Physical Downlink Control Channel (PDCCH) is used for mobile control information. This channel
is mainly characterized by its low error rate rather than a high data rate. The PDCCH carries a
message known as the Downlink Control Information (DCI), which contains resource assignments and
control information for a particular UE or group of UEs. Each PDCCH is transmitted using one or more
Control Channel Elements (CCEs).The PDCCH is mapped onto resource elements in up to the first
three OFDM symbols in the first slot of a sub frame.
The Physical Control Format Indicator Channel (PCFICH) carries the Control Format Indicator (CFI)
which indicates the number of OFDM symbols (typically 1, 2 or 3) used for transmission of control
channel information in each sub frame extending over of the entire bandwidth. Due to this flexibility,
the control channel overhead can be adjusted for different system´s configurations, traffic scenarios
and channel conditions.
Physical Hybrid ARQ Indicator Channel (PHICH) carries the HARQ ACK/NACK, which indicates
whether the eNodeB has correctly received a transmission on the PUSCH. The HARQ indicator is set
to 0 for a positive Acknowledgement (ACK) and 1 for a Negative Acknowledgement (NACK). This
information is repeated in each of three BPSK 8 symbols.
Like the PDCCH, the CCPCH robustness rather than a high data rate is the main concern in this
channel. The CCPCH carries cell-wide control information and the there is only one modulation format
available, QPSK. The CCPCH is transmitted exclusively on the 72 active subcarriers centred on the
DC subcarrier. CCPCH symbols are mapped to resource elements in increasing order of index k.
Convolutional coding is used in this channel.
32
2.6 Adaptive Modulation and Channel Coding
To optimize capacity and coverage for each User Equipment (UE), LTE adjusts the transmitted
information data rate (modulation scheme and channel coding rate) dynamically to match the radio
channel capacity for each user. Link adaptation is closely related to the choice of a specific channel
coding scheme used for Forward Error Correction (FEC). For the downlink data transmissions, the
eNodeB chooses the modulation scheme and code rate depending on a prediction of the downlink
communication channel quality. The quality channel indicator (CQI) describes the quality of the
communication channel and it is transmitted by the User Equipment (UE) in the uplink. CQI indicates
the adequate transmission data rate and it depends on the received signal to interference plus noise
ratio (SNIR) and on the UE characteristics.
The CQI is a 4 bit quantity and for a specific CQI index the eNodeB assigns:
A modulation scheme - A low index modulation scheme has a high degree of tolerance to
noise and interference but provides a low transmission rate and a high index modulation
scheme has a low degree of tolerance to noise and interference but provides a high
transmission rate.
A code rate - For a specific modulation, a low code rate will be used in a lower SNIR
communication channel whereas a high code rate will be used in a high SNIR communication
channel.
In LTE usually each user has assigned the same modulation scheme and channel coding.
The fifteen different CQI index and theirs correspondent modulation and code rate are in the following
table:
Table 5 – All the fifteen possible CQI index defined for LTE and characteristics
CQI Index Modulation Code rate Efficiency
(information
bits/symbol)
1 QPSK 78 0.1523
2 QPSK 120 0.2344
3 QPSK 193 0.3770
4 QPSK 308 0.6016
5 QPSK 449 0.8770
6 QPSK 602 1.1758
7 16 QAM 378 1.4766
8 16 QAM 490 1.9141
9 16 QAM 616 2.4063
10 64 QAM 466 2.7305
11 64 QAM 567 3.3223
33
12 64 QAM 666 3.9023
13 64 QAM 772 4.5234
14 64 QAM 873 5.1152
15 64 QAM 948 5.5547
In the previous mobile cellular system UMTS, the channel coding chosen was the turbo codes
because they allow a performance near the theoretical Shannon limit. In newer versions of the UMTS
the channel coding was enhanced by the ability to select different redundancy versions for HARQ
retransmissions.
LTE uses also turbo codes in channel coding but with a fewer enhanced aspects mainly because very
high transmission rates are used.
The following table shows the main channel coding features for both UMTS and LTE:
Table 6 – Channel coding features of UMTS and LTE used for data transmission
Channel Coding UMTS LTE
Constituent code Tailed, eight states, R = 1/3
mother code
Tailed, eight states, R = 1/3
mother code
Turbo interleaver Row/column permutation
Contention-free quadratic
permutation polynomial
(QPP) interleaver
Rate matching Performed on concatenated
code blocks
Virtual Circular Buffer (CB)
rate matching, performed per
code block
Hybrid ARQ
Redundancy Versions (RVs)
defined, Chase operation
allowed
RVs defined on virtual CB,
Chase
operation allowed
Control channel 256-state tailed
convolutional code
64-state tail-biting
convolutional
code, CB rate matching
Per-code-block operations Turbo coding only
CRC attachment, turbo
coding, rate
matching, modulation
mapping
The channel coding used in general control information uses convolutional coding instead of the turbo
coding because the code blocks are much smaller and thus there is no need of adding more
complexity to the system to support the turbo codes.
34
35
Chapter 3 Uplink
36
37
3.1 Single Carrier Frequency Division Multiple Access
Single Carrier Frequency Division Multiple Access (SC-FDMA) is used in LTE uplink rather than
OFDMA mainly due to its lower pick-to-average-ratio (PAPR). UE terminals have less power available
for their data transmission and thus SC-FDMA is more suitable.
In theory, an SC-FDMA signal can be generated in either the time domain or the frequency domain but
in time domain the signal will be less bandwidth efficiency. The SC-FDMA transmitter and receiver can
introduce distortion at the carrier frequency (DC in baseband). To prevent this problem, the
subcarriers are all frequency-shifted half of the subcarrier spacing (7.5 kHz).
The SC-FDMA transmitter is similar to the OFDM but has an additional DFT processing before the
OFDM processing. Unlike the standard OFDM where the each data symbol is carried by the individual
subcarriers, the SC-FDMA transmitter carries data symbols over a group of subcarriers transmitted
simultaneously. In other words, the group of subcarriers that carry each data symbol can be viewed as
one frequency band carrying data sequentially in a standard FDMA. Analysis has shown that the LTE
UE Radio Frequency Power Amplifier (RFPA) can be operated about 2 dB closer to the 1-dB
compression point than would otherwise be possible if OFDM were employed on the uplink.
However, the current working assumption is that LTE will use localized subcarrier mapping. This
decision was motivated by the fact that with localized mapping, it is possible to exploit frequency
selective gain via channel dependent scheduling (assigning uplink frequencies to UE based on
favourable propagation conditions).
It is possible to divide a basic SC-FDMA transmitter into several blocks where each block has a
unique function. The following figure shows a possible SC-FDMA transmitter block diagram:
Figure 15 – SC-FDMA transmitter block diagram
38
It is now explained for each of the nine blocks its main functions:
The first SC-FDMA block is the serial to parallel block which converts the bit stream into
several blocks of fixed number of bits and all the blocks will be modulated using the same
modulation scheme. The number of bits in all blocks depends on the modulation scheme
used. In LTE the number of bits for all block can be two, four or six bits.
The second SC-FDMA block is called the constellation mapping which converts the blocks of
bits into modulated symbols. The modulation schemes defined for LTE are QPSK, 16 QAM
and 64 QAM. As already was referred all modulated symbols will have the same modulation
scheme. The criterion to choose a specific modulation scheme rather than other will depend
on communication channel quality in the frequency band of the subcarrier carrying a specific
modulated symbol.
The third SC-FDMA block is the M-point DFT which applies the discrete Fourier transform to
the modulated symbols. The operation is similar to spreading the symbols over a specific
frequency band.
The fourth SC-FDMA block is called the subcarrier mapping which consists in assigning the
subcarriers in different ways. There are two possible ways of subcarrier mapping in SC-
FDMA, localized and distributed. In localized it is allocated M adjacent subcarriers to a user.
In distributed it is allocated equally spaced M subcarriers every Lth subcarrier. L must satisfy
the condition ML<N. In both cases in order to match the IFFT size it is appended with zeroes
the non-assigned subcarriers.
The fifth SC-FDMA block is the N-point IFFT block which applies the Inverse Fast Fourier
Transform to the output of the subcarrier mapping samples. If M=N, then DFT and IFFT
cancel each other and the modulated symbols are transmitted directly.
The sixth SC-FDMA block is the cyclic prefix block which consists in adding samples to
the N samples from the output of the IFFT. The number depends on the type of cyclic
prefix used and on the sampling frequency. LTE cyclic prefix can have two lengths namely
the normal cyclic prefix and the extended cycle prefix.
The seventh SC-FDMA block is the parallel to serial block and consists in converting the
parallel samples from the output of the cyclic prefix clock into a discrete time sequence which
represents the SC-FDMA time discrete baseband signal.
The seventh SC-FDMA block is the digital to analogue (D/A) block which converts the
discrete time signal into an analogue/continuous time signal.
The eighth SC-FDMA block is called the Radio block which basically up converts the
baseband signal to a radiofrequency signal.
39
Figure 16 – SC-FDMA receiver block diagram
It is now explained for each of the eight blocks its main functions:
The first block is the Radio block. This block will realize the inverse operation of the Radio
block mentioned above in the OFDM transmitter above. It is basically down converts the radio
signal into a continuous baseband signal.
The second block is the analogue to digital (A/D) block which converts the continuous time
received by the output of the radio block into a discrete time signal.
The third block is the serial to parallel block and consists in converting the discrete time
sequence into parallel sets of samples.
The fourth block has the task of removing the cyclic prefix samples from each of the sets
of samples received from the S/P block.
The fifth block is the N-point FFT block which applies the Fast Fourier Transform. The set of
the FFT output samples are in the frequency domain signal.
The sixth block is the subcarrier de-mapping and channel equalization block which consists in
doing the inverse operation of the subcarrier mapping block and the channel equalization is
supposed to compensate the amplitude and phase distortion caused by the communication
channel to the signal.
The seventh block is the IDFT block which has the inverse function of the DFT block of the
SC-FDMA transmitter.
The seventh block converts the constellation symbols into correct bits. It basically does the
demodulation of each set of symbols.
The eighth block is the P/S block which consists
40
3.2 Physical Uplink Channel Structure and Reference
Signals
There are three types of physical channels defined for the LTE uplink:
Physical Uplink Shared Channel (PUSCH)
Physical Uplink Control Channel (PUCCH)
Physical Random Access Channel (PRACH)
The Physical Uplink Shared Channel (PUSCH) carries data from the Uplink Shared Channel (UL-
SCH) transport channel and uses SC-FDMA. The channel code used is the turbo code with a code
rate r = 1/3, which can be adapted to a suitable final code rate by a rate-matching process. It also uses
a symbol-level channel interleaving which follows the scrambling using a length-31 Gold code.
In the PUSCH the resources are allocated on a sub-frame basis by the UL scheduler and subcarriers
are allocated in multiples of 12 (RBs). The PUSCH can use the three possible modulation formats
defined in LTE (QPSK, 16QAM and 64QAM).
The PUCCH carries uplink control information and it is never transmitting PUSCH data at the same
time. The control information carried by the PUCCH includes the channel quality information (CQI),
ACK/NACK, HARQ and uplink scheduling request. The PUCCH uses two modulation schemes: BPSK
and QPSK.
The Physical Random Access Channel is used for random access functions. When this physical
channel is used the downlink and uplink propagation delays are not known and therefore it cannot be
synchronized.
The channel coding used the LTE uplink is the r=1/3 turbo coding.
In LTE uplink there are two types of reference signals:
Demodulation Reference Signals (DM-RS) – These reference signals are mainly used for
enabling coherent signal demodulation at the eNodeB.
Sounding Reference Signal (SRS) – This reference signals is mainly used for determining
channel quality.
41
Chapter 4 Modem
42
43
4.1 Introduction
The main objective is to implement and simulate a LTE modem using the Matlab software and analyse
the results in order to test theoretical aspects of the OFDMA and the SC-FDMA. It will be simulated
both the uplink and downlink directions. There are some important considerations that will be present
in the simulations:
The input bit stream of the modem is supposed to be random (bit 1 and bit 0 both with a
probability of 0.5)
There will no channel coding involved
Both downlink and uplink directions will be modelled in baseband
Communication channel will be modelled by a Finite Impulse Response (FIR) filter and an
Addictive White Gaussian Noise(AWGN) model
The input reference signal used for channel estimation is based on the Zadoff-chu sequence
Guarantee always a bit error rate less than 0.001
No guard subcarriers are considered
It will be used the normal cyclic prefix because it is assumed we are in regular urban cell
scenario
In the LTE uplink simulation the SC-FDMA communication has DFT/IDFT length M equal to
the FFT/IFFT length N
The modulation scheme choice for each subcarrier or for all the subcarriers is based on the bit
loading formulas
The chosen numbers of subcarriers for simulation were 512, 1024 and 2048. These numbers
were chosen due to the fact they differ from each other by a factor of 2 which allows observing
more easily variations in the parameters with the number of subcarriers.
The OFDM transmitter and the OFDM receiver must be modelled as well as the communication
channel between them. The goal is to study the performance of the modem guaranteeing always an
error bit probability less than 0.001. To maximize the OFDM transmission (send the maximum bits
guaranteeing the bit error rate less than 0.001), it is useful to use a formula which gives the best
modulation technique for each subcarrier for a specific bit error rate (bit loading formulas).
As already said the communication channel will be modelled by a FIR filter and an AWGN channel
model as shown in the following diagram:
44
Figure 17 – Communication channel model
The FIR filter will be used to simulate the multipath propagation caused by multiple signal reflections
on obstacles. A general filter transfer function can be written using the following formula:
( ) ∑
∑
(22)
When N=0, there is no feedback in the filter, the output will only have dependency on the input and so
in this case it is called a FIR filter. In the case of N≠0, the filter is called an IIR filter.
The transfer function of the FIR filter will depend on the numbers of signal reflections and on the delay
spread of the channel. For example a FIR filter with the following b coefficients:
has two signal reflections (number of non-zero coefficient with the
exception of ) and has a delay spread time duration of M multiplied by the FIR filter tap delay. In the
example above M is equal to 6 which is equal to the identification number of the last b coefficient. The
coefficients´ values of the FIR filter transfer function used in the simulations were chosen taking into
account the typical channel models used in LTE.
The Additive White Gaussian Noise (AWGN) channel model is a random channel noise model with a
constant spectral density and a Gaussian distribution of amplitude and it will be used to simulate the
channel noise in the environment between the transmitter and the receiver. The Additive Gaussian
AWGN model will introduce phase and amplitude changes in the signal.
Now it will be described the sequence of the procedures used the Modem for downlink. First it will be
generated a random bit stream with a sufficient large number of bits in order to have more accurate
results. Then the bit stream will be divided into sub streams, each of them carried by a specific OFDM
subcarrier. Each OFDM subcarrier will have different modulation techniques according to each of the
subcarrier channel quality. For example if a specific channel has a Channel Quality Index (CQI) 8,
then the modulation scheme chosen for this channel will be 16 QAM according to the CQI table for
LTE. The CQI index depends mainly on the Signal to Noise Ratio (SNR.) The modulated symbols will
enter in the IFFT processing and from the output samples from the IFFT it will be added the cyclic
prefix samples. This baseband OFDM signal enters the communication channel.
45
The OFDM receiver like the OFDM transmitter will be modelled in almost the reverse way. First it will
be removed the cyclic prefix samples from the signal. After that the remaining samples will enter in the
FFT processing. The channel equalization is done dividing the FFT output samples by the channel
transfer function in the frequency domain (this procedure almost eliminates the distortion caused by
the communication channel because the communication channel noise is impossible to predict). The
output of the FFT processing after the channel equalization will be the modulated symbols
(constellation). To correctly demodulate each subcarrier, the receiver needs to previously know all the
modulation schemes used for each subcarrier. Finally, the original bit stream is compared with de
demodulated bit stream and it is obtained the bit errors. The bit error rate is obtained dividing the
number of bit errors by the number of all the transmitted bits.
In the following figure, there are illustrated a baseband LTE transmitter, the communication channel
and the LTE receiver for LTE downlink:
Figure 18 - OFDM baseband transmitter and receiver and the communication channel block diagram
46
4.2 Channel Estimation
The channel estimation procedure is done before transmitting any data bit. After that it starts
transmitting data through the communication channel. The channel estimation´s main goals differ for
each simulation section.
The main goals of the channel estimation for the downlink part1 and for the uplink are:
To estimate the channel transfer function
To estimate value of the Signal to Noise Ratio (SNR) for each subcarrier
The main goals of the channel estimation for the downlink part2 are:
To estimate the channel transfer function
To estimate value of the Noise Power for each subcarrier
The channel estimation is done by sending several identical reference signals (in the simulations the
number of signals sent is 80) based on the Zadoff-Chu sequence (root equal to 25 and length 63 )
through the communication channel. For example if it is done a simulation with 1024 subcarriers the
reference signal will be extension of the Zadoff-Chu sequence with 1024 samples ( repeating the
Zadoff-Chu 63 samples sequence until it reach the 1024 samples) The basic channel estimation
procedure is done correctly following the next steps for each of the 80 cycles:
The input discrete signal in the frequency domain is a signal based on the Zadoff-Chu
sequence but extended to the number of subcarriers
It is applied the Inverse Fast Fourier Transform (IFFT) to the signal
It is introduced the cyclic prefix
The resulting signal passes through the communication channel
The cyclic prefix is removed
It is applied the Fast Fourier Transform (FFT) to the signal
It is obtained the output response signal in the frequency domain
The procedure explained above conduces to obtain the parameters necessary to begin to transmit
data through the Modem. The calculations of the useful parameters are described below:
The approximate channel transfer function (frequency domain): It is obtained by dividing the
mean of the output responses in the frequency domain by the reference signal also in the
frequency domain.
The vector containing the power of all the subcarriers: It is the absolute value of the mean of
the output responses squared in the frequency domain.
The vector containing the noise of all the subcarriers: It is the variance of the output responses
in the frequency domain.
The vector containing the Signal to Noise Ratio (SNR) of all the subcarriers: It is obtained
dividing the power vector by the noise vector element by element.
47
4.3 Bit Loading
The Shannon theorem states that the maximum channel capacity for a certain Signal to Noise Ratio
with an arbitrary low error bit probability is given by the following expression:
(
) (22)
If we divide both members of the equation by the channel bandwidth B we obtain:
(
) (23)
The parameter b which is equal to
gives the maximum bits per symbol for that channel and this value
indicates the most suitable modulation technique. For example if there is a channel with a Signal to
Noise Ratio
, bits/symbol and so the best modulation technique for this transmission
is QPSK (2 bits/symbols) because it does not exceed the maximum theoretical bits/symbol limit.
If it is desired to know the maximum bits per symbol for a specific error probability, we have to add the
gap parameter Γ in the previous formula. The gap parameter is calculated using the following
expression:
( ⁄ )
(24)
is the inverse of the Q function.
Adding the gap parameter to the Shannon formula, we obtain:
( ⁄
) (25)
Which gives the maximum theoretical value if bits/symbol for a specific Signal to Noise Ratio and bit
error probability.
In a general M-QAM constellation where and b the number of bits per symbol is even, the
alphabets used are given by the expression below:
( ) ( ) * √
+ (26)
As an example, for a 16-QAM constellation the alphabets are the following:
{
} (27)
Below it will be explained how to calculate the average energy of an M-QAM constellation.
Firstly it will be calculated the sum of energy of the individual alphabets of the constellation. The
expression below gives that result:
48
∑ ∑ ( ) ( )
√
√
(28)
In order to find the average energy of an individual alphabet, it will be divided by M. Concluding the
average energy is given by:
( ) (29)
In a general M-PSK constellation where and b the number of bits in each constellation is even,
the alphabets used are:
( )
( ( )
) (
( )
) (30)
m is a natural number between 1 and M.
The average energy of the M-PSK constellation is equal √ because the energy of all the individual
alphabets is √ .
49
4.4 Downlink part 1
In the downlink simulations, the OFDM signal analysed is not the practical implementation of the LTE
downlink mainly because in these simulations each of OFDM subcarriers can have different
modulation schemes from each other. In the practical implementation of LTE downlink, the resources
are grouped into resource blocks as already was explained. Each of these resource blocks contains
twelve OFDM subcarriers, all using the same modulation scheme. The purpose of these downlink
simulations is to study a general OFDM signal in an outdoor environment.
4.4.1 Simulation
The first simulation has the following parameters:
Approximately 1000000 bits to be transmitted
512,1024 and 2048 OFDM subcarriers
Fir transfer function with the following coefficients: 1,4; 0; 0; 0; 0; 0; 0; 0; 0; 0,6; 0; 0; 0,8; 0; 0;
0; 0,9; 0; 0; 0; 0,8; 0; 0; 0; 0; 1,1; 0; 0; 0; 1,2.
The noise amplitude of the communication channel is 0,01
Transmission only if it is possible to guarantee a bit error rate smaller than 0.001
The main objective is to compare the frequency response of the FIR filter used to simulate the
communication channel and the number of bits transmitted per each OFDM subcarrier. It is expected
that the OFDM subcarriers in the frequency zones that suffer more attenuation by the communication
channel, transmit less number of bits per modulated symbol and the OFDM subcarriers in the
frequency zones that suffer less attenuation by the communication channel, transmit more number of
bits per modulated symbol. The number of bits per modulated symbols can have the values 2, 4 and 6
(corresponding to the modulation schemes QPSK, 16QAM and 64 QAM respectively) but also the 0
value in the case of no modulation scheme used which is the same of saying that no bits are
transmitted in that OFDM subcarrier because of the very high attenuation of the communication
channel in that frequency zone.
50
4.4.2 Results
Figure 19 – Number of bits/symbols transmitted per subcarrier for the case of 512 subcarriers with a
Signal to Noise Ratio of 27.7 dB
Figure 20 - Number of bits/symbols transmitted per subcarrier for the case of 1024 subcarriers with a
Signal to Noise Ratio of 24.8 dB
0 100 200 300 400 500 6000
1
2
3
4
5
6
0 200 400 600 800 1000 12000
1
2
3
4
5
6
51
Figure 21 - Number of bits/symbols transmitted per subcarrier for the case of 2048 subcarriers with a
Signal to Noise Ratio 21.7 dB
Figure 22 – FIR filter frequency response
These two graphics confirm the theoretical expectations in the way that the OFDM subcarriers
corresponding to the frequency zones in the FIR filter frequency response graphic with less
attenuation have more transmitted bits per modulated symbol on the three cases (512, 1024 and 2048
OFDM subcarriers).The last statement can be proved looking in the little zone at the lowest frequency
band where the FIR filter magnitude can be considered high and then observing the corresponding
frequency zone in the figures 19, 20 and 21, it is can be concluded that all the OFDM subcarriers
belonging to that zone use 64QAM which correspond to 6 bits per modulation symbol, the maximum
0 500 1000 1500 2000 25000
1
2
3
4
5
6
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1-3000
-2000
-1000
0
Normalized Frequency ( rad/sample)
Phase (
degre
es)
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1-40
-20
0
20
Normalized Frequency ( rad/sample)
Magnitude (
dB
)
52
value. Following the same logic it can be concluded looking at the FIR filter frequency response
graphic that in the frequency zones with more attenuation correspond that less transmitted bits per
modulated symbols or even no transmission when the attenuation is very high for the 19, 20 and 21
figures.
4.4.3 Simulation
The second simulation has the following parameters:
Approximately 1000000 bits to be transmitted
512, 1024 and 2048 OFDM subcarriers
Fir transfer function with the following coefficients: 1,4; 0; 0; 0; 0; 0; 0; 0; 0; 0,6; 0; 0; 0,8; 0; 0;
0; 0,9; 0; 0; 0; 0,8; 0; 0; 0; 0; 1,1; 0; 0; 0; 1,2.
Transmission only if it is possible to guarantee a bit error rate smaller than 0.001
The main objective is to measure the variation of the number of bits transmitted per OFDM symbol
with the global Signal to Noise Ratio. This global Signal to Noise Ratio is obtained by calculating the
mean Signal to Noise Ratio all the OFDM symbols. It is expected that the number of bits transmitted
per OFDM symbol increase with the increase of the global Signal to Noise Ratio because the bigger
the Signal to Noise Ratio is, more bits per OFDM symbol is possible to transmit according to the
Shannon formula already explained for each OFDM subcarrier. The number of bits transmitted per
OFDM symbol is the sum of all the bits transmitted per OFDM subcarrier. It is possible to calculate the
inferior and superior limits of the number of bits per OFDM subcarrier for the cases of 512, 1024 and
2048 OFDM subcarriers:
If the Signal to Noise Ratio is very low for all subcarriers, there will be transmitted no bits at all.
The inferior limit is 0.
If the Signal to Noise Ratio is very high for all subcarriers, the modulation technique used will
be 64QAM (6 bits/symbol) for any number of OFDM subcarriers. The overall number of bits
per OFDM symbol is 6×Nc = 6 Nc bits, where Nc is the number of OFDM subcarriers.
In summary, the variation of bits transmitted per OFDM symbol ranges between the following values:
For 512 subcarriers, the number of bits transmitted ranges between 0 and 3072;
For 1024 subcarriers, the number of bits transmitted ranges between 0 and 6144;
For 2048 subcarriers, the number of bits transmitted ranges between 0 and 12288.
53
4.4.4 Results
Figure 23 – Variation of the number of bits transmitted per OFDM symbol with the Signal to Noise Ratio in
dB for 512 subcarriers
Figure 24 - Variation of the number of bits transmitted per OFDM symbol with the Signal to Noise Ratio in
dB for 1024 subcarriers
0
500
1000
1500
2000
2500
3000
3500
15 20 25 30 35
N
u
m
b
e
r
o
f
b
i
t
s
Signal to Noise Ratio [dB]
0
1000
2000
3000
4000
5000
6000
7000
14 19 24 29 34
N
u
m
b
e
r
o
f
b
i
t
s
Signal to Noise Ratio [dB]
54
Figure 25 - Variation of the number of bits transmitted per OFDM symbol with the Signal to Noise Ratio in
dB for 2048 subcarriers
As expected the number of bits transmitted per OFDM symbol increase with the Signal to Noise Ratio
for the three cases (512, 1024 and 2048 subcarriers). It can be concluded from the simulations that
the number of bits transmitted per OFDM symbol has an approximately linear dependence with the
number of OFDM subcarriers which is the same of saying that for the same Signal to Noise Ratio, the
number, the number of bits transmitted per OFDM symbol doubles when the number of OFDM
subcarriers doubles for example.
4.4.5 Simulation
The third simulation has the following parameters:
Approximately 1000000 bits to be transmitted
512, 1024 and 2048 OFDM subcarriers
Fir transfer function with the following coefficients: 1,4; 0; 0; 0; 0; 0; 0; 0; 0; 0,6; 0; 0; 0,8; 0; 0;
0; 0,9; 0; 0; 0; 0,8; 0; 0; 0; 0; 1,1; 0; 0; 0; 1,2.
Transmission only if it is possible to guarantee a bit error rate smaller than 0.001
The objective is to measure the variation of the bit error rate with the global Signal to Noise Ratio. It
was expected that the bit error rate decrease with the increase of the Signal to Noise Ratio if there
was no variance of the modulation schemes for all the OFDM subcarriers. The behaviour of the
downlink simulation is: when there is sufficient Signal to Noise Ratio to guarantee a bit error rate less
than 0.001 for a higher order modulation scheme for a particular OFDM subcarrier, the modulation
changes. Every time an OFDM subcarrier changes to a higher order modulation scheme for the same
Signal to Noise Ration, the bit error rate increases. There are cases when the global Signal to Noise
Ratio increases, some OFDM subcarriers changes to higher order modulation schemes and so these
0
2000
4000
6000
8000
10000
12000
14000
15 20 25 30 35
N
u
m
b
e
r
o
f
b
i
t
s
Signal to Noise Ratio [dB]
55
subcarriers contribute to a higher bit error rate and the remaining subcarriers contribute to a lower bit
rate because the Signal to Noise Ratio increased. Thus it is very hard to predict an accurate behaviour
of the bit error rate although it is possible to say that from a certain high value of Signal to Noise Ratio
the bit error rate always decreases because when it is achieved the highest order modulation scheme
(64 QAM), if the Signal to Noise Ration increases the bit error rate will decrease.
The bit error rate will be always less than 0.001 and if it is not possible to guarantee this bit error rate
there will be no transmission.
4.4.6 Results
Figure 26 – Variation of the bit error rate with the Signal to Noise Ratio in dB for 512 subcarriers
Figure 27 – Variation of the bit error rate with the Signal to Noise Ratio in dB for 1024 subcarriers
0,00E+00
1,00E-05
2,00E-05
3,00E-05
4,00E-05
5,00E-05
6,00E-05
7,00E-05
8,00E-05
9,00E-05
15 20 25 30 35
B
i
t
e
r
r
o
r
r
a
t
e
Signal to Noise Ratio [dB]
0,00E+00
2,00E-05
4,00E-05
6,00E-05
8,00E-05
1,00E-04
1,20E-04
14 19 24 29 34
B
i
t
e
r
r
o
r
r
a
t
e
Signal to Noise Ratio [dB]
56
Figure 28 - Variation of the bit error rate with the Signal to Noise Ratio in dB for 2048 subcarriers
By observing the three graphics it can be concluded that the bit error rate decreases when the Signal
to Noise Ratio increases except in a little zone. The bit error rate value is also has expected never
more than 0.001 for all Signals to Noise Ratio values. If the simulations were done with a very low
Signal to Noise Ratio there was no transmission as explained before because it would not be possible
to guarantee a bit error rate less than 0.001.
0,00E+00
1,00E-05
2,00E-05
3,00E-05
4,00E-05
5,00E-05
6,00E-05
7,00E-05
8,00E-05
9,00E-05
1,00E-04
15 20 25 30 35
B
i
t
e
r
r
o
r
r
a
t
e
Signal to Noise Ratio [dB]
57
4.5 Downlink part 2
The main difference between the downlink part 2 simulations and the downlink part 1 simulations is
that the downlink part 2 assigns to each user a specific number of resource blocks instead of
transmitting in all the signal bandwidth like in the downlink part 1.As explained before, all the OFDM
subcarriers of the resource blocks belonging to the same user will have the same modulation scheme.
The channel estimation for the resource blocks belonging to a specific user will consist in calculating
the error bit probability for each subcarrier, adding all the values and then diving by the number of
subcarriers. The result gives the overall bit error probability.
4.5.1 Simulation
The simulation has the following parameters:
Approximately 1000000 bits to be transmitted
1024 OFDM subcarriers
Fir transfer function with the following coefficients: 1,4; 0; 0; 0; 0; 0; 0; 0; 0; 0,6; 0; 0; 0,8; 0; 0;
0; 0,9; 0; 0; 0; 0,8; 0; 0; 0; 0; 1,1; 0; 0; 0; 1,2.
Transmission only if it is possible to guarantee a bit error rate smaller than 0.001
The main objective is to measure the variation of the bit error rate with the Signal to Noise Ratio. It is
expected that the bit error rate decrease with the increase of the Signal to Noise Ratio for the same
modulation scheme. When the modem changes to a higher order modulation scheme the bit error rate
increases but always below of the 0.001 limit. In summary, the global expected behaviour is: from the
point when there is sufficient Signal to Noise Ration to transmit with the lowest order modulation
scheme (QPSK) until it changes to 16 QAM, the bit error rate decreases. Immediately when the
modulation scheme changes, the bit error rate increases to a value near the 0.001 limit. Then until the
modulation scheme changes again (16 QAM to 64 QAM in this case) the bit error rate will decrease
again. Again in the moment when the modulation scheme is changed to 64QAM the bit error rate
increases to a value near the 0.001 limit. From this point the bit error rate will decreases with the
Signal to Noise Ratio because there will be no more modulation scheme changes.
58
4.5.1 Results
Figure 29 - Variation of the bit error rate with the Signal to Noise Ratio in dB
Figure 30 – Variation of the Modulation scheme (bits per moduled symbol) with the Signal to Noise Ratio
in dB
As expected the bit error rate decreases with the Signal to Noise Ratio for the same modulation
scheme. The only bit error rate growth zone is when the modem changes to a higher order modulation
scheme.
0,00E+00
1,00E-04
2,00E-04
3,00E-04
4,00E-04
5,00E-04
6,00E-04
7,00E-04
8,00E-04
15 20 25 30 35
B
i
t
E
r
r
o
r
R
a
t
e
Signal to Noise Ratio [dB]
0
1
2
3
4
5
6
7
15 20 25 30 35
M
o
d
u
l
a
t
i
o
n
Signal to Noise Ratio [dB]
59
4.6 Uplink
To simulate the 4G LTE uplink, the SC-FDMA transmitter and the SC-FDMA receiver will be modelled
like the OFDM transmitter and receiver but with two additional blocks: the DFT and the IDFT blocks.
The following diagram the main blocks of the baseband simulation of the SC-FDMA:
Figure 31 – SC-FDMA baseband transmitter and receiver and the communication channel block diagram
The simulations presented in the uplink section will be just exclusively the variation of bit error rate
with the Signal to Noise Ratio. The channel estimation consists in calculating the sum of all the Signal
power in all after the channel compensation, the sum of all the Noise power after the channel
compensation. The global Signal to Noise Ratio will be the division of first quantity by the second.
4.6.1 Simulation
The simulation has the following parameters:
Approximately 1000000 bits to be transmitted
1024 OFDM subcarriers
Fir transfer function with the following coefficients: 1,4; 0; 0; 0; 0; 0; 0; 0; 0; 0,6; 0; 0; 0,8; 0; 0;
0; 0,9; 0; 0; 0; 0,8; 0; 0; 0; 0; 1,1; 0; 0; 0; 1,2.
Transmission only if it is possible to guarantee a bit error rate smaller than 0.001
The main objective is to measure the variation of the bit error rate with the Signal to Noise Ratio and
also the variation of the modulation scheme used with the Signal to Noise Ratio. It is expected, like in
the downlink that the bit error rate decreases with the Signal to Noise Ratio. The objective is also to
compare the behaviour of the graphic with the downlink´s simulations.
60
4.6.2 Results
Figure 32 - Variation of the bit error rate with the Signal to Noise Ratio in dB
Figure 33 - Variation of the Modulation scheme (bits per moduled symbol) with the Signal to Noise Ratio
in dB
The two graphics above show that for a specific modulation scheme in the SC-FDMA, the bit error rate
decreases with the Signal to Noise Ratio. This fact is due to the fact that the Modem is simulated in
order to achieve a bit error rate less than 0.001 and so when a specific Signal to Noise Ratio is
enough to achieve a bit error rate less than 0.001, the Modem can use a better modulation scheme.
When the Signal to Noise Ratio is to low it is impossible to transmit information because there is no
modulation scheme available to achieve a bit error rate less than 0.001.
As explained before BPSK, 16QAM and 64QAM correspond to 2 bits per symbol, 4 bits per symbol
and 6 bits per symbol respectively.
0,00E+00
2,00E-05
4,00E-05
6,00E-05
8,00E-05
1,00E-04
1,20E-04
1,40E-04
1,60E-04
1,80E-04
2,00E-04
24 29 34 39
B
i
t
E
r
r
o
r
R
a
t
e
Signal to Noise Ratio [dB]
0
1
2
3
4
5
6
7
24 29 34 39
M
o
d
u
l
a
t
i
o
n
Signal to Noise Ratio [dB]
61
4.7 Uplink vs Downlink
The Pick-to-Average-Ratio (PAPR) is obtained dividing the maximum value by the mean of the
samples of the ODFM/SC-FDMA signals before passing in the communication channel. It is an
important parameter because it shows the variation of the amplitude of a signal. Usually in
communication systems a high value of PAPR is bad because the amplifier produce a significant
distortion in the signal.
4.7.1 Simulation
The simulation has the following parameters:
Approximately 1000000 bits to be transmitted
1024 OFDM subcarriers
Fir transfer function with the following coefficients: 1,4; 0; 0; 0; 0; 0; 0; 0; 0; 0,6; 0; 0; 0,8; 0; 0;
0; 0,9; 0; 0; 0; 0,8; 0; 0; 0; 0; 1,1; 0; 0; 0; 1,2.
Transmission only if it is possible to guarantee a bit error rate smaller than 0.001
The main objective is to study the Pick-to-Average-Ratio (PAPR) for different number of subcarriers
either for OFDM and SC-FDMA.
4.7.2 Results
Figure 34 - Variance of the Pick to Average Power Ration (PAPR) with the number of OFDM subcarriers
6
6,5
7
7,5
8
8,5
512 1024 2048
P
A
P
R
OFDM subcarriers
62
Figure 35 - Variation of the Pick to Average Power Ration (PAPR) with the number of SC-FDMA subcarriers
It is clear that for all the situations analysed an OFDM signal has always a higher PAPR than a SC-
FDMA signal. The last statement confirms the theory. In the case of SC-FDMA, as expected, the
PAPR stays stable with different number of subcarriers. In the case of OFDM, the PAPR grows with
the increase of the number of OFDM subcarriers. It can be explained because the higher the value of
the peak in the OFDM signal is, higher is achieved when there are higher number of subcarriers
contributing constructively.
0
0,5
1
1,5
2
2,5
512 1024 2048
P
A
P
R
Number of SC-FDMA subcarriers
63
Chapter 5 Conclusion Although the real LTE downlink and uplink transmissions procedures are far more complex than the
ones used in the simulations, the objective was to retract as close as possible as to the reality both
uplink and downlink of LTE.
In the downlink simulations part 1 the main conclusions to take are the following:
OFDM subcarriers which suffer more attenuation by the communication channel carry less bits
Although the behaviour is not completely linear, it can be stated the higher the SNR is, the
greater number of bits is transmitted per OFDM symbol
The bit error rate decreases for almost the simulations with the SNR
In the downlink simulations part 2 the main conclusions are:
For the same modulation scheme the bit error rate decreases with SNR
There are some switch behaviour of the bit error rate when a higher order modulation scheme
is used increasing the bit error rate in that precise point
In the uplink simulations the main conclusions to take are:
The behaviour of the bit error rate is similar to the OFDMA simulations but in case situations
there is a need of guaranteeing a higher SNR to achieve the same bit error rate
In the downlink vs uplink the main conclusions are:
PAPR is always higher in LTE uplink (SC-FDMA) than in LTE downlink (OFDM) for all the
cases analysed
The higher number of OFDM subcarriers, the greater the value of PAPR is
The PAPR value doesn’t change with SC-FDMA subcarriers variation
64
65
References [1] Erik Dahlman, Stefan Parkvall, Johan Sköld and Per Beming,3G Evolution HSPA and LTE for
mobile broadband, Academic Press,2008
[2] Jim Zyren, Overview of the 3GPP Long Term Evolution Physical Layer (White Paper)
[3] Christopher Cox, AN INTRODUCTION TO LTE: LTE, LTE-ADVANCED, SAE and 4G Mobile
Communications, John Wiley & Sons, 2012
[4] Telesystem Innovations, LTE in a Nutshell: The Physical Layer (White Paper)
[5] Stefania Sesia and Issam Toufik and Matthew Baker,LTE – The UMTS Long Term Evolution
From Theory to Practice, John Wiley & Sons, 2011
[6] Moray Rumney, 3GPP LTE: Introducing Single-Carrier FDMA, Agilent Technologies, 2008
