OFDM Final

Ashish Kumar Meshram
Roll No. mt1402102002
M.Tech. Communication & Signal Processing
Discipline of Electrical EngineeringIIT – Indore | EE642 | Wireless Communication
Orthogonal Frequency Division Multiplexing
OFDM
DAB
DVB-T
IEEE 802.11a
IEEE 802.11g
IEEE 802.11n
IEEE 802.11ac
IEEE 802.11ad
IEEE 802.11af
IEEE 802.11ai
IEEE 802.11aq
IEEE 802.11ax
IEEE 802.16
IEEE 802.22
4G LTE

01IIT – Indore | EE642 | Wireless Communication
Contents
1
2
3
4
5
Current Scenario
Why from single to multi-carrier modulation schemes?
FDM and OFDM Overview
Multicarrier Modulation
Power Spectral Density of FDM and OFDM
Orthogonality
Modulation
Illustrative Example
OFDM Transreceiver
BER for AWGN and Rayleigh Channel
Broadcasting standards DAB and DVB-T
World Wide Usages of DAB & DVB-T
Wireless Local Area Network (WLAN) standard
Wireless Local Loop (WLL) standards
Inter-Symbol Interferences
Guard Interval
Guard Interval (Zero Padding)
Guard Interval (Cyclic Prefix)
Inter-Carrier Interferences
Further Issues
Time and Frequency Synchronization
Channel Estimation
Peak Average Power Reduction
1 Motivation
2 Introduction
Basic Principles3
4 Applications & Standards
5 Implementation Issues
References6

H. Rohling: A Flexible and Adaptive Air Interface for a 4G Communication Systems
Current Scenario
O F D M
Motivation Introduction Basic Principles Implementation IssuesApplications & Standards

MIMO-OFDM Wireless Communications with MATLAB, Yong Soo Cho, Jaekwon Kim, Won Young Yang, Chung-Gu Kang
In order to support the symbol rate of 𝑅 𝑠 symbols per second, the
minimum required bandwidth is the Nyquist bandwidth, which is
given by 𝑅 𝑠 2 Hz.
Coherence bandwidth is a statistical measurement of the range of
frequencies over which the channel can be considered "flat", or in
other words the approximate maximum bandwidth or frequency
interval over which two frequencies of a signal are likely to
experience comparable or correlated amplitude fading.
• Wider bandwidth is required to support a higher data rate
in a single-carrier transmission.
• As the signal bandwidth becomes larger than the
coherence bandwidth in the wireless channel, the link
suffers from multi-path fading, incurring the inter-symbol
interference (ISI).
• Requires a high-complexity equalizer to deal with the inter-
symbol interference problem in the multi-path fading
channel or equivalently, frequency-selective fading
channel.
Limitation of Single-Carrier Transmission for High Data Rate
MCM is considered to be spectrally efficient and it offers an elegant way
to deal with equalization of dispersive slowly fading channels.
Why from single to multi-carrier modulation schemes?

Frequency Division Multiplexing (FDM) and OFDM
FDM is a technique by which the total bandwidth available in a communication medium is divided into a series of
non-overlapping frequency sub-bands, each of which is used to carry a separate signal. These sub-bands can be
used independently with completely different information streams, or used dependently in the case of information
sent in a parallel stream. This allows a single transmission medium such as the radio spectrum, a cable or optical
fiber to be shared by multiple separate signals.
OFDM is a type of multicarrier modulation that divides a given channel into many parallel subchannels or subcarriers,
so that multiple symbols are sent in parallel.
Orthogonal frequency-division multiplexing (OFDM) is the modulation technique for European standards such as the
Digital Audio Broadcasting (DAB) and the Digital Video Broadcasting (DVB) systems. As such it has received much
attention and has been proposed for many other applications, including local area networks and personal
communication systems.
http://home.deib.polimi.it/spalvier/sistemi_di_comunicazione/integrazione_lezioni/ofdm_tutorial.htm

Multi-Carrier Modulation (MCM)
MCM is a method of transmitting data by splitting it into several components, and sending each of these
components over separate carrier signals. The individual carriers have narrow bandwidth , but the composite
signal can have broad bandwidth.
• MCM include relative immunity to fading caused by transmission over
more than one path at a time (multipath fading)
• Less susceptibility than single-carrier systems to interference caused
by impulse noise, and enhanced immunity to inter-symbol
interference
• Limitations include difficulty in synchronizing the carriers under
marginal conditions, and a relatively strict requirement that
amplification be linear.
Multi-Carrier and Spread Spectrum Systems, K Fazel, S Kaiser, 2e

Power Spectral Density of FDM and OFDM
Spectrum of first sub-carrier
OFDM Spectrum
𝑓
𝐻(𝑓) 2
Guard Band Guard Band
𝑓1 𝑓2 𝑓3
𝑓
𝐻(𝑓) 2
OFDM FDM

𝑒 𝑗2𝜋𝑓 𝑘 𝑡, 𝑒−𝑗2𝜋𝑓 𝑖 𝑡 =
1
0 ; 𝑜𝑡ℎ𝑒𝑟𝑤𝑖𝑠𝑒
; ∀ 𝑖𝑛𝑡𝑒𝑔𝑒𝑟 𝑘 = 𝑖
Consider the time-limited complex exponential signals 𝑒 𝑗2𝜋𝑓 𝑘 𝑡
𝑘=0
𝑁−1
which represent the different subcarriers
at 𝑓𝑘 = 𝑘 𝑇𝑠𝑦𝑚 in the OFDM signal, where 0 ≤ 𝑡 ≤ 𝑇𝑠𝑦𝑚
These signals are defined to be orthogonal if the integral of the products for their common (fundamental)
period is zero, that is,
Taking the discrete samples with the sampling instances at 𝑡 = 𝑛𝑇𝑠 = 𝑛𝑇𝑠𝑦𝑚 𝑁 , 𝑛 = 0,1,2, … , 𝑁 − 1
𝑒
𝑗2𝜋
𝑘
𝑇𝑠𝑦𝑚
𝑛𝑇𝑠
, 𝑒
−𝑗2𝜋
𝑖
𝑇𝑠𝑦𝑚
𝑛𝑇𝑠 =
1
0 ; 𝑜𝑡ℎ𝑒𝑟𝑤𝑖𝑠𝑒
; ∀ 𝑖𝑛𝑡𝑒𝑔𝑒𝑟 𝑘 = 𝑖
Orthogonality
The above orthogonality is an essential condition for the OFDM signal to be Inter-Carrier Interference (ICI) free.

OFDM modulation maps the message bits into a sequence of PSK or QAM symbols which will be subsequently converted
into 𝑁 parallel streams. Each of 𝑁 symbols from serial-to-parallel (S/P) conversion is carried out by the different subcarrier.
Modulation
Let 𝑋𝑙[𝑘] denote the 𝑙𝑡ℎ transmit symbol at the k𝑡ℎ subcarrier, 𝑙 = 0,1,2, … , ∞; 𝑘 = 0,1,2, … , 𝑁 − 1. Due to the S/P
conversion, the duration of transmission time for 𝑁 symbols is extended to 𝑁𝑇𝑠, which forms a single OFDM symbol with a
length of 𝑇𝑠𝑦𝑚 (i.e., 𝑇𝑠𝑦𝑚 = 𝑁𝑇𝑠).
Bank of
Modulator
𝑋[0]
𝑋[1]
𝑋[2]
𝑋[𝑁 − 1]
×
×
×
×
Input Bits
𝑑[𝑘]
𝑥 0
𝑥 1
𝑥 2
𝑥 𝑁 − 1
𝑥𝑙[𝑛] 𝑘=0
𝑁−1
Serial
To
Parallel
(S/P)
OFDM
Signal
𝑋𝑙[𝑘] 𝑘=0
𝑁−1
sin 2𝜋𝑓0 𝑛𝑇𝑠𝑦𝑚 𝑁
sin 2𝜋𝑓𝑁−1 𝑛𝑇𝑠𝑦𝑚 𝑁
𝑥𝑙 𝑛 =
𝑘=0
𝑁−1
𝑋𝑙 𝑘 sin 2𝜋𝑓𝑘 𝑛𝑇𝑠𝑦𝑚 𝑁 ; 𝑓𝑜𝑟 𝑛 = 0,1,2, … , 𝑁 − 1 … (1.1)

Modulation
𝑥𝑙 𝑛 =
𝑘=0
𝑁−1
𝑋𝑙[𝑘]𝑒 𝑗2𝜋𝑘 𝑛 𝑁
; 𝑓𝑜𝑟 𝑛 = 0,1,2, … , 𝑁 − 1
𝑥𝑙 𝑛 =
𝑘=0
𝑁−1
𝑋𝑙 𝑘 sin 2𝜋𝑘 𝑛 𝑁 ; 𝑓𝑜𝑟 𝑛 = 0,1,2, … , 𝑁 − 1
Eq. 1.1 can be discretized in frequency domain also as
… (1.2)
From Eq. (1.2) individual sinusoidal multipliers can be eliminated by use of IFFT/FFT. Thus can be expressed as
… (1.3)
Bank of
Modulator
𝑋[0]
𝑋[1]
𝑋[2]
𝑋[𝑁 − 1]
Input Bits
𝑑[𝑘]
𝑥𝑙[𝑛] 𝑘=0
𝑁−1
Serial
To
Parallel
(S/P)
OFDM
Signal
𝑋𝑙[𝑘] 𝑘=0
𝑁−1
IFFT

Illustrative Example
Gray
encoded
input data
Phase of
QPSK signal
(radian)
Coordinates of
message points
𝑠𝑖1 𝑠𝑖1
11 𝜋 4 + 𝐸 2 + 𝐸 2
01 3𝜋 4 − 𝐸 2 + 𝐸 2
00 5𝜋 4 − 𝐸 2 − 𝐸 2
10 7𝜋 4 + 𝐸 2 − 𝐸 2
𝑠𝑖 𝑡 = 𝐸 cos 2𝑖 − 1
𝜋
4
𝜙1(𝑡) − 𝐸 sin 2𝑖 − 1
𝜋
4
𝜙2(𝑡)
𝜙2 𝑡 =
2
𝑇
sin(2𝜋𝑓𝑐 𝑡)𝜙1 𝑡 =
2
𝑇
cos(2𝜋𝑓𝑐 𝑡)
1101
1000
𝐸 2
𝐸 2
− 𝐸 2
− 𝐸 2
𝑠0𝑠1
𝑠3𝑠2
𝜙1 𝑡
𝜙2 𝑡
QPSK Mapper
𝑋 𝑘 = −0−1i;−0−1i;−1+0i;−1+0i;0+1i;1+0i;1+0i;−0−1i;0+1i;−0−1i
QPSK Mapper Output
𝑋𝑙 𝑘 =
-0-1i
-0-1i
-1+0i
-1+0i
0+1i
1+0i
1+0i
-0-1i
0+1i
-0-1i
Serial to Parallel Output
𝑑 𝑘 = 1 0 1 0 1 1 1 1 0 1 0 0 0 0 1 0 0 1 1 0
Input Bit Stream
0.4000 - 0.2000i
0.3067 + 0.1284i
-0.4598 + 0.2794i
0.5362 + 0.0442i
0.2169 - 0.2520i
-0.4000 - 0.2000i
0.7040 - 0.2000i
0.1115 - 0.2000i
-0.3587 - 0.2000i
-0.0568 - 0.2000i
𝑥𝑙 𝑘 =
OFDM Symbols
Mapper
Serial
To
Parallel
(S/P)
𝑑 𝑘
𝑋 𝑘
IFFT
𝑋𝑙 𝑘 𝑥𝑙 𝑘
Number of Sub-Carrier, 𝑁 = 5

OFDM Transreceiver
Bank Of
Modulator
IFFT
Bank Of
Demodulator
FFT
Channel
Input
Output
Parallel
To
Serial
Serial
To
Parallel
Serial
To
Parallel
Parallel
To
Serial

𝑃𝑒 =
2(𝑀 − 1)
𝑀 log2 𝑀
Q
6𝐸 𝑏
𝑁0
∙
log2 𝑀
𝑀2 − 1
AWGN Channel
𝑃𝑒 =
𝑀 − 1
𝑀 log2 𝑀
Q 1 −
3𝛾 log2 𝑀 𝑀2 − 1
3𝛾 log2 𝑀 (𝑀2−1) + 1
Rayleigh Fading Channel
𝛾 =
𝐸 𝑏
𝑁0
BER for AWGN and Rayleigh Channel

Broadcasting standards DAB and DVB-T
Digital Audio Broadcasting (DAB) is a digital radio technology for broadcasting radio stations, used in several
countries across Europe and Asia Pacific.
Digital Video Broadcasting — Terrestrial (DVB-T) system transmits compressed digital audio, digital video and other data
in an MPEG transport stream, using coded orthogonal frequency-division multiplexing (COFDM or OFDM) modulation.
Parameter DAB DVB-T
Bandwidth (MHz) 1.5 8
Number of Sub-Carriers, 𝑁 192 (256 FFT) 384 (512 FFT) 1536 (2k FFT) 1705 (2k FFT) 6817 (8k FFT)
Symbol Duration, 𝑇𝑠 125 𝜇𝑠 250 𝜇𝑠 1 𝑚𝑠 224 𝜇𝑠 896 𝜇𝑠
Carrier Spacing, 𝐹𝑠(kHz) 8 4 1 4.464 1.116
Guard Interval, 𝑇𝑔 31 62 246 𝑇𝑠 32, 𝑇𝑠 16 , 𝑇𝑠 8, 𝑇𝑠 4
Modulation D-QPSK QPSK, 16-QAM, 64-QAM
FEC Coding Convolution with code rate 1 3 up to 3 4 Reed Solomon + Convolution with code rate 1 2 up to 7 8
Maximum Data Rate 1.7 Mbit/s 31.7 Mbit/s

http://en.wikipedia.org/wiki/File:Digital_Audio_Broadcasting.svg
http://upload.wikimedia.org/wikipedia/commons/thumb/b/bd/Digital_broadcast_standards.svg/1280px-Digital_broadcast_standards.svg.png
World Wide Usages of DAB & DVB-T
DAB
Countries with regular services
Countries with trials / tests
Countries with interest
DAB no longer used
DVB-T
DVB-T
ATSC, Advanced Television Systems Committee (ATSC) standards
ISDB-T, Integrated Services Digital Broadcasting-Terrestrial
DTMB, Digital Terrestrial Multimedia Broadcast

Wireless Local Area Network (WLAN) standard
Parameter IEEE 802.11a
Bandwidth (MHz) 20
Number of Sub-Carriers, 𝑁 52 (48 data + 4 pilots) (64 FFT)
Symbol Duration, 𝑇𝑠 4 𝜇𝑠
Carrier Spacing, 𝐹𝑠(kHz) 312.5
Guard Interval, 𝑇𝑔 0.8 𝜇𝑠
Modulation BPSK, QPSK, 16-QAM, and 64-QAM
FEC Coding Convolution with code rate 1 2 up to 3 4
Maximum Data Rate 54 Mbit/s
WLAN is a wireless computer network that links two or more devices using a wireless distribution method
(often spread-spectrum or OFDM radio) within a limited area such as a home, school, computer laboratory,
or office building. This gives users the ability to move around within a local coverage area and still be
connected to the network, and can provide a connection to the wider Internet

Wireless Local Loop (WLL) standards
Parameter IEEE 802.16d, ETSI HIPERMAN
Bandwidth (MHz) 1.5 to 28
Number of Sub-Carriers, 𝑁 256 OFDM 2048 OFDMA
Symbol Duration, 𝑇𝑠 (𝜇𝑠) 8 to 125 64 to 1024
Guard Interval, 𝑇𝑔 From 1/32 up to 1/4 of 𝑇𝑠
Modulation QPSK, 16-QAM, and 64-QAM
FEC Coding Reed Solomon + convolutional with code rate 1/2 up to 5/6
Maximum Data Rate Up to 26 Mbit/s
Wireless Local Loop (WLL), is the use of a wireless communications link as the connection for delivering plain old
telephone service (POTS) or Internet access (marketed under the term "broadband") to telecommunications customers

Inter-symbol interference (ISI) occurs when one OFDM symbol affects the next one due to the multi-path channel
Inter Symbol Interference
𝑓1 = 1 𝑇𝑠
𝑂𝐹𝐷𝑀 𝑆𝑦𝑚𝑏𝑜𝑙
ℎ0 ℎ1
𝑇𝑠 8
Suppose multi-path
channel with delay
be 𝑇𝑠 8
𝑓2 = 2 𝑇𝑠
𝑂𝐹𝐷𝑀 𝑆𝑦𝑚𝑏𝑜𝑙 𝑂𝐹𝐷𝑀 𝑆𝑦𝑚𝑏𝑜𝑙
𝑇𝑥 𝑆𝑖𝑔𝑛𝑎𝑙 𝑅𝑥 𝑆𝑖𝑔𝑛𝑎𝑙
Can be eliminated by using guard interval
Inter-Symbol Interference

In telecommunications, guard intervals are used to ensure that distinct transmissions do not interfere with one
another. These transmissions may belong to different users (as in TDMA) or to the same user (as in OFDM).
The purpose of the guard interval is to introduce immunity to propagation delays, echoes and reflections, to which
digital data is normally very sensitive.
• Zero Padding (ZP)
• Cyclic Prefix (CP)
pads the guard interval with zeros in an OFDM symbols
extends the OFDM symbols by copying the last samples of an OFDM symbols into its front
Guard Interval
The discrete length of the guard interval has to be 𝐿 𝑔 ≥
𝜏 𝑚𝑎𝑥
𝑇𝑠

• Guard Time eliminates ISI between neighboring OFDM symbols
• However each OFDM symbol suffers from inter-carrier interference (ICI)
• Guard time corresponds to a reduction of bit rate
𝑇𝑠 8
ℎ0 ℎ1
𝑇𝑠 8 𝑇𝑠 8
𝑇𝑥 𝑆𝑖𝑔𝑛𝑎𝑙 𝑅𝑥 𝑆𝑖𝑔𝑛𝑎𝑙
No ISI
Guard
Time
Guard Interval (Zero Padding)

Inter-Carrier Interference
×No Orthogonal Interference
×Orthogonal No Interference

copy
copy
Guard Interval (Cyclic Prefix)
+
ℎ0 ℎ1
𝑇𝑠 8
𝑇𝑥 𝑆𝑖𝑔𝑛𝑎𝑙
𝑅𝑥 𝑆𝑖𝑔𝑛𝑎𝑙

Further Issues
Time and Frequency Synchronization
Channel Estimation
Peak Average Power Reduction
Frequency offsets will be arising from the frequency mismatch of the transmitter and the receiver
oscillators and the existence of Doppler shift in the channel. In addition, due to the delay of signal
when transmitting in the channel, the receiver in general starts sampling a new frame at the
incorrect time instant. Therefore, it is important to estimate the frequency offset to minimize its
impact, and to estimate the timing offset at the receiver to identify the start time of each frame
and the FFT window position for each OFDM.
The received signal is usually distorted by the channel characteristics. In order to recover the
transmitted bits, the channel effect must be estimated and compensated in the receiver.
The transmit signals in an OFDM system can have high peak values in the time domain since many
subcarrier components are added via an IFFT operation. Therefore, OFDM systems are known to
have a high PAPR (Peak-to-Average Power Ratio), compared with single-carrier systems. In fact,
the high PAPR is one of the most detrimental aspects in the OFDM system, as it decreases the
SQNR (Signal-to-Quantization Noise Ratio) of ADC (Analog-to-Digital Converter) and DAC (Digital-
to-Analog Converter) while degrading the efficiency of the power amplifier in the transmitter. The
PAPR problem is more important in the uplink since the efficiency of power amplifier is critical
due to the limited battery power in a mobile terminal.

[1]. Multi-Carrier and Spread Spectrum Systems, K Fazel, S Kaiser, 2e
[2]. MIMO-OFDM Wireless Communications with MATLAB, Yong Soo Cho, Jaekwon Kim, Won Young Yang, Chung-Gu Kang
[3]. H. Rohling: A Flexible and Adaptive Air Interface for a 4G Communication Systems
References
[1]. http://home.deib.polimi.it/spalvier/sistemi_di_comunicazione/integrazione_lezioni/ofdm_tutorial.htm
Bibliography
Internet Resources

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