Page | DEPT OF ECE P . E . S I n s t i t u t e o f T e c h n o l o g y

B e n g a l u r u - 8 5

2014

ORTHOGONAL

FREQUENCY DIVISION

MULTIPLEXING

Kishan P B

Under-Graduate student in

Dept. of Electronics and Communication Engineering

PESIT, Bangalore – 560 085

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TABLE OF CONTENTS:

ABSTRACT……………………………………………………………………………ii

LIST OF FIGURES……………………………………………………………………iii

LIST OF TABLES……………………………………………………………………..iv

1. INTRODUCTION………………………………………………………..................1

2. PRINCIPAL OFDM SYSTEM……………………………………………………...2 - 4

3. PRACTICAL OFDM SYSTEM……………………………………………………..5 - 8

4. ADVANTAGES OF OFDM………………………………………………………...8

5. DISADVANTAGES OF OFDM…………………………………………………….9

6. FEW APPLICATIONS OF OFDM………………………………………………….9 - 10

7. CONCLUSION………………………………………………………………………10

8. FURTHER WORK BY AUTHOR…………………………………………………..11

9. REFERENCES………………………………………………………………………11 - 12

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ABSTRACT:

This report is an introduction to orthogonal frequency division multiplexing (OFDM). OFDM

is becoming the chosen modulation technique for wireless communications. OFDM can

provide large data rates with sufficient robustness to radio channel impairments. Many

research centers in the world have specialized teams working in the optimization of OFDM

for countless applications.

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LIST OF FIGURES:

Fig 2.1 Principal OFDM modulation block diagram 2

Fig 2.2 Serial to parallel conversion 3

Fig 2.3 Illustration of 3 subcarrier waveform 3

Fig 2.4 OFDM receiver 4

Fig 3.1 Practical OFDM Transmitter and Receiver system 5

Fig 3.2 Frequency response of raised-cosine filter with various roll-off factors 7

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LIST OF TABLES:

Table 1 Digital Audio Broadcasting (DAB) 9

Table 2 Wireless LANs 10

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1. INTRODUCTION

Recently, a worldwide convergence has occurred for the use of Orthogonal Frequency

Division Multiplexing (OFDM) as an emerging technology for high data rates. In particular,

many wireless standards (Wi-Max, IEEE802.11a, LTE, DVB) have adopted the OFDM

technology as a mean to increase dramatically future wireless communications. OFDM is a

particular form of Multi-carrier transmission and is suited for frequency selective channels

and high data rates. This technique transforms a frequency-selective wide-band channel into a

group of non-selective narrowband channels, which makes it robust against large delay

spreads by preserving orthogonality in the frequency domain. Moreover, the ingenious

introduction of cyclic redundancy at the transmitter reduces the complexity to only FFT

processing and one tap scalar equalization at the receiver.

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2. PRINCIPAL OFDM SYSTEM

I. Overview

Since the original OFDM model was proposed in the 1960s [1], the core structure of

OFDM has hardly changed. The key idea of OFDM is that a single user would make use of

all orthogonal subcarrier in divided frequency bands. Therefore, the data rate can be

increased significantly. Since the bandwidth is divided into several narrower subchannels,

each subchannel requires a longer symbol period. Therefore OFDM systems can overcome

the intersymbol interference (ISI) problem. As a consequence, the OFDM system can result

in lower bit error rates but higher data rates than conventional communication systems.

Nevertheless, OFDM technique has certain drawbacks [2], such as the increased system

complexity, which is associated with the generation of orthogonal subcarriers, and other new

problems, which might not occur in other modulation schemes. Such new problems include

the peak to average power ratio (PAPR) and inter-carrier interference (ICI).

II. OFDM Modulation [3]

As depicted in Fig 2.1, the input data stream is converted into N parallel data streams

through a serial-to-parallel port. The duration of the data is elongated by N times. Serial-to-

parallel conversion is depicted in Fig 2.2.

Fig 2.1 Principal OFDM modulation block diagram

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Fig 2.2 Serial to parallel conversion

III. Orthogonal Subcarriers

When the parallel symbol streams are generated, each stream would be modulated and

carried at different center frequencies as the traditional FDM scheme. The

subcarriers centered at frequencies in Fig.2.1 must be orthogonal to each other.

The definition of the orthogonality was given in [14] as

(1)

Where is the Dirac-Delta function.

In OFDM modulation, the subcarrier frequency is defined as

(2)

Where

(3)

Here

is the entire bandwidth, and is the number of subcarriers.

Substituting Eq.2 and Eq.3 into Eq.1, Orthogonality can easily be justified for

all . Fig 2.3 illustrates an example of subcarrier waveforms.

Fig 2.3 Illustration of 3 subcarrier waveform

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IV. Bandpass Signaling

After the modulation by orthogonal sub carriers, all N subcarrier waveforms were added

together to be up-converted to the pass-band. This resulting signal waveform will be

transmitted with a carrier frequency at 2.4G Hz, 5G Hz, 11G Hz or 60 G Hz. Then the band-

pass OFDM signal waveform would be sent to power amplifier and antennas.

Thus, the transmitted OFDM signal x(t) can be expressed as:

Where the s(n) represents the input data stream, T the symbol duration and fc the carrier

frequency. Traveling through a wireless channel, the distorted x(t) results in r ' (t), as shown

in Fig.2.4.

V. OFDM Demodulation

Fig 2.4 OFDM receiver

At the receiver, the received signal is down-converted to form a base-band signal first.

Then, low-pass filters and de-subcarriers are applied to separate subcarrier waveforms.

Orthogonality of sub-carriers will ensure that only the targeted subcarrier waveform will be

preserved in each sub-band. Ideally, the final detected symbols will be identical to those

transmitted in Fig.2.1.

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3. PRACTICAL OFDM SYSTEM

I. Overview

It was a complicated process to achieve N subcarrier oscillators, especially when the N was

large. Therefore, the principal OFDM system could not been widely used. Thanks to

IFFT/FFT-based algorithms introduced in 1980 [4], OFDM has become a popular wireless

modulation technique since after. The practical OFDM system is depicted in Fig 3.1

Fig 3.1 Practical OFDM Transmitter and Receiver system

II. Channel coding and Channel decoder

It is a technique used for controlling errors in data transmission over unreliable or noisy

communication channels. The central idea is the sender encodes their message in a redundant

way by using an error-correcting code (ECC). The American mathematician Richard

Hamming pioneered this field in the 1940s and invented the first error-correcting code in

1950: the Hamming (7,4) code.

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Main two categories of Channel coding -

Block codes work on fixed-size blocks (packets) of bits or symbols of predetermined

size. Practical block codes can generally be decoded in polynomial time to their block

length.

Convolutional codes work on bit or symbol streams of arbitrary length. They are most

often decoded with the Viterbi algorithm, though other algorithms are sometimes

used. Viterbi decoding allows asymptotically optimal decoding efficiency with

increasing constraint length of the convolutional code, but at the expense of

exponentially increasing complexity. A convolutional code can be turned into a block

code, if desired, by "tail-biting".

III. Symbol Map and De-map

The process of mapping the information bits onto the signal constellation plays a fundamental

role in determining the properties of the modulation.

An OFDM signal consists of a sum of sub-carriers, each of which contains -

M-ary phase shift keyed (PSK) signal.

Quadrature amplitude modulated (QAM) signal.

IV. FFT and IFFT

An FFT computes the DFT and produces exactly the same result as evaluating the DFT

definition directly; the only difference is that an FFT is much faster.

Let x0, ...., xN-1 be complex numbers. The DFT is defined by the formula

Evaluating this definition directly requires O(N

2) operations.

The well-known radix-2 Cooley–Tukey algorithm for FFT and IFFT [5], for N a power of 2,

can compute the same result with only O( ) complex multiplications (again,

ignoring simplifications of multiplications by 1 and similar) and O( ) complex

additions.

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V. Cyclic extension (prefix) and Remove cyclic extension (prefix).

It refers to the prefixing of a symbol with a repetition of the end. Although the receiver is

typically configured to discard the cyclic prefix samples, the cyclic prefix serves two

purposes [6].

As a guard interval, it eliminates the Inter-Symbol Interference (ISI) from the

previous symbol.

As a repetition of the end of the symbol, it allows the linear convolution of a

frequency-selective multipath channel to be modelled as circular convolution, which

in turn may be transformed to the frequency domain using a discrete Fourier

transform. This approach allows for simple frequency-domain processing, such as

channel estimation and equalization.

VI. Raised cosine window (or filter).

The raised-cosine filter is a filter frequently used for pulse-shaping in digital modulation

due to its ability to minimise ISI. Its name stems from the fact that the non-zero portion of the

frequency spectrum of its simplest form (β = 1) is a cosine function, 'raised' up to sit above

the (horizontal) axis.

Fig 3.2 Frequency response of raised-cosine filter with various roll-off factors [7]

VII. Timing and frequency synchronisation

This by itself is a vast topic

Timing Offsets (TOs) of different users that are caused by path delay differences

between different users and imperfect timing synchronization

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Carrier Frequency Offsets (CFOs) of different users that are induced by Doppler

effects and/or poor oscillator alignments can destroy orthogonality among subcarriers

at the receiver and cause multiuser interference (MUI)

Main aim of this block in the receiver side is to synchronise the above two offsets [8].

VIII. ADC and DAC

Analog to Digital Converter – [9]

Digital to Analog Converter – [10]

IX. RF-RX and TX module

An RF module (radio frequency module) is a (usually) small electronic circuit used to

transmit and/or receive radio signals on one of a number of carrier frequencies. RF modules

are widely used in electronic design owing to the difficulty of designing radio circuitry. Good

electronic radio design is notoriously complex because of the sensitivity of radio circuits and

the accuracy of components and layouts required achieving operation on a specific frequency.

Design engineers will design a circuit for an application which requires radio communication

and then "drop in" a radio module rather than attempt a discrete design, saving time and

money on development.

4. ADVANTAGES OF OFDM [11]

Immunity to delay spread

1. Symbol duration >> channel delay spread

2. Guard interval

Resistance to frequency selective fading

Each subchannel is almost flat fading

Simple equalization

Each subchannel is almost flat fading, so it only needs a one-tap equalizer to

overcome channel effect.

Efficient bandwidth usage

The subchannel is kept orthogonality with overlap.

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5. DISADVANTAGES OF OFDM [11]

The problem of synchronization

1. Symbol synchronization

Timing errors

Carrier phase noise

2. Frequency synchronization

Sampling frequency synchronization

Carrier frequency synchronization

Need FFT units at transmitter, receiver

The complexity of computations

6. FEW APPLICATIONS OF OFDM

Digital Audio Broadcasting (DAB)

DAB is an European standard for digital broadcasting that is intended to replace the current

analog technologies such as AM and FM. It was standardized by the European

Telecommunications Institute (ETSI) in 1995 [12]. DAB has got four transmission modes

with different parameters as shown in the table 1.

Mode –I Mode –II Mode –III Mode –IV

# of sub-carriers 1536 384 192 768

Sub-carrier Spacing 1KHz 4KHz 8KHz 2KHz

Symbol Time 1.246 ms 311.5 us 155.8 us 623 us

Guard Time 246 us 61.5 us 30.8 us 123 us

Carrier Frequency < 375 MHz < 1.5 GHz <3 GHz < 1.5 GHz

Transmitter Separation < 96 km < 24 km < 12 km < 48 km

Table 1

Digital Video Broadcasting (DVB)

Digital Video Broadcasting (DVB) is a standard for broadcasting Digital Television over

satellites, cables and thorough terrestrial (wireless) transmission. DVB was standardized by

the ETSI in 1997 [13].

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Wireless LANs

Wireless LANs are one of the most important applications of OFDM. A lot of standards have

been proposed for Wireless LANs during the past decade, most of them based on spread-

spectrum schemes. In July 1998, IEEE Wireless LAN standardization group IEEE

802.11 standardized a scheme based on OFDM operating in the 5-GHz band. It is interesting

to note that this standard is one of the first packet-based one to use OFDM. The parameters of

this WLAN standard are given in table 2.

Data Rate 6,9,12,18,24,36,48,54 Mbps

Modulation BPSK, QPSK, 16-QAM, 64 QAM

Coding Rate 1/2, 2/3,3/4

# of Sub-Carriers 52

# of pilots 4

OFDM Symbol Duration 4 us

Guard Interval 800 ns

Sub-Carrier Spacing 312.5 kHz

3 dB bandwidth 16.56 MHz

Channel Spacing 20 MHz

Table 2

OFDMA

Finally, it is also possible to use OFDM for multiple-access too. This technique is called

OFDMA and is implemented by providing each user with a small number of sub-carriers.

Even though this technique is similar to FDMA, it avoids the use of large guard bands that

are used to prevent adjacent channel interference.

7. CONCLUSION

OFDM has several interesting properties that suit its use over Wireless channels and hence

many Wireless standards have started to use OFDM for modulation and multiple access. The

principal and practical methods of generation and demodulation of OFDM were analyzed.

Application of OFDM such MC-CDMA, DAB, DVB, WLAN etc.., were briefly discussed.

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8. FURTHER WORK BY THE AUTHOR

OFDM simulation in MATLAB.

Explanation of ADSL (Asymmetric digital subscriber line) which uses OFDM

concept.

9. REFERENCES

[1] R.W. Chang, “Synthesis of band- limited orthogonal signals for multichannel data

transmission” Bell Sys. Tech. Journal, vol. 45, Dec. 1966

[2] K. Thomas and H. Lajos, “Adaptive Multicarrier Modulation: A

Convenient Framework for Time-Frequency Processing in Wireless Communications”

IEEE processing of the IEEE, vol. 88, No.5, pp.611-640, May 2000

[3] Yao Xiao, “Orthogonal Frequency Division Multiplexing Modulation and Inter-carrier

Interference Cancellation”, M.S., Institute of Automation, May 2003

[4] Weinstein, S. and Ebert, P.; “Data Transmission by Frequency-Division Multiplexing

Using the Discrete Fourier Transform” IEEE Trans. on Commun. vol. 19 Issue: 5. Oct.1971

[5] John G. Proakis and Dimitris G. Manolakis, “Digital signal processing”, Pearson Prentice

Hall, 2007 - Technology & Engineering.

[6] M. D. Nisar, W. Utscick, H. Nottensteiner, and T. Hindelang, “Channel Estimation and

Equalization of OFDM Systems with Insufficient Cyclic Prefix,” in 65th IEEE Vehicular

Technology Conference, Apr 2007.

[7] Simon S. Haykin, “Digital communications”, Wiley, 08-Mar-1988 - Technology &

Engineering.

[8] K. Raghunath, Yogendra U. Itankar, A. Chockalingam, and Ranjan K. Mallik, “BER

Analysis of Uplink OFDMA in the Presence of Carrier Frequency and Timing Offsets on

Rician Fading Channels”, IEEE Trans. on Vehicular Technology, vol. 60, no. 9, pp. 4392-

4402, November 2011.

[9] http://en.wikipedia.org/wiki/Analog-to-digital_converter

[10] http://en.wikipedia.org/wiki/Digital-to-analog_converter

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[11] L. Hanzo, W. Webb and T. Keller, “Single- and multi-carrier quadrature amplitude

modulation – Principles and applications for personal communications”, WLANs and

broadcasting, John Wiley & Sons, Ltd, 2000.

[12] ETSI, “Radio Broadcasting Systems: Digital Audio Broadcasting to Mobile, Portable

and Fixed Receivers”, European Telecommunication Standard, ETS 300-401, Feb.

1995.

[13] ETSI, “Digital Video Broadcasting: Framing Structure, Channel Coding and

Modulation for Digital Terrestrial Television”, European Telecommunication

Standard, EN 300-744, Aug 1997.