OFDM tutorial

Introduction to OrthogonalFrequency Division Multiplexing

(OFDM)Harald Haas and Birendra Ghimire

Advanced Digital Communications c©The University of Edinburgh, 2009 – p. 1/18

Literature

S. B. Weinstein, et al., "Data Transmission by Frequency-Division Multiplexing Usingthe Discrete Fourier Transform", IEEE transactions on communication technology,vol. 19, no. 5, Oct. 1971. KEY PAPER

J. A. C. Bingham, Multicarrier Modulation for Data Transmission: An Idea WhoseTime Has Come", IEEE Communications Magazine, vol. 28, no. 5, May 1990.

H. Sari, "Transmission techniques for digital terrestrial TV broadcasting", IEEECommunications Magazine, vol. 33, no. 2, Feb. 1995.

H. Rohling, et al., "Performance comparison of different multiple access schemes forthe downlink of an OFDM communication system", 47th IEEE Vehicular TechnologyConference, May 1997.

S. Hara, et al., "Overview of multicarrier CDMA", IEEE Communications Magazine,vol. 35, no. 12, Dec. 1997.


Application of OFDM

OFDM is the modulation/multiplexing technology for:

Broadband access via plain old telephone system (POTS) copper wiring. e.g.ADSL, SDSL, VDSL (OFDM is also called discrete multitone (DMT))

Certain Wi–Fi systems: IEEE 802.11a/g

Digital Audio Broadcasting (DAB): EUREKA 147, Digital Radio Mondiale, HDRadio, T-DMB and ISDB-TSB.

Digital Video Broadcasting (DVB): Terrestrial digital TV systems like DVB-T,DVB-H, T-DMB and ISDB-T.

IEEE 802.16 or WiMAX Wireless MANs.

IEEE 802.20 or Mobile Broadband Wireless Access (MBWA) systems.

Flash-OFDM cellular systems.

Certain Ultra wideband (UWB) systems.

Power line communication (PLC).

Multimedia over Coax Alliance (MoCA) home networking.

Emerging systems like WINNER ...etc


OFDM Transmission Block

S/P

Conversion

IFFT

(OFDM

Modulation)

P/S

Conversion

+

Addition of

Guard Interval

D/A

Converter

RF

Up

converterChannel

Channel

Equalization

RF

Down

converter

A/D

Converter

S/P

Conversion

+

Removal of

Guard Interval

IFFT

(OFDM

Demodulation)

P/S

Conversion

Data

Stream

Data

Stream

Interference

+ Noise+

Figure 1: OFDM transmission chain.


Multiple Access Schemes

Time slots

Ban

dwid

th

Time Division Multiple Access

(a) Time division multiple access

Time

Ban

dwid

th

Frequency Division Multiple Access

Guard band

Guard band

Guard band

Guard band

Guard band

Guard band

Guard band

(b) Frequency division multiple access

Figure 2: TDMA and FDMA illustration

OFDM + FDMA = OFDMA

OFDMA uses OFDM as modulation and FDMA as multiple access scheme.


−10 −5 0 5 10Frequency Index

Frequency Division Multiple Access

(a) Frequency division multiple access

−5 −4 −3 −2 −1 0 1 2 3 4 5

−0.2

0

0.2

0.4

0.6

0.8

1

Frequency Index

Nor

mal

ized

Am

plitu

de

Orthogonal Frequency Division Multiplexing

(b) Orthogonal Frequency division multiple access

Figure 3: Comparison of FDMA and OFDMA

FDMA requires guard bands to avoid inter–carrier interference (ICI)

OFDMA exploits the orthogonality of subcarriers


Motivation

The data rate typical for a 3G system is:

144 kbps (vehicular)

384 kbps (pedestrian)

2 Mbps (indoor)

4G system envisions a data rate of:

100 Mbps for mobile

1 Gbps for fixed links

If single carrier modulation (SCM) were used, the symbol duration will around 2orders of magnitude smaller.


Effect of smaller symbol

Using SCM, for 3G data rates of 144 kbps, 384 kbps and 2 Mbps, the symboldurations are 6.94 ms, 2.6 ms, 0.5 µs respectively. (Assuming 1 bit per symbol).

For data rates of 100 Mbps and 1 Gbps (envisioned data rates for 4G system), thesymbol durations are 10 ns and 1 ns respectively if SCM is used with 1 bit persymbol.

Ignoring channel impairments, multiple access interference (MAI), impulse noise isalso a factor in degradation of performance.

Impulse noise has a pulse duration, burst duration and inter-burst duration time of250 ns, 1 µs and 10 ms respectively.

The symbol duration is therefore significantly smaller compared to the pulse durationof the impulse noise. Depending on the amplitude of the impulse noise, quite a fewsymbols would be badly affected.


Frequency selective channel

Typical bandwidth for OFDM systems is between 20 MHz to 100 MHz.

Such broadband channels exhibit a wider degree of frequency selectivity comparedto a narrow–band channel.

0 10 20 30 40 50 600

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

Subchannel index

Cha

nnel

tran

sfer

func

tion

|H(f

)|

Frequency selective channel

Figure 4: Frequency selective channel.

Locally flat fading sub–channels can be obtained by dividing the signal bandwidthinto smaller sub–channels.


OFDM

The system bandwidth (B) is divided into N subcarriers, each having a bandwidth of( BN

).

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Frequency Index

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ized

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For the same data rate and modulation technique, the symbol duration will beTS = N · TB, where TB is the symbol duration for the broadband system.

Simpler equalizers such as zero forcing can be used for equalization.

Spectral efficiency is increased as the subcarriers overlap with each other.


Orthogonality of Signals

−3 −2 −1 0 1 2 3

−0.8

−0.6

−0.4

−0.2

0

0.2

0.4

0.6

0.8

Angle in radians (θ)

sin(

θ)

Sine curve

−ve area

+ve area

(a) Area under sine curve

−3 −2 −1 0 1 2 3−1

−0.8

−0.6

−0.4

−0.2

0

0.2

0.4

0.6

0.8

Angle in radians (θ)

cos(

θ)

Cosine curve

−ve area

+ve area

−ve area

(b) Area under cosine curve

The area under one period of a sine or a cosine wave is zero

The area under the product of two sinusoids with frequency of an integer number ofthe fundamental frequency (ω) is also 0.

∫

−

T

2

−

T

2

sin(kω t) · sin(lω t) = 0

Such sinusoids are said to be "Orthogonal" to one another.



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−0.2

0

0.2

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Frequency Index

Nor

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SamplingInstant

Orthogonality in OFDM system means that all the subcarriers other than theintended one go through 0 at the sampling instant.

Both frequency and time synchronization are vital.

Frequency offset and jitter cause inter-carrier interference (ICI) in the systembecause the contribution from other subcarriers at such sampling instant is not 0.



−5 −4 −3 −2 −1 0 1 2 3 4 5

−0.2

0

0.2

0.4

0.6

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Frequency Index

Nor

mal

ized

Am

plitu

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(c) Frequency synchronized

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0

0.2

0.4

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Subchannel index

Nor

mal

ised

rec

eive

d si

gnal

Incorrect Synchronisation

Sampling Instant

(d) Frequency not synchronized

Frequency shift causes intercarrier interferences.

One cause of frequency shift is due to doppler.

Orthogonality is realized with FFT/IFFT - output is a sum of orthogonal signals.


Realization of Orthogonality

An OFDM system takes a data stream and splits it into N parallel data streams

each at a rate 1N

of the original rate.

each stream is then mapped to a tone at a unique frequency and combinedtogether using the inverse fast fourier transform (IFFT) to yield the time-domainwaveform to be transmitted.


OFDM transmitter

The transmitted signal can be written in equivalent low–pass description as:

x(t) =1√TS

N−1∑

k=0

sk(n)ej2πfkt nTS ≤ t < (n + 1)TS

where, sk is the baseband modulated signal (i.e. QAM, PAM or PSK modulated.)

As every subcarrier is orthogonal to one another in an OFDM system, we have,

1

TS

∫ TS

0ej2π(fk−fl)tdt =

1 k = l

0 k 6= l

The minimum carrier spacing between two adjacent subcarriers(∆f = fk+1 − fk = 1

TS)

Hence the low-pass equivalent of the transmitted signal is:

x(t) =1√TS

N−1∑

k=0

sk(n)ej2πk t

TS nTS ≤ t < (n + 1)TS


Signal in Frequency Domain

x(t) =1√TS

N−1∑

k=0

sk(n)ej2πk t

TS nTS ≤ t < (n + 1)TS

To get the signal representation in frequency domain, Fourier Transform of x(t) isobtained:

X(f, nTS) =1

TS

∫ (n+1)TS

nTS

x(t)ej2πftdt

= e−jθn

N−1∑

k=0

sk(n)sinc(fTS − k)

The symbol sk(n) can be obtained directly by sampling X(f, nTS) at f = kT

X(k

TS

, nTS) = sk(n), k = 0, 1, · · · , N − 1

Any offset in frequency causes cross-talk over the subcarriers.


Detection of OFDM symbols

The received signal is given by r(t) = x(t) + z(t), where z(t) is the interference andNoise added to the received signal.

The baseband symbol is detected by taking FFT of the received signal.

rk(n) =1√TS

∫ (n−1)TS

nTS

r(t)e−j2πk t

TS dt

= sk(n) + Ik(n)

Now the baseband symbol is zero-forced (equalised) and sliced to recover datasymbols.


OFDM tutorial

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