ch.6 ofdm principles - mercury.kau.ac.krmercury.kau.ac.kr/hrpark/lecture/2012년...

CH.6 OFDM Principles

1Korea Aerospace University Mobile Communications Lab.

CH.6 OFDM Principles

Contents

� Overview of the OFDM Technique

� Block Diagram of an OFDM Transceiver

� Generation of Sub-carriers Using the IFFT

� Demodulation Using the FFT

� Guard Time and Cyclic Extension

� Windowing


� Windowing

� Design Example of OFDM Systems

� OFDM-based Multiple Access Schemes

Overview of the OFDM Technique [1],[2]

� Recently, mobile internet and multimedia services rapidly increase

==> High rate data transmission is essential!

� In case of transmitting high rate data through single carrier systems,

the ISI (inter-symbol interference) is inevitable due to the channel

delay spread, as shown in Fig. 6.1.

� The inter-symbol interference can be reduced by multi-carrier

transmission which divides a high speed data stream into several

parallel lower rate data streams prior to transmission.


parallel lower rate data streams prior to transmission.

� OFDM (orthogonal frequency division multiplexing) is a special case

of multi-carrier transmission techniques that the spectra of sub-

carriers are overlapped.

� OFDM is the only transmission technique accepted for the fourth

generation mobile communication systems:

� WCDMA-LTE

� WiBro evolution (IEEE 802.16m)

� UMB (Ultra Mobile Broadband, IEEE 802.20)

Overview of the OFDM Technique (cont.)


Fig. 6.1 Illustration of the inter-symbol interference due to delay spread


� In a classical multi-carrier transmission, the total frequency band

is divided into N non-overlapping frequency sub-channels

==> may reduce the spectrum efficiency due to the guard band and

may require several oscillators and pulse-shaping filters.


Fig. 6.2 A classical multi-carrier transmission scheme


� In OFDM, however, the spectra of sub-carriers are overlapped ==>

no guard band and no pulse-shaping

f


0f

1Kf −2f1f0f

1Kf −2f1f

f

f

Fig. 6.3 Spectra of multi-carrier signals and OFDM signals


� The sub-carriers in OFDM signals are arranged so that the

sidebands of individual sub-carriers overlap but the signals are

received without inter-channel (or -carrier) interference (ICI).


Fig. 6.4 Spectra of an OFDM sub-channel and total OFDM channel

(a) Spectrum of an OFDM sub-channel (b) Spectrum of total OFDM channel


� Key advantages of OFDM

� Robust against inter-symbol interference

� Reduced H/W complexity since it does not require complicated equalizers

and pulse-shaping filters

� Can be implemented easily by using FFT / IFFT processors

� Drawbacks compared with a single carrier transmission

� Relatively large PAPR (peak-to-average power ratio) ==> reduced


� Relatively large PAPR (peak-to-average power ratio) ==> reduced

efficiency of the power amplifier

� More sensitive to the frequency offset and phase noise

Block Diagram of an OFDM Transceiver [1]

Symbolmapping


Fig. 6.5 Block diagram of an OFDM transceiver

Symboldemap.

Generation of Sub-carriers Using the IFFT [1],[2]

S/P+d

i

exp(j2πfot)

( )s tɶ

� An OFDM signal consists of a sum of sub-carriers that are modulated by using

PSK or QAM.


Fig. 6.6 A simplified OFDM modulator

S/P+d

i

exp(j2πf1t)

exp(j2πfNc-1t)

( )s tɶ

, 1 /if i f f T= ∆ ∆ =

T: OFDM symbol duration

Generation of Sub-carriers Using the IFFT (cont.)

� A complex baseband OFDM signal can be written as

( )1

0

( ) exp 2 , 0

( ) 0, 0 or

cN

i

i

s t d j i ft t T

s t t t T

π−

=

= ∆ ≤ ≤

= < >

∑ɶ

ɶ

( )s tɶ


id cN

T f∆

: complex PSK or QAM symbols, : number of used sub-carriers

: effective OFDM symbol duration, : sub-carrier spacing


� The complex baseband signal is in fact nothing more than the inverse Fourier

transform of N input symbols.

Let Then,, 0, 1, 2, , 1.t n t n N= ∆ = −⋯

( )

( )

1

0

1

( ) exp 2

exp 2 / , ( 1/ )

c

c

N

i

i

N

i

s n t d j i fn t

d j in t T f T

π

π

−

=

−

∆ = ∆ ∆

= ∆ ∆ =

∑

∑

ɶ


( )

( )

( )

{ }

0

1

0

1

0

exp 2 / , ( 1/ )

exp 2 / , ( )

exp 2 / , 0 for , 1, ,

sample of the IDFT of , : DFT

c

i

i

N

i

i

N

i i c c

i

i

d j in t T f T

d j in N T N t

d j in N d i N N N

N nth d N

π

π

π

=

−

=

−

=

= ∆ ∆ =

= = ∆

= = = +

⇒ ×

∑

∑

∑ ⋯

size

� Note that Nc is the number of used subcarriers, while N is the DFT size.


� The amplitude spectrum of the square pulse with a duration T is equal to the

sinc function, which has zeros for all frequencies f that are integer multiples

of 1/T.

� At the maximum of each sub-carrier spectrum, all other sub-carrier spectra are

zero.


Fig. 6.7 Spectra of the individual sub-carriers

Demodulation Using the FFT [1],[2]

� Demodulation is equivalent to DFT.

� Orthogonality between sub-carriers

� Each sub-carrier has exactly an integer number of cycles in the interval T.

� The number of cycles between adjacent sub-carriers differs by exactly one.


Fig. 6.8 Example of four sub-carriers within one OFDM symbol

0 T

Demodulation Using the FFT (cont.)

� Demodulation for the sub-carrier k

1

00th subcarrier

1

0 0

exp 2 exp 2

( )exp 2

c

c

T N

i

i

k

TN

i k

i

k itj t d j dt

T T

i kd j t dt d T

T

π π

π

−

=

−

=

−

− = =

∑∫

∑ ∫

��


since

0 0iT

= ∫

0

0

( ) exp 2 , for

( )exp 2 0, for

T

T

i kj t dt T i k

T

i kj t dt i k

T

π

π

− = =

− = ≠

∫

∫

� Obviously, demodulation for all subcarriers can be performed by the FFT.

Guard Time and Cyclic Extension [1],[2]

� In order to avoid inter-symbol interference, a guard time should be introduced

for each OFDM symbol.

� The guard time should be chosen larger than the expected maximum multi-

path delay.

� The guard time could consist of no signal at all. However, in this case, the

problem of inter-carrier interference (ICI) would arise due to the loss of

orthogonality between sub-carriers, as shown in Fig. 6.9.


� To avoid the ICI, the OFDM symbol should be cyclically extended in the guard

time.

Guard Time and Cyclic Extension (cont.)


Fig. 6.9 Effect of multi-paths in case of zero signal in the guard time


copy


Fig. 6.10 OFDM symbol with cyclic extension


� The orthogonality is maintained by using cyclic extension as shown in Fig. 6.11.

� However, the orthogonality becomes lost if the multi-path delay is larger than

the guard time since the phase transitions of the delayed path may fall within

the FFT interval of the receiver.


Fig. 6.11 Example of an OFDM signal with cyclic extension: three sub-carriers

in a two-ray multi-path channel with the delay smaller than guard time



Fig. 6.12 16-QAM constellation for a 48-subcarrier OFDM link with a two-ray

multi-path channel, the second ray being 6dB lower than the first one

(a) delay < guard time, (b) delay exceeds 3% of the FFT interval

(c) delay exceeds 10% of the FFT interval

Windowing [1],[2]

� An OFDM signal consists of a number of unfiltered sub-carriers.

� Therefore, the out-of-band spectrum decreases rather slowly, with the speed

depending on the number of sub-carriers, as shown below.


Fig. 6.13 PSD without windowing for 16, 64, 256 sub-carriers

Windowing (cont.)

� To make the spectrum go down more rapidly, windowing can be applied to

individual OFDM symbols.

� Mostly used is the raised cosine window, which is defined as

( )

( )

0.5 0.5 cos /( ) , 0

( ) 1.0,

0.5 0.5 cos ( ) /( ) , (1 )

s s

s s

s s s s

t T t T

w t T t T

t T T T t T

π π β ββ

π β β

+ + ≤ ≤

= ≤ ≤ + − ≤ ≤ +


where ββββ is the roll-off factor.

Fig. 6.14 OFDM cyclic extension and windowing

Windowing (cont.)


Fig. 6.15 Spectra for raised cosine windowing with roll-off factor

0, 0.025, 0.05, and 0.1 (64 sub-carriers)

Windowing (cont.)

� Larger roll-off factors improve the spectrum further, at the cost, however, of a

decreased delay spread tolerance.

� Instead of windowing, it is possible to use virtual carriers by nulling the sub-

carriers around the edge of the spectrum.


Fig. 6.16 OFDM symbol windows for a two-ray multi-path channel,

showing ICI and ISI

Design Example of OFDM Systems [1]

� The choice of various OFDM parameters is a tradeoff between various, often

conflicting, requirements.

� Usually, there are three main requirements for the design of OFDM systems;

bandwidth, bit rate, and tolerable delay spread.

� As a first rule for design, the guard time should be at least four times the rms

delay spread.

� Also, to minimize the SNR loss caused by the guard time, it is desirable to

have the symbol duration much larger than the guard time.


have the symbol duration much larger than the guard time.

� However, a larger symbol duration means more sub-carriers with a smaller

sub-carrier spacing, a larger implementation complexity, and more sensitivity

to phase noise and frequency offset, as well as an increased peak-to-average

power ratio (PAPR).

� Hence, a practical design choice is to make the symbol duration around five

times the guard time.

� The number of sub-carriers may be determined by the required bit rate divided

by the bit rate per sub-carrier.

Design Example of OFDM Systems (cont.)

� As an example, suppose we want to design an OFDM system with the

following requirements.

� Bit rate: 20Mbps

� Tolerable delay spread: 200ns

� Bandwidth < 15MHz

- Guard time: delay spread x 4 = 800ns

- Total OFDM symbol duration: guard time (800ns) x 6 = 4.8µµµµs


- Total OFDM symbol duration: guard time (800ns) x 6 = 4.8µµµµs ==> FFT interval = 4.0µµµµs

- Sub-carrier spacing: 1/(4.0µµµµs) = 250kHz

- 15MHz / 250kHz = 60: number of used sub-carriers should be smaller than 60

- 20Mbps x 4.8us = 96bits per symbol

� 16-QAM, ½ coding: 48 sub-carriers are needed.

� QPSK without coding: 48 sub-carriers

� FFT size = 64

OFDM-Based Multiple Access Schemes


OFDM-TDMA OFDM-FDMA OFDM-CDMA (MC-CDMA)

Fig. 6.17 OFDM-based multiple access schemes

References

1. R. V. Nee and R. Prasad, OFDM for Wiress Multimedia Communications,

Artech House Publishers, 2000.

2. L. Hanjo, M. Munster, B. J. Choi, T. Keller, OFDM and MC-CDMA for

Broadband Multi-User Communications, WLANs, and Broadcasting, John

and Wiley, 2003.


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