CH. 7 OFDM Principles - mercury.kau.ac.krmercury.kau.ac.kr/hrpark/lecture/2012년...

1Korea Aerospace University Mobile Communications Lab.

CH. 7 OFDM Principles


ContentsContents

Overview of 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

Design Example of OFDM Systems

OFDM-based Multiple Access Schemes


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

Recently, the demand for mobile internet and multimedia services is growing exponentially ==> High rate data transmission is essential!

In case of transmitting the high rate data through single carrier systems, the ISI (inter-symbol interference) is inevitable due to channel delay spread, as shown in Fig. 7.1.

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.

OFDM (orthogonal frequency division multiplexing) is a special case of multi-carrier transmission techniques that the spectra of sub-carriers are overlapped.

OFDM is a transmission technique of prominent fourth generation mobile communication systems:

WCDMA-LTE

WiBro evolution (IEEE 802.16m)

UMB (Ultra Mobile Broadband, IEEE 802.20)


Overview of OFDM Technique (cont.)Overview of OFDM Technique (cont.)

Fig. 7.1 Illustration of Inter-symbol interference



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 guard band and may require several oscillators and pulse-shaping filters.

Fig. 7.2 A classical multi-carrier transmission scheme



In OFDM, the spectra of sub-carriers are overlapped ==> no guard band and pulse shaping

0f

1Kf −2f1f0f

1Kf −2f1f

f

f

Fig. 7.3 Spectra of multi-carrier signals and OFDM signals



Fig. 7.4 Spectra of an OFDM sub-channel and total OFDM channel

The sub-carriers in OFDM signals are arranged so that the sidebands of individual sub-carriers overlap and the signals are received without inter-channel (or -carrier) interference (ICI).

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



Key advantages of OFDM

Robust against inter-symbol interference and narrowband 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 transmissionRelatively large PAPR (peak-to-average power ratio) ==> reduced power efficiency of the RF amplifier

More sensitive to the frequency offset and phase noise


Block Diagram of an OFDM Transceiver [1]Block Diagram of an OFDM Transceiver [1]

Fig. 7.5 Block diagram of an OFDM transceiver

Symbolmapping

Symboldemap.


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

Fig. 7.6 A simplified OFDM modulator

S/P+di

exp(j2πfot)

exp(j2πf1t)

exp(j2πfNc-1t)

( )s t

, 1 /if i f f T= Δ Δ =

An OFDM signal consists of a sum of sub-carriers that are modulated by using PSK or QAM.

T: OFDM symbol duration


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

ii

s t d j i ft t T

s t t t T

π−

=

= Δ ≤ ≤

= < >

∑

id cN

T fΔ

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

: effective OFDM symbol duration, : sub-carrier spacing

( )s t



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= Δ = −

( )

( )

( )

( )

{ }

1

0

1

0

1

0

1

0

( ) exp 2

exp 2 / , ( 1/ )

exp 2 / , ( )

exp 2 / , 0 for , 1, ,

sample of the IDFT of , : DFT

c

c

c

N

ii

N

ii

N

ii

N

i i c ci

i

s n t d j i fn t

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

π

−

=−

=−

=−

=

Δ = Δ Δ

= Δ Δ =

= = Δ

= = = +

⇒ ×

∑

∑

∑

∑ 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. 7.7 Spectra of the individual sub-carriers


Demodulation Using the FFT [1],[2]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. 7.8 Example of four sub-carriers within one OFDM symbol

0 T


Demodulation Using the FFT (cont.)Demodulation Using the FFT (cont.)

Demodulation for the sub-carrier k

since

1

00th subcarrier

1

0 0

exp 2 exp 2

( )exp 2

c

c

T N

ii

k

TN

i ki

k itj t d j dt

T T

i kd j t dt d T

T

π π

π

−

=

−

=

⎛ ⎞ ⎛ ⎞−⎜ ⎟ ⎜ ⎟⎝ ⎠ ⎝ ⎠

−⎧ ⎫= =⎨ ⎬⎩ ⎭

∑∫

∑ ∫

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

In order to eliminate inter-symbol interference almost completely, 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. 7.9.

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


Guard Time and Cyclic Extension (cont.)Guard Time and Cyclic Extension (cont.)

Fig. 7.9 Effect of multi-paths in case of zero signal in the guard time



Fig. 7.10 OFDM symbol with cyclic extension

copy



Fig. 7.11 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

The orthogonality is maintained by using cyclic extension as shown in Fig. 7.11.

However, the orthogonality become 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. 7.12 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]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. 7.13 PSD without windowing for 16, 64, 256 sub-carriers


Windowing (cont.)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

where β is the roll-off factor.

( )

( )

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

⎧ + + ≤ ≤⎪= ≤ ≤⎨⎪ + − ≤ ≤ +⎩

Fig. 7.14 OFDM cyclic extension and windowing



Fig. 7.15 Spectra for raised cosine windowing with roll-off factor0, 0.025, 0.05, and 0.1 (64 sub-carriers)



Fig. 7.16 OFDM symbol windows for a two-ray multi-path channel,showing ICI and ISI

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.


Design Example of OFDM Systems [1]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 rmsdelay 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.

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.)Design Example of OFDM Systems (cont.)

As an example, suppose we want to design an OFDM system with thefollowing 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 = 4.8μs ==> FFT interval = 4.0μs

- Sub-carrier spacing: 1/(4.0μs) = 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 SchemesOFDM-Based Multiple Access Schemes

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

Fig. 7.17 OFDM-based multiple access schemes


ReferencesReferences

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.

CH. 7 OFDM Principles - mercury.kau.ac.krmercury.kau.ac.kr/hrpark/lecture/2012년...

Documents

Transcript of CH. 7 OFDM Principles - mercury.kau.ac.krmercury.kau.ac.kr/hrpark/lecture/2012년...