Broadband Communication Systems 521316S 7. Basics for OFDM

Contents • Why OFDM? • Basic Features of OFDM Systems • • • •

OFDM Signal Generation Modulation and Coding OFDM in Multipath Channels Design Aspects of OFDM Systems – Cyclic Prefix, Carrier Spacing • OFDM Signal Spectrum and Spectrum Limitation • Advantages and Disadvatages of OFDM • Summary

2

Why OFDM?

Multicarrier Transmission • Basic ideas: – Avoid ISI by multiplexing high rate data stream into several lower rata streams – by utilising several distinct frequency bands

=> Frequency division Multiplexing (FDM) Ch.1

Ch.2

Ch.3

Ch.4

Ch.5

Ch.6

Ch.7

Ch.8

Ch.9

Ch.10

frequency

Basic FDM based systems (like FDMA) require quard bands.

4

Parallel Transmissions to Avoid Channel Caused Distortions

5

Concept of Parallel Transmission

 Freq. 1

Freq. 1

 S/P

Binary low-speed data

Freq. 2

Sum

P/S

Freq. 2

Binary highspeed data

 Freq. N

Freq. N

6

Bandwidth Efficiency Basic FDM scheme Ch.1

Ch.2

Ch.3

Ch.4

Ch.5

Ch.6

Ch.7

Ch.8

Ch.9

Ch.10

frequency

Basic FDM based systems require quard bands.

Orthogonal FDM Ch.2 Ch.4 Ch.6 Ch.8 Ch.10 Ch.1 Ch.3 Ch.5 Ch.7 Ch.9

Saving of bandwidth

frequency

By allowing TX bands to overlap, guard bands are not needed and the same system bandwidth can be used to increase the transmission rate.

7

Bandwidth Efficiency (2) FDM

OFDM

BW = 2R

BW = 2R

-R

R

f

N=1 -R

R

BW = 3/2R

BW = 2R

f

N=2

f -R

-3R/4 - R/4 R/4 3R/4

R

BW = 4/3R

-2R/3 - R/3 R/3 2R/3

f

BW = 2R

f

N=3

f - R - R/3

R/3

R

8

Single Carrier vs. Multicarrier

9

Singlecarrier vs. Multicarrier (2) EXAMPLE • Data rate 10 Mbps with BPSK => B=10 MHz • Channel with max. delay spread of 10 ms

• Singlecarrier scheme: Ts,sc=1/10MHz=0.1 ms ISI will extend over 100 symbol intervals • Multicarrier scheme with 1000 subcarriers: Ts,mc=1000 *Ts,sc =100 ms ISI will extend over 0.1 symbol interval SC scheme will require very long time domain equalizer, which 10 is not necessarily needed in the MC scheme.

Single Carrier vs. Multicarrier (3) N carriers Channel Guard bands

B Pulse length ~1/B – Data are transmited over only one carrier

Drawbacks

B Pulse length ~ N/B – Data are shared among several carriers and simultaneously transmitted Advantages

– Selective Fading

– Flat Fading per carrier

– Very short pulses

– N long pulses

– ISI is compartively long

– ISI is comparatively short

– EQs are then very long

– no EQs or N short EQs needed - Improved spectral efficiency

– Poor spectral efficiency because of band guards

11

Single Carrier vs. Multicarrier (4)

12

Some Historical Highlights • First multicarrier systems were HF military radio links in 1957 (Collins KINEPLEX). • Bell Labs filed the first OFDM patent in 1966 and published the first article. • 1971 Weinstein presents the idea on using FFT to generate OFDM signal. • 1985 Cimini describes the principle how to apply OFDM in mobile communication systems. • 1980-1990 evolution of digital subscriber line (DSL) technologies. • 1995 DAB standard; the first OFDM standard. • 1997 DVB-T standard finalised. • 1998 Digital • 1999 OFDM based WLAN standards (802.11a) for 5 GHz. • 2004 Wi-Max standard (802.16a) based on OFDM is finalised. • 2004 Multiband OFDM Alliance (MBOA) established to promote OFDM for ultrawideband standard (www.multibandofdm.org). • 2004 ETSI approves digital AM radio standard based on OFDM. • 2006 OFDM is chosen for 3G-LTE standard as the air-interface concept. • 2007 OFDM seems to be the strongest candidate for 4G mobile phone systems air-interface. 13

Basic features of OFDM systems

OFDM Signal

15

OFDM Signal (2)

16

OFDM Signal (3) • Example: 4 orthogonal subcarriers

17

Proof of Orthogonality

18

Proof of Orthogonality (2) • Each OFDM block (or OFDM symbol) contains subcarriers which are non-zero over Ts,mc. • Spectrum of one OFDM symbol is convolution of sinc-pulse with Dirac pulses at subcarrier frequencies => Other pulses are zeros at the maximum point of each subcarrier signal.

19

Proof of Orthogonality (3) ~ r (t ) 



S

i  

i ,1

cos 1t  Si , 2 cos(2t   )

T

2 cos(1t )~ r (t )dt 0

T

T

0

0

 2Si ,1  cos 1t cos 1tdt  2Si , 2  cos 1t cos(2t   )dt T

 Si ,1  2Si , 2  cos[(2  1 )t   ]dt 0

0



(1  2 )  2

1 T

20

Spectrum of OFDM Signal rect(t/Ts,mc) -Df

Df Df f.

Ts,mc

2/Ts,mc

At the optimum sampling instants, inter-channel interference (ICI) is zero. 1

2 Df ....

N

Df

* f.



...

ICI=0

1 2 ... N

f

21

Spectrum of OFDM Signal (2)

22

OFDM Signal Generation

OFDM Signal Revisted  1 s(t )  w(t  iTs ,mc )   i    N 

window function, which can be also something else than rect( )

N 1

S k 0

i ,k

e

j 2kt / Ts ,mc

  

Ts ,mc  NTs ,sc

f 24

Some Mathematical Definitions 

• Fourier Transform:

H( f ) 

 h(t )  e

 j 2ft

dt

t  

N 1

• Discrete Fourier Transform:

X ( k )   x ( n)  e

 j 2kn / N

n 0

• Inverse DFT:

1 x ( n)  N

N 1

j 2kn / N X ( k )  e  n 0

25

Comparison of IDFT and DiscreteTime Presentation for OFDM Signal • IDFT:

1 N 1 j 2kn / N x ( n)   X ( k )  e N n 0

• OFDM signal:

1 si ,n  si (n  Dt )  N

N 1

j 2nkDfDt S  e  i ,k k 0

Df  Dt 

1 Ts ,mc



Ts ,mc N



1  N

N 1

j 2nk / N S  e  i ,k k 0

1 N

OFDM signal can be produced by using IDFT!  OFDM modulator relatively simple 26 to implement by using IFFT

Simplified Modulator Demodulator Pair (QAM) encoder

IDFT

...

S2P

...

binary data

...

TX P2S

D/A + IF/RF

channel

DFT

...

P2S

(QAM) decoder

...

binary data

...

RX S2P

D/A + IF/RF

27

Modulation and Coding

Modulation • The power of OFDM is the avoidance of ISI and ICI under earlier defined conditions. • OFDM does suffer from frequency selective fading and interference as any other systems. • The difference of OFDM is, however, that the whole information symbol can be lost if, e.g., a deep fade occurs at a subcarrier of interest.

29

Adaptive Modulation • OFDM gives opportunity to use different data modulation an d TX power for each subcarrier. • This is called adaptive bit loading.

64QAM 16QAM QPSK BPSK

30

Adaptive Modulation (2) • Unlike in DMT, wireless OFDM systems rely on channel coding and subcarrier interleaving to cope with channel frequency selectivity caused errors. • Narrowband interrence can be suppressed e.g. by neglecting subcarriers exceeding a pre-determined threshold. • When using adaptive modulation, somewhat weaker channel coding can be applied. • When adaptive modulation is NOT used, channel coding requirements remain the same as in any wireless system. 31

QAM Constellation Q

Q

I

I

64QAM

256QAM 32

QAM Constellation (2) • QAM is typically used in OFDM systems because QAM is bandwidth efficient modulation in flat fading channels when large constellation sizes can be used due to relatively small channel caused distortions  Multilevel modulation requiring coherent demodulation can be applied and channel estimation needed in coherent demodulation is relatively simple.

33

2D coding and interleaving dataflow

Map data symbols To 2D matrix time

freq.

Transmit

34

OFDM in Multipath Channels

What Happens in Multipath Channel? • Although OFDM modulation almost eliminates ISI, multipath propagation causes distortion and loss of some orthogonality: One OFDM ”frame” or ”block” contains M+1 OFDM symbols. Direct wave

Symbol M-1

Delayed wave #1

Symbol M-1

Delayed wave #2

Symbol M-1

Delayed wave #3

Symbol M-1

Delayed wave #4

Symbol M-1

Received wave

Symbol M-1 Contaminated area by delayed waves

Symbol M

Symbol M

Symbol M Symbol M Symbol M

Symbol M Non-contaminated area by delayed wave

Symbol M+1

Symbol M+1

Symbol M+1 Symbol M+1 Symbol M+1

Symbol M+1

< Symbol M

36

What Happens in Multipath Channel? (2) • Multipath caused distortion can be made smaller by introducing guard time: Part of subcarrier #2 causing ICI on subcarrier #1 Subcarrier #1

Orthogonality is not lost due to delay (phase shift), but because not full signal cycles (2) are used in demodulation.

Delayed subcarrier #2

Guard Time

FFT Integration Time = Ts,mc=1/Carrier Spacing OFDM Symbol Length

37

What Happens in Multipath Channel? (3) • Introduction of guard time solve inter OFDM-symbol interference (called ISI):

Direct wave

Symbol M-1

Delayed wave #1

Symbol M-1

Delayed wave #2

Symbol M-1

Delayed wave #3

Symbol M-1

Delayed wave #4

Symbol M-1

Received wave

Symbol M-1

Guard interval

Symbol M

Guard interval

Symbol M

Guard interval

Contaminated area by delayed wave

Guard interval Guard interval

Symbol M Symbol M Symbol M

Guard interval

Symbol M+1

Guard interval

Symbol M+1

Guard interval

Symbol M+1

Guard interval Guard interval

Symbol M

Symbol M+1 Symbol M+1

Symbol M+1

Non-contaminated > Symbol M area by delayed wave

38

What Happens in Multipath Channel? (4) • Introduce cyclic prefix to maintain orthogonality between subcarriers and avoid ISI within one OFDM symbol (called inter carrier interference ICI): Complete OFDM Symbol Data part of OFDM Symbol

Next OFDM Symbol

Guard interval alone Guard interval, G > τmax Using empty spaces as guard interval at the beginning of each symbol Complete OFDM Symbol Data part of OFDM Symbol

Next OFDM Symbol

Guard with cyclic prefix Cyclic prefix, CP = G > τmax End of symbol is copied to the beginning of each symbol

39

What Happens in Multipath Channel? (5) • NO ISI and ICI occur, if guard interval is longer than channel delay spread. • The loss of energy because of the discarded energy in the cyclic prefix is: SNRloss  10 log10 1  Tcp T



40

What Happens in Multipath Channel? (6) • An example with 16 carriers in a two path channel:

41

What Happens in Multipath Channel? (7) • Cyclic prefix has to be larger than the delay spread of the channel. • Example: OFDM link with 48 subcarriers, 16-QAM, 2-ray multipath channel (0dB and -6dB) – (a) multipath delay < Tcp – (b) multipath delay exceeds Tcp by 3% of FFT interval – (c) multipath delay exceeds Tcp by 10% of FFT interval

(a)

(b)

(c)

42

Design Aspects of OFDM Systems – Cyclic Prefix, Carrier Spacing

Basic System Design Parameters • Basic parameters for designing an OFDM System: –number of subcarriers, –guard time, OFDM symbol duration, –subcarrier spacing, –modulation type per subcarrier and –the type of forward error correction coding

44

OFDM System Requirements • Choice of basic parameters is influenced by the system requirements: –Available bandwidth, –Required bit rate, –Tolerable delay spread and –Max. Doppler values

• Channel time-frequency correlation functions influence on pilot symbol placing strategy (to be discussed later). 45

Choice of OFDM Parameters 1. 2. 3.

Delay spread dictates guard interval Tcp Symbol duration: to minimize SNR loss due to using cyclic prefix, it is desirable to have T >> Tcp Larger Ts means: • • • •

4.

more subcarriers with a smaller subcarrier spacing larger implementation complexity more sensitivity to phase noise and frequency offset increased peak-to-average power ratio (PAPR)

After Tcp and Ts fixed, the number of subcarriers N: • N = BW(-3dB) / Df, Df = 1 /(T – Tcp) or • N = required bit rate / bit rate per subcarrier, the bit rate per subcarrier is defined by the modulation type, coding rate and symbol rate 46 [ FFT integration time = OFDM symbol duration without cp ]

Choice of OFDM Parameters (2)

47

Choice of OFDM Parameters (3)

48

Choice of OFDM Parameters (4)

49

Choice of OFDM Parameters (5)

TOFDM=T

50

Example Design for OFDM • Determine parameters for OFDM system operating under the following conditions: • bit rate Rb 20 Mbps • tolerable rms delay spread  200 ns • System bandwidth B  15 MHz • Loss due to cyclic prefix max. 1 dB

51

Example Design for OFDM (2) • Let’s choose Tcp=800 ns*), to allow for timing errors SNRloss=0.8 dB Cp length should be 2-4 times max. delay spread, depending on the data mod. and ch. coding robustness against ICI. *)

52

Example Design for OFDM (3) • Then subcarrier spacing becomes Df=1/T = 250 kHz • Number of subcarriers becomes: – N=B/Df = 15 MHz/250 kHz = 60 • IFFT/FFT of size 64 should be chosen • To achieve 20 Mbps, each transmitted OFDM symbol (including cp) must carry 96 bits of information (96/4.8ms = 20Mbps) S

53

Example Design for OFDM (4) • 16-QAM with rate 1/2 coding gives 4*1/2*N/4.8ms= 20 Mbps => N=48 subcarriers for data • QPSK with rate 3/4 coding gives 2*3/4*N/4.8ms= 20 Mbps => N=64 subcarriers for data • However, 64 subcarriers would mean bandwidth of 64*250kHz=16MHz • The first option is selected to maintain under 15MHz bandwidth (48*250kHz=12MHz). 54

Example Design for OFDM (5) • The receiver operates by using samples. Hence an integer number of samples must be collected both from FFT interval and OFDM symbol interval: 64-FFT => sampling freq. 64*250kHz=16MHz, BUT 16MHz*0.8ms=12.8 samples for cp • The parameters need to be readjusted to meet this requirement.

55

Example Design for OFDM (6) Sampling rate is Rs  N FFT / TFFT s , thenit must also be Rs  N cp / Tcp N FFT N cp N FFT    N cp   Tcp . TFFT Tcp TFFT

To make sure that Ploss  1dB, N 64 N cp  FFT  Tcp   0,8ms  16.5. TFFT 3.1ms

TFFT=TS Let's select N cp  13. Now the modified FFT integration interval is TFFT  3.938ms (resulting in Ploss  0.99dB) and the new sampling frequency is Rs  13 / 0.8ms  16.25MHz 56

Example Design for OFDM (7) • The bandwidth constraint needs to be rechecked since the carrier spacing is slightly modified: Df=253.90625kHz => (16-QAM needs 48 carriers for data) B=12.1875MHz. • Data rate requirement is achieved since OFDM symbol interval is now a bit shorter.

57

Example Design for OFDM (8) • How the system parameters would be changed if the channel delay spread is 1ms and the number of subcarriers is kept the same? • Let’s assume that 0.6 ms is enough to cover timing errors etc. => Tcp=1.6ms

1.6ms T  7.8ms 1/ 10 1  10

• Let’s choose T = 8.4 ms => SNRloss= 0.9dB • Then subcarrier spacing becomes Df=1/TS = 147 kHz 58

Example Design for OFDM (9) • 48 subcarriers results in 48* 147 kHz = 7 MHz system bandwidth.

• 16-QAM with rate 1/2 coding gives 4*1/2*48/8.4ms= 11.4 Mbps • QPSK with rate 5/6 coding gives 2*5/6*48/8.4ms= 9.5 Mbps • The larger delay spread causes lowering the data rate and lowering the system bandwidth if the number of subcarriers is kept constant. 59

Example Design for OFDM (10) • How the data rate of 20Mbps can be maintained with system bandwidth of 15 Mbps for delayspread of max. 1 ms? Tcp=1.6ms and TS = 6.8 ms The subcarrier spacing is Df=1/TS ~ 147 kHz Number of subcarriers is N=B/Df = 15 MHz/147 kHz = 102 IFFT/FFT of size 128 should be chosen. 16-QAM with rate 1/2 coding gives 4*1/2*102/8.4ms=24.3Mbps • QPSK with rate 5/6 coding gives 2*5/6*102/8.4ms= 20.2 Mbps • • • • •

When higher delayspreads must be tolerated, OFDM symbol length must be increased to avoid large performance loss due to cyclic prefix. This in turn results in narrower subcarrier spacing => synchronisation problems 60 and larger number of subcarriers => increased complexity due to larger FFT

Discussion on the Choice of Parameters • The guard interval often isn't negligible compared to the OFDM data symbol length (often, it's 1/4th of the useful symbol size). Why not use a very long OFDM data symbol after a guard interval in order to decrease the redundancy (i.e. to minimise the loss due to cyclic prefic) ? – Subcarrier spacing is inverse of the OFDM symbol length – Subcarriers would be more closely spaced to keep bandwith constant => tighter frequency and phase synchronisation requirements 61

Discussion on the Choice of Parameters (2) • If we define an OFDM system for a quasi-AWGN-channel context (i.e. channel impulse response is short) - so, the data throughput can be increased by choosing a short guard interval. – Long enough cyclic prefix relaxes timing requirements – TX and RX filters also cause extra delay, i.e., lengthening of channel impulse response  Longer cyclic prefix makes system implementation easier • CP >> channel delay spread 62

Comparison Between MC and SC Systems • Implementation complexity single carrier vs. multicarrier – in SC systems: equalization dominates (necessary when delay spread larger than 10% of the symbol duration) – the need for equalization in MC systems is only at higher symbol rates -- lower symbol rates: only CPC (Common phase correction)

• OFDM implementation complexity – dominated by the FFT (however, FFT circuits, ASICs, etc. available) – simpler FFT algorithms such as CORDIC can be used (no need for full multiplications)

• SCMC Duality – problems in SC systems in time domain = problems in MC system in frequency domain and vice versa. 63

OFDM Signal Spectrum and Spectrum Limitation

Windowing • Out of band power does not decrease rapidly enough without additional bandlimitation:

Number of subcarriers

65

Windowing (2) • Without windowing, out-ofband spectrum decreases slowly, according to sinc function. • Windowing means multiplication of OFDM symbolsamples by corresponding window function. • Raised cosine (RC) function is the most typical window function.

PSD for different RC roll-off factors. 66

Windowing (3) •

How to construct an OFDM signal in practice: – Nc input data values padded with zeros to get N input samples – The last Tprefix samples of the IFFT output are inserted at the start of the OFDM symbol – The first Tpostfix samples are appended to the end – multiplication by a raised cosine window – add new OFDM symbol to previous one with a delay and overlap region T ( = roll-off factor of the raised cosine window) T =TS+T cp T prefix

T

TS

T

postfix

67

Windowing (4) • Faster PSD decay (i.e. larger roll-off factors) decreases the system tolerance to multipath by T. • Example: two-path channel

Multipath delay

Total guard period reduced by T 68

Windowing (5) • Windowing means multiplication in time-domain => frequency domain convolution. • Filtering is convolution in time-domain => multiplication in frequency domain. • Both techniques can be applied to OFDM, but windowing results in simpler implementation than digital filtering.

69

Spectrum Limitation • As was shown earlier, windowing is used to obtain faster decaying out-of band energy. • Besides windowing (or filtering), some other techniques maybe used as well. • So called filterbank based schemes utilise different orthogonal base from normal Fourier base (usage of sinusoidals and rectangular windows).

70

Spectrum Limitation (2)

Spectra for 5 carriers in a regular OFDM system.

71

Spectrum Limitation (3)

72 Spectra for 5 carriers in a wavelet based OFDM system.

Spectrum Limitation (4) -13 dB

-38 dB

Orthogonality lost, but spectrum more densily packed.

PSDs for 5 carrier OFDM systems.

73

Spectrum Limitation (5)

74

PSDs for standard and paraunitary filterbank based OFDM systems.

Spectrum Limitation (6)

PSDs for regular OFDM and paraunitary filterbank based OFDM subcarriers. NOTE: both retain orthogonality

75

Discussion on Different OFDM Systems • Normal OFDM systems relying on cyclic prefix will encounter ISI in channels with larger delay spreads than used as design parameter. => Some sort of equaliser maybe need in practice or => Cyclic prefix must be made long enough to guarantee that ISI is not a problem

• By using some filter bank based modulation, PSD sidelobe level can be made smaller

synchronisation errors cause smaller loss. • Wavelet based OFDM loses orthogonality, but provides improved spectral efficiency since: – Mainlobe is narrower => more dense packing of spectrum – No need for cyclic prefix due to very low sidelobe level • Nevertheless, standard Fourier based OFDM is applied in practice due to rather simple implementation via IFFT/FFT 76 algorithms.

Advantages and Disadvatages of OFDM

Pros and Cons + • Resistance to frequency selective channels => higher data rates • Allows for simple techniques for reducing ISI and ICI almost completely • Equalization typically simple • Less sensitive to time offsets • Good protection against narrowband interference • Efficient use of spectrum by allowing overlap • Single-frequency networks => attractive to broadcasting

• Sensitive to carrier frequency offsets • Sensitive to phase noise • Large Peak-to-Average Power Ratio (PAPR) -> reduces the power efficiency of RF amplifiers

78

Complete Block Diagramm Binary input data

Coding

Interleaving

Timing and Frequency Synchronization

Remove CP

QAM Mapping

S/P

ADC

Pilot Insertion

S/P

IFFT

RF RX

Channel

FFT

P/S

Channel Correction

QAM Demapping

P/S

RF TX

Deinterleaving

Add CP and windowing

DAC Binary output data

Decoding

79

Summary • OFDM schemes utilize simultaneous transmission of parallel low data rate orthogonal channels. • OFDM modulator/demodulator can be implemented by using simple IDFT/DFT algorithms implemented by IFFT/FFT. • Cyclic prefix (cp) is used to avoid inter-carrier interference in multipath channels; delay spread dictates the length of cp. • Basic OFDM signal design includes determination of the cp and OFDM symbol lenghts, number of subcarriers, subcarrier spacing as well as normal coding and modulation design. • Windowing is used to lower OFDM signal spectrum sidelobe level. • By using more generic filterbank based schemes, the spectral characteristics can be improved (at the cost of 80 implementation complexity).