11/5/00 p. 1 postacademic course on telecommunications module-3 transmission marc moonen lecture-7...

Module-3 Transmission Marc MoonenLecture-7 Multi-tone Modulation K.U.Leuven/ESAT-SISTA

11/5/00p. 1

Postacademic Course on Telecommunications

Module-3 : Transmission

Lecture-7 (11/5/00)

Marc Moonen

Dept. E.E./ESAT, K.U.Leuven

[email protected]

www.esat.kuleuven.ac.be/sista/~moonen/


Module-3 Transmission Marc MoonenLecture-7 Multi-tone Modulation K.U.Leuven-ESAT/SISTA

11/5/00p. 2

Lecture 7-8 : Multi-tone Modulation

Lecture 7 : Overview• Driver application : ADSL (VDSL) modems

Modem technology : voice-band vs. xDSL

Communication impairments• DMT principles

Preliminaries

IFFT/FFT-based modulation/demodulation

The magic `prefix’ trick



11/5/00p. 3

Lecture 7-8 : Multi-tone Modulation

Lecture 8 : Overview• ADSL/VDSL revisited

Specs, spectrum, FDM vs. EC, P-to-A,…• Equalization Time-domain equalization

Frequency-domain equalization

• Windowing Receiver windowing, Transmitter windowing

• Echo Cancellation Time-domain echo cancellation

Time+frequency-domain echo cancellation

`Joint shortening’



11/5/00p. 4

Acknowledgement

Lecture partly adopted from

Module T2

`Digital Communication Principles’

M.Engels, M. Moeneclaey, G. Van Der Plas

1998 Postgraduate Course on Telecommunication

Special thanks to G. Van der Plas (Alcatel)

Lecture partly co-authored by

Thierry Pollet, Alcatel Telecom, CRC, Antwerp (B)



11/5/00p. 5

Driver Application: ADSL (VDSL) Modems

References:• J.A.C. Bingham, `The theory and practice of

modem design’, Wiley, 1980• J.A.C. Bingham, `Multicarrier modulation for

data transmission, an idea whose time has come’, IEEE Communications Magazine, May 1990, pp.5-14

• W.Y. Chen, `DSL simulation techniques and standards development for digital subscriber line systems’, Macmillan, 1998

• ...



11/5/00p. 6


Modem Technology :

• …1970 : development of efficient modulation techniques for transmission over band limited channels, spurred by military applications (-> … 9.6 kbits/sec)

• 1970-1980 : Semiconductor technology (size & power reduction)• 1980-1990 : Introduction of coding techniques

(-> … 19.2 kbits/sec)• 1990-2000 : reaching Shannon limit (-> 33kbits/sec, asymmetric

56kbits/sec modems)

• 1995-… : ADSL (8Mbits/sec downstream, 60 kbits/sec upstream) • 2000-… : VDSL (52Mbits/sec downstream, 6Mbits/sec upstream), ...



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Performance improvement results from:• improved telephone channel quality (digital switches, etc.) • improved modulation/coding techniques (QAM, trellis

coded modulation (TCM), echo cancellation (EC), adaptive equalization,…)

• semiconductor technology

19721976198419891996

4.8kbits/sec (V.27) 9.6kbits/sec (V.29) 9.6kbits/sec (V.32)19.2kbits/sec (V.33b)33.6kbits/sec (V.34)

8-PSK 16-QAM 32-QAM/TCM 64-QAM/TCM128-QAM/TCM

simplexsimplexEC-duplexEC-duplexEC-duplex



11/5/00p. 8


PS: duplexing techniques• Frequency division duplexing (FDD)

`downstream’ = central office -> remote user

`upstream’ = remote user -> central office

• Time division duplexing (TDD) :

`ping-pong’

• Full duplex with echo-cancellation (EC)

(see also Lecture-6/8)

up down

frequency

up down

time

up & down

time & frequency



11/5/00p. 9


PS: echo cancellation for full-duplex

(see Lecture-6/8)



11/5/00p. 10


Voice-band modems : Shannon capacity limit (Lecture-2)

• In analog public switched telephone network

SNR > 28dB (signal-to-noise ratio)

BW > 2400 Hz (bandwidth)

...Hence capacity approx. 22.4 kbits/sec

• In digital public switched telephone network

SNR > 34 dB (signal-to-noise ratio)

BW > 3200 Hz (bandwidth)

...Hence capacity approx. 35 kbits/sec

)(.3

)1(log.its/sec)Capacity(b 2 dBSNRBW

SNRBW

100Hz 3600Hz



11/5/00p. 11


Digital Subscriber Line (DSL) Technologies:• HDSL : `High Speed Digital Subscriber Line’

…2Mbits/sec on 2 or 3 pairs• ADSL : `Asymmetric Digital Subscriber Line’

…8Mbits/sec down, 60kbits/sec up on 1 pair

uses frequency band up to approx. 1 MHz• SDSL : `High Speed Digital Subscriber Line’

…2Mbits/sec symmetrical on 1 pair• VDSL : `Very High Speed Digital Subscriber Line’

…52Mbits/sec down, 6Mbits/sec up on 1 pair

uses frequency band up to approx. 10 MHz



11/5/00p. 12


• ADSL : `Asymmetric Digital Subscriber Line’

…-1993: ADSL spurred by interest in video-on-demand (VOD)

1995 : ADSL/VOD interest decline

1996 : ADSL technology trials prove viability.

1997-... : ADSL deployment, reoriented to data applications,

as telco’s reaction to cable operators offering high-

speed internet access with cable modems.



11/5/00p. 13


• ADSL : `Asymmetric Digital Subscriber Line’

• VDSL : `Very High Speed Digital Subscriber Line’

BackboneNetwork

AccessNode max 3.5…5 km

BackboneNetwork

AccessNode

max 0.3…1.5 km

cabinet (ONU)

optical fiber

copper wire

copper wire



11/5/00p. 14


• Distance/bitrate trade-off (upstream)

distance (km)1 2 3 4

10

20

30

40

bitrate(Mbits/

sec)

ADSL

VDSL



11/5/00p. 15


Communication Impairments :• Frequency-dependent cannel attenuation

introduces inter-symbol interference (ISI)• Coupling between wires in same or adjacent

binders introduces crosstalk Near-end Xtalk (NEXT)

Far-end Xtalk (FEXT)

useful signal

FEXTNEXT



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Communication Impairments :



11/5/00p. 17


Communication Impairments (continued) :• Xtalk from other systems e.g. HPNA (Home Phone Network Alliance) vs. VDSL• Radio Frequency Interference (RFI) e.g. AM broadcast, amateur radio• Noise e.g. impulsive noise (=high bursts of short duration)• Echo due to hybrid impedance mismatch

Conclusion: Need advanced modulation, DSP,etc. !



11/5/00p. 18


Line Codes (modulation technique) :• ADSL (ANSI standard)

DMT (`Discrete Multi-tone Modulation’, a.k.a. multi-carrier modulation, orthogonal frequency division multiplexing (OFDM))

256 different `carriers’, each of them QAM-modulated, see below.

• VDSL

DMT or single carrier (CAP/QAM) systems ? =undecided..



11/5/00p. 19


Line Codes (modulation technique) :• DMT (Preview) : Multiple carriers are QAM-modulated with

a low-rate bit stream. The high-rate bit stream is thus carried by dividing it into hundreds of low-rate streams. Modulation/demodulation by FFT/IFFT (see below)



11/5/00p. 20


• ADSL (Preview)

DAC

S/P

FFT

FEQ

IFFT P/S

Tx clock

Discreteequivalent

channel

Rx clock

p(t)

Tx filter Channel Rx filter

ch(t) r(t) ADC



11/5/00p. 21

DMT Principles: Preliminaries

• DMT `inspiration’ : see Lecture 2

Postacademic Course on Telecommunicat ions

Module-3 Transmission Marc MoonenLecture-2 Limits of Communication K.U.Leuven-ESAT/SISTA

20/4/00p. 20

Channel Capacity (frequency-selective channels)

n(t)

+

channel

s(t) R(f)=H(f).S(f)+N(f)

H(f)

• Example: frequency-selective AWGN-channel

received SNR is frequency-dependent!

f

H(f)

B-B



11/5/00p. 22

DMT Principles : Preliminaries



Module-3 Transmission Marc MoonenLecture-2 Limits of Communication K.U.Leuven-ESAT/SISTA

20/4/00p. 21

Channel Capacity (frequency-selective channels)

• Divide bandwidth into small bins of width df,such that H(f) is approx. constant over df

• Capacity is

optimal transmit power spectrum?

f

H(f)

B-B

second

bits).

)(

)()(1(log

2

22

2 dff

ffH

n

x

0

B



11/5/00p. 23

DMT Principles : Preliminaries



Module-3 Transmission Marc MoonenLecture-3 Transmitter Design K.U.Leuven-ESAT/SISTA

27/4/00p. 9

Preliminaries : Passband vs. baseband transmission (IV)

Bandpass transmission:

• note that modulatedsignal has 2x largerbandwidth, henceinefficient scheme !

• solution = accommodate2 baseband signals in 1bandpass signal :

I =`in-phase signal’Q=`quadrature signal’

such that energy in BP isenergy in LP

2



11/5/00p. 24

DMT Principles: IFFT/FFT-based modulation

`Multi-tone’/`multi-carrier’ = modulate different carriers at the same time:

• (=complex envelope) modulates fo

- subscript `m’ refers to m-th symbol (frame)

- this is one `tone’ • similarly, modulate 2.fo, 3.fo, …, N.fo

- N `tones’

- highest frequency N.fo = Fs/2, with Fs sampling

frequency (for baseband DMT)• each tone carries a number of bits (0,1,2,…) depending upon its SNR

(`bit loading’)

Nmmm aaa ,...,, 32

QIm sjsa .1



11/5/00p. 25


Modulation is realized by means of 2N-point

Inverse Discrete Fourier Transform (I-DFT) : example N=4

`*’ = complex conjugate

domainfrequency in symbolth -m

*1

*2

*3

4

3

2

1

0

matrixDFT inverse

49423528211470

42363024181260

35302520151050

2824201612840

211815129630

14121086420

76543210

00000000

domainin time symbolth m

7

6

5

4

3

2

1

0

.

m

m

m

m

m

m

m

m

m

m

m

m

m

m

m

m

a

a

a

a

a

a

a

a

WWWWWWWW

WWWWWWWW

WWWWWWWW

WWWWWWWW

WWWWWWWW

WWWWWWWW

WWWWWWWW

WWWWWWWW

s

s

s

s

s

s

s

s

NjeW

.

realreal



11/5/00p. 26


• I-DFT is implemented by means of 2N-point (inverse)

Fast Fourier Transform (I-FFT)

- complexity is O(N.logN) instead of O(N^2)

- fast hardware available

• Time-domain symbols are transmitter over channel

• Receiver : demodulation with inverse operation, i.e. FFT (i.o. I-FFT)



11/5/00p. 27


• DMT-transmission block scheme (revisited):

DAC

Tx clock

S/P

FFT

FEQ

IFFT P/S

0

Discreteequivalent

channel

Rx clock

p(t)

Tx filter Channel Rx filter

ch(t) r(t) ADC



11/5/00p. 28

DMT Principles: The Magic Prefix Trick

Additional feature : before transmission, a `prefix’

is added to each time-domain

symbol, i.e. the last

samples are copied and

put up front :

domain-in time symbolth -m

7

6

5

4

3

2

1

0

in -addprefix

88

22

sequence dtransmitte

7

6

5

4

3

2

1

0

8

7

.0

m

m

m

m

m

m

m

m

x

x

m

m

m

m

m

m

m

m

m

m

s

s

s

s

s

s

s

s

I

I

s

s

s

s

s

s

s

s

s

s

)2 (example



11/5/00p. 29


Prefix insertion :



11/5/00p. 30


Prefix insertion : • in the receiver, the samples corresponding to the

prefix are removed (=unused) :

S/P

FFT

FEQ

IFFT P/S

0

Discreteequivalent

channel



11/5/00p. 31


• if channel impulse response has length L (= L non-zero taps) and ( is prefix length), then all `transient effects’ between symbols are confined to the prefix period :

1L

Tx-side Rx-side

Tone 3

Tone 2

Tone 1

Tone 0

Tone 3

Tone 2

Tone 1

Tone 0

Prefix From IFFT Guardband To FFT

*

ch(t)

r(t)s(t)



11/5/00p. 32


• Magic trick fails if

-> transient effects within sample sequence that is

fed into FFT

-> this results in

inter-symbol-interference (ISI) = interference

from previous symbol(s) (same carrier)

inter-carrier interference (ICI) = interference

from other carriers

(`carrier orthogonality destroyed’)

(see also Lecture 8)

1L



11/5/00p. 33


• In the receiver, after removing the samples corresponding to the prefix, the i-th tone is observed, multiplied by a factor H(i.fo), i.e. the channel response for frequency f=i.fo (=`simplified statement’)

• `Prefix trick’ based on a linear convolution (filtering by channel impulse response) being turned into a circular convolution, which corresponds to component-wise multiplication in frequency domain (=statement to be ignored)



11/5/00p. 34


The mathematics behind this are as follows :

• assume N=4, prefix-length=2 (cfr. supra) assume channel impulse response is

• received samples are…

22

110210 .. ,...0,0,,, zhzhhH(z)hhh

22110 ... kkkk shshshr

transmitted signal at time kreceived signal at time k



11/5/00p. 35


Received samples for symbol m, after removing prefix :

m symbolfor sequence dtransmitte

7

6

5

4

3

2

1

0

8

7

matrix channel

012

012

012

012

012

012

012

012

m symbolfor samples received

7

6

5

4

3

2

1

0

0000000

0000000

0000000

0000000

0000000

0000000

0000000

0000000

m

m

m

m

m

m

m

m

m

m

m

m

m

m

m

m

m

m

s

s

s

s

s

s

s

s

s

s

hhh

hhh

hhh

hhh

hhh

hhh

hhh

hhh

r

r

r

r

r

r

r

r



11/5/00p. 36


...This is equivalent with :

7

6

5

4

3

2

1

0

matrix channel modified

012

012

012

012

012

012

201

120

m symbolfor samples received

7

6

5

4

3

2

1

0

.

00000

00000

00000

00000

00000

00000

00000

00000

m

m

m

m

m

m

m

m

m

m

m

m

m

m

m

m

s

s

s

s

s

s

s

s

hhh

hhh

hhh

hhh

hhh

hhh

hhh

hhh

r

r

r

r

r

r

r

r



11/5/00p. 37


• The modified channel matrix is a so-called `circulant’ matrix (constant along the diagonals & `wrapped around’)

• Theorem : every circulant matrix C is diagonalized by a DFT & I-DFT matrix :

PS: Proof by MatLab (try it, it always works!)

PPS: This is an eigenvalue (singular value) decomposition

(remember from high school maths?)

• Diagonal matrix has DFT of first column of C on its main diagonal, i.e. Hi=H(i.fo) !

)).(matrix diagonal).(( DFTIDFTC



11/5/00p. 38


…By substituting this :

*1

*2

*3

4

3

2

1

0

nfreq.domaiin matrix channel

7

6

5

4

3

2

1

0

nfreq.domaiin symbol received

7

6

5

4

3

2

1

0

.

0000000

0000000

0000000

0000000

0000000

0000000

0000000

0000000

.

m

m

m

m

m

m

m

m

m

m

m

m

m

m

m

m

a

a

a

a

a

a

a

a

H

H

H

H

H

H

H

H

r

r

r

r

r

r

r

r

DFT



11/5/00p. 39


• …which means that after removing the prefix-samples and performing a DFT in the receiver, the obtained samples are equal to the transmitted (`frequency-domain’) symbols, up to a channel attenuation Hi (for tone-i).

• Hence `channel equalization’ may be performed `in the frequency domain’, by component-wise divisions (divide by Hi for tone-i).

=`1-taps FEQ’ (frequency-domain equalization) • Conclusion: if , DMT-modulation leads to

a simple (trivial) channel equalization problem.

…otherwise, see Lecture-8.

1L



11/5/00p. 40


• PS : compare with transmitter & receiver transformation for MIMO-transmission (singular value decomposition of channel response matrix, etc., see Lecture-2)

S/P

FFT

FEQ

IFFT P/S

0

Discreteequivalent

channel

11/5/00 p. 1 postacademic course on telecommunications module-3 transmission marc moonen lecture-7...

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