1. Module-3 : Transmission Lecture-7 (11/5/00)
Marc Moonen
Dept. E.E./ESAT, K.U.Leuven
Module-3 Transmission Marc Moonen
Lecture-7 Multi-tone Modulation K.U.Leuven/ESAT-SISTA

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

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

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

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

6. Driver Application: ADSL (VDSL) Modems
Modem Technology :
…1970 : development of efficient modulation techniques for transmission over band limited channels, spurred by military applications (-> … 9.6 kbits/sec)
: Semiconductor technology (size & power reduction)
: Introduction of coding techniques
(-> … 19.2 kbits/sec)
: 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), ...
Module-3 Transmission Marc Moonen
Lecture-7 Multi-tone Modulation K.U.Leuven-ESAT/SISTA

7. Driver Application: ADSL (VDSL) Modems
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
Module-3 Transmission Marc Moonen
Lecture-7 Multi-tone Modulation K.U.Leuven-ESAT/SISTA

8. Driver Application: ADSL (VDSL) Modems
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
Module-3 Transmission Marc Moonen
Lecture-7 Multi-tone Modulation K.U.Leuven-ESAT/SISTA

9. Driver Application: ADSL (VDSL) Modems
PS: echo cancellation for full-duplex
(see Lecture-6/8)
Module-3 Transmission Marc Moonen
Lecture-7 Multi-tone Modulation K.U.Leuven-ESAT/SISTA

10. Driver Application: ADSL (VDSL) Modems
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 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
100Hz
3600Hz
Module-3 Transmission Marc Moonen
Lecture-7 Multi-tone Modulation K.U.Leuven-ESAT/SISTA

11. Driver Application: ADSL (VDSL) Modems
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
Module-3 Transmission Marc Moonen
Lecture-7 Multi-tone Modulation K.U.Leuven-ESAT/SISTA

12. Driver Application: ADSL (VDSL) Modems
ADSL : `Asymmetric Digital Subscriber Line’
…-1993: ADSL spurred by interest in video-on-demand (VOD)
: ADSL/VOD interest decline
: ADSL technology trials prove viability.
: ADSL deployment, reoriented to data applications,
as telco’s reaction to cable operators offering high-
speed internet access with cable modems.
Module-3 Transmission Marc Moonen
Lecture-7 Multi-tone Modulation K.U.Leuven-ESAT/SISTA

13. Driver Application: ADSL (VDSL) Modems
ADSL : `Asymmetric Digital Subscriber Line’
VDSL : `Very High Speed Digital Subscriber Line’
Backbone
Network
Access
Node
max 3.5…5 km
copper wire
cabinet (ONU)
Access
Node
Backbone
Network
optical fiber
copper wire
max 0.3…1.5 km
Module-3 Transmission Marc Moonen
Lecture-7 Multi-tone Modulation K.U.Leuven-ESAT/SISTA

14. Driver Application: ADSL (VDSL) Modems
Distance/bitrate trade-off (upstream)
bitrate
(Mbits/sec) 40
VDSL 30 20 10
ADSL 1 2 3 4
distance (km)
Module-3 Transmission Marc Moonen
Lecture-7 Multi-tone Modulation K.U.Leuven-ESAT/SISTA

15. Driver Application: ADSL (VDSL) Modems
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
FEXT
NEXT
Module-3 Transmission Marc Moonen
Lecture-7 Multi-tone Modulation K.U.Leuven-ESAT/SISTA

16. Driver Application: ADSL (VDSL) Modems
Communication Impairments :
Module-3 Transmission Marc Moonen
Lecture-7 Multi-tone Modulation K.U.Leuven-ESAT/SISTA

17. Driver Application: ADSL (VDSL) Modems
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. !
Module-3 Transmission Marc Moonen
Lecture-7 Multi-tone Modulation K.U.Leuven-ESAT/SISTA

18. Driver Application: ADSL (VDSL) Modems
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..
Module-3 Transmission Marc Moonen
Lecture-7 Multi-tone Modulation K.U.Leuven-ESAT/SISTA

19. Driver Application: ADSL (VDSL) Modems
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)
Module-3 Transmission Marc Moonen
Lecture-7 Multi-tone Modulation K.U.Leuven-ESAT/SISTA

20. Driver Application: ADSL (VDSL) Modems
ADSL (Preview)
IFFT
P/S
S/P
Discrete
equivalent
channel
FFT
FEQ
DAC
p(t)
ch(t)
r(t)
ADC
Tx filter
Channel
Rx filter
Tx clock
Rx clock
Module-3 Transmission Marc Moonen
Lecture-7 Multi-tone Modulation K.U.Leuven-ESAT/SISTA

21. DMT Principles: Preliminaries
DMT `inspiration’ : see Lecture 2
Module-3 Transmission Marc Moonen
Lecture-7 Multi-tone Modulation K.U.Leuven-ESAT/SISTA

22. DMT Principles : Preliminaries
DMT `inspiration’ : see Lecture 2
Module-3 Transmission Marc Moonen
Lecture-7 Multi-tone Modulation K.U.Leuven-ESAT/SISTA

23. DMT Principles : Preliminaries
DMT `inspiration’ : see Lecture 3
Module-3 Transmission Marc Moonen
Lecture-7 Multi-tone Modulation K.U.Leuven-ESAT/SISTA

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’)
Module-3 Transmission Marc Moonen
Lecture-7 Multi-tone Modulation K.U.Leuven-ESAT/SISTA

25. DMT Principles: IFFT/FFT-based modulation
Modulation is realized by means of 2N-point
Inverse Discrete Fourier Transform (I-DFT) : example N=4
`*’ = complex conjugate
real
real
Module-3 Transmission Marc Moonen
Lecture-7 Multi-tone Modulation K.U.Leuven-ESAT/SISTA

26. DMT Principles: IFFT/FFT-based modulation
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)
Module-3 Transmission Marc Moonen
Lecture-7 Multi-tone Modulation K.U.Leuven-ESAT/SISTA

27. DMT Principles: IFFT/FFT-based modulation
DMT-transmission block scheme (revisited):
S/P
FFT
FEQ
IFFT
P/S
Discrete
equivalent
channel
DAC
p(t)
ch(t)
r(t)
ADC
Tx filter
Channel
Rx filter
Tx clock
Rx clock
Module-3 Transmission Marc Moonen
Lecture-7 Multi-tone Modulation K.U.Leuven-ESAT/SISTA

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

29. DMT Principles: The Magic Prefix Trick
Prefix insertion :
Module-3 Transmission Marc Moonen
Lecture-7 Multi-tone Modulation K.U.Leuven-ESAT/SISTA

30. DMT Principles: The Magic Prefix Trick
Prefix insertion :
in the receiver, the samples corresponding to the prefix are removed (=unused) :
S/P
FFT
FEQ
IFFT
P/S
Discrete
equivalent
channel
Module-3 Transmission Marc Moonen
Lecture-7 Multi-tone Modulation K.U.Leuven-ESAT/SISTA

31. DMT Principles: The Magic Prefix Trick
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 :
Tx-side
Rx-side
Tone 3
Tone 2
Tone 1
Tone 0
Tone 3
Tone 2
Tone 1
Tone 0
ch(t) *
s(t)
r(t)
Prefix
From IFFT
Guardband
To FFT
Module-3 Transmission Marc Moonen
Lecture-7 Multi-tone Modulation K.U.Leuven-ESAT/SISTA

32. DMT Principles: The Magic Prefix Trick
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)
Module-3 Transmission Marc Moonen
Lecture-7 Multi-tone Modulation K.U.Leuven-ESAT/SISTA

33. DMT Principles: The Magic Prefix Trick
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)
Module-3 Transmission Marc Moonen
Lecture-7 Multi-tone Modulation K.U.Leuven-ESAT/SISTA

34. DMT Principles: The Magic Prefix Trick
The mathematics behind this are as follows :
assume N=4, prefix-length=2 (cfr. supra) assume channel impulse response is
received samples are…
transmitted signal at time k
received signal at time k
Module-3 Transmission Marc Moonen
Lecture-7 Multi-tone Modulation K.U.Leuven-ESAT/SISTA

35. DMT Principles: The Magic Prefix Trick
Received samples for symbol m, after removing prefix :
Module-3 Transmission Marc Moonen
Lecture-7 Multi-tone Modulation K.U.Leuven-ESAT/SISTA

36. DMT Principles: The Magic Prefix Trick
...This is equivalent with :
Module-3 Transmission Marc Moonen
Lecture-7 Multi-tone Modulation K.U.Leuven-ESAT/SISTA

37. DMT Principles: The Magic Prefix Trick
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) !
Module-3 Transmission Marc Moonen
Lecture-7 Multi-tone Modulation K.U.Leuven-ESAT/SISTA

38. DMT Principles: The Magic Prefix Trick
…By substituting this :
Module-3 Transmission Marc Moonen
Lecture-7 Multi-tone Modulation K.U.Leuven-ESAT/SISTA

39. DMT Principles: The Magic Prefix Trick
…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.
Module-3 Transmission Marc Moonen
Lecture-7 Multi-tone Modulation K.U.Leuven-ESAT/SISTA

40. DMT Principles: The Magic Prefix Trick
PS : compare with transmitter & receiver transformation for MIMO-transmission (singular value decomposition of channel response matrix, etc., see Lecture-2)
IFFT
P/S
S/P
Discrete
equivalent
channel
FFT
FEQ
Module-3 Transmission Marc Moonen
Lecture-7 Multi-tone Modulation K.U.Leuven-ESAT/SISTA