lecture8.ppt

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Postacademic Course on
Telecommunications
Module-3 Transmission Marc Moonen
Lecture-8 Multi-tone Modulation K.U.Leuven/ESAT-SISTA
Module-3 : Transmission
Lecture-8 (11/5/00)
Marc Moonen
Dept. E.E./ESAT, K.U.Leuven
marc.moonen@esat.kuleuven.ac.be
www.esat.kuleuven.ac.be/sista/~moonen/

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Lecture-8 Multi-tone Modulation K.U.Leuven-ESAT/SISTA
Lecture 8 : Overview
• ADSL/VDSL revisited
Specs, spectra, FDM vs. echo, bit loading, 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’

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Acknowledgement
-Lecture partly adopted from
Module T2
`Digital Communication Principles’
M.Engels, M. Moeneclaey, G. Van der Plas
1998 Postgraduate Course on Telecommunications
Special thanks to G. Van der Plas (Alcatel)
-Lecture partly co-authored by
Thierry Pollet, Alcatel Telecom, CRC, Antwerp (B)

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ADSL/VDSL Revisited
• ADSL-DMT Transmission block scheme (see Lecture-7)

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ADSL/VDSL Revisited : Specs
ADSL specs (=ANSI standard)
• 256 carriers
• 512-point (I)FFT’s (or `similar’)
• prefix length = 32
• carrier spacing fo= 4.3215 kHz
• basic sampling rate is 2.21 MHz (=512*4.3215k)
VDSL specs (=proposal)
• up to 4096 carriers
• same carrier spacing
• etc.

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ADSL/VDSL Revisited : Spectrum
• ADSL spectrum :

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• ADSL spectrum :
FDD-ADSL
(=frequency division
duplex)
EC-ADSL
(=overlapping up- and
downstream band)

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• VDSL spectrum :
Power
spectrum
unused tones
due to line conditions
tone spacing
(4.3 kHz)
POTS/
ISDN
17.6 MHz
1.1 MHz
Frequency
Up
Down

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• VDSL spectrum :
flexible setting up- & downstream rates
Upstream
Downstream
Frequency
Medium line
Long line
Short line

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ADSL/VDSL Revisited : Channel
• ADSL channel attenuation, crosstalk, noise

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ADSL/VDSL Revisited : Channel
• VDSL channel attenuation, crosstalk, noise, RFI:
Next dominated environment + several RF interferers

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ADSL/VDSL Revisited: Bit Loading
Bit loading and gain settings :
• QAM constellation size for each tone depends on SNR
measured at the receiver
Guarantees optimal capacity in all operation conditions (loops, noise).

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Bit loading and gain settings
• Transmit power optimization to obtain BER=10^-7 on each
tone

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Bit loading and gain settings
• Transmit power optimization to obtain BER=10^-7 on each
tone (continued)
1 0
1 3
1 6
1 9
2 2
2 5
2 8
- 3
- 2
- 1
0
1
2
3
4
SNR
gain
5 bits
4 bits
3 bits
2 bits
1 bits

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ADSL/VDSL Revisited: P-to-A
Peak-to-average problem
• DMT signals have large dynamic range :

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ADSL/VDSL Revisited: P-to-A
Peak-to-average problem (continued)
• large dynamic range implies large quantization
steps in A/D & D/A, etc.
Remedies
• tone structure : redundant tones, modulated with
linear combination of other tones, such that time-
domain signals have lower dynamic range
• receiver re-design : receiver compensates for
clipping non-linearity (part of `channel model’)
• ...

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Equalization
Problem Statement :
• ISI/ICI-free transmission if
L is channel impulse response length
is prefix length
• In ADSL : prefix-length is 32 samples
channel length is….500 samples (approx.) !!!
Solution :
• Insert time-domain equalizer for channel shortening
1


L


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Equalization
Time-domain equalization :
ps: in Lecture 5, (zero-forcing) equalization means `shortening
to 1 non-zero tap’ (cfr. H(z).C(z)=1)
ps: complexity !
Example: 32 taps @ 2.2 MHZ -> 70 Mflops...

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Equalization
Time-domain equalization :

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Equalization
Time-domain equalization
• additional design parameter :
synchronization delay
(=`positioning’ of shortened channel impulse response)


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Time-Domain Equalization (TEQ)
• Equalizer design :
- Possible optimization criterion is overall capacity, i.e. sum
of transmitted bits (with BER 10^-7) on all carriers together.
- Number of bits loaded onto 1 carrier is a function of the
received SNR for that carrier.
- SNR for 1 carrier is function of SNR at TEQ-output.
- Leads to highly non-linear optimization criterion.
Iterative non-linear optimization procedures usually lead to
(sub-optimal) local minima.
- Need simpler optimization criterion.

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• Equalizer design (continued):
- Alternative optimization criterion is time-domain
minimum mean squared error criterion based on….
channel impulse response
target impulse response
time-domain equalizer
synchronization delay (p20)

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- minimum mean squared error criterion is...
i.e., for a given TEQ-length (e.g. 16 taps),
find TEQ-coefficients such that cascade
(`convolution’) of CIR and TEQ is as close as
possible to a (delayed) TIR with non-zero
coefficients ( = prefix length)
 
2
,
min e
E
TIR
TEQ
1




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-This leads to a least squares problem a la the
least squares problems for equalizer design in Lecture-6.
- Have to include a constraint to avoid trivial (TEQ=TIR=0)
solution, e.g. impose `normalized’ TIR or `normalized’ TEQ
- Constrained least squares problem equivalent to
eigenvalue problem (solved iteratively)
 
2
,
min e
E
TIR
TEQ

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• Resulting structure (TEQ + 1-taps FEQ)
example: ADSL-TEQs with 16…64 taps

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• Problem with TEQ-receiver :
- MMSE criterion does correspond to optimizing overall
bit-rate. Leads to unpredictable behavior (sometimes lower
bit-rate with longer TEQ…)
- Obtained bit-rate heavily (and unpredictably)
depends on chosen synchronization delay
- In practice : modem start-up procedure does not allow for
searching for optimal delay within a range.
Hence can pick only one delay, and then have to be lucky..

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Frequency-Domain Equalization (FEQ)
• Alternative structure based on `per-tone
equalization’ :
- each tone had its own TEQ, but implemented
after the FFT (and combined with 1-taps FEQ)
- overall `FEQ’ (=TEQ + 1-taps FEQ) can be designed to
optimize SNR for each tone separately.
Hence true overall bit-rate optimization.
- Smooth behavior (as a function of synchronization delay)
- Computational complexity = comparable
- Implementation based on sliding FFT properties

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Frequency-Domain Equalization (FEQ)
• `Per-tone’ equalization structure :
`difference terms’
cfr. sliding FFT
properties

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Windowing (VDSL)
Problem Statement :
Transmit spectrum for 1 tone has high side-lobes, that
generate interference (e.g.NEXT) in other systems.
Receiver DFT may be viewed as filter bank, each filter has
high side-lobes, hence picks up interference in a broad
frequency range
Solution : Reduce transmit/receive side-lobes by
(time-domain) windowing

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Windowing (VDSL)
Windowing basic principle = extend symbol length +
apply `symmetric’ weighting around original symbol edges

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Windowing (VDSL)
Windowing at the transmitter:
Reduces frequency domain side-lobes
Reduces the out of band power of the NEXT signal
Allows for digital duplexing
Guarantees spectral compatibility with ADSL , HPNA,…
Symbol body
CP CS
DMT symbol CP: cyclic prefix
CS: cyclic suffix

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DMT symbol
Symbol body
Windowing (VDSL)
Windowing at the receiver :
Reduces Inter Symbol Interference (ISI)
Reduces susceptibility to RFI
ps: This is equivalent to per-tone equalization (=per-tone
optimized window).

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Windowing (VDSL)
DMT-based VDSL-transceiver :
additional features : analog & digital RFI-cancellation,
egress spectrum control, ...

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Echo Cancellation
• Problem Statement :
ADSL with overlapping up- and downstream bands requires
echo cancellation (adaptive filter)
Main problem = complexity
example : echo path with 500 taps @ 2.2 MHz -> ...Gflops

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Echo Cancellation
• Time-domain echo cancellation :
Adaptive filter (see Lecture 6) has complexity > 2M
(M is number of filter taps).
Leads to too high computational complexity
• Time + Frequency domain echo cancellation :
Part of the cancellation is brought to the frequency-
domain (after the FFT).
Leads to complexity reduction with a factor ..4…8.
• Conclusion : Overlapping up- & downstream bands
difficult to implement (@reasonable cost)
• PS : EC in FDD-system with reduced front-end filter specs

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Echo Cancellation
• PS: alternative solutions
- `Joint Shortening’ :
Design TEQ such that echo channel impulse response
length is shortened, together with transmission channel
impulse response length.
Allows for shorter (cheaper) echo cancellation filter.
- `Per-tone’ echo cancellation : optimize TEQ + echo filter
for each tone separately (=true SNR optimization!).
Allows for shorter (cheaper) echo cancellation filter

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Conclusion
• Investigated additional features in ADSL/VDSL
systems
- Equalization
- Windowing
- Echo Cancellation
- …
• Confirms importance of digital signal
processing techniques in present-day high-
performance communication systems
(`box full of maths/DSP’,cfr. Lecture-1)

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Assignment 4.1
• Recommended (optional) reading:
J.A.C. Bingham, `Multicarrier modulation for data
transmission, an idea whose time has come’, IEEE
Communications Magazine, May 1990, pp.5-14

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Assignment 4.2
Echo Cancellation in an FDD/ADSL-system ?
• Assume an FDD/ADSL transceiver sending an upstream signal (lower
tones) and receiving a downstream signal (higher tones)
• Assume the downstream path as well as the echo path is shorter than
the prefix length, and the up- & downstream signals being perfectly
(symbol-)synchronized. Investigate the effect of the echo...
• Assume the echo path is longer than the prefix. Investigate the effect of
the echo...
• Assume the echo path is shorter than the prefix, but that the two
signals are not (symbol-)synchronized. Investigate the effect of the
echo…

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Assignment 4.2
Echo Cancellation in an FDD/ADSL-system ?
(continued)
• Is it possible to have (symbol-)synchronization at the two ends of the
line (i.e. in the remote terminal as well as in central office) ?
• Conclusion: which extra features to be introduced in FDD modems.
Echo cancellation or… ?
• To be solved by using your brains and/or pen&paper (i.e. write down a
few formulas) and/or your favorite simulation tool….

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