Module-3 : Transmission Lecture-8 (11/5/00)

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Module-3 Transmission Marc Moonen Lecture-8 Multi-tone Modulation K.U.Leuven/ESAT- SISTA

11/5/00 p. 1 Postacademic Course on

Telecommunications

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 : 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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Postacademic Course on Telecommunications

Module-3 Transmission Marc Moonen Lecture-8 Multi-tone Modulation K.U.Leuven- ESAT/SISTA

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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/VDSL Revisited : Spectrum

• ADSL spectrum :

FDD-ADSL

(=frequency division duplex)

EC-ADSL

(=overlapping up- and

downstream band)

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ADSL/VDSL Revisited : Spectrum

• 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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ADSL/VDSL Revisited : Spectrum

• 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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ADSL/VDSL Revisited: Bit Loading

Bit loading and gain settings

• Transmit power optimization to obtain BER=10^-7 on each tone

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ADSL/VDSL Revisited: Bit Loading

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

- 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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Time-Domain Equalization (TEQ)

• 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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Time-Domain Equalization (TEQ)

• Equalizer design (continued):

- 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

_TEQ,_TIR

E e

 1

 

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Time-Domain Equalization (TEQ)

• Equalizer design (continued):

-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

_TEQ,_TIR

E e

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Time-Domain Equalization (TEQ)

• Resulting structure (TEQ + 1-taps FEQ)

example: ADSL-TEQs with 16…64 taps

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Time-Domain Equalization (TEQ)

• 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….