on the relation between time-domain equalizers and per-tone equalizers for dmt-based systems koen...
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On the Relation Between Time-On the Relation Between Time-Domain Equalizers and Per-Tone Domain Equalizers and Per-Tone
Equalizers for DMT-Based SystemsEqualizers for DMT-Based Systems
Koen Vanbleu, Geert Ysebaert, Gert Cuypers, Marc Moonen
Katholieke Universiteit Katholieke Universiteit Leuven, ESATLeuven, ESAT//SCD-SISTA, BelgiumSCD-SISTA, Belgium
April 16, 2004
IEEE Benelux Signal Processing SymposiumHilvarenbeek, the Netherlands
Koen Vanbleu, Geert Ysebaert, Gert Cuypers, Marc Moonen
Katholieke Universiteit Katholieke Universiteit Leuven, ESATLeuven, ESAT//SCD-SISTA, BelgiumSCD-SISTA, Belgium
April 16, 2004
IEEE Benelux Signal Processing SymposiumHilvarenbeek, the Netherlands
On On Equalization Alternatives and Equalization Alternatives and their Relations for ADSL Modemstheir Relations for ADSL Modems
3
OverviewOverview
• ADSL Basics
What? Multicarrier modulation
Transmitter/Receiver
• ADSL Equalizer Design
Problem Description
Current Equalizers (TD-MMSE)
Bit rate Maximizing Equalizers (FD-MMSE criterion)
Relations
5
IntroductionIntroduction
Broadband communication over telephone line ADSL (Asymmetric Digital Subscriber Line) ADSL2 / ADSL2+ (Second-Generation ADSL) VDSL (Very high bit rate Digital Subscriber Line) Bit rate is function of the line length
Upstream
Downstream
CustomerCentral
• ADSL Basics - Intro - DMT Transmitter - Why
Equalization? - DMT Receiver
• ADSL Equalizer Design
- Problem Description
- Current Equalizers
- Bit rate Maximizing
Equalizers - Relations
Down Up Line length
Frequency band
ADSL 6 Mbps 640 kbps 3.7 km 1.1 MHz
ADSL2+
15 Mbps 1.5 Mpbs 1.8 km 2.2 MHz
VDSL 52 Mbps 2.3 Mbps < 1 km 12 MHz
6
• Traditional telephony (POTS) still available over the same wire.
Multicarrier ModulationMulticarrier Modulation
• Assign different frequency bins to up- and downstream directions
f (kHz)
POTS UP DOWN
4 25 138 1104
e.g. ADSL
• Digital multicarrier modulation scheme: Discrete Multitone (DMT)
• ADSL Basics - Intro - DMT Transmitter - Why
Equalization? - DMT Receiver
• ADSL Equalizer Design
- Problem Description
- Current Equalizers
- Bit rate Maximizing
Equalizers - Relations
7
Discrete Multitone: TransmitterDiscrete Multitone: Transmitter
...
P/S
CP
lx
Cyclic Prefix
• ADSL Basics - Intro - DMT Transmitter - Why
Equalization? - DMT Receiver
• ADSL Equalizer Design
- Problem Description
- Current Equalizers
- Bit rate Maximizing
Equalizers - Relations
00
11
10
01
Re
Im
2 bits
Re
Im
4 bits
bits Data symbols (QAM)
0
IDFT
N-point
.
.
.
.
.
.
...
IDFT modulation (Inverse Discrete Fourier Transform)
N12/ N
nkx ,ˆ
Blocktransmission!
8
Why Equalization?Why Equalization?
channel
ly
lnnoise
...
P/S
CP
lxIDFT
N-point
.
.
.
.
.
.
...
N
12/ N
Transmitter
Why equalization?“Invert” channel
distortion while not boosting noise
• ADSL Basics - Intro - DMT Transmitter - Why
Equalization? - DMT Receiver
• ADSL Equalizer Design
- Problem Description
- Current Equalizers
- Bit rate Maximizing
Equalizers - Relations
nkx ,ˆ
9l
h
Discrete Multitone: ReceiverDiscrete Multitone: Receiver
00
11
10
01Re
Im
2 bits
Re
Im
4 bits
bits
Data symbols
channel h
lnnoise
lylx
• ADSL Basics - Intro - DMT Transmitter - Why
Equalization? - DMT Receiver
• ADSL Equalizer Design
- Problem Description
- Current Equalizers
- Bit rate Maximizing
Equalizers - Relations
wh
lCP length + 1
...S/P
CP
.
.
.DFT
N-point
DFT demodulation
.
.
.
Frequency Domain
Equalizer
1 tap / tonex
x
x
nd~
TEQ w
tapsT
Time Domain
Equalizer
10
DMT Equalization: DMT Equalization: Problem DescriptionProblem Description
S/P
CP
... DFT
FEQ
TEQ w
ly
T taps
...
...
1 tap/tone
N-point
To maximize bit rate:
n
nbtones
toneonbits
00
11
10
01
Re
Im
2 bits
• ADSL Basics - Intro - DMT Transmitter - Why
Equalization? - DMT Receiver
• ADSL Equalizer Design
- Problem Description
- Current Equalizers
- Bit rate Maximizing
Equalizers - Relations
nknk ex ,,~~
FEQ
n n
nSNR
tones2
)(1log
w
is hard with time-domain equalizer w
nd~
where
2,
2
,
)(~
~
)(w
w
nk
nkn
eE
xESNR Residual ISI/ICI
Noise (RFI/XT/etc.)
11
Current ADSL EqualizersCurrent ADSL Equalizers• ADSL Basics - Intro - DMT Transmitter - Why
Equalization? - DMT Receiver
• ADSL Equalizer Design
- Problem Description
- Current Equalizers
- Bit rate Maximizing
Equalizers - Relations
Channel shortenerse.g. time-domain MMSE-TEQ design
l
h
Channel h
lnnoise
lxly
No bit rate optimization!
wh
CP length + 1
l
TEQ w
Constrained linear least-squares based MMSE-TEQ
wbxwybw,
on constraint s.t.min1
0
2
L
l
Tl
Tl
TIR = target impulse response of (CP-length+1)
delay TIR b
le
-
12
wy
wY
,
)(
k
k
Bit rate Maximizing Equalizers:Bit rate Maximizing Equalizers:Per-tone equalizationPer-tone equalization• ADSL Basics
- Intro - DMT Transmitter - Why
Equalization? - DMT Receiver
• ADSL Equalizer Design
- Problem Description
- Current Equalizers
- Bit rate Maximizing
Equalizers Per-tone equalization BM-TEQ
- Relations
DFTN-point
TEQ w
tapsT
Time Domain Equalize
r
wy
wY
,
)(~~̂
,
k
knnnk Fdx
.
.
.
x
x
x
nd~
FEQ
nkx ,~̂
ly
.
.
.
wy
,k
N
N
N
N
.
.
.
wy
wY
,
)(
k
knF
13
Bit rate Maximizing Equalizers:Bit rate Maximizing Equalizers:Per-tone equalizationPer-tone equalization
ly
S/P
N
N
N
...N
N
N
...1T
...
...
...
DFT
N-point
T
DFTN-pointsliding
wy
wY
,
)(~~̂
,
k
knnnk Fdx
PTEQ ...
• ADSL Basics - Intro - DMT Transmitter - Why
Equalization? - DMT Receiver
• ADSL Equalizer Design
- Problem Description
- Current Equalizers
- Bit rate Maximizing
Equalizers Per-tone equalization BM-TEQ
- Relations
)( knF Y n
nkn dFw
wY )~
()(
n
T –tap linear combiner
w for each tone
nkx ,~̂
14
Bit rate Maximizing Equalizers:Bit rate Maximizing Equalizers:Per-tone equalizationPer-tone equalization
21
0,
~
~)(min
K
knk
d
nkn xF
n
n
ww
wY
• Least-squares criterion per tone: “design TEQ per tone”
• Optimizes the SNR per tone Performs always better than a TEQ
• Efficient computation: exploit sliding DFT structure
similar complexity as TEQ
• ADSL Basics - Intro - DMT Transmitter - Why
Equalization? - DMT Receiver
• ADSL Equalizer Design
- Problem Description
- Current Equalizers
- Bit rate Maximizing
Equalizers Per-tone equalization BM-TEQ
- Relations
15
Bit rate Maximizing (BM) Bit rate Maximizing (BM) Equalizers:Equalizers:
Time-domain equalizationTime-domain equalization• ADSL Basics - Intro - DMT Transmitter - Why
Equalization? - DMT Receiver
• ADSL Equalizer Design
- Problem Description
- Current Equalizers
- Bit rate Maximizing
Equalizers Per-tone equalization BM-TEQ
- Relations
21
0,
~
21
0,
~)(min)(~min
K
knk
d
nkn
K
knnk xFe
n
nn
www
wYwPTEQ:
n n
nSNR
tones2 1logmax where
2,
2
,
)/(~
~
)/(
nnk
nknn
eE
xESNR
wwww
BM-TEQ:
21
0 tones,~
,
~)(~
min
K
k nnkknnn
dxFd
n
wYw
with )~()( ,nknn egSNRf
TEQly S/P
CP
... DFT
FEQ
T taps
...
...
N-pointnd
~
x
x
16
Bit rate Maximizing Equalizers:Bit rate Maximizing Equalizers:Time-domain equalizationTime-domain equalization• ADSL Basics
- Intro - DMT Transmitter - Why
Equalization? - DMT Receiver
• ADSL Equalizer Design
- Problem Description
- Current Equalizers
- Bit rate Maximizing
Equalizers Per-tone equalization BM-TEQ
- Relations
21
0 tones,~
,
21
0 tones,~
,
~)(~
min
)~
,(~min
K
k nnkknnn
d
K
k nnnkn
d
xFd
de
n
n
wY
w
w
w
with )),~
(~()( , wnnknn degSNRf
Iteratively-reweighted separable non-linear least squares-based
frequency-domain MMSE-TEQ design
17
Relation between ADSL Relation between ADSL equalizersequalizers• ADSL Basics
- Intro - DMT Transmitter - Why
Equalization? - DMT Receiver
• ADSL Equalizer Design
- Problem Description
- Current Equalizers
- Bit rate Maximizing
Equalizers - Relations
(Channel shortening) TD-MMSE-TEQ: constrained linear LS
FD-MMSE-TEQ: constrained linear LS or separable NL-LS
Block transmission/CP/Multicarrier
Bit rate maximization
BM-TEQ: iteratively reweighted separable NL-LS
PTEQ: linear LS
Only 1 toneRemarkable
correspondence between generalized eigenvalue
problems
18
Relation between ADSL Relation between ADSL equalizersequalizers• ADSL Basics
- Intro - DMT Transmitter - Why
Equalization? - DMT Receiver
• ADSL Equalizer Design
- Problem Description
- Current Equalizers
- Bit rate Maximizing
Equalizers - Relations
TD-MMSE-TEQReal FD-MMSE-TEQ 1Complex FD-MMSE-TEQ 1Real FD-MMSE-TEQ 2Complex FD-MMSE-TEQ 2Real BM-TEQ Complex BM-TEQ Real PTEQComplex PTEQ
19
Relation between ADSL Relation between ADSL equalizersequalizers• ADSL Basics
- Intro - DMT Transmitter - Why
Equalization? - DMT Receiver
• ADSL Equalizer Design
- Problem Description
- Current Equalizers
- Bit rate Maximizing
Equalizers - Relations
(Channel shortening) TD-MMSE-TEQ: constrained linear LS
FD-MMSE-TEQ: constrained linear LS or separable NL-LS
Block transmission/CP/Multicarrier
Bit rate maximization
BM-TEQ: iteratively reweighted separable NL-LS
PTEQ: linear LS
Only 1 toneRemarkable
correspondence between generalized eigenvalue
problems