bitrate maximizing time-domain equalizer design for dmt-based systems koen vanbleu promotor: marc...
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Bitrate Maximizing Time-Bitrate Maximizing Time-Domain Equalizer Design for Domain Equalizer Design for
DMT-based SystemsDMT-based SystemsKoen Vanbleu
Promotor: Marc MoonenCoauthors: Geert Ysebaert, Gert Cuypers, Katleen Van Acker
KULeuven, ESAT SCD-SISTA, BelgiumKULeuven, ESAT SCD-SISTA, BelgiumICC 2003
2
OverviewOverview
• ADSL Basics� What?� Transmitter/Receiver
• ADSL Equalizer Design� Problem Description� Current Equalizers� Bitrate Maximizing Equalizers
• Conclusions
3
IntroductionIntroduction
• Communication at high rates towards customer� telephone wire, cable, fiber, wireless
• Communication over telephone wire� Evolution: ever increasing bitrates� E.g. Time to download 10 Mbyte file
Modem Time56 Kbps
Voice band modem
24 minutes
128 Kbps ISDN 10 minutes6 Mbps ADSL 13 seconds52 Mbps VDSL 1.5 seconds
• ADSL Basics - Intro - DMT Transmitter - Why
Equalization? - DMT Receiver
• ADSL Equalizer Design
- Problem Description
- Current Equalizers
- Bitrate Maximizing
Equalizers
• Conclusions
4
IntroductionIntroduction
• Broadband communication over telephone line� ADSL (Asymmetric Digital Subscriber Line)� VDSL (Very high bit rate Digital Subscriber Line)� Bitrate is function of the line length
Upstream
Downstream
CustomerCentral
300 m6.4 Mbps52 MbpsVDSL
3 km640 Kbps6 MbpsADSL
Line lengthUpDown Frequency band1.1 MHz8.8 MHz
• ADSL Basics - Intro - DMT Transmitter - Why
Equalization? - DMT Receiver
• ADSL Equalizer Design
- Problem Description
- Current Equalizers
- Bitrate Maximizing
Equalizers
• Conclusions
5• Traditional telephony (POTS) still available
over the same wire.
Modulation and DuplexingModulation and Duplexing
• Assign different frequency bins to up- and downstream directions� Frequency Division Duplexing (FDD)� Overlap: Echo Cancellation (EC)
f (kHz)
POTS UP DOWN POTS UP&DOWN
DOWN
4 25 138 1104 f (kHz)4 25 138 1104
e.g. ADSL
• Multicarrier modulation scheme: Discrete Multitone (DMT)
• ADSL Basics - Intro - DMT Transmitter - Why
Equalization? - DMT Receiver
• ADSL Equalizer Design
- Problem Description
- Current Equalizers
- Bitrate Maximizing
Equalizers
• Conclusions
6
Discrete Multi Tone: TransmitterDiscrete Multi Tone: Transmitter
00
11
10
01Re
Im
2 bits
Re
Im
4 bits
bits Data symbols (QAM)
...
P/S
CP
kx
Cyclic Prefix
0
IFFTN-point
.
.
.
.
.
.
...
IFFT modulation(Inverse Fast Fourier Transform)
N12/ N
• ADSL Basics - Intro - DMT Transmitter - Why
Equalization? - DMT Receiver
• ADSL Equalizer Design
- Problem Description
- Current Equalizers
- Bitrate Maximizing
Equalizers
• Conclusions
7
Why Equalization?Why Equalization?
channel
ky
knnoise
...
P/S
CP
kxIFFTN-point
.
.
.
.
.
.
...
N
12/ N
nX
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
- Bitrate Maximizing
Equalizers
• Conclusions
8
Discrete Multi Tone: ReceiverDiscrete Multi Tone: Receiver
00
11
10
01Re
Im
2 bits
Re
Im
4 bits
bits
Data symbols
...S/P
CP
.
.
.FFT
N-point
FFT demodulation
.
.
. FEQ
Unbiased Frequency
Domain Equalizer
1 tap / tone
.
.
.channel h
knnoise
kykxTEQ w
tapsT
Time Domain
Equalizer
• ADSL Basics - Intro - DMT Transmitter - Why
Equalization? - DMT Receiver
• ADSL Equalizer Design
- Problem Description
- Current Equalizers
- Bitrate Maximizing
Equalizers
• Conclusions
k
kh kk wh
CP length + 1k
9
DMT Equalization: DMT Equalization: Problem DescriptionProblem Description
S/P
CP... FFT FE
QTEQ w
ky
T taps
...
...
1 tap/tone
N-point
To maximize bitrate:
n
nbtones
toneonbits
00
11
10
01
Re{X}
Im{X}
2 bits
• ADSL Basics - Intro - DMT Transmitter - Why
Equalization? - DMT Receiver
• ADSL Equalizer Design
- Problem Description
- Current Equalizers
- Bitrate Maximizing
Equalizers
• Conclusions
nnn EXZ
FEQ Dn
n n
nn DSNRtones
2),(1log w
is hard with time-domain equalizer w
where 2
2
),(),(
nn
nnn
DEE
XEDSNR
ww
10
Current ADSL Equalizers (1)Current ADSL Equalizers (1)• ADSL Basics - Intro - DMT Transmitter - Why
Equalization? - DMT Receiver
• ADSL Equalizer Design
- Problem Description
- Current Equalizers
- Bitrate Maximizing
Equalizers
• Conclusions
• Channel shorteners, e.g. MMSE-based TEQ [Al-Dhahir, Cioffi]
Channel h
knnoise
kxTEQ w
ky
delay TIR b
ke
bwbw,
oron constraint s.t.min 2keE
TIR = target impulse response of (CP-length+1)
MMSE criterion ADSL bitrate maximization
11
Current ADSL Equalizers (2)Current ADSL Equalizers (2)• ADSL Basics - Intro - DMT Transmitter - Why
Equalization? - DMT Receiver
• ADSL Equalizer Design
- Problem Description
- Current Equalizers
- Bitrate Maximizing
Equalizers
• Conclusions
• Approximate Bitrate Maximizing TEQs [Al-Dhahir], [Evans]
S/P
CP... FFT FEQ Dn
TEQ wky
T taps
...
...
1 tap/tone
N-point nnn EXZ
n n
nSNRbtones
2 1logMaximize
based on SNR at FFT output
2
21
)(),(
),()(
whw
hww
nn
nnn
NIE
XDESNR
residual ISI/ICI noise
Approximations!
12
• Approximate Bitrate Maximizing TEQs (continued)
2
21
)(),(
),()(
whw
hww
nn
nnn
NIE
XDESNR
residual ISI/ICI noiseExamples of approximations :
•
• Signal component in SNR does not only depend on `windowed’ (shortened) channel impulse response
• : do not forget DFT leakage (ICI)!
nnn WHD 1
nN
• ADSL Basics - Intro - DMT Transmitter - Why Equalization? - DMT Receiver
• ADSL Equalizer Design - Problem Description - Current Equalizers - Bitrate Maximizing Equalizers
• Conclusions
Current ADSL Equalizers (3)Current ADSL Equalizers (3)
13nnnnnnn XYDXZDE )(),( wwthen
= residual ISI/ICI+noise sources (XT, RFI, …)
n n
nn DSNRbtones
2),(1log w
Bitrate Maximizing Equalizers Bitrate Maximizing Equalizers (1)(1)• ADSL Basics
- Intro - DMT Transmitter - Why
Equalization? - DMT Receiver
• ADSL Equalizer Design
- Problem Description
- Current Equalizers
- Bitrate Maximizing
Equalizers
• Conclusions
S/P
CP... FFT FEQ Dn
TEQ wky
T taps
...
...
N-point nnn EXZ
where 2
2
),(),(
nn
nnn
DEE
XEDSNR
ww
Maximize
)(wnY
AND
*2
)( nn
nn XYE
XED
w
14
Bitrate Maximizing Equalizers Bitrate Maximizing Equalizers (2)(2)
Exact bitrate maximizing (BM-)TEQ cost function
• Nonlinear cost function in w only with An and Bn
• tone dependent matrices• function of signal statistics
• ADSL Basics - Intro - DMT Transmitter - Why
Equalization? - DMT Receiver
• ADSL Equalizer Design
- Problem Description
- Current Equalizers
- Bitrate Maximizing
Equalizers
• Conclusions • Recursive Gauss-Newton updating algorithm:• attains good local optimum• adaptivity (to track channel/noise changes)• however: high complexity
15
Bitrate Maximizing Equalizers Bitrate Maximizing Equalizers (3)(3)• ADSL Basics
- Intro - DMT Transmitter - Why
Equalization? - DMT Receiver
• ADSL Equalizer Design
- Problem Description
- Current Equalizers
- Bitrate Maximizing
Equalizers
• Conclusions
Bitrate maximizing equalizers:
• Bitrate maximizing (single) TEQ: NG = all used tones nonlinear cost function
• “Per group” equalization: BM-TEQ w per group SG of NG tones nonlinear cost function
• “Per tone” equalization: NG = 1 tone (advantageous) linear MMSE problem
[Vanacker, Leus, Moonen]
HIGHERBITRATE
16
Bitrate Maximizing Equalizers Bitrate Maximizing Equalizers (4)(4)• ADSL Basics
- Intro - DMT Transmitter - Why
Equalization? - DMT Receiver
• ADSL Equalizer Design
- Problem Description
- Current Equalizers
- Bitrate Maximizing
Equalizers
• Conclusions
Simulations
Bitrate Maximizing-TEQPer-Tone Equalizer
MMSE-based TEQsApprox. Bitrate Max. TEQs
17
ConclusionsConclusions• ADSL Basics - Intro - DMT Transmitter - Why
Equalization? - DMT Receiver
• ADSL Equalizer Design
- Problem Description
- Current Equalizers
- Bitrate Maximizing
Equalizers
• Conclusions
• ADSL Equalizer Design
• Truly Bitrate Maximizing Per-Group Equalizer• Time-Domain Equalizer (1 group of tones)• Per-Tone Equalizer (groups of 1 tone)
• Recursive Gauss-Newton algorithm • Good local optimum• Complex
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