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Maximizing Data Rate of Discrete Multitone Systems Using Time Domain Equalization Design. Milo š Milo š evi ć. Ph.D. Defense. Committee Members Prof. Ross Baldick Prof. Gustavo de Veciana Prof. Brian L. Evans (advisor) Prof. Edward J. Powers Prof. Robert A. van de Geijn. Outline. - PowerPoint PPT Presentation

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Maximizing Data Rate of Discrete Multitone SystemsMaximizing Data Rate of Discrete Multitone SystemsUsing Time Domain Equalization DesignUsing Time Domain Equalization Design

Miloš Milošević

Committee Members

Prof. Ross Baldick

Prof. Gustavo de Veciana

Prof. Brian L. Evans (advisor)

Prof. Edward J. Powers

Prof. Robert A. van de Geijn

Ph.D. Defense

2

OutlineOutline• Broadband access technologies

• Background– Multicarrier modulation

– Channel and noise

– Equalization

• Contributions – Model subchannel SNR at multicarrier demodulator output

– Data rate optimal filter bank equalizer

– Data rate maximization finite impulse response equalizer

• Simulation results

• Conclusions and future work

3

Broadband Access TechnologiesBroadband Access Technologies• Wireless Local Area Network

– Standardized in 1997

– 15M adaptors sold (2002)

– 4.4M access points sold (2002)

– Up to 54 Mbps data rate

– Data security issues

• Cable Network

– Video broadcast since 1948

– Data service standardized 1998

– Shared coaxial cable medium: data security is an issue

– 42-850 MHz downstream (for broadcast), 5-42 MHz upstream

– Data Over Cable Service Interface Specifications 2.0 (2002)• Downstream 6.4 MHz channel: up to 30.72 Mbps (shared)

• Upstream 6.4 MHz channel: up to 30.72 Mbps (shared)

Standard Modulation Data Rate Carrier

802.11 Single carrier 2 Mbps 2.4 GHz

802.11a Multicarrier 54 Mbps 5.2 GHz

802.11b Single carrier 11 Mbps 2.4 GHz

802.11g Multicarrier 54 Mbps 2.4 GHz

4

Digital Subscriber Line (DSL) StandardsDigital Subscriber Line (DSL) Standards• Dedicated link

over copper twisted pair

• “Last mile”

• Widely deployed: North America, West. Europe, South Korea (35M lines)

• In US cable leads2 : 1 industry3 : 1 consumer

xDSL Modulation Data Rate BandHDSL Single 1544 kbps (N.A.)

2320 kbps (Europe)

2 x 1168 kbps (Europe)

3 x 784 kbps (Europe)

193 kHz

580 kHz

292 kHz

196 kHz

SDSL Single 1.544 kbps <386 kHz

ADSL (1998)

Multicarrier

<256 tones

6144 (8192) kbps down

786 (640) kbps up

1104 MHz

ADSL Lite

(1998)

Multicarrier

<128 tones

1536 kbps down

512 kbps up

552 kHz

VDSL

(2003)

Single or Multicarrier <4092 tones

13 Mbps (N.A.) sym.

22/3 Mbps (N.A.) asym.

14.5 Mbps (N.A.) sym.

23/4 Mbps (N.A.) asym.

12 MHz

(N.A.) - North America

5

DSL Broadband AccessDSL Broadband Access

ATM - Asynchronous Transfer ModeDMT - Discrete MultitoneDSLAM - Digital Subscriber Line Access MultiplexerLAN – Local Area NetworkPSTN - Public Switched Telephone Network

Splitter

DMT Modem

Telephone

Wireless Modem

Wireless Modem

Home Hub

Local Area Network

Home Wireless LAN

Splitter

Voice Switch

PSTN

DSLAM

ATM Switch

Internet

Router

Set-top box

Customer Premises

Central Office

downstream

upstreamPC

6

OutlineOutline• Broadband access technologies

• Background– Multicarrier modulation

– Channel and noise

– Equalization

• Contributions – Model subchannel SNR at multicarrier demodulator output

– Data rate optimal filter bank equalizer

– Data rate maximization finite impulse response equalizer

• Simulation results

• Conclusions and future work

7

Multicarrier ModulationMulticarrier Modulation• Frequency division multiplexing for transmission

• Carrier frequencies are spaced in regular increments up to available system bandwidth– Discrete multitone (DMT) modulation

– Orthogonal frequency division multiplexing

Serial-to-Parallel

Converter

M bits

mn bits

Encoding

Encoding

Encoding

m2 bits

m1 bits

f1

f2

fn

To physical medium

Bit rate is M fsymbol bits/s

Transmit filter

-fx fx

8

Discrete Multitone Transmitter Discrete Multitone Transmitter S

eria

l-to-

Par

alle

l

QA

Men

cod

er

Mirr

or d

ata

and

N-I

FF

T

Add Cyclic Prefix

Digital-to-Analog Converter +

Transmit Filter

N/2 subchannels(complex-valued)

Bits

00101

Par

alle

l-to-

Ser

ial

To Physical Medium

N coefficients(real-valued) N + coefficients

copy

I

Q iX

00101

sym

bo

l

sym

bo

lC

P

symbolCP

CP: Cyclic PrefixFFT: Fast Fourier TransformQAM: Quadrature Amplitude Modulation : cyclic prefix length

9

Channel and NoiseChannel and Noise• Channel model

– Finite impulse response (FIR) filter

– Additive noise sources

• Channel noise sources– White noise

– Near-end echo

– Near-end crosstalk (NEXT)

– Intersymbol interference (ISI)

• Model other noise not introduced by the channel– Analog-to-digital and digital-to-analog quantization error

– Digital noise floor introduced by finite precision arithmetic

Channel Equalizer

White Noise, ISI, NEXT, Echo, Quantization Error

Digital Noise Floor

Input

Output

10

InterferenceInterference• Intersymbol interference (ISI) occurs if channel impulse

response longer than cyclic prefix (CP) length + 1– Received symbol is weighted sum of neighboring symbols

– Weights determined by channel impulse response

– Causes intercarrier interference

• Solution: Use channel shortening filter

Tx Symbol Tx Symbol Tx Symbol

Rx Symbol Rx Symbol Rx Symbol

* channel

=

CP

Tx Symbol Tx Symbol Tx Symbol

Rx Symbol Rx Symbol Rx Symbol

* channel

=* filter

11

Channel Shortening FilterChannel Shortening Filter• Called time-domain equalizer (generally an FIR filter)

• If shortened channel length at most cyclic prefix length + 1– symbol channel FFT(symbol) x FFT(channel)– Division by FFT(channel) can undo linear time-invariant

frequency distortion in the channel

Channel impulse response

Shortened channel impulse response

Transmission delay

12

TEQtime

domain equalizer

QAMdecoder

Frequencydomain

equalizer= invert channel

N-FFTand

removemirrored

data

Discrete Multitone Receiver Discrete Multitone Receiver

Remove Cyclic Prefix

Receive Filter+Analog-to-Digital

Converter

N/2 subchannels

Bits

00101

Ser

ial-t

o-P

aral

lel

From Physical Medium

Par

alle

l-to-

Ser

ial

N coefficientsN + coefficients

ADSL downstream upstream 32 4 N 512 64

13

z-

h + w

b

-x y e

n

+

• Minimize E{eTe}

Error: e = x*b - y*w

Equalized channel: h*w

Pick channel delay and length of

b to shorten length of h*w

Minimum mean squared error

solution satisfies:

• DisadvantagesDeep notches in shortened channel

frequency response Long equalizer reduces bit rateDoes not consider bit rate or noise

Minimum Mean Squared Error MethodMinimum Mean Squared Error Method

yyxy RwRb TT

|DFT{h*w}|

Virtual path

Chow & Cioffi, 1992

14

Maximum Shortening SNR MethodMaximum Shortening SNR Method• Minimize energy leakage outside shortened channel length

• Disadvantages– Does not consider bit rate

or channel noise

– Long equalizer reduces bit rate

– Requires generalizedeigenvalue solution orCholesky decomposition

– Cannot shape TEQ accordingto frequency domain needs

Yellow – leads to Hwall

Gray – leads to Hwin

sample number

Channel h (blue line)

1 s.t. min winTwin

Twall

Twall

T wHHwwHHww

wHwHHwwhh wallwinshort *

Melsa, Younce & Rohrs, 1996

DistortionSignal

15

Minimum ISI MethodMinimum ISI Method• Extends Maximum Shortening SNR method

– Adds frequency domain weighting of ISI

– Weight according to subchannel SNR; favors high SNR subchannels

– Does not minimize ISI in unused subchannels

• Minimizes weighted sum of subchannel ISI power under constraint that power of signal is constant

qk is kth column vector of N-length Discrete Fourier Transform matrix

(*)H is the Hermitian (conjugate transpose)

• Method is not optimal as it does not consider system bit rate

1 s.t. min winTwin

Twall

2/

1

H

,

,Twall

T

wHHwwHqqHww

N

kk

kn

kxk S

S

Subchannel SNR

Arslan, Kiaei & Evans, 2000

16

Dual-path Time Domain EqualizerDual-path Time Domain Equalizer• Received signal passes through two parallel time domain

equalizers – One time domain equalizer designed to minimize ISI over the

system bandwidth– Other time domain equalizer designed for particular frequency

band, e.g. by using Minimum Intersymbol Interference method

• Time domain equalizers are designed using sub-optimal methods

FEQ – Frequency domain equalizer

TEQ 1

TEQ 2

FFT

FFT

Subchannel SNR

Comparison

FEQReceived Signal

Ding, Redfern & Evans, 2002

17

Per-tone EqualizerPer-tone Equalizer• Transfers time

domain equalizer operations to frequency domain

• Combined complex multi-tap equalizer

• Each tone (subchannel) equalized separately

SlidingN-point

FFT

yN+M-1

yN+M-2

y0

Z1

Z2

w1,0 w1,1 wi,M-1

0

w2,0 w2,1 w2,M-1

0

wN/2,0 wN/2,1 wN/2,M-1

0 ZN/2

N+M-1

N/2

y – received symbol; M – subchannel equalizer length; w – complex equalizer;Zk – received subsymbol in subchannel k; Sliding FFT - efficient implementation of M fast Fourier transforms on M columns of convolution matrix of y with w

Acker, Leus, Moonen, van der Wiel & Pollet, 2001

18

OutlineOutline• Broadband access technologies

• Background– Multicarrier modulation

– Channel and noise

– Equalization

• Contributions – Model subchannel SNR at multicarrier demodulator output

– Data rate optimal filter bank equalizer

– Data rate maximization finite impulse response equalizer

• Simulation results

• Conclusions and future work

19

Interference-free Symbol at FFT OutputInterference-free Symbol at FFT Output• FFT of circular convolution of channel and discrete

multitone symbol in kth subchannel

is the desired subsymbol in subchannel k at FFT output is desired symbol circular convolution matrix for delay H is channel convolution matrix

qk is kth column vector of N-length FFT matrix

• Received subsymbol in kth subchannel after FFT

is symbol convolution matrix (includes contributions from previous, current, and next symbol)

G(*) is convolution matrix of source of noise or interference

Dk is digital noise floor, which is not affected by TEQ

wHUqY circHD kk

circU

DkY

kkk D wGGGGGHUqY ADCEchoFEXTNEXTWhiteISIHR

ISIU

Contribution #1

20

Model SNR at Output of DemodulatorModel SNR at Output of Demodulator• Proposed subchannel SNR model at demodulator output

– Ratio of quadratic functions in equalizer coefficients w

• Bits per frame as a nonlinear function of equalizer taps.

– Multimodal for more than two-tap w

– Nonlinear due to log and flooring operations

– Requires integer maximization

– Ak and Bk are Hermitian symmetric

• Maximizing bint is an unconstrained optimization problem

wBw

wAw

YYYY

YYw

T

T

k

k

kkkk

kkk ~

~

)]()E[(

])E[()(SNR

DRHDR

DHD

Contribution #1

Ik k

k

Ik k

kbwBw

wAwww

T

T

22int log

SNR1log

21

Data Rate Optimal Filter BankData Rate Optimal Filter Bank• Find optimal time domain equalizer for every subchannel

• Generalized eigenvalue problem

• Bit rate of bank of optimal time domain equalizer filters

kkk

kkk

kkk

kkkk

kk wBw

wAw

wBw

wAww

wwT

T

T

T

2opt maxarglogmaxarg

kkkkkkkkk for λλfor λ satisfies optoptoptoptopt wBwAw

Ik kkk

kkkboptTopt

optTopt

2intopt log

wBw

wAw

Contribution #2

22

TEQ Filter Bank

Filter Bank Equalizer ArchitectureFilter Bank Equalizer Architecture

Goertzel Filter Bank

G0

G1

GN/2-1

y0

y1

yN/2-1

Y0

Y1

YN/2-1

Frequency Domain

Equalizer

FEQ0

FEQ1

FEQN/2-1

Z0

Z1

ZN/2-1

w0

w1

wN/2-1

x

CP

CP

CP

Received frame

TEQinput DFT output

Contribution #2

23

• Advantages– Provides a new achievable upper bound on bit rate performance

– Single FIR can only perform at par or worse

– Supports different subchannel transmission delays

– Can modify frequency and phase offsets in multiple carriers by adapting carrier frequencies of Goertzel filters

– Easily accommodates equalization of groups of tones with a common filter with corresponding drop in complexity

• Disadvantages - computationally intensive – Requires up to N/2 generalized eigenvalue solutions during

transceiver initialization

– Requires up to N/2 single FIR and as many Goertzel filters

Filter Bank SummaryFilter Bank Summary

Contribution #2

24

• Find single FIR that performs as well as the filter bank

• Maximizing b(w) more tractable than maximizing bint(w)

• Maximizer of b(w) may be the maximizer of bint(w)– Conjecture is that it holds true for 2- and 3-tap w

– Hope is that it holds for higher dimensions

• Maximizing sum of ratios is an open research problem

Data Rate Maximization Single FIR DesignData Rate Maximization Single FIR Design

Ik k

kbwBw

wAww

T

T

2log

Contribution #3

25

• Gradient-based optimization of b(w)– Find gradient root corresponding to a local maximum

– Start with a good initial guess of equalizer taps w

– No guarantee of finding global maximum of b(w)

• Initial guess: filter bank FIR wkopt resulting in highest b(w)

• Parameterize problem to make it easier to find desired root

– H() is a convex, non-increasing

function of vector – Solution reached when H() = 0

– Solution corresponds to local maximum closest to initial point

Data Rate Maximization Single FIR DesignData Rate Maximization Single FIR Design

wBAwλ

ww IkkkkkH λrmax)( T

1,2

wwBw

wAww

wAww

T

T

T

kk

kk

kkr

SNR)(

2log

2)(

Contribution #3

26

Equalizer Implementation ComplexityEqualizer Implementation Complexity

• Per tone equalizer and single FIR similar complexity

• Filter bank has high complexity

• Example shownN = 512

fsymbol = 4 kHz

fs=2.208 MHz

M = 3

= 32

Subsystem Multiply/adds*

Words/symbol

Single FIR

FIR 6.6e6 6

FFT 36.9e6 2048

FEQ 4.1e6 1024

Total 46.7e6 3078

FilterBank

FIR 1700e6 771

Goertzel 1000e6 2048

FEQ 4.1e6 1024

Total 2704.1e6 3843

Per ToneEqualizer

FFT 36.9e6 2112

Sliding FFT 8.2e6 512

Combiner 12.3e6 1024

Total 57.4e6 3648

fsymbol – Symbol rate fs – Sample rate M – Equalizer length * – Calculations assume N/2 data populated subchannels

27

Filter Bank Simulation ResultsFilter Bank Simulation Results• Search to find filter length just before diminishing returns

– ADSL parameters except no constraints on bit allocation

– ADSL carrier serving area (CSA) lines used

• Optimal transmission delay found using line searchCSA loop Data Rate opt TEQ Size

1 11.417 Mbps 15 8

2 12.680 Mbps 22 12

3 10.995 Mbps 26 8

4 11.288 Mbps 35 6

5 11.470 Mbps 32 16

6 10.861 Mbps 20 8

7 10.752 Mbps 34 13

8 9.615 Mbps 35 11

28

Proposed vs. Other Equalization DesignsProposed vs. Other Equalization Designs• Percentage of filter bank data rates for same filter length

– Each table entry averaged over TEQ lengths 2-32

– ADSL parameters with NEXT modeled as 49 ADSL disturbers

LS PTE – Least-squares Per-Tone Equalizer; UEC – Unit energy Constraint; UTC – Unit Tap Constraint

CSA loop Single FIR Min-ISI LS PTE MMSE-UEC MMSE-UTC

1 99.6% 97.5% 99.5% 86.3% 84.4%

2 99.6% 97.3% 99.5% 87.2% 85.8%

3 99.5% 97.3% 99.6% 83.9% 83.0%

4 99.3% 98.2% 99.1% 81.9% 81.5%

5 99.6% 97.2% 99.5% 88.6% 88.9%

6 99.5% 98.3% 99.4% 82.7% 79.8%

7 98.8% 96.3% 99.6% 75.8% 78.4%

8 98.7% 97.5% 99.2% 82.6% 83.6%

Average 99.3% 97.5% 99.4% 83.6% 83.2%

29

Data Rate vs. Equalizer Filter LengthData Rate vs. Equalizer Filter Length• CSA loop 2 data rates for different equalizer filter lengths

– Standard ADSL parameters

– NEXT modeled as 49 disturbers

expanded

30

Spectrally Flat Equalizer ResponseSpectrally Flat Equalizer Response• Some design

methods attempt to achieve flatness using empirical design constraints

• Example: CSA loop 4 SNR for Single FIR, MBR and Min-ISI – MBR and Min-ISI

place nulls in SNR (lowers data rate)

– Proposed Single FIR avoids nulls

Detail

Blue - Single FIR Red – Min-ISIGreen - MBR

MBR – Maximum Bit Rate Time Domain Equalizer Design

31

Data Rate vs. Transmission DelayData Rate vs. Transmission Delay• Transmission delay:

not known, TEQ design parameter

• MMSE: Bit rate does not change smoothly as function of delay

– Optimal delay not easily chosen prior to actual design

– Exhaustive search of delay values needed

• Single FIR: Bit rate changes smoothly as function of delay – Example: CSA loop 1 – “Sweet spot” increases with filter length– Optimal bit rate for range of delays

0 10 20 30 40 50 60 70 80 90 1000

2

4

6

8

10

12

Bit

Rat

e (M

bp

s)

Transmission Delay

- M=3

- M=10

- M=30

32

ConclusionsConclusions• Subchannel SNR model noise sources not in other methods

– Crosstalk and echo

– Analog-to-digital conversion noise and digital noise floor

• Optimal time domain equalizer filter bank– Bit rate in each subchannel maximized by separate TEQ filter

– Provides achievable upper bound on bit rate performance

– Available in freely distributable Discrete Multitone Time Domain Equalizer Matlab Toolbox by Embedded Signal Processing Laboratory (http://signal.ece.utexas.edu)

• Data maximization single time domain equalizer– Achieves on average 99.3% of optimal filter bank performance

– Outperforms state of the art Min-ISI by 2% and MMSE by 15%

– Similar performance to least-squares per-tone equalizer

33

Future WorkFuture Work

• Further research into architectures where equalizers are assigned to spectral bands instead for each subchannel

• Possibility of integrating time domain equalization with the adjustment of Discrete Fourier Transform carrier frequencies to maximize subchannel SNR

• Adaptive and numerically inexpensive implementation of Min-ISI method that removes TEQ length constraint of the original method

34

Publications in Discrete MultitonePublications in Discrete Multitone

• Journal papers– M. Milosevic, L. F. C. Pessoa, B. L. Evans, and R. Baldick, “Optimal

time domain equalization design for maximizing data rate of discrete multitone systems,” accepted for publication in IEEE Trans. On Signal Proc.

– M. Milosevic, T. Inoue, P. Molnar, and B. L. Evans, “Fast unbiased echo canceller update during ADSL transmission,” to be published in IEEE Trans. on Comm., April 2003.

– R. K. Martin, K. Vanbleu, M. Ding, G. Ysebaert, M. Milosevic, B. L. Evans, M. Moonen, and C. R. Johnson, Jr., “Multicarrier Equalization: Unification and Evaluation Part I,” to be submitted to IEEE Trans. On Signal Proc.

– R. K. Martin, K. Vanbleu, M. Ding, G. Ysebaert, M. Milosevic, B. L. Evans, M. Moonen, and C. R. Johnson, Jr., “Multicarrier Equalization: Unification and Evaluation Part II,” to be submitted to IEEE Trans. On Signal Proc.

35

Publications in Discrete MultitonePublications in Discrete Multitone

• Conference papers– M. Milosevic, L. F. C. Pessoa, and B. L. Evans, “Simultaneous

multichannel time domain equalizer design based on the maximum composite shortening SNR,” in Proc. IEEE Asilomar Conf. on Sig., Sys., and Comp., vol. 2, pp. 1895-1899, Nov. 2002.

– M. Milosevic, L. F. C. Pessoa, B. L. Evans, and R. Baldick, “Optimal time domain equalization design for maximizing data rate of discrete multitone systems,” in Proc. IEEE Asilomar Conf. on Sig., Sys., and Comp., vol. 1, pp. 377-382, Nov. 2002.

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