Combat%20Inter-Symbol%20Interference%20with%20Equalization

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Equalization for Discrete Multitone Transceivers
Güner Arslan Ph.D. Defense Committee Prof.
Ross Baldick Prof. Alan C. Bovik Prof. Brian L.
Evans, advisor Prof. Joydeep Ghosh Dr. Sayfe
Kiaei Prof. Edward J. Powers
2
Outline

• Introduction to high-speed wireline digital
  communications
• Problem Increase ADSL transceiver bit rate by
  increasing performance of the time-domain
  equalizer (TEQ) in the receiver
• Contribution 1 New model for equalized channel
• Contribution 2 Optimal channel capacity TEQ
• Contribution 3 Closed-form near-optimal TEQ
• Simulation results
• Summary and future work

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Introduction
Residential Applications
Business Applications
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Standards for High-Speed Digital Communications
Courtesy of Shawn McCaslin (Cicada Semiconductor,
Austin, TX)
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Intersymbol Interference (ISI)

• Ideal channel
• Impulse response is an impulse
• Frequency response is flat
• Non-ideal channel causes ISI
• Channel memory
• Magnitude and phase variation
• Received symbol is weighted sum of neighboring
  symbols
• Weights are determined by channel impulse
  response

Channel
Receivedsignal
Transmit signal
Threshold at zero
1
1
1
1
Detected signal
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Combat ISI with Equalization

• Problem Channel frequency response is not flat
• Solution Use equalizer to flatten channel
  frequency response

• Zero-forcing equalizer
• Inverts channel
• Flattens frequency response
• Amplifies noise
• Minimum mean squared error (MMSE) equalizer
• Optimizes trade-off between noise amplification
  and ISI
• Decision-feedback equalizer
• Increases complexity
• Propagates error

MMSE Equalizer frequency response
Zero-forcing Equalizer frequency response
Channel frequency response
Magnitude (dB)
Frequency
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Multicarrier Modulation

• Divide broadband channel into many narrowband
  subchannels
• No intersymbol interference (ISI) in subchannels
  if channel gain is constant in every subchannel
• Discrete Multitone (DMT) modulation
• Multicarrier modulation based on fast Fourier
  transform (FFT)
• Standardized for ADSL and proposed for VDSL

channel frequency response
magnitude
carrier
subchannel
frequency
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Multicarrier Modulation

• Advantages
• Efficient use of bandwidth without full channel
  equalization
• Robust against impulsive noise and narrowband
  interference
• Dynamic rate adaptation
• Disadvantages
• Transmitter High signal peak-to-average power
  ratio
• Receiver Sensitive to frequency and phase offset
  in carriers
• Active areas of research
• Pulse shapes of subchannels (orthogonal,
  efficient realization)
• Channel equalizer design (increase capacity,
  reduce complexity)
• Synchronization (timing recovery, symbol
  synchronization)
• Bit loading (allocation of bits in each
  subchannel)

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Eliminating ISI in DMT
copy
copy
s y m b o l ( i1)
CP
CP
s y m b o l i
CP Cyclic Prefix
N samples
v samples

• Convolve stream of samples with channel
• Symbols are spread out in time
• No ISI if channel length is shorter than v1
  samples
• Symbols are distorted in frequency
• Cyclic prefix converts linear convolution into
  circular convolution
• Division in FFT domain can undo distortion if
  channel length is less than v1 samples
• Time domain equalizer shortens channel length
• Frequency domain equalizer inverts channel
  frequency response

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Discrete Multitone Transmitter and Receiver
N/2 subchannels
N subchannels (N 512 for ADSL)
DAC and transmit filter
serial to parallel
QAM encoder
mirror data and N-IFFT
add cyclic prefix
parallel to serial
TRANSMITTER
channel
RECEIVER
N subchannels
N/2 subchannels
parallel to serial
QAM decoder
invert channel frequency domain equalizer
N-FFT and remove mirrored data
serial to parallel
remove cyclic prefix
receive filter and ADC
TEQ time domain equalizer
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Problem Definition and Contributions

• Problem
• Find a TEQ design method that maximizes channel
  capacity at the TEQ output
• Proposed solution
• Decompose equalized channel into signal, noise,
  and ISI paths
• Model subchannel SNR based on this decomposition
• Write channel capacity as a function of TEQ taps
• Develop design methods to maximize channel
  capacity
• Contributions
• A new model for subchannel SNR
• Optimal maximum channel capacity (MCC) TEQ design
  method
• Near-optimal minimum ISI TEQ design method

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Minimum Mean Squared Error (MMSE) MethodChow,
Cioffi, 1992

• Minimize mean squared error Eek where ekbk-?
  - hkwk
• Chose length of bk to shorten length of hkwk
• Disadvantages
• Does not consider channel capacity
• Zeros low SNR bands
• Deep notches in equalizer frequency response

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Maximum Shortening SNR (MSSNR) MethodMelsa,
Younce, Rohrs, 1996

• For each possible position of a window of ?1
  samples,

• Disadvantages
• Does not consider channel capacity
• Requires Cholesky decomposition and eigenvector
  calculation
• Does not take channel noise into account

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Capacity of a Multicarrier Channel

• Each subchannel modeled as white Gaussian noise
  channel

• Define geometric SNR

• Channel capacity of a multicarrier channel

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Maximum Geometric SNR MethodAl-Dhahir, Cioffi,
1996

• Maximize approximate geometric SNR
• Disadvantages
• Subchannel SNR definition ignores ISI
• Objective function ignores interdependence of b
  and w
• Requires solution of nonlinear constrained
  optimization problem
• Based on MMSE method same drawbacks as MMSE
  method
• Ad-hoc parameter MSEmax has to be tuned for
  different channels

nk
rk
xk
ek
h
w


-
z-?
b
zk
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Comparison of Existing Methods
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Contribution 1New Subchannel Model Motivating
Example

• Received signal
• x is transmitted signal
• Symbols a b
• Symbol length
• N 4
• Length of
• L 4
• Cyclic prefix
• v 1
• Delay
• ? 1

Tail
ISI
signal
ISI
noise
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Contribution 1Proposed Subchannel SNR Model

• Partition equalized channel into signal path, ISI
  path, noise path

nk
rk
yk
xk
h
w

xk
h
w
x
Signal
gk
xk
h
w
x
ISI
1-gk
nk
w
noise
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Contribution 1Subchannel SNR Definition

• SNR in i th subchannel is defined as

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Contribution 2Optimal Maximum Channel Capacity
(MCC) TEQ

• Channel capacity as a nonlinear function of
  equalizer taps
• Maximize nonlinear function to obtain the optimal
  TEQ
• Good performance measure for any TEQ design
  method
• Not an efficient TEQ design method in
  computational sense

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Contribution 2MCC TEQ vs. Geometric TEQ
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Contribution 3Near-optimal Minimum-ISI
(min-ISI) TEQ

• ISI power in ith subchannel is
• Minimize ISI power as a frequency weighted sum of
  subchannel ISI
• Constrain signal path gain to one to prevent
  all-zero solution
• Solution is a generalized eigenvector of X and Y
• Possible weightings
• Performance virtually equal to that of the
  optimal method
• Generalizes MSSNR method by weighting in
  frequency domain

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Contribution 3Min-ISI TEQ vs. MSSNR TEQ

• Min-ISI weights ISI power with the SNR
• Residual ISI power should be placed in high noise
  frequency bands

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Contribution 3Efficient Implementations of
Min-ISI Method

• Generalized eigenvalue problem can solved with
  generalized power iteration
• Recursively calculate diagonal elements of X and
  Y from first column Wu, Arslan, Evans, 2000

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Bit Rate vs. Number of TEQ Taps

• Min-ISI, MCC, and MSSNR perform close to Matched
  Filter Bound (MFB) even with small TEQ sizes
• Geometric and MMSE TEQ require 20 taps to achieve
  90 of MFB performance
• Geometric TEQ gives little improvement over MMSE
  TEQ
• Two-tap min-ISI TEQ outperforms 21-tap MMSE TEQ

TEQ taps
cyclic prefix (?) 32 FFT size (N) 512 coding
gain 4.2 dB margin 6 dB input power 14
dBm noise power -113 dBm/Hz, crosstalk noise
10 ADSL disturbers
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Bit Rate vs. Number of TEQ Taps

• Min-ISI and MCC give virtually same performance
• Min-ISI and MCC outperform MSSNR by 2
• 9 taps is enough for best performance for
  min-ISI, MCC, and MSSNR TEQs
• No performance gain for more than 9 taps

TEQ taps
cyclic prefix (?) 32 FFT size (N) 512 coding
gain 4.2 dB margin 6 dB input power 14
dBm noise power -113 dBm/Hz, crosstalk noise
10 ADSL disturbers
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Bit Rate vs. Cyclic Prefix Size

• Min-ISI, MCC, and MSSNR perform close to MFB
• Geometric and MMSE TEQ require cyclic prefix of
  30 samples
• Geometric TEQ gives worse performance for short
  cyclic prefix
• Performance drops because cyclic prefix does not
  carry new information
• MSSNR does not work for cyclic prefix smaller
  than the number of TEQ taps

TEQ taps 17 FFT size (N) 512 coding gain 4.2
dB margin 6 dB input power 14 dBm noise power
-113 dBm/Hz, crosstalk noise 10 ADSL disturbers
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Simulation Results

• Min-ISI, MCC, and MSSNR require cyclic prefix of
  17 samples to hit matched filter bound
  performance
• Geometric and MMSE TEQs do not work with 2 taps
  even with a cyclic prefix of 32 samples
• Geometric TEQ gives lower performance for small
  cyclic prefix length
• Min-ISI TEQ with 3-sample cyclic prefix
  outperforms MMSE TEQ with 32-sample cyclic prefix

TEQ taps 2 FFT size (N) 512 coding gain 4.2
dB margin 6 dB input power 14 dBm noise power
-113 dBm/Hz, crosstalk noise 10 ADSL disturbers
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Simulation Results for 17-tap TEQ
Cyclic prefix length of 32 FFT size
(N) 512 Coding gain 4.2 dB Margin 6 dB
Input power 14 dBm Noise power -113
dBm/Hz Crosstalk noise 10 ADSL disturbers
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Simulation Results for Two-Tap TEQ
Cyclic prefix length of 32 FFT size
(N) 512 Coding gain 4.2 dB Margin 6 dB
Input power 14 dBm Noise power -113
dBm/Hz Crosstalk noise 10 ADSL disturbers
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Summary

• Design TEQ to maximize channel capacity
• No previous method truly maximizes channel
  capacity
• New subchannel SNR model
• Partitions the equalized channel into signal,
  noise, and ISI paths
• Enables to write channel capacity as a function
  of equalizer taps
• New maximum channel capacity TEQ design method
• Good benchmark for all design methods
• Requires nonlinear optimization
• New minimum-ISI design method
• Virtually same performance as the optimal method
• Fast implementation using recursive calculations

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MATLAB DMTTEQ Toolbox

• Toolbox features ten TEQ design methods
• Available at http//signal.ece.utexas.edu/arslan/
  dmtteq/

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Future Research

• End-to-end optimization of channel capacity
• Joint optimization of bit loading and TEQ
• On-line adaptation of TEQ taps to track changes
  in channel
• Analysis of TEQ design methods
• Effect of analog transmit/receive filters and A/D
  and D/A converters
• Analyze performance under channel estimation
  errors
• Fixed-point analysis
• Extension to MCC and min-ISI methods
• Taking into account the noise floor
• Modifications to subchannel SNR model
• Optimal frequency domain weighting in min-ISI
  method

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Capacity of Additive White Gaussian Noise Channel

• Maximum theoretical capacity of an additive white
  Gaussian noise channel (no inter-symbol
  interference) is

• Maximum achievable capacity can be defined as

• ? SNR gap between theoretical and practical
  capacity
• Modulation method
• Coding gain
• Probability of error
• Margin for unaccounted distortions

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Publications

• G. Arslan, B. L. Evans, and S. Kiaei,
  Equalization for Discrete Multitone
  Transceivers to Maximize Channel Capacity'', IEEE
  Trans. on Signal Processing, submitted on April
  17, 2000.
• B. Lu, L. D. Clark, G. Arslan, and B. L. Evans,
  Discrete Multitone Equalization Using Matrix
  Pencil and Divide-and-Conquer Methods'', IEEE
  Trans. on Signal Processing, submitted on May 30,
  2000.
• J. Wu, G. Arslan, and B. L. Evans, Efficient
  Matrix Multiplication Methods to Implement a
  Near-Optimum Channel Shortening Method for
  Discrete Multitone Transceivers'', IEEE Asilomar
  Conf. on Signals, Systems, and Computers, Oct. 29
  - Nov. 1, 2000, Pacific Grove, CA.
• B. Lu, L. D. Clark, G. Arslan, and B. L. Evans,
  Fast Time-Domain Equalization for Discrete
  Multitone Modulation Systems'', IEEE Digital
  Signal Processing Workshop, Oct. 15-18, 2000,
  Hunt, TX.
• G. Arslan, B. L. Evans, and S. Kiaei, Optimum
  Channel Shortening for Multicarrier
  Transceivers'', IEEE Int. Conf. on Acoustics,
  Speech, and Signal Processing, Jun. 5-9, 2000,
  vol. 5, pp. 2965-2968, Istanbul, Turkey.

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Acronyms

• LAN Local area network
• MCC Maximum channel capacity
• MFB Matched filter bound
• min-ISI Minimum ISI
• MMSE Minimum MSE
• MSE Mean squared error
• MSSNR Maximum SSNR
• QAM Quadrature amplitude modulation
• SNR Signal-to-noise ratio
• SSNR shortening SNR
• TEQ Time domain equalizer
• VDSL Very-high-speed DSL

• ADC Analog digital converter
• ADSL Asymmetric DSL
• CAD Computer aided design
• CP Cyclic prefix
• DAC Digital-analog converter
• DMT Discrete multitone
• DSL Digital subscriber line
• FFT Fast Fourier transform
• HDSL High-speed DSL
• IFFT Inverse FFT
• ISDN Integrated service digital network
• ISI Intersymbol interference