Maximizing%20Data%20Rate%20of%20Discrete%20Multitone%20Systems%20Using%20Time%20Domain%20Equalization%20Design

1
Maximizing Data Rate of Discrete Multitone
SystemsUsing Time Domain Equalization Design

• Miloš Miloševic

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
2
Outline

• 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 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
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Digital 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 Band
HDSL 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 lt386 kHz
ADSL (1998) Multicarrier lt256 tones ? 6144 (8192) kbps down ? 786 (640) kbps up 1104 MHz
ADSL Lite (1998) Multicarrier lt128 tones ? 1536 kbps down ? 512 kbps up 552 kHz
VDSL (2003) Single or Multicarrier lt4092 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
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DSL Broadband Access
Internet
Home Wireless LAN
Local Area Network
Router
Home Hub
ATM Switch
DMT Modem
DSLAM
Set-top box
downstream
Splitter
Splitter
PC
upstream
Voice Switch
Telephone
Customer Premises
ATM - Asynchronous Transfer ModeDMT - Discrete
MultitoneDSLAM - Digital Subscriber Line Access
MultiplexerLAN Local Area NetworkPSTN -
Public Switched Telephone Network
PSTN
Central Office
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Outline

• 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 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

Transmit filter
m1 bits
Encoding
Serial-to-Parallel Converter
To physical medium
f1
m2 bits
M bits
Encoding
f2
mn bits
Encoding
Bit rate is M fsymbol bits/s
fn
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Discrete Multitone Transmitter
Serial-to-Parallel
QAM encoder
Mirror data and N-IFFT
Add Cyclic Prefix
Parallel-to-Serial
Bits
Digital-to-Analog Converter Transmit Filter
00101
N/2 subchannels(complex-valued)
To Physical Medium
N coefficients(real-valued)
N n coefficients
symbol
Q
copy
00101
I
CP Cyclic PrefixFFT Fast Fourier
TransformQAM Quadrature Amplitude Modulation
n cyclic prefix length
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Channel 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

White Noise, ISI, NEXT, Echo, Quantization Error
Output
Equalizer
Channel
Input
Digital Noise Floor
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Interference

• 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

CP
Tx Symbol
Tx Symbol
Tx Symbol

channel

Rx Symbol
Rx Symbol
Rx Symbol
Tx Symbol
Tx Symbol
Tx Symbol

channel


filter
Rx Symbol
Rx Symbol
Rx Symbol
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Channel 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
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Discrete Multitone Receiver
Frequency domain equalizer invert channel
N-FFT and remove mirrored data
Remove Cyclic Prefix
Serial-to-Parallel
TEQ time domain equalizer
Receive Filter Analog-to-Digital Converter
From Physical Medium
N/2 subchannels
N coefficients
N n coefficients
Parallel-to-Serial
QAM decoder
Bits
00101
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Minimum Mean Squared Error Method
Chow Cioffi, 1992
n

• Minimize EeTe
• Error e xb? - yw
• Equalized channel hw
• Pick channel delay D and length of b? to shorten
  length of hw
• Minimum mean squared error solution satisfies
• Disadvantages
• Deep notches in shortened channel frequency
  response
• Long equalizer reduces bit rate
• Does not consider bit rate or noise

y
e
x
h
w


-
z-?
b
Virtual path
DFThw
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Maximum Shortening SNR Method
Melsa, Younce Rohrs, 1996

• Minimize energy leakage outside shortened channel
  length
• Disadvantages
• Does not consider bit rateor channel noise
• Long equalizer reduces bit rate
• Requires generalizedeigenvalue solution
  orCholesky decomposition
• Cannot shape TEQ accordingto frequency domain
  needs

Distortion
Signal
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Minimum ISI Method
Arslan, Kiaei Evans, 2000

• 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

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Dual-path Time Domain Equalizer
Ding, Redfern Evans, 2002

• 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
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Per-tone Equalizer
Acker, Leus, Moonen, van der Wiel Pollet, 2001

• Transfers time domain equalizer operations to
  frequency domain
• Combined complex multi-tap equalizer
• Each tone (subchannel) equalized separately

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

• 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

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Interference-free Symbol at FFT Output
Contribution 1

• 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 D
• 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

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Model SNR at Output of Demodulator
Contribution 1

• 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

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Data Rate Optimal Filter Bank
Contribution 2

• Find optimal time domain equalizer for every
  subchannel
• Generalized eigenvalue problem
• Bit rate of bank of optimal time domain equalizer
  filters

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Filter Bank Equalizer Architecture
Contribution 2
y0
Y0
Z0
TEQ Filter Bank
Goertzel Filter Bank
Frequency Domain Equalizer
w0
CP
y1
Y1
Z1
w1
CP
x
Received frame
yN/2-1
YN/2-1
ZN/2-1
wN/2-1
CP
TEQ
input
DFT
output
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Filter Bank Summary
Contribution 2

• 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

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Data Rate Maximization Single FIR Design
Contribution 3

• 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

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Data Rate Maximization Single FIR Design
Contribution 3

• 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(l) is a convex, non-increasing
• function of vector l
• Solution reached when H(l) 0
• Solution corresponds to local maximum closest to
  initial point

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Equalizer Implementation Complexity
Subsystem Multiply/adds Words/symbol
Single FIR FIR 6.6e6 6
Single FIR FFT 36.9e6 2048
Single FIR FEQ 4.1e6 1024
Single FIR Total 46.7e6 3078
FilterBank FIR 1700e6 771
FilterBank Goertzel 1000e6 2048
FilterBank FEQ 4.1e6 1024
FilterBank Total 2704.1e6 3843
Per ToneEqualizer FFT 36.9e6 2112
Per ToneEqualizer Sliding FFT 8.2e6 512
Per ToneEqualizer Combiner 12.3e6 1024
Per ToneEqualizer Total 57.4e6 3648

• Per tone equalizer and single FIR similar
  complexity
• Filter bank has high complexity
• Example shown
• N 512
• fsymbol 4 kHz
• fs2.208 MHz
• M 3
• n 32

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

CSA loop Data Rate Dopt 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
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Proposed 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

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
LS PTE Least-squares Per-Tone Equalizer UEC
Unit energy Constraint UTC Unit Tap Constraint
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Data Rate vs. Equalizer Filter Length

• CSA loop 2 data rates for different equalizer
  filter lengths
• Standard ADSL parameters
• NEXT modeled as 49 disturbers

expanded
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Spectrally 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

Blue - Single FIR Red Min-ISI Green - MBR
Detail
MBR Maximum Bit Rate Time Domain Equalizer
Design
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Data 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

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Conclusions

• 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

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Future 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

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Publications 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.

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Publications 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.