Equalization for ADSL Transceivers by 82c6qUJC

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									          Equalizer Design to Maximize
          Bit Rate in ADSL Transceivers
                                            Prof. Brian L. Evans
                                     Dept. of Electrical and Comp. Eng.
                                      The University of Texas at Austin
                                        http://signal.ece.utexas.edu
                                         Last modified November 30, 2009
       UT graduate students: Mr. Aditya Chopra, Mr. Yousof Mortazavi
 UT MS/PhD grads: Dr. Güner Arslan (ST-Ericcson), Dr. Biao Lu (OpenSpirit),
Dr. Ming Ding (Broadcom), Dr. Milos Milosevic (Schlumberger), Mr. Alex Olson
(Schlumberger), Dr. Zukang Shen (Datang Mobile), and Dr. Ian Wong (Nat. Inst.)
UT senior design students: Mr. Wade Berglund, Mr. Jerel Canales, Mr. David J.
Love, Mr. Ketan Mandke, Mr. Scott Margo, Ms. Esther Resendiz, Mr. Jeff Wu
Other collaborators: Dr. Lloyd D. Clark, Prof. C. Richard Johnson, Jr. (Cornell),
 Prof. Sayfe Kiaei (ASU), Prof. Rick Martin (AFIT), Prof. Marc Moonen (KU
     Leuven), Dr. Lucio F. C. Pessoa (Freescale), Dr. Arthur J. Redfern (TI)
                                Introduction

        Interne
            t               Digital Subscriber Line (DSL)
                                       Broadband Access

        DSLAM              Downstream
                         (higher data rate)

 Service  DSL                                        DSL
Provider modem
                                                    modem
                            Upstream
   Voice
                  LPF                           LPF
   Switch
                                                  Customer Premises


    Telephone           DSLAM - Digital Subscriber Line Access Multiplexer
     Network            LPF – Lowpass Filter (passes voiceband frequencies)
                                                                              2
                                   Introduction

   Discrete Multitone (DMT) DSL Standards
ADSL – Asymmetric DSL
  Maximum data rates supported in G.DMT standard (ideal case)
      Echo cancelled: 14.94 Mbps downstream, 1.56 Mbps upstream
      Frequency division multiplexing (FDM): 13.38 Mbps downstream, 1.56 Mbps upstream
  Widespread deployment in US, Canada, Western Europe, and Hong Kong
      Central office providers only installing frequency-division multiplexed (FDM)
      ADSL:cable modem market
        1:2 in US & 2:1 worldwide                                     G.DMT Asymmetric
                                                                ADSL DMT VDSL
  ADSL+ 8 Mbps downstream min.                              0.025 – 1.1 0.138 – 12
                                         Data band
  ADSL2 doubles analog bandwidth                                  MHz        MHz
                                         Upstream
VDSL – Very High Rate DSL                subcarriers
                                                                     32            256
  Asymmetric                             Downstream
                                                                    256     2048/4096
      Faster G.DMT FDM ADSL              subcarriers
      2m subcarriers m  [8, 12]         Target up-
                                                               1 Mbps          3 Mbps
  Symmetric: 13, 9, or 6 Mbps            stream rate
                                         Target down-
  Optional 12-17 MHz band                                      8 Mbps      13/22 Mbps
                                         stream rate
                                                                                         3
                                   Outline
    • Multicarrier modulation
    • Conventional equalizer training methods
        – Minimum Mean Squared Error design                            [Stanford]

        – Maximum Shortening Signal-to-Noise Ratio design               [Tellabs]

        – Maximum Bit Rate design (optimal)                           [UT Austin]

        – Minimum Inter-symbol Interference design (near-optimal) [UT Austin]
    • Per-tone equalizer                    [Catholic University, Leuven, Belgium]
    • Dual-path equalizer                                            [UT Austin]
    • Conclusion
Message                                                                    Received
bit stream                                                                 bit stream
                                                 Equalizer
             Transmitter       Channel
                                                     Receiver
                                                                                     4
                            Multicarrier Modulation

                  Single Carrier Modulation
• Ideal (non-distorting) channel over transmission band
   – Flat magnitude response
   – Linear phase response: delay is constant for all spectral components
   – No intersymbol interference

• Impulse response for ideal channel over all frequencies
   – Continuous time: g d(t-T)        Channel
                                              nk
                                                    Equalizer
   – Discrete time: g d[k-D]     xk              yk           rk    ek
                                        h     +       w           +
• Equalizer                  Training                         +
                                                                -
   – Shortens channel         sequence
     impulse response                                  Ideal Channel
     (time domain)          Receiver
   – Compensates for        generates                 z-D         g
     frequency distortion       xk
     (frequency domain)
                                        Discretized Baseband System
                                                                            5
                                  Multicarrier Modulation

                           Multicarrier Modulation
• Divide channel into narrowband subchannels
   – No inter-symbol interference (ISI) in subchannels if constant gain
     within every subchannel and if ideal sampling
                                                                    sampled
• Discrete multitone modulation                   pulse               sinc
                                                            DTFT-1
   – Baseband transmission
   – Based on fast Fourier transform (FFT)                  w                              k
   – Standardized for ADSL and VDSL            -w       w
                                                                            sin w c k )
                                                            c       c


                                                 channel
                                                                               k
  magnitude




                                                                carrier

                                                                          subchannel



              Subchannels are 4.3 kHz wide in ADSL and VDSL                 frequency
                                                                                               6
                                         Multicarrier Modulation

     Multicarrier Modulation by Inverse FFT Filter Bank
                      j 2 f1 t            complex-valued                j 2
                                                                                1
                e                                                               N
                                                                                  k
                                                                     e
  X1     g(t)        x                                       X1          x
                     j 2 f 2 t           complex-valued                 j 2
                                                                                2
                e                                                               N
                                                                                  k
                                                                     e
  X2     g(t)        x                         Discrete      X2          x
                                     +          time                                    +


                    j 2 f N / 2 t             real-valued              j 2
                                                                               N /2
                e                                                               N
                                                                                    k
                                                                    e
X N /2   g(t)        x                                    X N /2         x

         g(t) : pulse shaping filter                  Xi : ith subsymbol from encoder
                                                                                            7
                                     Multicarrier Modulation

             Discrete Multitone Modulation Symbol
 • N/2 subsymbols are in general complex-valued                       Quadrature
      – ADSL uses 4-level Quadrature Amplitude                                      Xi
        Modulation (QAM) during training
      – ADSL uses QAM of 22, 23, 24, …, 215 levels                           In-phase
        during data transmission

 • Multicarrier modulation using inverse FFT                             QAM
                                      X0                       x0
                                      X1                       x1
   Mirror and                         X2         N-point       x2      Yields one
    conjugate                                    Inverse              symbol of N
  N/2–1 complex                    XN/2            Fast               real-valued
   subsymbols                                    Fourier                samples
                                     X2*        Transform
                                     X1*                       xN-1


X i e j wi n  X i*e- j wi n  2 X i cos( i n  X i )
                                        w                                                8
                             Multicarrier Modulation

         Discrete Multitone Modulation Frame
• Frame is sent through D/A converter and transmitted
   – Frame is the symbol with cyclic prefix prepended
   – Cyclic prefix (CP) consists of last n samples of the symbol

                     copy                              copy

        CP       s y m b o l i            CP      s y m b o l i+1

     v samples       N samples                          ADSL G.DMT Values
                                         N     16            Down      Up
   – CP reduces throughput by factor of                    stream stream
                                        N  v 17
                                                         n      32      4
• Linear convolution of frame with                      N              64
                                                               512
  channel impulse response
   – Is circular convolution if channel length is CP length plus one or shorter
   – Circular convolution       frequency-domain equalization in FFT domain
   – Time-domain equalization to reduce effective channel length and ISI
                                                                                  9
                            Multicarrier Modulation

 Eliminating ISI in Discrete Multitone Modulation
• Time domain equalizer (TEQ)                           n1
   – Finite impulse response (FIR) filter                             channel
                                                                      impulse
   – Effective channel impulse response:                             response
     convolution of TEQ impulse response
     with channel impulse response                                  effective
• Frequency domain equalizer (FEQ)                                   channel
                                                                     impulse
   – Compensates magnitude/phase distortion                         response
     of equalized channel by dividing each FFT
     coefficient by complex number                     D

   – Generally updated during data transmission        D: transmission delay
• ADSL G.DMT equalizer training                        n: cyclic prefix length
   – Reverb: same symbol sent 1,024 to 1,536 times     ADSL G.DMT Values
   – Medley: aperiodic pseudo-noise sequence of             Down      Up
     16,384 symbols for subchannel SNR estimation          stream stream
   – Receiver returns number                            n      32      4
                                            SNR i 
     of bits (0-15) to transmit bi  log 2 1 
                                                  
                                                Γi 
                                                       N      512     64
     each subchannel i                            
                                                                                 10
                                    Multicarrier Transceivers

                ADSL Transceiver: Data Transmission
                            N/2 subchannels N real samples                     2.208 MHz
                       quadrature
                                          mirror
      Bits             amplitude                           add                     D/A +
                                           data
                S/P    modulation                         cyclic      P/S        transmit
 00110                                     and
                         (QAM)                            prefix                   filter
                                          N-IFFT
                        encoder

TRANSMITTER                           each block programmed in lab and
                                      covered in one full lecture                channel
                                      each block covered in one full lecture
RECEIVER
                 N/2 subchannels        N real samples
                        invert        N-FFT                             time
                       channel                                                    receive
                                       and             remove         domain
              QAM         =                                                         filter
P/S                                  remove         S/P cyclic       equalizer
             decoder   frequency                                                       +
                                     mirrored           prefix          (FIR
                         domain                                                     A/D
                        equalizer      data                            filter)
                                     
                        
                              conventional ADSL equalizer structure
                                                                                             11
                                   Outline
    • Multicarrier modulation
    • Conventional equalizer training methods
        – Minimum Mean Squared Error design                         [Stanford]

        – Maximum Shortening Signal-to-Noise Ratio design            [Tellabs]

        – Maximum Bit Rate design (optimal)                       [UT Austin]

        – Minimum Inter-symbol Interference design (near-optimal) [UT Austin]
    • Per-tone equalizer
    • Dual-path equalizer
    • Conclusion
Message                                                                Received
bit stream                                                             bit stream
                                                Equalizer
             Transmitter       Channel
                                                    Receiver
                                                                                 12
                                Conventional Equalizer

     Minimum Mean Squared Error TEQ Design
                  nk
       Channel              TEQ
xk                     yk            rk      ek
          h       +         w         - +

         z-D                b
                                      bk-D
• Minimize E{ek2} [Chow & Cioffi, 1992]
     – Chose length of b (e.g. n+1) to shorten length of h * w
   – b is eigenvector of minimum eigenvalue of symmetric         Rxy is cross
     channel-dependent matrix R D  R xx - R xy R -1 R yx
                                                  yy             correlation
   – Minimum MSE when R yy w  R xy b where w  0                  matrix
• Disadvantages
     – Does not consider bit rate
     – Deep notches in equalized frequency response      Why?
                                                                                13
                               Conventional Equalizer

         Infinite Length MMSE TEQ Analysis
• As TEQ length goes to
  infinity, RD becomes
  Toeplitz [Martin et al. 2003]
    – Eigenvector of minimum
      eigenvalue of symmetric
      Toeplitz matrix has zeros
      on unit circle [Makhoul 1981]
    – Zeros of target impulse
      response b on unit circle
      kills n subchannels

• Finite length TEQ plot
                                                         [Martin et al., 2004]
    – Each trace is a different zero of b
    – Distance of 32 zeros of b to unit circle averaged
                                                         Longer MMSE
      over 8 ADSL test channels for each TEQ length TEQ may be worse
    – Zeros cluster at 0.01 and 10-4 from UC for TEQ lengths 32 and 100
                                                                             14
                           Conventional Equalizer

      Maximum Shortening SNR TEQ Design
• Minimize energy leakage outside shortened channel length
• For each possible position of window [Melsa, Younce & Rohrs, 1996]
                                      energy inside window after TEQ 
      maxSSNR in dB)  max 10 log10 
                                      energy outside window after TEQ 
                                                                       
       w                 w
                                                                      
                                                        n1

              h            w                                         channel
                                                                     impulse
                                                                    response
• Equivalent to noise-free MMSE TEQ
                                                                   effective
• Disadvantages                                                     channel
   – Does not consider channel noise                                impulse
                                                                   response
   – Does not consider bit rate
   – Deep notches in equalized frequency response            D
     (zeros of target impulse response near unit circle kill subchannels)
   – Requires Cholesky decomposition, which is computationally-intensive and
     does not allow TEQ lengths longer than cyclic prefix
                                                                               15
                                    Conventional Equalizer

          Maximum Shortening SNR TEQ Design
• Choose w to minimize energy outside window of desired length
     Locate window to capture maximum channel impulse response energy
                   nk                   T
                                              h wall h wall  w H wall H wall w  wT Aw
                                                      T   T

                           yk           rk
xk
           h         +          w             hT h win  wT HT H win w  wT Bw
                                               win           win


     hwin, hwall : equalized channel within and outside the window
• Objective function is shortening SNR (SSNR)
                              wT Bw 
   maxSSNR)  max 10 log10  T       subject to wT Bw  1
                              w Aw 
                                    
    w             w


      Cholesky decomposition of B to find eigenvector
      for minimum generalized eigenvalue of A and B          C    B ) A
                                                                       -1
                                                                              B T
                                                                                    )
                                                                                    -1




     wopt    B)q
                 T
                     -1
                          min   q min : eigenvector of min eigenvalue of C
                                                                                          16
                            Conventional Equalizer

               Modeling Achievable Bit Rate
• Bit allocation bounded by subchannel SNRs: log(1 + SNRi / Gi)
• Model ith subchannel SNR [Arslan, Evans & Kiaei, 2001]
                  signal power                         Used in Maximum
  SNR i 
           noise power  ISI power                      Bit Rate Method
                           S x,i  signal transferfunction
  SNRi 
           Sn,i  noise transferfunction  S x,i  ISI transferfunction
  S x,i : transmitted signal power in subchanneli
  Sn,i : channel noise power in subchanneli
                                                    S x ,i signal 2
• Divide numerator and                                     Hi
  denominator of SNRi by noise SNR                 S n ,i
                                              i
  power spectral density Sn,i                     noise 2    S x ,i ISI   2
                                                Hi                 Hi
                                                             S n ,i
  Used in Minimum               Conventional
        ISI Method            subchannel SNRi
                                                                              17
                                 Conventional Equalizer

           Maximum Bit Rate (MBR) TEQ Design
• Subchannel SNR as nonlinear function of equalizer taps w
  H isignal  q iH GHw                         H     2
                                       S x,i qi GHw          wT Ai w
                       SNRi                             2 
  H i  qi DHw
                                             2
     ISI      H
                              S n,i qi Fw  S x,i qi DHw
                                     H              H        wT Bi w
                                                                           qi
   H inoise  q iH Fw                                     GT        Sx,i    H   G
                                 Ai =     HT                   qi                   H
   qi is ith row of DFT matrix
                      q                                                    qi
            FT Sn,i Hi            F                       DT        Sx,i   H
                                                                                D
Bi =           qi                     +   HT                   qi                   H


• Maximize nonlinear function of bits/symbol with respect to w
                      N /2
                                    1 wT A i w
               bDMT   log 2 ( 1 
                                                  Fractional bits
                                               )
                      i 1          G wT Bi w    for optimization
    – Good performance measure for comparison of TEQ design methods
    – Not an efficient TEQ design method in computational sense
                                                                                        18
                               Conventional Equalizer

           Minimum-ISI (Min-ISI) TEQ Design
• Rewrite subchannel SNR                             S x ,i signal 2
  [Arslan, Evans & Kiaei, 2001]                             Hi
                                                     S n ,i
            ISI power weighted in       SNR i 
                                                   noise 2    S x ,i ISI 2
             frequency domain by                 Hi                 Hi
          inverse of noise spectrum                           S n ,i
• Generalize MSSNR method by weighting ISI in frequency
                                     ISIi   Ki qi DHw  wT Xw
                                                              2
   – Minimize frequency weighted                   H
      sum of subchannel ISI power        i            i
    – Penalize ISI power in high conventional SNR subchannels: K i  S x ,i / S n ,i
    – Constrain signal path gain to one
      to prevent all-zero solution for w   | h signal |2 | GHw |2  w T Yw  1
    – Solution is eigenvector of minimum generalized eigenvalue of X and Y
• Iterative Min-ISI method [Ding et al. 2003]
    – Avoids Cholesky decomposition by using adaptive filter theory
    – Designs arbitrary length TEQs without loss in bit rate
    – Overcomes disadvantages of Maximum SSNR method
                                                                                   19
                                   Outline
    • Multicarrier modulation
    • Conventional equalizer training methods
        – Minimum Mean Squared Error design
        – Maximum Shortening Signal-to-Noise Ratio design
        – Maximum Bit Rate design (optimal)
        – Minimum Inter-symbol Interference design (near-optimal)
    • Per-tone equalizer                    [Catholic University, Leuven, Belgium]
    • Dual-path equalizer
    • Conclusion
Message                                                                    Received
bit stream                                                                 bit stream
                                                 Equalizer
             Transmitter       Channel
                                                     Receiver
                                                                                     20
                                 Per-Tone Equalizer

   Drawbacks to Using Single FIR Filter for TEQ
• Conventional                                  N real    N/2 complex
  equalizer                                    samples      samples
                                                       N-FFT      invert
                        time
                                    remove              and      channel
                      domain
                     equalizer       cyclic S/P       remove        =
                                                                 frequency
                        (FIR         prefix           mirrored
                                                                   domain
                       filter)                          data      equalizer

• Equalizes all tones in combined fashion: may limit bit rate
• Output of conventional equalizer for tone i computed using
  sequence of linear operations
                            Zi = Di rowi(QN ) Y w                       Yw
                                                                     represents
   Di is the complex scalar value of one-tap FEQ for tone i         convolution
   QN is the N  N complex-valued FFT matrix
   Y is an N  Lw real-valued Toeplitz matrix of received samples
   w is a Lw  1 column vector of real-valued TEQ taps
                                                                                  21
                                       Per-Tone Equalizer

             Frequency-Domain Per Tone Equalizer
• Rewrite equalized FFT coefficient for each of N/2 tones
     [Van Acker, Leus, Moonen, van de Wiel, Pollet, 2001]

       Zi = Di rowi(QN ) Y w = rowi(QN Y) ( w Di ) = rowi(QN Y) wi
      – Take sliding FFT to produce N  Lw matrix product QN Y
      – Design wi for each tone

                           N+n

                 z-1
                                                             W1,0    W1,1     W1,2     W1,Lw-
                                         Sliding                                         1

                                         N-Point
N + Lw – 1
channels         z-1                      FFT
                           N+n          (Lw-frame)
                                                            WN/2,0   WN/2,1   WN/2,2   WN/2,Lw-1
                 z-1
 y                         N+n                              FEQ is a linear combiner
                                                            of up to N/2 Lw-tap FEQs
                                                                                                   22
                                   Outline
    • Multicarrier modulation
    • Conventional equalizer training methods
        – Minimum Mean Squared Error design
        – Maximum Shortening Signal-to-Noise Ratio design
        – Maximum Bit Rate design (optimal)
        – Minimum Inter-symbol Interference design (near-optimal)
    • Per-tone equalizer
    • Dual-path equalizer                                           [UT Austin]
    • Conclusion
Message                                                                  Received
bit stream                                                               bit stream
                                                Equalizer
             Transmitter       Channel
                                                    Receiver
                                                                                  23
                              Dual-Path Equalizer

    Dual-Path Time Domain Equalizer (DP-TEQ)
                        [Ding, Redfern & Evans, 2002]

• First FIR TEQ equalizes entire available bandwidth
• Second FIR TEQ tailored for subset of subchannels
   – Subchannels with higher SNR
   – Subchannels difficult to equalize, e.g. at boundary of upstream and
     downstream channels in frequency-division multiplexed ADSL
• Minimum ISI method is good match for second FIR TEQ

            TEQ 1            FFT               Path
                                             Selection
                                             for each       FEQ
                                            Subchannel
            TEQ 2            FFT
• Path selection for each subchannel is fixed during training
• Up to 20% improvement in bit rate over MMSE TEQs
• Enables reuse of VLSI designs of conventional equalizers
                                                                           24
                                             Simulation Results

                  Simulation Results for 17-Tap Equalizers
                                                                         Parameters
                                                                  Cyclic prefix length 32
                                                                  FFT size (N)         512
                                                                  Coding gain (dB)       4.2
                                                                  Margin (dB)            6
Bit rate (Mbps)




                                                                  Input power (dBm) 23
                                                                  Noise power (dBm/Hz)
                                                                                      -140
                                                                  Crosstalk noise
                                                                         24 ISDN disturbers

                                                                       Downstream
                      Carrier serving area (CSA) test loop
                                                                       transmission
Figure 1 in [Martin, Vanbleu, Ding, Ysebaert, Milosevic, Evans, Moonen & Johnson, Oct. 2005]
UNC(b) means unit norm constraint on target impulse response b, i.e. || b || = 1
MDS is Maximum Delay Spread design method [Schur & Speidel, 2001]
                                                                                               25
                                            Simulation Results

                  Simulation Results for 17-Tap Equalizers
                                                                        Parameters
                                                                 Cyclic prefix length 32
                                                                 FFT size (N)         512
                                                                 Coding gain (dB)       4.2
Bit Rate (Mbps)




                                                                 Margin (dB)            6
                                                                 Input power (dBm) 23
                                                                 Noise power (dBm/Hz)
                                                                                     -140
                                                                 Crosstalk noise
                                                                        24 ISDN disturbers

                                                                      Downstream
                     Carrier Serving Area (CSA) Test Loop
                                                                      transmission
Figure 3 in [Martin, Vanbleu, Ding, Ysebaert, Milosevic, Evans, Moonen & Johnson, Oct. 2005]
MDR is Maximum Data Rate design method [Milosevic et al., 2002]
BM-TEQ is Bit Rate Maximizing design method [Vanbleu et al., 2003]
PTEQ is Per Tone Equalizer structure and design method [Acker et al., 2001]                    26
                                                               Simulation Results

                                     Estimated Computational Complexity

Computational Complexity in 10 log10(MACs)




                                                            Equalizer Design Algorithm

                                             MAC means a multiplication-accumulation operation
                                                                                                 27
                                      Simulation Results

   Bit Rate vs. Training Complexity Tradeoffs
                  6.6


                  6.5


                  6.4
Bit Rate (Mbps)



                  6.3
                                                                        SymMinSSNR
                                                                        SymMMSE
                  6.2
                                                                        MinSSNR
                                                                        SymMinISI
                  6.1
                                                                        MMSE
                                                                        MinISI
                   6                                                    MDS
                                                                        DualPath
                  5.9


                  5.8


                  5.7


                  5.6
                        4.5   5        5.5         6       6.5     7

                        Training Complexity in log10(MACs)
                    MAC means a multiplication-accumulation operation                28
                              Simulation Results

   Achievable Bit Rate vs. Delay Parameter

    Bit rate (Mbps)




                      Delay Parameter D for CSA Test Loop 4
Large plateau of near-optimal delays (optimal choice requires search)
One choice is to set the delay parameter equal to cyclic prefix length
                                                                         29
                                  Conclusion

            Contributions by Research Group
• New methods for single-path time-domain equalizer design
   – Maximum Bit Rate method maximizes bit rate (upper bound)
   – Minimum Inter-Symbol Interference method (real-time, fixed-point)

• Minimum Inter-Symbol Interference TEQ design method
   – Generalizes Maximum Shortening SNR by frequency weighting ISI
   – Improve bit rate in an ADSL transceiver by change of software only
   – Implemented in real-time on three fixed-point digital signal processors:
     Motorola 56000, TI TMS320C6200 and TI TMS320C5000
       http://www.ece.utexas.edu/~bevans/projects/adsl
• New dual-path time-domain equalizer
   – Achieves bit rates between conventional and per tone equalizers
   – Lower implementation complexity in training than per tone equalizers
   – Enables reuse of ASIC designs

                                                                                30
                                   Conclusion

         UT Austin Matlab DMTTEQ Toolbox 3.1
• Single-path, dual-path, per-tone & TEQ filter bank equalizers
    Available at http://www.ece.utexas.edu/~bevans/projects/adsl/dmtteq/

                                                                      18 design
                                                                      methods

                                                                       default
                                                                     parameters
                                                                        from
                                                                       G.DMT
                                                                        ADSL
                                                              23
                                                             -140
                                                                      standard

  various                                                              different
performance                                                            graphical
 measures                                                                views

                                                                                  31
                                  Conclusion

               UT Austin ADSL2 Simulator 1.1

1. Simulation
   controls
2. Simulation
   state indicator
3. Description
   window
4. Simulation
   parameters
5. Performance
   indicators



     http://users.ece.utexas.edu/~bevans/projects/adsl/simulator/index.html

                                                                              32
Backup Slides
                                   Introduction

              Applications of Broadband Access
                                 Residential
Application                     Downstream Upstream Willing to pay   Demand
                                rate (kb/s)   rate (kb/s)            Potential
Database Access                           384           9  High      Medium
On-line directory; yellow pages           384           9  Low         High
Video Phone                             1,500       1,500  High      Medium
Home Shopping                           1,500          64  Low       Medium
Video Games                             1,500       1,500 Medium     Medium
Internet                                3,000         384  High      Medium
Broadcast Video                         6,000           0  Low         High
High definition TV                     24,000           0  High      Medium

                                   Business
Application                     Downstream Upstream Willing to pay   Demand
                                rate (kb/s)   rate (kb/s)            Potential
On-line directory; yellow pages           384           9 Medium       High
Financial news                          1,500           9 Medium       Low
Video phone                             1,500       1,500  High        Low
Internet                                3,000         384  High        High
Video conference                        3,000       3,000  High        Low
Remote office                           6,000       1,500  High      Medium
LAN interconnection                    10,000     10,000  Medium     Medium
Supercomputing, CAD                    45,000     45,000   High        Low
                                                                                 34
                                       Introduction

                         Selected DSL Standards
Standard Meaning                  Data Rate       Mode    Applications
ISDN     Integrated Services         144 kbps   Symmetric Internet Access, Voice, Pair
         Digital Network                                  Gain (2 channels)
T1       T-Carrier One             1.544 Mbps Symmetric Enterprise, Expansion,
         (requires two pairs)                             Internet Service
HDSL     High-Speed Digital        1.544 Mbps Symmetric Pair Gain (12 channels),
         Subscriber Line                                  Internet Access, T1/E1
         (requires two pairs)                             replacement
HDSL2 Single Line HDSL             1.544 Mbps Symmetric Same as HDSL except pair
                                                          gain is 24 channels
G.Lite    Splitterless          up to 1.5 Mbps Downstream Internet Access, Digital
ADSL      Asymmetric Digital    up to 512 kbps Upstream Video
          Subscriber Line
G.DMT     Asymmetric Digital    up to 10 Mbps Downstream Internet Access, Digital
ADSL      Subscriber Line        up to 1 Mbps Upstream Video
VDSL      Very High-Speed       up to 22 Mbps Downstream Internet Access, Digital
          Digital Subscriber     up to 3 Mbps Upstream Video, Broadcast Video
          Line                  up to 13 Mbps Symmetric

              Courtesy of Shawn McCaslin (National Instruments, Austin, TX)
                                                                                         35
                            Introduction

            A Digital Communications System


Message                                                  Message
              Encoder                       Decoder
 Source                     Noise                         Sink



             Modulator     Channel         Demodulator

             Transmitter                     Receiver


 •   Encoder maps a group of message bits to data symbols
 •   Modulator maps these symbols to analog waveforms
 •   Demodulator maps received waveforms back to symbols
 •   Decoder maps the symbols back to binary message bits
                                                                   36
                               Introduction

              Intersymbol Interference (ISI)
                                                                      2.1
• Ideal channel
                                                                   1.7
   – Impulse response is impulse
                                       111 1       1              1
   – Flat frequency response                           .7                     .7
                                                         .4              .1
• Non-ideal channel                            *              =
   – Causes ISI                          Channel       Received
   – Channel memory                -1    impulse        signal
   – Magnitude and phase     Transmitted response
     variation                  signal
                                              Threshold
• Received symbol is weighted                  at zero
  sum of neighboring symbols                                       11 1 1 1
   – Weights are determined by channel
     impulse response
                                                                  Detected
                                                                   signal
                                                                                   37
                               Introduction

               Combat ISI with Equalization
• Equalization because channel response is not flat
• Zero-forcing equalizer
   – Inverts channel
   – Flattens freq. response           Zero-forcing     MMSE
                                         equalizer     equalizer
   – Amplifies noise                    frequency     frequency
                                                      response
• MMSE equalizer                        response

   – Optimizes trade-off                 Channel
                                        frequency
     between noise                      response
     amplification and ISI
• Decision-feedback
  equalizer
   – Increases complexity
   – Propagates error


                                                                   38
              Introduction

           Cyclic Prefix




Repeated                             cyclic
 symbol                              prefix




    *
                                         to be
                                       removed


   =
                             equal
                                                 39
                             Multicarrier Modulation

        Open Issues for 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
• Open issues
   –   Pulse shapes of subchannels (orthogonal, efficient realization)
   –   Channel equalizer design (increase bit rate, reduce complexity)
   –   Synchronization (timing recovery, symbol synchronization)
   –   Bit loading (allocation of bits in each subchannel)
   –   Echo cancellation


                                                                         40
                            Conventional Equalizer

                         TEQ Algorithm
• ADSL standards
   – Set aside 1024 frames (~.25s) for TEQ estimation
   – Reserved ~16,000 frames for channel and noise estimation for the
     purpose of SNR calculation
• TEQ is estimated before the SNR calculations
• Noise power and channel impulse response can be
  estimated before time slot reserved for TEQ if the TEQ
  algorithm needs that information




                                                                        41
                             Conventional Equalizer

Single-FIR Time-Domain Equalizer Design Methods
• All methods below perform optimization at TEQ output
• Minimizing the mean squared error
    – Minimize mean squared error (MMSE) method [Chow & Cioffi, 1992]
    – Geometric SNR method [Al-Dhahir & Cioffi, 1996]
• Minimizing energy outside of shortened (equalized)
  channel impulse response
    – Maximum Shortening SNR method [Melsa, Younce & Rohrs, 1996]
    – Divide-and-conquer methods [Lu, Evans, Clark, 2000]
    – Minimum ISI method [Arslan, Evans & Kiaei, 2000]
• Maximizing bit rate [Arslan, Evans & Kiaei, 2000]
• Implementation
    – Geometric SNR is difficult to automate (requires human intervention)
    – Maximum bit rate method needs nonlinear optimization solver
    – Other methods implemented on fixed-point digital signal processors
                                                                             42
                                  Conventional Equalizer

       Minimum Mean Squared Error (MMSE) TEQ
                    nk

xk
                         yk             rk      ek         
                                                      w  w0 w1  wLw -1      ]   T

                              w
                                                       b  b0 b1  bn ] T
            h       +                   - +

           z-D                b
                                         bk-D
                                                      ˆ    
                                                      b  0D | bT | 0Lh -D-n -1   ]   T


                          ˆ      ˆ    ˆ
           MSE  {ek }  bT R xxb - 2bT R xy w  wT R yy w
                    2


         minimum MSE is achieved only if bT R xy  wT Ryy
                 ˆ                       ˆ ˆ    ]    ˆ
           MSE  bT R xx - R xy R -1 R yx b  bT R x|yb
                                  yy


         Define RD  OT Rx|yO then MSE  b R Δb
                                          T


O selects the proper part out of Rx|y corresponding to the delay D


                                                                                          43
                             Conventional Equalizer

Near-optimal Minimum-ISI (Min-ISI) TEQ Design
• Generalizes MSSNR method by frequency weighting ISI
                                                          2
  – ISI power in ith subchannel is ISIi  S x ,i q iH DHw
   – Minimize ISI power as a frequency weighted sum of subchannel ISI
                      ISIi   Ki q DHw  wT Xw
                                          H           2
                                          i
                       i          i
   – Constrain signal path gain to one to prevent all-zero solution
                      | h signal |2 | GHw |2  w T Yw  1
   – Solution is a generalized eigenvector of X and Y

• Possible weightings
                                                                         S x ,i
   – Amplify ISI objective function in subchannels with low       Ki 
     noise power (high SNR) to put ISI in low SNR bins:             S n ,i
   – Set weighting equal to input power spectrum:             K i  S x ,i
   – Set weighting to be constant in all subchannels (MSSNR): K i  1

• Performance virtually equal to MBR (optimal) method
                                                                                  44
                          Conventional Equalizer

    Efficient Implementations of Min-ISI Method
• Generalized eigenvalue problem can solved with
  generalized power iteration:          Xwk 1  Ywk
• Recursively calculate diagonal elements of X and Y from
  first column [Wu, Arslan, Evans, 2000] Method      Bit Rate MACs
                                            Original       99.6%   132,896
                                            Recursive      99.5%    44,432

                                            Row-rotation   99.5%    25,872

                                            No-weighting   97.8%    10,064




                                                                             45
                               Conventional Equalizer

    Motivation for Divide-and-Conquer Methods
• Fast methods for implementing Maximum SSNR method
• Maximum SSNR Method
   – For each D, maximum SSNR method requires
      • Multiplications: ( L  7 ) L  5 L2  25 L3
                            h       w     w       w
                               6       2      3
      • Additions:             5       3      25
                         ( Lh - ) Lw - L2  L3
                                           w       w
                               6       2       3
       • Divisions:       L2
                           w

   – Exhaustive search for the optimal delay D
                  0  D  Lh  Lw -n - 2  0  D  499
• Divide Lw TEQ taps into (Lw - 1) two-tap filters in cascade
   – Design first two-tap filter then second and so forth (greedy approach)
• Develop heuristic to estimate the optimal delay

                                                                              46
                           Conventional Equalizer

              Divide-and-Conquer Approach
• The ith two-tap filter is initialized as either
                                          1
   – Unit tap constraint (UTC)       wi   
                                           gi 
                                          sin  i 
   – Unit norm constraint (UNC)     wi  
                                         cos i  

• Calculate best gi or i by using a greedy approach either by
   – Minimizing     1  (Divide-and-conquer TEQ minimization)
                  SSNR
   – Minimizing energy in hwall (Divide-and conquer TEQ cancellation)

• Convolve two-tap filters to obtain TEQ


                                                                        47
                                       Conventional Equalizer

   Divide-and-Conquer TEQ Minimization (UTC)
• At ith iteration, minimize Ji over gi

                                   a1,i                 a2 ,i   1 
                          1 gi ] 
                 T
               w i Aw i            a2 , i               a3,i   g i  a1,i  2a2,i g i  a3,i g i2
                                                                 
           Ji  T       
               w i Bw i            b1,i                 b2,i   1  b1,i  2b2,i g i  b3,i g i2
                          1 gi ] 
                                  b2,i                  b3,i   g i 
                                                               


• Closed-form solution

                            - a3,i b1,i - a1,i b3,i )                   D
            g i 1, 2 )                                 
                            2a3,i b2,i - a2,i b3,i )        2a3,i b2,i - a2,i b3,i )
            D  a3,i b1,i - a1,i b3,i ) - 4a3,i b2,i - a2,i b3,i )a2,i b1,i - a1,i b2,i )
                                             2




                                                                                                       48
                               Conventional Equalizer

   Divide-and-Conquer TEQ Minimization (UNC)
• At ith iteration, minimize Ji over i

                                             a1,i       a2 ,i            1 
                          sin  i 1 i ])                     sin  i   
                 T
               w i Aw i                      a 2 ,i     a3,i  
                                                                                 
                                                                           i  
           Ji  T       
               w i Bw i                      b1,i       b2,i            1 
                          sin  i 1 i ])                     sin  i   
                                            b2,i        b3,i  
                                                              
                                                                                
                                                                          i  
                                      a1,i    a2 ,i   1 
                             1 i ]                                           Calculate i in
                                      a2 ,i   a3,i  i 
                                                                             the same way
                           
                                      b1,i    b2,i   1                      as gi for UTC
                             1 i ] 
                                               b3,i  i 
                                                                                version of this
                                     b2,i                                      method
                   sin  i                  1               1
• where      wi             sin  i cos sin    sin  i  
                  cos i                  i     i            i

                                                                                                  49
                             Conventional Equalizer

   Divide-and-Conquer TEQ Cancellation (UTC)
• At ith iteration, minimize Ji over gi


                                                                )
              J i  h wallh wall   hi -1 k )  g i hi -1 k - 1) ,
                    ~T ~             ~                ~            2




                                                            
                                  kS

             S  1, 2,, D, D  n  2,, Lh
                                          ~
                                                      i -1




• Closed-form solution for the ith two-tap FIR filter
                              ~            ~
                             hi -1 (k - 1)hi -1 (k )
                  g i  - kS      ~2
                                  hi -1 (k - 1)
                                 kS




                                                                        50
                                Conventional Equalizer

   Divide-and-Conquer TEQ Cancellation (UNC)
• At ith iteration, minimize Ji over I
                ~T ~
                                      
          J i  h wallh wall   hi -1 k )sin  i  hi -1 k - 1) cos i ,
                                 ~                   ~                    2
                                                                               )
                                                            
                                kS

          S  1, 2,, D, D n  2,, Lh
                                      ~
                                                      i -1




• Closed-form solution

                                      a2                                   a2 
         sin  i   0.51  2                 , cos   0.51                  
                                  a  4b  2          i
                                                                                2 
                                                                           a  4b 
                                                                            2
                                                                    

                                         )
         a   hi -1 k ) - hi -1 k - 1) , b   hi -1 (k - 1) hi -1 (k )
                  ~2        ~2                     ~            ~
             kS                              kS



                                                                                       51
                           Conventional Equalizer

                Computational Complexity
• Computational complexity for each candidate D
          Method                                 Memory    G.DMT
                                                    (words)    ADSL
     Maximum             120379 118552        441      1899
                                                              Lh = 512
     SSNR
     DC-TEQ-mini-         53240     52980      60       563    n = 32
     mization (UTC)                                           Lw = 21
     DC-TEQ-can-          42280     42160      20       555
     cellation (UNC)
     DC-TEQ-can-          41000     40880      20       554
     cellation (UTC)
• Divide-and-conquer methods vs. maximum SSNR method
   – Reduces multiplications, additions, divisions, and memory
   – No matrix calculations (saves on memory accesses)
   – Avoids matrix inversion, and eigenvalue and Cholesky decompositions


                                                                           52
                                 Conventional Equalizer

        Heuristic Search for the Optimal Delay
• Estimate optimal delay D before computing TEQ taps
                                 energy inside a window of original h
            D ratio  arg max
                          D     energy outside a window of original h

• Total computational cost
   – Multiplications:   Lh
   – Additions:         3Lh - 3
   – Divisions:  Lh
• Performance of heuristic vs. exhaustive search
   – Reduce computational complexity by factor of 500
   – 2% loss in SSNR for TEQ with four taps or more
   – 8% loss in SSNR for two-tap TEQ


                                                                        53
                             Conventional Equalizer

               Comparison of Earlier Methods
Method                             MMSE               MSSNR     Geometric
                               Advantages
Maximize bit rate                                                  
Minimize ISI                                            
Bit Rate                        Low-medium             High    Low-medium
                             Disadvantages
Nonlinear optimization                                             
Computational complexity             Low              Medium      High
Artificial constraints                                            
Ad-hoc parameters                                                  
Lowpass frequency response                                        
Unrealistic assumptions                                            


                                                                            54
                   Conventional Equalizer

         MBR TEQ vs. Geometric TEQ
Method                               MBR       Geometric
                     Advantages
Maximize channel capacity                        
Minimize ISI                           
Bit rate                            optimal   Low-medium
                   Disadvantages
Low-pass frequency response                       
Computationally complex                          
Artificial constraints                            
Ad-hoc parameters                                 
Nonlinear optimization                           
Unrealistic assumptions                           

                                                           55
                               Conventional Equalizer

                 Min-ISI TEQ vs. MSSNR TEQ
           Method                                 Min-ISI   MSSNR
                                  Advantages
           Maximize channel capacity
           Minimize ISI                                      
           Frequency domain weighting                   
           Bit rate                     high                 high
                            Disadvantages
           Computationally complex    very high              high
  • Min-ISI weights ISI power with the SNR
      – Residual ISI power should be placed in high noise frequency bands
                                         1                  1
                                             0.1 SNR50 
                                      SNR50                      0.09
SNR i 
              signal power              10                10  1
        noise power  ISI power          1                  1
                                SNR 2       10 SNR2             0.9
                                        0.1               0.1  1     56
                              Conventional Equalizer

           Bit Rate vs. Cyclic Prefix (CP) Size
• Matched filter
  bound decreases
  because CP has no
  new information
• Min-ISI and MBR
  achieve bound with
  16-sample CP
• Other design
  methods are erratic
• MGSNR better for
  15-28 sample CPs
     TEQ taps (Lw)   17
     FFT size (N)    512         input power     23 dBm
     coding gain     4.2 dB      noise power     -140 dBm/Hz
     margin          6 dB        crosstalk noise 8 ADSL disturbers
                                                                     57
                           Conventional Equalizer

                      Simulation Results
• Min-ISI, MBR, and
  MSSNR achieve
  matched filter
  bound owith CP of
  27 samples
• Min-ISI with 13-
  sample CP beats
  MMSE with 32-
  sample CP
• MMSE is worst
      TEQ taps (Lw)   3
      FFT size (N)    512       input power     23 dBm
      coding gain     4.2 dB    noise power     -140 dBm/Hz
      margin          6 dB      crosstalk noise 8 ADSL disturbers
                                                                    58
                               Per-Tone Equalizer

                  Bit Allocation Comparison
• AWG 26 Loop:
  12000 ft + AWGN
Equalizer       Bit Rate
Per Tone      5.7134 Mbps
MBR           5.4666 Mbps
MSSNR         5.2903 Mbps
Min ISI       5.2586 Mbps
ARMA          4.5479 Mbps
MMSE          4.4052 Mbps

• Simulation
   – NEXT from 24 DSL disturbers
   – 32-tap equalizers: least squares training used for per-tone equalizer
                                                                             59
   Per-Tone Equalizer

Subchannel SNR




                        60
                                    Per-Tone Equalizer

         Frequency-Domain Per-Tone Equalizer
• Rearrange computation of FFT coefficient for tone i
  [Van Acker, Leus, Moonen, van de Wiel, Pollet, 2001]

                     Zi = Di rowi(QN ) Y w = rowi(QN Y) ( w Di )
   QN Y produces N  Lw complex-valued matrix produced by sliding FFT
   Zi is inner product of ith row of QN Y (complex) and w Di (complex)
   TEQ has been moved into FEQ to create multi-tap FEQ as linear combiner
• After FFT demodulation, each tone equalized separately
   Equalize each carrier independently of other carriers (N/2 carriers)
   Maximize bit rate at output of FEQ by maximizing subchannel SNR
• Sliding FFT to produce N  Lw matrix product QN Y
   Receive one ADSL frame (symbol + cyclic prefix) of N + n samples
   Take FFT of first N samples to form the first column
   Advance one sample
   Take FFT of N samples to form the second column, etc.
                                                                            61
                                            Per-Tone Equalizer

    Per-Tone Equalizer: Implementation Complexity
Conventional     Real MACs          Words               Parameter          Symbol     Value
TEQ                  Lw fs           2 Lw               Sampling rate        fs     2.208 MHz
FFT            2 N log2(N) fsym      4N                 Symbol rate         fsym      4 kHz
FEQ                4 Nu fsym         4 Nu               TEQ length           Lw       3-32

                                                        Symbol length        N         512
Per Tone        Real MACs              Words
                                                        Subchannels used     Nu        256
FFT            2 N log2(N) fsym      4N+2n
                                                        Cyclic prefix        n         32
Sliding FFT 2 (Lw – 1) N fsym               N           length
Combiner        4 Lw Nu fsym        2 (Lw + 1) Nu


Modified.        Real MACs                  Adds           Words
Per Tone
FFT             2 N log2(N) fsym                            4N

Differencing                           (Lw – 1) fsym       Lw – 1

Combiner       2 (Lw + 1) Nu fsym                         2 Lw Nu

                                                                                                62
                  Dual-Path Equalizer

Dual-Path TEQ (Simulated Channel)



                  Optimized for subchannel 2-250




 Optimized for subchannel 2-30




                                                   63
            Motorola CopperGold ADSL Chip
•   Announced in March 1998
•   5 million transistors, 144 pins, clocked at 55 MHz
•   1.5 W power consumption
•   DMT processor consists
    – Motorola MC56300 DSP core
    – Several application specific ICs
        • 512-point FFT
        • 17-tap FIR filter for time-domain channel equalization based on MMSE
          method (20 bits precision per tap)
• DSP core and memory occupies about 1/3 of chip area




                                                                                 64

								
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