1、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,UT graduate students: Mr. Zukang Shen, Mr. Daifeng Wang, Mr. Ian Wong UT Ph.D. graduates: Dr. Gner Arslan (Silicon Labs), D
2、r. Biao Lu (Schlumberger), Dr. Ming Ding (Bandspeed), Dr. Milos Milosevic (Schlumberger) UT senior design students: Wade Berglund, Jerel Canales, David J. Love, Ketan Mandke, Scott Margo, Esther Resendiz, Jeff Wu Other collaborators: Dr. Lloyd D. Clark (Schlumberger), Prof. C. Richard Johnson, Jr. (
3、Cornell), Prof. Sayfe Kiaei (ASU), Prof. Rick Martin (AFIT), Prof. Marc Moonen (KU Leuven), Dr. Lucio F. C. Pessoa (Motorola), Dr. Arthur J. Redfern (Texas Instruments),Last modified August 8, 2005,2,Digital Subscriber Line (DSL) Broadband Access,Customer Premises,downstream,upstream,Voice Switch,Ce
4、ntralOffice,DSLAM,DSL modem,DSL modem,LPF,LPF,Internet,DSLAM - Digital Subscriber Line Access Multiplexer LPF Lowpass Filter (passes voiceband frequencies),Telephone Network,Introduction,3,Discrete Multitone (DMT) DSL Standards,ADSL Asymmetric DSL Maximum data rates supported in G.DMT standard (idea
5、l 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:cab
6、le modem market 1:2 in US & 2:1 worldwide ADSL+ 8 Mbps downstream min. ADSL2 doubles analog bandwidth VDSL Very High Rate DSL Asymmetric Faster G.DMT FDM ADSL 2m subcarriers m 8, 12 Symmetric: 13, 9, or 6 Mbps Optional 12-17 MHz band,2003,2003,2003,1997,Introduction,4,Outline,Multicarrier modulation
7、 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, Be
8、lgium Dual-path equalizer UT Austin Conclusion,5,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 freque
9、ncies Continuous time: Discrete time: Equalizer Shortens channel impulse response (time domain) Compensates for frequency distortion (frequency domain),g dk-D,Discretized Baseband System,g d(t-T),Multicarrier Modulation,6,Multicarrier Modulation,Divide channel into narrowband subchannels No inter-sy
10、mbol interference (ISI) in subchannels if constant gain within every subchannel and if ideal sampling Discrete multitone modulation Baseband transmission Based on fast Fourier transform (FFT) Standardized for ADSL and VDSL,subchannel,frequency,magnitude,carrier,DTFT-1,pulse,sinc,w,k,wc,-wc,channel,S
11、ubchannels are 4.3 kHz wide in ADSL and VDSL,Multicarrier Modulation,7,Multicarrier Modulation by Inverse FFT Filter Bank,x,x,x,+,g(t),g(t),g(t),x,x,x,+,Discrete time,g(t) : pulse shaping filter Xi : ith subsymbol from encoder,Multicarrier Modulation,8,Discrete Multitone Modulation Symbol,N/2 subsym
12、bols are in general complex-valued ADSL uses 4-level Quadrature Amplitude Modulation (QAM) during training ADSL uses QAM of 22, 23, 24, , 215 levels during data transmission Multicarrier modulation using inverse FFT,In-phase,Quadrature,QAM,N-point Inverse Fast Fourier Transform,X1,X2,X1*,x0,x1,x2,xN
13、-1,X2*,XN/2,X0,Multicarrier Modulation,Xi,Mirror and conjugate N/21 complex subsymbols,Yields one symbol of N real-valued samples,9,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
14、last n samples of the symbolCP reduces throughput by factor of Linear convolution of frame with 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 effe
15、ctive channel length and ISI,N samples,v samples,CP,CP,s y m b o l i,s y m b o l i+1,copy,copy,Multicarrier Modulation,10,Eliminating ISI in Discrete Multitone Modulation,Time domain equalizer (TEQ) Finite impulse response (FIR) filter Effective channel impulse response: convolution of TEQ impulse r
16、esponse with channel impulse response Frequency domain equalizer (FEQ) Compensates magnitude/phase distortion of equalized channel by dividing each FFT coefficient by complex number Generally updated during data transmission ADSL G.DMT equalizer training Reverb: same symbol sent 1,024 to 1,536 times
17、 Medley: aperiodic pseudo-noise sequence of 16,384 symbols Receiver returns number of bits (0-15) to transmit each subchannel i,Multicarrier Modulation,11,P/S,QAM demod decoder,invert channel = frequency domain equalizer,S/P,quadrature amplitude modulation (QAM) encoder,mirror data and N-IFFT,add cy
18、clic prefix,P/S,D/A + transmit filter,N-FFT and remove mirrored data,S/P,remove cyclic prefix,TRANSMITTER,RECEIVER,N/2 subchannels,N real samples,N real samples,N/2 subchannels,time domain equalizer (FIR filter),receive filter + A/D,channel,ADSL Transceiver: Data Transmission,Bits,00110,conventional
19、 ADSL equalizer structure,Multicarrier Modulation,12,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 Interferenc
20、e design (near-optimal) UT Austin Per-tone equalizer Dual-path equalizer Conclusion,13,Minimize Eek2 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 channel-dependent matrix Minimum MSE when where Disadvantages Does not
21、consider bit rate Deep notches in equalized frequency response,Minimum Mean Squared Error TEQ Design,z-,h,+,w,b,-,xk,yk,ek,rk,nk,+,bk-D,TEQ,Channel,Conventional Equalizer,Why?,Rxy is cross correlation matrix,14,Infinite Length MMSE TEQ Analysis,As TEQ length goes to infinity, RD becomes Toeplitz Mar
22、tin 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 Each trace is a different zero of b Distance of 32 zeros of b to unit circle averaged over
23、 8 ADSL test channels for each TEQ length Zeros cluster at 0.01 and 10-4 from UC for TEQ lengths 32 and 100,Longer MMSE TEQ may be worse,Conventional Equalizer,15,Maximum Shortening SNR TEQ Design,Minimize energy leakage outside shortened channel length For each possible position of window Melsa, Yo
24、unce & Rohrs, 1996Equivalent to noise-free MMSE TEQ Disadvantages Does not consider channel noise Does not consider bit rate Deep notches in equalized frequency response (zeros of target impulse response near unit circle kill subchannels) Requires Cholesky decomposition, which is computationally-int
25、ensive and does not allow TEQ lengths longer than cyclic prefix,Conventional Equalizer,16,Maximum Shortening SNR TEQ Design,hwin, hwall : equalized channel within and outside the window Objective function is shortening SNR (SSNR),Choose w to minimize energy outside window of desired length Locate wi
26、ndow to capture maximum channel impulse response energy,Cholesky decomposition of B to find eigenvector for minimum generalized eigenvalue of A and B,Conventional Equalizer,17,Modeling Achievable Bit Rate,Bit allocation bounded by subchannel SNRs: log(1 + SNRi / Gi) Model ith subchannel SNR Arslan,
27、Evans & Kiaei, 2001Divide numerator and denominator of SNRi by noise power spectral density Sn,i,Conventional subchannel SNRi,Used in Maximum Bit Rate Method,Used in Minimum ISI Method,Conventional Equalizer,18,Maximum Bit Rate (MBR) TEQ Design,Subchannel SNR as nonlinear function of equalizer taps
28、wMaximize nonlinear function of bits/symbol with respect to wGood performance measure for comparison of TEQ design methods Not an efficient TEQ design method in computational sense,qi is ith row of DFT matrix,Fractional bits for optimization,Conventional Equalizer,19,Minimum-ISI (Min-ISI) TEQ Design
29、,Rewrite subchannel SNR Arslan, Evans & Kiaei, 2001Generalize MSSNR method by weighting ISI in frequency Minimize frequency weighted sum of subchannel ISI power Penalize ISI power in high conventional SNR subchannels: Constrain signal path gain to one to prevent all-zero solution for w Solution is e
30、igenvector 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,ISI power weighted in frequency domain
31、 by inverse of noise spectrum,Conventional Equalizer,20,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)
32、Per-tone equalizer Catholic University, Leuven, Belgium Dual-path equalizer Conclusion,21,Drawbacks to Using Single FIR Filter for TEQ,Conventional equalizerEqualizes all tones in combined fashion: may limit bit rate Output of conventional equalizer for tone i computed using sequence of linear opera
33、tions Zi = Di rowi(QN ) Y w Di is the complex scalar value of one-tap FEQ for tone i 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,Y w represents convolution,Per-Tone Equalizer,22,Frequency-Domai
34、n 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,Per-Tone Equalizer,23,Outline,Multi
35、carrier 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,24,Dual-P
36、ath 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-divisio
37、n multiplexed ADSL Minimum ISI method is good match for second FIR TEQPath 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,Dual-Path Equalizer,25,Simulation Results for 17-Tap Equalizers,
38、Parameters Cyclic prefix length 32 FFT size (N) 512 Coding gain (dB) 4.2 Margin (dB) 6 Input power (dBm) 23 Noise power (dBm/Hz)-140 Crosstalk noise 24 ISDN disturbers,Figure 1 in Martin, Vanbleu, Ding, Ysebaert, Milosevic, Evans, Moonen & Johnson, Oct. 2005,Downstream transmission,Simulation Result
39、s,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,Carrier serving area (CSA) test loop,Bit rate (Mbps),26,Simulation Results for 17-Tap Equalizers,Parameters Cyclic prefix length 32 FFT size (N) 512 Coding
40、 gain (dB) 4.2 Margin (dB) 6 Input power (dBm) 23 Noise power (dBm/Hz)-140 Crosstalk noise 24 ISDN disturbers,Figure 3 in Martin, Vanbleu, Ding, Ysebaert, Milosevic, Evans, Moonen & Johnson, Oct. 2005,Downstream transmission,MDR is Maximum Data Rate design method Milosevic et al., 2002,BM-TEQ is Bit
41、 Rate Maximizing design method Vanbleu et al., 2003,PTEQ is Per Tone Equalizer structure and design method Acker et al., 2001,Simulation Results,Carrier Serving Area (CSA) Test Loop,Bit Rate (Mbps),27,Estimated Computational Complexity,Simulation Results,Equalizer Design Algorithm,Computational Comp
42、lexity in 10 log10(MACs),MAC means a multiplication-accumulation operation,28,Achievable Bit Rate vs. Delay Parameter,Simulation Results,Large plateau of near-optimal delays (optimal choice requires search) One choice is to set the delay parameter equal to cyclic prefix length,Delay Parameter D for
43、CSA Test Loop 4,Bit rate (Mbps),29,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 G
44、eneralizes 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 TMS320C5000New dual-path time-domain equalizer Achieves bit r
45、ates between conventional and per tone equalizers Lower implementation complexity in training than per tone equalizers Enables reuse of ASIC designs,http:/www.ece.utexas.edu/bevans/projects/adsl,Conclusion,30,Single-path, dual-path, per-tone & TEQ filter bank equalizers Available at http:/www.ece.ut
46、exas.edu/bevans/projects/adsl/dmtteq/,Matlab DMTTEQ Toolbox 3.1,various performance measures,default parameters from G.DMT ADSL standard,different graphical views,-140,23,Conclusion,18 design methods,Backup Slides,32,Residential,Business,Applications of Broadband Access,Introduction,33,Selected DSL
47、Standards,Courtesy of Shawn McCaslin (National Instruments, Austin, TX),Introduction,34,Discrete Multitone DSL Standards,Discrete multitone (DMT) modulation uses multiple carriers ADSL Asymmetric DSL (G.DMT) Asymmetric: 8 Mbps downstream and 1 Mbps upstream Data band: 25 kHz 1.1 MHz Maximum data rat
48、es possible in standard (ideal case) Echo cancelled: 14.94 Mbps downstream, 1.56 Mbps upstream Frequency division multiplexing: 13.38 Mbps downstream, 1.56 Mbps up Widespread deployment in US, Canada, Western Europe, Hong Kong Central office providers only installing frequency-division ADSL ADSL mod
49、ems have about 1/3 of market, and cable modems have 2/3 VDSL Very High Rate DSL Asymmetric: either 22/3 or 13/3 Mbps downstream/upstream Symmetric: 13, 9, or 6 Mbps each direction Data band: 1 12 MHz DMT and single carrier modulation supported DMT VDSL essentially higher speed version of G.DMT ADSL,
