Maximizing Data Rate of Discrete Multitone Systems Using Time Domain Equalization Design Miloš Milošević Committee Members Prof. Ross Baldick Prof. Gustavo de Veciana Prof. Brian L. Evans (advisor) Prof. Edward J. Powers Prof. Robert A. van de Geijn Ph.D. Defense

2 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 – MHz downstream (for broadcast), 5-42 MHz upstream –Data Over Cable Service Interface Specifications 2.0 (2002) Downstream 6.4 MHz channel: up to Mbps (shared) Upstream 6.4 MHz channel: up to Mbps (shared) StandardModulationData RateCarrier Single carrier2 Mbps2.4 GHz aMulticarrier54 Mbps5.2 GHz bSingle carrier11 Mbps2.4 GHz gMulticarrier54 Mbps2.4 GHz

4 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 leads 2 : 1 industry 3 : 1 consumer xDSLModulationData RateBand HDSLSingle1544 kbps (N.A.) 2320 kbps (Europe) 2 x 1168 kbps (Europe) 3 x 784 kbps (Europe) 193 kHz 580 kHz 292 kHz 196 kHz SDSLSingle  kbps <386 kHz ADSL (1998) Multicarrier <256 tones  6144 (8192) kbps down  786 (640) kbps up 1104 MHz ADSL Lite (1998) Multicarrier <128 tones  1536 kbps down  512 kbps up 552 kHz VDSL (2003) Single or Multicarrier <4092 tones  13 Mbps (N.A.) sym.  22/3 Mbps (N.A.) asym.  14.5 Mbps (N.A.) sym.  23/4 Mbps (N.A.) asym. 12 MHz (N.A.) - North America

5 DSL Broadband Access ATM - Asynchronous Transfer Mode DMT - Discrete Multitone DSLAM - Digital Subscriber Line Access Multiplexer LAN – Local Area Network PSTN - Public Switched Telephone Network Splitter DMT Modem Telephone Wireless Modem Home Hub Local Area Network Home Wireless LAN Splitter Voice Switch PSTN DSLAM ATM Switch Internet Router Set-top box Customer Premises Central Office downstream upstream PC

6 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 Serial-to- Parallel Converter M bits m n bits Encoding m 2 bits m 1 bits f1f1 f2f2 fnfn To physical medium Bit rate is M f symbol bits/s Transmit filter -f x fxfx

8 Discrete Multitone Transmitter Serial-to- Parallel QAM encoder Mirror data and N -IFFT Add Cyclic Prefix Digital-to-Analog Converter + Transmit Filter N/2 subchannels (complex-valued) Bits Parallel-to-Serial To Physical Medium N coefficients (real-valued) N + coefficients copy I Q symbol CP symbol CP CP: Cyclic Prefix FFT: Fast Fourier Transform QAM: Quadrature Amplitude Modulation : cyclic prefix length

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

10 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 Tx Symbol Rx Symbol * channel = CP Tx Symbol Rx Symbol * channel = * filter

11 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

12 TEQ time domain equalizer QAM decoder Frequency domain equalizer = invert channel N -FFT and remove mirrored data Discrete Multitone Receiver Remove Cyclic Prefix Receive Filter+ Analog-to-Digital Converter N/2 subchannels Bits Serial-to-Parallel From Physical Medium Parallel-to- Serial N coefficients N + coefficients

13 z-z- h + w b - x y e n + Minimize E{e T e} Error: e = x*b  - y*w Equalized channel: h*w Pick channel delay  and length of b  to shorten length of h*w Minimum mean squared error solution satisfies: Disadvantages Deep notches in shortened channel frequency response Long equalizer reduces bit rate Does not consider bit rate or noise Minimum Mean Squared Error Method | DFT {h*w}| Virtual path Chow & Cioffi, 1992

14 Maximum Shortening SNR Method Minimize energy leakage outside shortened channel length Disadvantages –Does not consider bit rate or channel noise –Long equalizer reduces bit rate –Requires generalized eigenvalue solution or Cholesky decomposition –Cannot shape TEQ according to frequency domain needs Yellow – leads to H wall Gray – leads to H win sample number Channel h (blue line) Melsa, Younce & Rohrs, 1996 DistortionSignal

15 Minimum ISI Method Extends Maximum Shortening SNR method –Adds frequency domain weighting of ISI –Weight according to subchannel SNR; favors high SNR subchannels –Does not minimize ISI in unused subchannels Minimizes weighted sum of subchannel ISI power under constraint that power of signal is constant q k is k th 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 Subchannel SNR Arslan, Kiaei & Evans, 2000

16 Dual-path Time Domain Equalizer Received signal passes through two parallel time domain equalizers –One time domain equalizer designed to minimize ISI over the system bandwidth –Other time domain equalizer designed for particular frequency band, e.g. by using Minimum Intersymbol Interference method Time domain equalizers are designed using sub-optimal methods FEQ – Frequency domain equalizer TEQ 1 TEQ 2 FFT Subchannel SNR Comparison FEQ Received Signal Ding, Redfern & Evans, 2002

17 Per-tone Equalizer Transfers time domain equalizer operations to frequency domain Combined complex multi- tap equalizer Each tone (subchannel) equalized separately Sliding N-point FFT y N+M-1 y N+M-2 y0y0 Z1Z1 Z2Z2 w1,0w1,0 w1,1w1,1 w i,M-1 0 w2,0w2,0 w2,1w2,1 w 2,M-1 0 w N/2,0 w N/2,1 w N/2,M-1 0 Z N/2 N+M-1 N/2 y – received symbol; M – subchannel equalizer length; w – complex equalizer; Z k – received subsymbol in subchannel k; Sliding FFT - efficient implementation of M fast Fourier transforms on M columns of convolution matrix of y with w Acker, Leus, Moonen, van der Wiel & Pollet, 2001

18 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

19 Interference-free Symbol at FFT Output FFT of circular convolution of channel and discrete multitone symbol in k th subchannel is the desired subsymbol in subchannel k at FFT output is desired symbol circular convolution matrix for delay  H is channel convolution matrix q k is k th column vector of N-length FFT matrix Received subsymbol in k th 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 D k is digital noise floor, which is not affected by TEQ Contribution #1

20 Model SNR at Output of Demodulator Proposed subchannel SNR model at demodulator output –Ratio of quadratic functions in equalizer coefficients w Bits per frame as a nonlinear function of equalizer taps. –Multimodal for more than two-tap w –Nonlinear due to log and flooring operations –Requires integer maximization –A k and B k are Hermitian symmetric Maximizing b int is an unconstrained optimization problem Contribution #1

21 Data Rate Optimal Filter Bank Find optimal time domain equalizer for every subchannel Generalized eigenvalue problem Bit rate of bank of optimal time domain equalizer filters Contribution #2

22 TEQ Filter Bank Filter Bank Equalizer Architecture Goertzel Filter Bank G0G0 G1G1 G N/2-1 y0y0 y1y1 y N/2-1 Y0Y0 Y1Y1 Y N/2-1 Frequency Domain Equalizer FEQ 0 FEQ 1 FEQ N/2-1 Z0Z0 Z1Z1 Z N/2-1 w0w0 w1w1 w N/2-1 x CP Received frame TEQinputDFT output Contribution #2

23 Advantages –Provides a new achievable upper bound on bit rate performance –Single FIR can only perform at par or worse –Supports different subchannel transmission delays –Can modify frequency and phase offsets in multiple carriers by adapting carrier frequencies of Goertzel filters –Easily accommodates equalization of groups of tones with a common filter with corresponding drop in complexity Disadvantages - computationally intensive –Requires up to N/2 generalized eigenvalue solutions during transceiver initialization –Requires up to N/2 single FIR and as many Goertzel filters Filter Bank Summary Contribution #2

24 Find single FIR that performs as well as the filter bank Maximizing b(w) more tractable than maximizing b int (w) Maximizer of b(w) may be the maximizer of b int (w) –Conjecture is that it holds true for 2- and 3-tap w –Hope is that it holds for higher dimensions Maximizing sum of ratios is an open research problem Data Rate Maximization Single FIR Design Contribution #3

25 Gradient-based optimization of b(w) –Find gradient root corresponding to a local maximum –Start with a good initial guess of equalizer taps w –No guarantee of finding global maximum of b(w) Initial guess: filter bank FIR w k opt resulting in highest b(w) Parameterize problem to make it easier to find desired root –H( ) is a convex, non-increasing function of vector –Solution reached when H( ) = 0 –Solution corresponds to local maximum closest to initial point Data Rate Maximization Single FIR Design Contribution #3

26 Equalizer Implementation Complexity Per tone equalizer and single FIR similar complexity Filter bank has high complexity Example shown N = 512 f symbol = 4 kHz f s =2.208 MHz M = 3  = 32 SubsystemMultiply/adds*Words/ symbol Single FIR FIR6.6e66 FFT36.9e62048 FEQ4.1e61024 Total46.7e63078 Filter Bank FIR1700e6771 Goertzel1000e62048 FEQ4.1e61024 Total2704.1e63843 Per Tone Equalizer FFT36.9e62112 Sliding FFT8.2e6512 Combiner12.3e61024 Total57.4e63648 f symbol – Symbol rate f s – Sample rate M – Equalizer length * – Calculations assume N/2 data populated subchannels

27 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 loopData Rate  opt TEQ Size Mbps Mbps Mbps Mbps Mbps Mbps Mbps Mbps3511

28 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 LS PTE – Least-squares Per-Tone Equalizer; UEC – Unit energy Constraint; UTC – Unit Tap Constraint CSA loopSingle FIRMin-ISILS PTEMMSE-UECMMSE-UTC 199.6%97.5%99.5%86.3%84.4% 299.6%97.3%99.5%87.2%85.8% 399.5%97.3%99.6%83.9%83.0% 499.3%98.2%99.1%81.9%81.5% 599.6%97.2%99.5%88.6%88.9% 699.5%98.3%99.4%82.7%79.8% 798.8%96.3%99.6%75.8%78.4% 898.7%97.5%99.2%82.6%83.6% Average 99.3%97.5%99.4%83.6%83.2%

29 Data Rate vs. Equalizer Filter Length CSA loop 2 data rates for different equalizer filter lengths –Standard ADSL parameters –NEXT modeled as 49 disturbers expanded

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

31 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 Bit Rate (Mbps) Transmission Delay - M=3 - M=10 - M=30

32 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 ( Data maximization single time domain equalizer –Achieves on average 99.3% of optimal filter bank performance –Outperforms state of the art Min-ISI by 2% and MMSE by 15% –Similar performance to least-squares per-tone equalizer

33 Future Work Further research into architectures where equalizers are assigned to spectral bands instead for each subchannel Possibility of integrating time domain equalization with the adjustment of Discrete Fourier Transform carrier frequencies to maximize subchannel SNR Adaptive and numerically inexpensive implementation of Min-ISI method that removes TEQ length constraint of the original method

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

35 Publications in Discrete 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 , Nov –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 , Nov