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Maximizing Bitrate: Time-Domain Equalizer Design for DMT-based Systems

This paper explores the design of time-domain equalizers for DMT-based systems to enhance bitrate efficiency. It covers ADSL and VDSL basics, equalizer design challenges, and solutions for maximizing bitrates. The evolution of broadband communication over telephone lines is examined, focusing on optimizing data transmission rates. Various equalization techniques are discussed, including minimizing channel distortion and optimizing frequency bins allocation. Key topics include CP noise reduction, channel shorteners, and approximations for bitrate maximization. The study concludes with insights on improving ADSL equalizers for enhanced performance.

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Maximizing Bitrate: Time-Domain Equalizer Design for DMT-based Systems

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  1. Bitrate Maximizing Time-Domain Equalizer Design for DMT-based Systems Koen Vanbleu Promotor: Marc Moonen Coauthors: Geert Ysebaert, Gert Cuypers, Katleen Van Acker KULeuven, ESAT SCD-SISTA, Belgium ICC 2003

  2. Overview • ADSL Basics • What? • Transmitter/Receiver • ADSL Equalizer Design • Problem Description • Current Equalizers • Bitrate Maximizing Equalizers • Conclusions

  3. Introduction • ADSL Basics • - Intro • - DMT Transmitter • - Why Equalization? • - DMT Receiver • ADSL Equalizer Design • - Problem Description • - Current Equalizers • - Bitrate Maximizing • Equalizers • Conclusions • Communication at high rates towards customer • telephone wire, cable, fiber, wireless • Communication over telephone wire • Evolution: ever increasing bitrates • E.g. Time to download 10 Mbyte file

  4. Introduction Down Up Line length ADSL 6 Mbps 640 Kbps 3 km VDSL 52 Mbps 6.4 Mbps 300 m Downstream Central Customer Upstream • ADSL Basics • - Intro • - DMT Transmitter • - Why Equalization? • - DMT Receiver • ADSL Equalizer Design • - Problem Description • - Current Equalizers • - Bitrate Maximizing • Equalizers • Conclusions • Broadband communication over telephone line • ADSL (Asymmetric Digital Subscriber Line) • VDSL (Very high bit rate Digital Subscriber Line) • Bitrate is function of the line length

  5. Modulation and Duplexing • Multicarrier modulation scheme: Discrete Multitone (DMT) e.g. ADSL UP &DOWN POTS UP DOWN POTS DOWN 4 25 138 1104 f (kHz) 4 25 138 1104 f (kHz) • ADSL Basics • - Intro • - DMT Transmitter • - Why Equalization? • - DMT Receiver • ADSL Equalizer Design • - Problem Description • - Current Equalizers • - Bitrate Maximizing • Equalizers • Conclusions • Assign different frequency bins to up- and downstream directions • Frequency Division Duplexing (FDD) • Overlap: Echo Cancellation (EC) • Traditional telephony (POTS) still available over the same wire.

  6. Discrete Multi Tone: Transmitter bits Data symbols (QAM) Cyclic Prefix CP Im 0 10 00 ... ... Re 11 01 2 bits N-point P/S Im IFFT Re ... ... 4 bits IFFT modulation (Inverse Fast Fourier Transform) • ADSL Basics • - Intro • - DMT Transmitter • - Why Equalization? • - DMT Receiver • ADSL Equalizer Design • - Problem Description • - Current Equalizers • - Bitrate Maximizing • Equalizers • Conclusions

  7. Why Equalization? CP noise ... ... channel N-point P/S IFFT ... ... Transmitter • ADSL Basics • - Intro • - DMT Transmitter • - Why Equalization? • - DMT Receiver • ADSL Equalizer Design • - Problem Description • - Current Equalizers • - Bitrate Maximizing • Equalizers • Conclusions Why equalization? “Invert” channel distortion while not boosting noise

  8. ADSL Basics • - Intro • - DMT Transmitter • - Why Equalization? • - DMT Receiver • ADSL Equalizer Design • - Problem Description • - Current Equalizers • - Bitrate Maximizing • Equalizers • Conclusions Discrete Multi Tone: Receiver Unbiased Frequency Domain Equalizer 1 tap / tone Data symbols Im bits 10 00 CP ... noise Re 11 01 ... 2 bits ... ... Im FEQ channel h TEQ w N-point S/P FFT Re Time Domain Equalizer taps 4 bits FFT demodulation CP length + 1

  9. DMT Equalization: Problem Description TEQ w CP where is hard with time-domain equalizer w • ADSL Basics • - Intro • - DMT Transmitter • - Why Equalization? • - DMT Receiver • ADSL Equalizer Design • - Problem Description • - Current Equalizers • - Bitrate Maximizing • Equalizers • Conclusions Im{X} 10 00 Re{X} T taps 1 tap/tone N-point 11 01 ... ... ... S/P FEQ Dn FEQ FFT 2 bits To maximize bitrate:

  10. Current ADSL Equalizers (1) noise Channel h TEQ w delay TIR b • ADSL Basics • - Intro • - DMT Transmitter • - Why Equalization? • - DMT Receiver • ADSL Equalizer Design • - Problem Description • - Current Equalizers • - Bitrate Maximizing • Equalizers • Conclusions • Channel shorteners, e.g. MMSE-based TEQ [Al-Dhahir, Cioffi] TIR = target impulse response of (CP-length+1) MMSE criterion  ADSL bitrate maximization

  11. Current ADSL Equalizers (2) T taps 1 tap/tone TEQ w N-point ... ... ... S/P FEQ Dn FFT CP Approximations! based on SNR at FFT output residual ISI/ICI noise • ADSL Basics • - Intro • - DMT Transmitter • - Why Equalization? • - DMT Receiver • ADSL Equalizer Design • - Problem Description • - Current Equalizers • - Bitrate Maximizing • Equalizers • Conclusions • Approximate Bitrate Maximizing TEQs [Al-Dhahir], [Evans] Maximize

  12. Current ADSL Equalizers (3) • ADSL Basics • - Intro • - DMT Transmitter • - Why Equalization? • - DMT Receiver • ADSL Equalizer Design • - Problem Description • - Current Equalizers • - Bitrate Maximizing • Equalizers • Conclusions • Approximate Bitrate Maximizing TEQs (continued) residual ISI/ICI noise Examples of approximations : • Signal component in SNR does not only depend on `windowed’ (shortened) channel impulse response • : do not forget DFT leakage (ICI)!

  13. Bitrate Maximizing Equalizers (1) TEQ w CP AND then = residual ISI/ICI+noise sources (XT, RFI, …) • ADSL Basics • - Intro • - DMT Transmitter • - Why Equalization? • - DMT Receiver • ADSL Equalizer Design • - Problem Description • - Current Equalizers • - Bitrate Maximizing • Equalizers • Conclusions T taps N-point ... ... ... S/P FEQ Dn FFT Maximize where

  14. Bitrate Maximizing Equalizers (2) • ADSL Basics • - Intro • - DMT Transmitter • - Why Equalization? • - DMT Receiver • ADSL Equalizer Design • - Problem Description • - Current Equalizers • - Bitrate Maximizing • Equalizers • Conclusions Exact bitrate maximizing (BM-)TEQ cost function • Nonlinear cost function in wonly with Anand Bn • tone dependent matrices • function of signal statistics • Recursive Gauss-Newton updating algorithm: • attains good local optimum • adaptivity (to track channel/noise changes) • however: high complexity

  15. Bitrate Maximizing Equalizers (3) • ADSL Basics • - Intro • - DMT Transmitter • - Why Equalization? • - DMT Receiver • ADSL Equalizer Design • - Problem Description • - Current Equalizers • - Bitrate Maximizing • Equalizers • Conclusions • Bitrate maximizing equalizers: • Bitrate maximizing (single) TEQ: NG = all used tones  nonlinear cost function • “Per group” equalization: BM-TEQ w per group SG of NG tones  nonlinear cost function • “Per tone” equalization: NG= 1 tone •  (advantageous) linear MMSE problem [Vanacker, Leus, Moonen] HIGHER BITRATE

  16. Bitrate Maximizing Equalizers (4) • ADSL Basics • - Intro • - DMT Transmitter • - Why Equalization? • - DMT Receiver • ADSL Equalizer Design • - Problem Description • - Current Equalizers • - Bitrate Maximizing • Equalizers • Conclusions Simulations Per-Tone Equalizer Bitrate Maximizing-TEQ MMSE-based TEQs Approx. Bitrate Max. TEQs

  17. Conclusions • ADSL Basics • - Intro • - DMT Transmitter • - Why Equalization? • - DMT Receiver • ADSL Equalizer Design • - Problem Description • - Current Equalizers • - Bitrate Maximizing • Equalizers • Conclusions • ADSL Equalizer Design • Truly Bitrate Maximizing Per-Group Equalizer • Time-Domain Equalizer (1 group of tones) • Per-Tone Equalizer (groups of 1 tone) • Recursive Gauss-Newton algorithm • Good local optimum • Complex

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