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Per-Tone Algorithms for ADSL Transceivers

Per-Tone Algorithms for ADSL Transceivers. PhD-students: Koen Vanbleu, Geert Ysebaert Supervisor: Marc Moonen Email: {moonen, vanbleu, ysebaert}@esat.kuleuven.ac.be Presentation: ftp://ftp.esat.kuleuven.ac.be/sista/ysebaert/presentations/ KULeuven, ESAT SCD-SISTA, Belgium. October 22, 2002.

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Per-Tone Algorithms for ADSL Transceivers

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  1. Per-Tone Algorithms for ADSL Transceivers PhD-students:Koen Vanbleu, Geert Ysebaert Supervisor:Marc Moonen Email:{moonen, vanbleu, ysebaert}@esat.kuleuven.ac.be Presentation:ftp://ftp.esat.kuleuven.ac.be/sista/ysebaert/presentations/ KULeuven, ESAT SCD-SISTA, Belgium October 22, 2002

  2. General Overview • Basic Principles • Per Tone Equalization • Per Tone Echo Cancellation • Per Tone Radio Frequency Interference (RFI) Mitigation • Per Tone Crosstalk Mitigation • Conclusions

  3. Overview • Principles • Equalization • Echo • RFI • Crosstalk • Conclusions • Basic Principles • Introduction • DMT • Transmitter structure • Receiver structure • Cyclic Prefix trick • Data Model

  4. Introduction • Principles • Intro • DMT • Data model • Equalization • Echo • RFI • Crosstalk • 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

  5. Introduction Down Up Line length ADSL 6 Mbps 640 Kbps 3 km VDSL 52 Mbps 6.4 Mbps 300 m Downstream Central Customer Upstream • Principles • Intro • DMT • Data model • Equalization • Echo • RFI • Crosstalk • 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

  6. Duplexing e.g. ADSL UP &DOWN POTS UP DOWN POTS DOWN 4 25 138 1104 f (kHz) 4 25 138 1104 f (kHz) • Principles • Intro • DMT • Data model • Equalization • Echo • RFI • Crosstalk • 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.

  7. 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) • Principles • Intro • DMT • Data model • Equalization • Echo • RFI • Crosstalk • Conclusions

  8. Discrete Multi Tone: Receiver Data symbols Im bits 1 tap / tone 10 00 Time Domain Equalizer CP ... Re 11 01 taps ... ... 2 bits ... Im FEQ TEQ N-point S/P FFT Re 4 bits FFT demodulation • Principles • Intro • DMT • Data model • Equalization • Echo • RFI • Crosstalk • Conclusions

  9. Discrete Multi Tone: Cyclic Prefix CP To demodulator To demodulator • Principles • Intro • DMT • Data model • Equalization • Echo • RFI • Crosstalk • Conclusions `short’ channel `long’ channel

  10. Influence of the channel behind the FFT: Short channel: amplitude- en phase change for each tone separately Discrete Multi Tone: Interference Im Im Im Re Re Re • Long channel: interference between data symbols of different tones and different symbol periods • Principles • Intro • DMT • Data model • Equalization • Echo • RFI • Crosstalk • Conclusions

  11. Data model FIR channel add cyclic prefix synchronization delay Symbol length Prefix length Equalizer length Symbol period IDFT-matrix • Principles • Intro • DMT • Data model • Equalization • Echo • RFI • Crosstalk • Conclusions received samples function of transmitted data symbols noise

  12. Overview • Principles • Equalization • Echo • RFI • Crosstalk • Conclusions • Equalization • “Pre FFT” Equalization • TEQ: several design algorithms • See talk Prof. B. Evans • “Post FFT” Equalization • Equalization Per Tone • Structure and Initialization

  13. Time Domain Equalization (TEQ) T taps 1 tap/tone N-point TEQ ... ... ... S/P FEQ FFT CP ... ... D- line with down samplers • Principles • Equalization • TEQ • Per Tone • Echo • RFI • Crosstalk • Conclusions Original structure of time domain equalizer + FEQs:

  14. TEQ: Channel Shortening • Principles • Equalization • TEQ • Per Tone • Echo • RFI • Crosstalk • Conclusions • Channel Shortening [Al-Dhahir, Cioffi, Evans, Melsa, …] • Finding `optimal’ TEQ leads to non-linear optimization • Most channel shortening schemes are not equivalent to bitrate optimization • Resulting bitrate is often sensitive to synchronization delay • All tones are equalized in the same way  limited capacity • Limited memory: T-taps TEQ and 1-taps FEQ per used tone

  15. Per Tone Equalization (PTEQ) • From TEQ to Equalization Per Tone [Van Acker] The received data symbol for tone i after equalization is given by with Y an NxT Toeplitz matrix with received data samples After applying the associativity of the matrix product, we get Equalization Per Tone (PT-EQ) • Principles • Equalization • TEQ • Per Tone • Echo • RFI • Crosstalk • Conclusions

  16. PT-EQ: Structure S/P ... ... sliding ... PT-EQ ... N-punt FFT N-punt ... ... T –taps filter w for each tone FFT i • PTEQ-inputs: T successive FFT’s per DMT-symbol • Efficient calculation with `sliding FFT’ • Cheap implementation using first FFT en T-1 real difference terms (t=2...T). • Principles • Equalization • TEQ • Per Tone • Echo • RFI • Crosstalk • Conclusions

  17. PTEQ: Structure ... ... ... N-punt ... ... PTEQ ... FFT T –taps filter v for each tone i • PTEQ=linear combiner with T inputs per tone: 1 FFT-output and T-1 real difference terms wv i i • Principles • Equalization • TEQ • Per Tone • Echo • RFI • Crosstalk • Conclusions

  18. PTEQ: Complexity TEQ and FEQ PTEQ O(Fs(T+1/2)+NlogN) O(Fs(T+1)+NlogN) (multiplications) • Principles • Equalization • TEQ • Per Tone • Echo • RFI • Crosstalk • Conclusions • Complexity during data transmission is comparable with TEQ-complexity for the sameT: • TEQ • 1 (real) T-taps TEQ @ sample frequency Fs • 1 FFT operation @ symbol frequency Fs/(N+n) • (complex) 1-taps FEQ/used tone @ Fs/(N+n) • PTEQ • 1 FFT operation @ Fs/(N+n) • (complex) T-taps PTEQ/used tone @ Fs/(N+n) • Complexity reductions are possible by varying T per tone. • PTEQ requires more memory than TEQ.

  19. PTEQ: Initialization • Adaptive initialization using training sequence minimization of the sum of quadratic errors • with LMS: convergence too slow • with RLS: fast convergence, very complex • with combination of RLS and LMS: fast convergence, lower complexity than full RLS [Ysebaert] • Principles • Equalization • TEQ • Per Tone • Echo • RFI • Crosstalk • Conclusions • Optimization of SNR with quadratic cost function per tone • Direct initialization using channel and noise characteristics: • Optimal MMSE solution per tone • Too expensive

  20. Simulations 6 x 10 3.5 3 2.5 2 Bitrate (bits/s) 1.5 1 0.5 0 -40 -30 -20 -10 0 10 20 30 Delayd 32-taps PT-EQ 8-taps PT-EQ 32-taps TEQ 8-taps TEQ • Principles • Equalization • TEQ • Per Tone • Echo • RFI • Crosstalk • Conclusions Comparison of PT-EQ and TEQ for 4km line, downstream • Down: • N=512, n=32, • Fs=2.2 MHz, • tones 39-256 • Bitrate versus delay • MMSE solution for PTEQ • TEQ-init. with MMSE channel shortening with |b|=1

  21. Simulations • Principles • Equalization • TEQ • Per Tone • Echo • RFI • Crosstalk • Conclusions Adaptive initialization T1.601#13line+24DSL NEXT, downstream • Bitrate as a function of the number of training symbols for PT-EQ • T=32, d=-8

  22. Overview • Principles • Equalization • Echo • RFI • Crosstalk • Conclusions • Echo cancellation (EC) • Problem formulation • Principles of EC • Echo cancellation per tone (PTEC)

  23. EC: Problem Formulation echo-canceller • Principles • Equalization • Echo • Problem formulation • EC principle • PTEC • RFI • Crosstalk • Conclusions • Hybrid couples transmitter and receiver to the same line • Imperfectly balanced hybrid can cause leakage (echo) of the transmitted signal into the received signal. • Solutions: • Assign different frequencies for transmitted and received signal (FDD). • Cancel the echo (EC). DMT-tx hybrid telephone line Echo DMT-rx

  24. Principle of Echo Cancellation N-IFFT N-FFT CP CP P/S TEC hybride FEQ S/P TEQ • Principles • Equalization • Echo • Problem formulation • EC principle • PTEC • RFI • Crosstalk • Conclusions • Echo canceller has 2 tasks: • Modeling the echo path (adaptively). • Remove the estimate of the echo signal from the received signal. • Original approaches: - time domain EC (TEC) - mixed time/frequency EC [Ho, Cioffi]

  25. Per Tone Echo Cancellation (PTEC) • Principles • Equalization • Echo • Problem formulation • EC principle • PTEC • RFI • Crosstalk • Conclusions • Structure [Van Acker] • Starting point: modem with equalization and echo cancellation in time domain (TEQ en TEC). • This structure is modified analogously to `TEQ to PT-EQ conversion’, i.e. TEQ and TEC are shifted behind FFT. • Goal: bitrate optimization

  26. Per Tone Echo Cancellation (PTEC) PTEC N-FFT N-IFFT N-FFT CP P/S D-line with downsamp. D-line with downsamp. D-line with downsamp. D-line with downsamp. PTEQ • Principles • Equalization • Echo • Problem formulation • EC principle • PTEC • RFI • Crosstalk • Conclusions

  27. PT-EC: Complexity • Cost function • Cost function contains optimal joint shortening per tone • SNR per tone is maximized PT-EC PT-EQ • Principles • Equalization • Echo • Problem formulation • EC principle • PTEC • RFI • Crosstalk • Conclusions • Complexity of PT-EC filtering • Similar to time domain EC (for same filter length) • Optimization of filter length per tone • Extra FFT-operation on echo reference signal

  28. Simulations 6 x 10 3.4 3.2 3 2.8 Bitrate (bits/s) 2.6 2.4 2.2 2 0 50 100 150 200 250 T E 32-taps PTEQ 2*16-taps PTEQ 32-taps PTEQ, no echo 2*16-taps PTEQ, no echo • Principles • Equalization • Echo • Problem formulation • EC principle • PTEC • RFI • Crosstalk • Conclusions Echo cancellation per tone for 4 km line, downstream • FDM with tx- and rx-filters of low order • Bitrate as a function of the length of the echo filter (PT-EC) • Comparable with 400 taps time domain EC

  29. Overview • Principles • Equalization • Echo • RFI • Crosstalk • Conclusions • Radio frequency interference mitigation • Problem definition • Receiver structure (in brief) Window incorporated PTEQ (WI-PTEQ) • Simulation results

  30. RFI interference problem • Principles • Equalization • Echo • RFI • Problem formulation • WI-PTEQ • Crosstalk • Conclusions • Downstream band overlaps with e.g. AM broadcast bands which causes narrowband interference. • Contrary to popular belief: affects lots of tones • Reason? High DFT filter bank side lobes. • Solution? Windowing functions.

  31. PTEQ + windowing: Structure [Cuypers] • Principles • Equalization • Echo • RFI • Problem formulation • WI-PTEQ • Crosstalk • Conclusions

  32. Simulation results • Principles • Equalization • Echo • RFI • Problem formulation • WI-PTEQ • Crosstalk • Conclusions • Nice gain for low number of taps • ADSL T1.601#13 standard loop • RFI at 630, 740, 800, 980, 1100, 1160, 308 kHz

  33. Overview • Principles • Equalization • Echo • RFI • Crosstalk • Conclusions • Per tone alien crosstalk mitigation • Problem definition • Principles of cyclostationarity • Receiver structure PTEQ combined with FRESH filtering • Simulation results

  34. Problem Formulation: Per-tone Alien Crosstalk Mitigation TX TX TX TX Near-end XT User 1 RX RX RX RX Far-endXT Desired User 2 Binder Remote terminals Central office • Principles • Equalization • Echo • RFI • Crosstalk • Problem formulation • Principle • Receiver structure • Conclusions • Crosstalk (XT)

  35. Problem Formulation • Principles • Equalization • Echo • RFI • Crosstalk • Problem formulation • Principle • Receiver structure • Conclusions • Crosstalk (XT): reduces the SNR in each frequency bin • Crosstalk types: • Self XT: caused by other ADSL systems • Alien XT: caused by copper wire transmission systems with different modulation scheme occupying (partially) same frequency band • Alien crosstalk examples: • in ADSL: HDSL and SDSL XT (baseband) • in VDSL: HPNA (QAM passband)

  36. Principles of Cyclostationarity DSL symbol blocks k k+1 k+2 XT symbols Non-integer relation between DSL and XT symbol rate • Principles • Equalization • Echo • RFI • Crosstalk • Problem formulation • Principle • Receiver structure • Conclusions • What makes alien XT particular? •  Sampling offset between DSL and XT changes from DSL block to block • XT “nonstationary”, i.e. time varying, w.r.t. DSL symbol rate • Processing varies from DSL block to block? • No: exploit XT cyclostationarity(*) in “frequency domain” ((*) with large period: e.g. 100s of symbols)

  37. Principles of Cyclostationarity PSD(f) EBW EBW f -fs -fs/2 fs fs/2 Same information about signal! • Principles • Equalization • Echo • RFI • Crosstalk • Problem formulation • Principle • Receiver structure • Conclusions • Received PSD of cyclostationary signals with excess bandwidth (EBW) • E.g. SDSL XT, symbol rate of fs=1.04MHz, 100% EBW Determined by pulse shape and channel

  38. Principles of Cyclostationarity uncorrelated correlated PSD(f) y’ = + shiftedADSL EBW f fs/2 fs • Principles • Equalization • Echo • RFI • Crosstalk • Problem formulation • Principle • Receiver structure • Conclusions • Mitigate the cyclostationary SDSL from a received signal y PSD(f) y = + ADSL EBW f fs fs/2 by optimal combined filtering of y and frequency shifted version y’ (shift = fs) [Gardner]

  39. Receiver Structure XT canceller CP Overall structure = time varying time invariant filters • Principles • Equalization • Echo • RFI • Crosstalk • Problem formulation • Principle • Receiver structure • Conclusions • From classical TEQ to TEQ with alien crosstalk mitigation: 1 tap/tone N-points ... ... ... S/P FFT FEQ TEQ • Only prior knowledge required: fs=crosstalker symbol rate

  40. Per-Tone Receiver for Alien Crosstalk Mitigation N-FFT N-FFT XT canceller D-line with downsamp. D-line with downsamp. D-line with downsamp. D-line with downsamp. • Principles • Equalization • Echo • RFI • Crosstalk • Problem formulation • Principle • Receiver structure • Conclusions • From “pre-FFT” to “post-FFT” (cfr. from TEQ to PTEQ) PTEQ

  41. Simulation Results • Principles • Equalization • Echo • RFI • Crosstalk • Problem formulation • Principle • Receiver structure • Conclusions • Bitrate as a function of loop length (26AWG loops) • SDSL crosstalker • Up to 100 % gain around 3000m

  42. Conclusions • Principles • Equalization • Echo • RFI • Crosstalk • Conclusions • Evolution in equalization • TEQ: Simple initialization, low memory requirements, little relation with bit rate, unpredictable behaviour • PTEQ: Optimize SNR per tone, comparable complexity, high memory requirements • Per tone echo canceling • PTEC: Optimize SNR per tone, apply the same trick as for PTEQ • Radio frequency interference • Solution based on PTEQ + windowing (WI-PTEQ) • Crosstalk mitigation • Solution based on PTEQ + FREquency SHift PTEQ (FRESH)

  43. Time-/frequency domain EC N-IFFT N-FFT CP CP P/S Time dom. EC hybrid freq. dom. EC FEQ TEQ S/P • Principles • Equalization • Echo • Problem formulation • EC principle • PTEC • RFI • Crosstalk • Conclusions • Time-/frequency domain EC [Ho, Cioffi] • Adaptation of EC filter: in frequency domain • Removing echo: partially in time- and frequency domain • Efficient implementation of time domain EC

  44. Double talk problem N-IFFT N-IFFT Freq. EC Update CES hybrid FEQ 1/FEQ N-FFT TEQ • Principles • Equalization • Echo • Problem formulation • EC principle • PTEC • RFI • Crosstalk • Conclusions • Far end signal causes excess MSE in EC coefficient update • LMS step size has to be lowered to average out far end signal  reduced convergence speed = double talk problem • Solution: cancellation of far end signal prior to EC update [Ysebaert] C P CP

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