Per-Tone Algorithms for ADSL Transceivers PhD-students: Koen Vanbleu, Geert Ysebaert Supervisor: Marc Moonen {moonen, vanbleu, 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

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

4Introduction 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 Principles –Intro –DMT –Data model Equalization Echo RFI Crosstalk Conclusions ModemTime 56 Kbps Voice band modem 24 minutes 128 Kbps ISDN10 minutes 6 Mbps ADSL13 seconds 52 Mbps VDSL1.5 seconds

5Introduction 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 Upstream Downstream CustomerCentral 300 m6.4 Mbps52 MbpsVDSL 3 km640 Kbps6 MbpsADSL Line lengthUpDownFrequency band 1.1 MHz 8.8 MHz Principles –Intro –DMT –Data model Equalization Echo RFI Crosstalk Conclusions

6 Traditional telephony (POTS) still available over the same wire.Duplexing Assign different frequency bins to up- and downstream directions  Frequency Division Duplexing (FDD)  Overlap: Echo Cancellation (EC) f (kHz) POTSUPDOWNPOTS UP &DOWN DOWN f (kHz) e.g. ADSL Principles –Intro –DMT –Data model Equalization Echo RFI Crosstalk Conclusions

7 Discrete Multi Tone: Transmitter Re Im 2 bits Re Im 4 bits bitsData symbols (QAM)... P/S CP Cyclic Prefix 0 IFFT N -point IFFT modulation (Inverse Fast Fourier Transform) Principles –Intro –DMT –Data model Equalization Echo RFI Crosstalk Conclusions

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

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

10 Discrete Multi Tone: Interference Influence of the channel behind the FFT: Short channel: amplitude- en phase change for each tone separately Re Im Re Im Re Im 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 noisetransmitted data symbols IDFT-matrix received samples add cyclic prefixFIR channel synchronization delay function of Symbol length Prefix length Equalizer length Symbol period Principles –Intro –DMT –Data model Equalization Echo RFI Crosstalk Conclusions

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

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

14 TEQ: Channel Shortening 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 Principles Equalization –TEQ –Per Tone Echo RFI Crosstalk Conclusions

15 Per Tone Equalization (PTEQ) From TEQ to Equalization Per Tone [Van Acker] with Y an N x T Toeplitz matrix with received data samples The received data symbol for tone i after equalization is given by 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 S/P... PT-EQ: Structure Efficient calculation with `sliding FFT’ PTEQ-inputs: T successive FFT’s per DMT-symbol Cheap implementation using first FFT en T-1 real difference terms (t=2...T).... FFT N -punt FFT N -punt sliding T –taps filter w for each tone PT-EQ... i Principles Equalization –TEQ –Per Tone Echo RFI Crosstalk Conclusions

17 PTEQ: Structure... FFT N -punt... PTEQ... 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 w v ii Principles Equalization –TEQ –Per Tone Echo RFI Crosstalk Conclusions

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

19 PTEQ: Initialization Optimization of SNR with quadratic cost function per tone Direct initialization using channel and noise characteristics:  Optimal MMSE solution per tone  Too expensive 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

20Simulations x 10 6 Delay  Bitrate (bits/s) 32-taps PT-EQ 8-taps PT-EQ 32-taps TEQ 8-taps TEQ Comparison of PT-EQ and TEQ for 4km line, downstream Down: N =512, =32, Fs =2.2 MHz, tones Bitrate versus delay MMSE solution for PTEQ TEQ-init. with MMSE channel shortening with | b |=1 Principles Equalization –TEQ –Per Tone Echo RFI Crosstalk Conclusions

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

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

23 EC: Problem Formulation 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 DMT-rx hybrid echo-canceller Echo telephone line Principles Equalization Echo –Problem formulation –EC principle –PTEC RFI Crosstalk Conclusions

24 Principle of Echo Cancellation 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] FEQ N -IFFTCPP/S N -FFT CP S/P TEC TEQ hybride Principles Equalization Echo –Problem formulation –EC principle –PTEC RFI Crosstalk Conclusions

25 Per Tone Echo Cancellation (PTEC) 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 Principles Equalization Echo –Problem formulation –EC principle –PTEC RFI Crosstalk Conclusions

26 Per Tone Echo Cancellation (PTEC) N -FFTPTEC  -line with downsamp.  -line with downsamp. N -IFFTCPP/S N -FFTPTEQ  -line with downsamp.  -line with downsamp. Principles Equalization Echo –Problem formulation –EC principle –PTEC RFI Crosstalk Conclusions

27 PT-EC: Complexity 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 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

28Simulations 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 Principles Equalization Echo –Problem formulation –EC principle –PTEC RFI Crosstalk Conclusions

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

30 RFI interference problem 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. Principles Equalization Echo RFI –Problem formulation –WI-PTEQ Crosstalk Conclusions

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

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

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

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

35 Problem Formulation 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) Principles Equalization Echo RFI Crosstalk –Problem formulation –Principle –Receiver structure Conclusions

36 k DSL symbol blocks XT symbols k+1k+2 Non-integer relation between DSL and XT symbol rate Principles of Cyclostationarity 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 ) Principles Equalization Echo RFI Crosstalk –Problem formulation –Principle –Receiver structure Conclusions

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

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

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

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

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

42Conclusions 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) Principles Equalization Echo RFI Crosstalk Conclusions

43 Time-/frequency domain EC 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 N -IFFT hybridfreq. dom. EC CPP/S N -FFTCPS/P Time dom. EC TEQ FEQ Principles Equalization Echo –Problem formulation –EC principle –PTEC RFI Crosstalk Conclusions

44 Double talk problem N -IFFT hybrid CP N -FFT CP CESTEQ FEQ 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] Freq. EC Update 1/FEQ N -IFFT Principles Equalization Echo –Problem formulation –EC principle –PTEC RFI Crosstalk Conclusions