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On the Relation Between Time-Domain Equalizers and Per-Tone Equalizers for DMT-Based Systems Koen Vanbleu, Geert Ysebaert, Gert Cuypers, Marc Moonen Katholieke Universiteit Leuven, ESAT/SCD-SISTA, Belgium April 16, 2004 IEEE Benelux Signal Processing Symposium Hilvarenbeek, the Netherlands

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Koen Vanbleu, Geert Ysebaert, Gert Cuypers, Marc Moonen Katholieke Universiteit Leuven, ESAT/SCD-SISTA, Belgium April 16, 2004 IEEE Benelux Signal Processing Symposium Hilvarenbeek, the Netherlands On Equalization Alternatives and their Relations for ADSL Modems

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3Overview ADSL Basics What? Multicarrier modulation Transmitter/Receiver ADSL Equalizer Design Problem Description Current Equalizers (TD-MMSE) Bit rate Maximizing Equalizers (FD-MMSE criterion) Relations

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4Introduction Communication at high rates towards customer telephone wire, cable, fiber, wireless Communication over telephone wire Evolution: ever increasing bit rates E.g. Time to download 10 Mbyte file ModemTime 56 Kbps Voice band modem 24 minutes 128 Kbps ISDN10 minutes 6 Mbps ADSL13 seconds 52 Mbps VDSL1.5 seconds ADSL Basics - Intro - DMT Transmitter - Why Equalization? - DMT Receiver ADSL Equalizer Design - Problem Description - Current Equalizers - Bit rate Maximizing Equalizers - Relations

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5Introduction Broadband communication over telephone line ADSL (Asymmetric Digital Subscriber Line) ADSL2 / ADSL2+ (Second-Generation ADSL) VDSL (Very high bit rate Digital Subscriber Line) Bit rate is function of the line length Upstream Downstream CustomerCentral ADSL Basics - Intro - DMT Transmitter - Why Equalization? - DMT Receiver ADSL Equalizer Design - Problem Description - Current Equalizers - Bit rate Maximizing Equalizers - Relations DownUpLine lengthFrequency band ADSL6 Mbps640 kbps3.7 km1.1 MHz ADSL2+15 Mbps1.5 Mpbs1.8 km2.2 MHz VDSL52 Mbps2.3 Mbps< 1 km12 MHz

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6 Traditional telephony (POTS) still available over the same wire. Multicarrier Modulation Assign different frequency bins to up- and downstream directions f (kHz) POTSUPDOWN 4251381104 e.g. ADSL Digital multicarrier modulation scheme: Discrete Multitone (DMT) ADSL Basics - Intro - DMT Transmitter - Why Equalization? - DMT Receiver ADSL Equalizer Design - Problem Description - Current Equalizers - Bit rate Maximizing Equalizers - Relations

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7 Discrete Multitone: Transmitter... P/S CP Cyclic Prefix ADSL Basics - Intro - DMT Transmitter - Why Equalization? - DMT Receiver ADSL Equalizer Design - Problem Description - Current Equalizers - Bit rate Maximizing Equalizers - Relations 00 11 10 01 Re Im 2 bits Re Im 4 bits bitsData symbols (QAM) 0 IDFT N -point............... IDFT modulation (Inverse Discrete Fourier Transform) Block transmission!

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8 Why Equalization? channel noise... P/S CP IDFT N -point............... Transmitter Why equalization? “Invert” channel distortion while not boosting noise ADSL Basics - Intro - DMT Transmitter - Why Equalization? - DMT Receiver ADSL Equalizer Design - Problem Description - Current Equalizers - Bit rate Maximizing Equalizers - Relations

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9 Discrete Multitone: Receiver 00 11 10 01 Re Im 2 bits Re Im 4 bits bits Data symbols channel h noise ADSL Basics - Intro - DMT Transmitter - Why Equalization? - DMT Receiver ADSL Equalizer Design - Problem Description - Current Equalizers - Bit rate Maximizing Equalizers - Relations CP length + 1... S/P CP...... DFT N -point DFT demodulation...... Frequency Domain Equalizer 1 tap / tone x x x TEQ w taps Time Domain Equalizer

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10 DMT Equalization: Problem Description S/P CP... DFT FEQ TEQ w T taps... 1 tap/tone N -point To maximize bit rate: 00 11 10 01 Re Im 2 bits ADSL Basics - Intro - DMT Transmitter - Why Equalization? - DMT Receiver ADSL Equalizer Design - Problem Description - Current Equalizers - Bit rate Maximizing Equalizers - Relations FEQ is hard with time-domain equalizer w where Residual ISI/ICI Noise (RFI/XT/etc.)

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11 Current ADSL Equalizers ADSL Basics - Intro - DMT Transmitter - Why Equalization? - DMT Receiver ADSL Equalizer Design - Problem Description - Current Equalizers - Bit rate Maximizing Equalizers - Relations Channel shorteners e.g. time-domain MMSE-TEQ design Channel h noise No bit rate optimization! CP length + 1 TEQ w Constrained linear least-squares based MMSE-TEQ TIR = target impulse response of (CP-length+1) delay TIR b -

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12 Bit rate Maximizing Equalizers: Per-tone equalization ADSL Basics - Intro - DMT Transmitter - Why Equalization? - DMT Receiver ADSL Equalizer Design - Problem Description - Current Equalizers - Bit rate Maximizing Equalizers Per-tone equalization BM-TEQ - Relations DFT N -point TEQ w taps Time Domain Equalizer...... x x x FEQ............

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13 Bit rate Maximizing Equalizers: Per-tone equalization S/P... DFT N -point DFT N -point sliding PTEQ... ADSL Basics - Intro - DMT Transmitter - Why Equalization? - DMT Receiver ADSL Equalizer Design - Problem Description - Current Equalizers - Bit rate Maximizing Equalizers Per-tone equalization BM-TEQ - Relations n T –tap linear combiner w for each tone

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14 Bit rate Maximizing Equalizers: Per-tone equalization Least-squares criterion per tone: “design TEQ per tone” Optimizes the SNR per tone Performs always better than a TEQ Efficient computation: exploit sliding DFT structure similar complexity as TEQ ADSL Basics - Intro - DMT Transmitter - Why Equalization? - DMT Receiver ADSL Equalizer Design - Problem Description - Current Equalizers - Bit rate Maximizing Equalizers Per-tone equalization BM-TEQ - Relations

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15 Bit rate Maximizing (BM) Equalizers: Time-domain equalization ADSL Basics - Intro - DMT Transmitter - Why Equalization? - DMT Receiver ADSL Equalizer Design - Problem Description - Current Equalizers - Bit rate Maximizing Equalizers Per-tone equalization BM-TEQ - Relations PTEQ: where BM-TEQ: with TEQ S/P CP... DFT FEQ T taps... N -point x x

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16 Bit rate Maximizing Equalizers: Time-domain equalization ADSL Basics - Intro - DMT Transmitter - Why Equalization? - DMT Receiver ADSL Equalizer Design - Problem Description - Current Equalizers - Bit rate Maximizing Equalizers Per-tone equalization BM-TEQ - Relations with Iteratively-reweighted separable non-linear least squares-based frequency-domain MMSE-TEQ design

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17 Relation between ADSL equalizers ADSL Basics - Intro - DMT Transmitter - Why Equalization? - DMT Receiver ADSL Equalizer Design - Problem Description - Current Equalizers - Bit rate Maximizing Equalizers - Relations (Channel shortening) TD-MMSE-TEQ: constrained linear LS FD-MMSE-TEQ: constrained linear LS or separable NL-LS Block transmission/CP/MulticarrierBit rate maximization BM-TEQ: iteratively reweighted separable NL-LS PTEQ: linear LS Only 1 tone Remarkable correspondence between generalized eigenvalue problems

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18 Relation between ADSL equalizers ADSL Basics - Intro - DMT Transmitter - Why Equalization? - DMT Receiver ADSL Equalizer Design - Problem Description - Current Equalizers - Bit rate Maximizing Equalizers - Relations TD-MMSE-TEQ Real FD-MMSE-TEQ 1 Complex FD-MMSE-TEQ 1 Real FD-MMSE-TEQ 2 Complex FD-MMSE-TEQ 2 Real BM-TEQ Complex BM-TEQ Real PTEQ Complex PTEQ

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19 Relation between ADSL equalizers ADSL Basics - Intro - DMT Transmitter - Why Equalization? - DMT Receiver ADSL Equalizer Design - Problem Description - Current Equalizers - Bit rate Maximizing Equalizers - Relations (Channel shortening) TD-MMSE-TEQ: constrained linear LS FD-MMSE-TEQ: constrained linear LS or separable NL-LS Block transmission/CP/Multicarrier Bit rate maximization BM-TEQ: iteratively reweighted separable NL-LS PTEQ: linear LS Only 1 tone Remarkable correspondence between generalized eigenvalue problems

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