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**Module-3 : Transmission Lecture-7 (11/5/00)**

Marc Moonen Dept. E.E./ESAT, K.U.Leuven Module-3 Transmission Marc Moonen Lecture-7 Multi-tone Modulation K.U.Leuven/ESAT-SISTA

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**Lecture 7-8 : Multi-tone Modulation**

Lecture 7 : Overview Driver application : ADSL (VDSL) modems Modem technology : voice-band vs. xDSL Communication impairments DMT principles Preliminaries IFFT/FFT-based modulation/demodulation The magic `prefix’ trick Module-3 Transmission Marc Moonen Lecture-7 Multi-tone Modulation K.U.Leuven-ESAT/SISTA

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**Lecture 7-8 : Multi-tone Modulation**

Lecture 8 : Overview ADSL/VDSL revisited Specs, spectrum, FDM vs. EC, P-to-A,… Equalization Time-domain equalization Frequency-domain equalization Windowing Receiver windowing, Transmitter windowing Echo Cancellation Time-domain echo cancellation Time+frequency-domain echo cancellation `Joint shortening’ Module-3 Transmission Marc Moonen Lecture-7 Multi-tone Modulation K.U.Leuven-ESAT/SISTA

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**Acknowledgement Lecture partly adopted from Module T2**

`Digital Communication Principles’ M.Engels, M. Moeneclaey, G. Van Der Plas 1998 Postgraduate Course on Telecommunication Special thanks to G. Van der Plas (Alcatel) Lecture partly co-authored by Thierry Pollet, Alcatel Telecom, CRC, Antwerp (B) Module-3 Transmission Marc Moonen Lecture-7 Multi-tone Modulation K.U.Leuven-ESAT/SISTA

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**Driver Application: ADSL (VDSL) Modems**

References: J.A.C. Bingham, `The theory and practice of modem design’, Wiley, 1980 J.A.C. Bingham, `Multicarrier modulation for data transmission, an idea whose time has come’, IEEE Communications Magazine, May 1990, pp.5-14 W.Y. Chen, `DSL simulation techniques and standards development for digital subscriber line systems’, Macmillan, 1998 ... Module-3 Transmission Marc Moonen Lecture-7 Multi-tone Modulation K.U.Leuven-ESAT/SISTA

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**Driver Application: ADSL (VDSL) Modems**

Modem Technology : …1970 : development of efficient modulation techniques for transmission over band limited channels, spurred by military applications (-> … 9.6 kbits/sec) : Semiconductor technology (size & power reduction) : Introduction of coding techniques (-> … 19.2 kbits/sec) : reaching Shannon limit (-> 33kbits/sec, asymmetric 56kbits/sec modems) 1995-… : ADSL (8Mbits/sec downstream, 60 kbits/sec upstream) 2000-… : VDSL (52Mbits/sec downstream, 6Mbits/sec upstream), ... Module-3 Transmission Marc Moonen Lecture-7 Multi-tone Modulation K.U.Leuven-ESAT/SISTA

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**Driver Application: ADSL (VDSL) Modems**

Performance improvement results from: improved telephone channel quality (digital switches, etc.) improved modulation/coding techniques (QAM, trellis coded modulation (TCM), echo cancellation (EC), adaptive equalization,…) semiconductor technology Module-3 Transmission Marc Moonen Lecture-7 Multi-tone Modulation K.U.Leuven-ESAT/SISTA

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**Driver Application: ADSL (VDSL) Modems**

PS: duplexing techniques Frequency division duplexing (FDD) `downstream’ = central office -> remote user `upstream’ = remote user -> central office Time division duplexing (TDD) : `ping-pong’ Full duplex with echo-cancellation (EC) (see also Lecture-6/8) up down frequency up down time up & down time & frequency Module-3 Transmission Marc Moonen Lecture-7 Multi-tone Modulation K.U.Leuven-ESAT/SISTA

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**Driver Application: ADSL (VDSL) Modems**

PS: echo cancellation for full-duplex (see Lecture-6/8) Module-3 Transmission Marc Moonen Lecture-7 Multi-tone Modulation K.U.Leuven-ESAT/SISTA

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**Driver Application: ADSL (VDSL) Modems**

Voice-band modems : Shannon capacity limit (Lecture-2) In analog public switched telephone network SNR > 28dB (signal-to-noise ratio) BW > 2400 Hz (bandwidth) ...Hence capacity approx kbits/sec In digital public switched telephone network SNR > 34 dB (signal-to-noise ratio) BW > 3200 Hz (bandwidth) ...Hence capacity approx. 35 kbits/sec 100Hz 3600Hz Module-3 Transmission Marc Moonen Lecture-7 Multi-tone Modulation K.U.Leuven-ESAT/SISTA

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**Driver Application: ADSL (VDSL) Modems**

Digital Subscriber Line (DSL) Technologies: HDSL : `High Speed Digital Subscriber Line’ …2Mbits/sec on 2 or 3 pairs ADSL : `Asymmetric Digital Subscriber Line’ …8Mbits/sec down, 60kbits/sec up on 1 pair uses frequency band up to approx. 1 MHz SDSL : `High Speed Digital Subscriber Line’ …2Mbits/sec symmetrical on 1 pair VDSL : `Very High Speed Digital Subscriber Line’ …52Mbits/sec down, 6Mbits/sec up on 1 pair uses frequency band up to approx. 10 MHz Module-3 Transmission Marc Moonen Lecture-7 Multi-tone Modulation K.U.Leuven-ESAT/SISTA

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**Driver Application: ADSL (VDSL) Modems**

ADSL : `Asymmetric Digital Subscriber Line’ …-1993: ADSL spurred by interest in video-on-demand (VOD) : ADSL/VOD interest decline : ADSL technology trials prove viability. : ADSL deployment, reoriented to data applications, as telco’s reaction to cable operators offering high- speed internet access with cable modems. Module-3 Transmission Marc Moonen Lecture-7 Multi-tone Modulation K.U.Leuven-ESAT/SISTA

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**Driver Application: ADSL (VDSL) Modems**

ADSL : `Asymmetric Digital Subscriber Line’ VDSL : `Very High Speed Digital Subscriber Line’ Backbone Network Access Node max 3.5…5 km copper wire cabinet (ONU) Access Node Backbone Network optical fiber copper wire max 0.3…1.5 km Module-3 Transmission Marc Moonen Lecture-7 Multi-tone Modulation K.U.Leuven-ESAT/SISTA

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**Driver Application: ADSL (VDSL) Modems**

Distance/bitrate trade-off (upstream) bitrate (Mbits/sec) 40 VDSL 30 20 10 ADSL 1 2 3 4 distance (km) Module-3 Transmission Marc Moonen Lecture-7 Multi-tone Modulation K.U.Leuven-ESAT/SISTA

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**Driver Application: ADSL (VDSL) Modems**

Communication Impairments : Frequency-dependent cannel attenuation introduces inter-symbol interference (ISI) Coupling between wires in same or adjacent binders introduces crosstalk Near-end Xtalk (NEXT) Far-end Xtalk (FEXT) useful signal FEXT NEXT Module-3 Transmission Marc Moonen Lecture-7 Multi-tone Modulation K.U.Leuven-ESAT/SISTA

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**Driver Application: ADSL (VDSL) Modems**

Communication Impairments : Module-3 Transmission Marc Moonen Lecture-7 Multi-tone Modulation K.U.Leuven-ESAT/SISTA

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**Driver Application: ADSL (VDSL) Modems**

Communication Impairments (continued) : Xtalk from other systems e.g. HPNA (Home Phone Network Alliance) vs. VDSL Radio Frequency Interference (RFI) e.g. AM broadcast, amateur radio Noise e.g. impulsive noise (=high bursts of short duration) Echo due to hybrid impedance mismatch Conclusion: Need advanced modulation, DSP,etc. ! Module-3 Transmission Marc Moonen Lecture-7 Multi-tone Modulation K.U.Leuven-ESAT/SISTA

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**Driver Application: ADSL (VDSL) Modems**

Line Codes (modulation technique) : ADSL (ANSI standard) DMT (`Discrete Multi-tone Modulation’, a.k.a. multi-carrier modulation, orthogonal frequency division multiplexing (OFDM)) 256 different `carriers’, each of them QAM-modulated, see below. VDSL DMT or single carrier (CAP/QAM) systems ? =undecided.. Module-3 Transmission Marc Moonen Lecture-7 Multi-tone Modulation K.U.Leuven-ESAT/SISTA

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**Driver Application: ADSL (VDSL) Modems**

Line Codes (modulation technique) : DMT (Preview) : Multiple carriers are QAM-modulated with a low-rate bit stream. The high-rate bit stream is thus carried by dividing it into hundreds of low-rate streams. Modulation/demodulation by FFT/IFFT (see below) Module-3 Transmission Marc Moonen Lecture-7 Multi-tone Modulation K.U.Leuven-ESAT/SISTA

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**Driver Application: ADSL (VDSL) Modems**

ADSL (Preview) IFFT P/S S/P Discrete equivalent channel FFT FEQ DAC p(t) ch(t) r(t) ADC Tx filter Channel Rx filter Tx clock Rx clock Module-3 Transmission Marc Moonen Lecture-7 Multi-tone Modulation K.U.Leuven-ESAT/SISTA

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**DMT Principles: Preliminaries**

DMT `inspiration’ : see Lecture 2 Module-3 Transmission Marc Moonen Lecture-7 Multi-tone Modulation K.U.Leuven-ESAT/SISTA

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**DMT Principles : Preliminaries**

DMT `inspiration’ : see Lecture 2 Module-3 Transmission Marc Moonen Lecture-7 Multi-tone Modulation K.U.Leuven-ESAT/SISTA

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**DMT Principles : Preliminaries**

DMT `inspiration’ : see Lecture 3 Module-3 Transmission Marc Moonen Lecture-7 Multi-tone Modulation K.U.Leuven-ESAT/SISTA

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**DMT Principles: IFFT/FFT-based modulation**

`Multi-tone’/`multi-carrier’ = modulate different carriers at the same time: (=complex envelope) modulates fo - subscript `m’ refers to m-th symbol (frame) - this is one `tone’ similarly, modulate 2.fo, 3.fo, …, N.fo - N `tones’ - highest frequency N.fo = Fs/2, with Fs sampling frequency (for baseband DMT) each tone carries a number of bits (0,1,2,…) depending upon its SNR (`bit loading’) Module-3 Transmission Marc Moonen Lecture-7 Multi-tone Modulation K.U.Leuven-ESAT/SISTA

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**DMT Principles: IFFT/FFT-based modulation**

Modulation is realized by means of 2N-point Inverse Discrete Fourier Transform (I-DFT) : example N=4 `*’ = complex conjugate real real Module-3 Transmission Marc Moonen Lecture-7 Multi-tone Modulation K.U.Leuven-ESAT/SISTA

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**DMT Principles: IFFT/FFT-based modulation**

I-DFT is implemented by means of 2N-point (inverse) Fast Fourier Transform (I-FFT) - complexity is O(N.logN) instead of O(N^2) - fast hardware available Time-domain symbols are transmitter over channel Receiver : demodulation with inverse operation, i.e. FFT (i.o. I-FFT) Module-3 Transmission Marc Moonen Lecture-7 Multi-tone Modulation K.U.Leuven-ESAT/SISTA

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**DMT Principles: IFFT/FFT-based modulation**

DMT-transmission block scheme (revisited): S/P FFT FEQ IFFT P/S Discrete equivalent channel DAC p(t) ch(t) r(t) ADC Tx filter Channel Rx filter Tx clock Rx clock Module-3 Transmission Marc Moonen Lecture-7 Multi-tone Modulation K.U.Leuven-ESAT/SISTA

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**DMT Principles: The Magic Prefix Trick**

Additional feature : before transmission, a `prefix’ is added to each time-domain symbol, i.e. the last samples are copied and put up front : Module-3 Transmission Marc Moonen Lecture-7 Multi-tone Modulation K.U.Leuven-ESAT/SISTA

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**DMT Principles: The Magic Prefix Trick**

Prefix insertion : Module-3 Transmission Marc Moonen Lecture-7 Multi-tone Modulation K.U.Leuven-ESAT/SISTA

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**DMT Principles: The Magic Prefix Trick**

Prefix insertion : in the receiver, the samples corresponding to the prefix are removed (=unused) : S/P FFT FEQ IFFT P/S Discrete equivalent channel Module-3 Transmission Marc Moonen Lecture-7 Multi-tone Modulation K.U.Leuven-ESAT/SISTA

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**DMT Principles: The Magic Prefix Trick**

if channel impulse response has length L (= L non-zero taps) and ( is prefix length), then all `transient effects’ between symbols are confined to the prefix period : Tx-side Rx-side Tone 3 Tone 2 Tone 1 Tone 0 Tone 3 Tone 2 Tone 1 Tone 0 ch(t) * s(t) r(t) Prefix From IFFT Guardband To FFT Module-3 Transmission Marc Moonen Lecture-7 Multi-tone Modulation K.U.Leuven-ESAT/SISTA

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**DMT Principles: The Magic Prefix Trick**

Magic trick fails if -> transient effects within sample sequence that is fed into FFT -> this results in inter-symbol-interference (ISI) = interference from previous symbol(s) (same carrier) inter-carrier interference (ICI) = interference from other carriers (`carrier orthogonality destroyed’) (see also Lecture 8) Module-3 Transmission Marc Moonen Lecture-7 Multi-tone Modulation K.U.Leuven-ESAT/SISTA

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**DMT Principles: The Magic Prefix Trick**

In the receiver, after removing the samples corresponding to the prefix, the i-th tone is observed, multiplied by a factor H(i.fo), i.e. the channel response for frequency f=i.fo (=`simplified statement’) `Prefix trick’ based on a linear convolution (filtering by channel impulse response) being turned into a circular convolution, which corresponds to component-wise multiplication in frequency domain (=statement to be ignored) Module-3 Transmission Marc Moonen Lecture-7 Multi-tone Modulation K.U.Leuven-ESAT/SISTA

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**DMT Principles: The Magic Prefix Trick**

The mathematics behind this are as follows : assume N=4, prefix-length=2 (cfr. supra) assume channel impulse response is received samples are… transmitted signal at time k received signal at time k Module-3 Transmission Marc Moonen Lecture-7 Multi-tone Modulation K.U.Leuven-ESAT/SISTA

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**DMT Principles: The Magic Prefix Trick**

Received samples for symbol m, after removing prefix : Module-3 Transmission Marc Moonen Lecture-7 Multi-tone Modulation K.U.Leuven-ESAT/SISTA

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**DMT Principles: The Magic Prefix Trick**

...This is equivalent with : Module-3 Transmission Marc Moonen Lecture-7 Multi-tone Modulation K.U.Leuven-ESAT/SISTA

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**DMT Principles: The Magic Prefix Trick**

The modified channel matrix is a so-called `circulant’ matrix (constant along the diagonals & `wrapped around’) Theorem : every circulant matrix C is diagonalized by a DFT & I-DFT matrix : PS: Proof by MatLab (try it, it always works!) PPS: This is an eigenvalue (singular value) decomposition (remember from high school maths?) Diagonal matrix has DFT of first column of C on its main diagonal, i.e. Hi=H(i.fo) ! Module-3 Transmission Marc Moonen Lecture-7 Multi-tone Modulation K.U.Leuven-ESAT/SISTA

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**DMT Principles: The Magic Prefix Trick**

…By substituting this : Module-3 Transmission Marc Moonen Lecture-7 Multi-tone Modulation K.U.Leuven-ESAT/SISTA

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**DMT Principles: The Magic Prefix Trick**

…which means that after removing the prefix-samples and performing a DFT in the receiver, the obtained samples are equal to the transmitted (`frequency-domain’) symbols, up to a channel attenuation Hi (for tone-i). Hence `channel equalization’ may be performed `in the frequency domain’, by component-wise divisions (divide by Hi for tone-i). =`1-taps FEQ’ (frequency-domain equalization) Conclusion: if , DMT-modulation leads to a simple (trivial) channel equalization problem. …otherwise, see Lecture-8. Module-3 Transmission Marc Moonen Lecture-7 Multi-tone Modulation K.U.Leuven-ESAT/SISTA

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**DMT Principles: The Magic Prefix Trick**

PS : compare with transmitter & receiver transformation for MIMO-transmission (singular value decomposition of channel response matrix, etc., see Lecture-2) IFFT P/S S/P Discrete equivalent channel FFT FEQ Module-3 Transmission Marc Moonen Lecture-7 Multi-tone Modulation K.U.Leuven-ESAT/SISTA

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