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11/5/00 p. 1 Postacademic Course on Telecommunications Module-3 Transmission Marc Moonen Lecture-7 Multi-tone Modulation K.U.Leuven/ESAT-SISTA Module-3 : Transmission Lecture-7 (11/5/00) Marc Moonen Dept. E.E./ESAT, K.U.Leuven

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Postacademic Course on Telecommunications 11/5/00 p. 2 Module-3 Transmission Marc Moonen Lecture-7 Multi-tone Modulation K.U.Leuven-ESAT/SISTA 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

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Postacademic Course on Telecommunications 11/5/00 p. 3 Module-3 Transmission Marc Moonen Lecture-7 Multi-tone Modulation K.U.Leuven-ESAT/SISTA 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’

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Postacademic Course on Telecommunications 11/5/00 p. 4 Module-3 Transmission Marc Moonen Lecture-7 Multi-tone Modulation K.U.Leuven-ESAT/SISTA 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)

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Postacademic Course on Telecommunications 11/5/00 p. 5 Module-3 Transmission Marc Moonen Lecture-7 Multi-tone Modulation K.U.Leuven-ESAT/SISTA 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,

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Postacademic Course on Telecommunications 11/5/00 p. 6 Module-3 Transmission Marc Moonen Lecture-7 Multi-tone Modulation K.U.Leuven-ESAT/SISTA 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),...

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Postacademic Course on Telecommunications 11/5/00 p. 7 Module-3 Transmission Marc Moonen Lecture-7 Multi-tone Modulation K.U.Leuven-ESAT/SISTA 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

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Postacademic Course on Telecommunications 11/5/00 p. 8 Module-3 Transmission Marc Moonen Lecture-7 Multi-tone Modulation K.U.Leuven-ESAT/SISTA 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) updown frequency updown time up& down time & frequency

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Postacademic Course on Telecommunications 11/5/00 p. 9 Module-3 Transmission Marc Moonen Lecture-7 Multi-tone Modulation K.U.Leuven-ESAT/SISTA Driver Application: ADSL (VDSL) Modems PS: echo cancellation for full-duplex (see Lecture-6/8)

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Postacademic Course on Telecommunications 11/5/00 p. 10 Module-3 Transmission Marc Moonen Lecture-7 Multi-tone Modulation K.U.Leuven-ESAT/SISTA 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 100Hz3600Hz

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Postacademic Course on Telecommunications 11/5/00 p. 11 Module-3 Transmission Marc Moonen Lecture-7 Multi-tone Modulation K.U.Leuven-ESAT/SISTA 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

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Postacademic Course on Telecommunications 11/5/00 p. 12 Module-3 Transmission Marc Moonen Lecture-7 Multi-tone Modulation K.U.Leuven-ESAT/SISTA Driver Application: ADSL (VDSL) Modems ADSL : `Asymmetric Digital Subscriber Line’ …-1993: ADSL spurred by interest in video-on-demand (VOD) 1995 : ADSL/VOD interest decline 1996 : 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.

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Postacademic Course on Telecommunications 11/5/00 p. 13 Module-3 Transmission Marc Moonen Lecture-7 Multi-tone Modulation K.U.Leuven-ESAT/SISTA 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 Backbone Network Access Node max 0.3…1.5 km cabinet (ONU) optical fiber copper wire

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Postacademic Course on Telecommunications 11/5/00 p. 14 Module-3 Transmission Marc Moonen Lecture-7 Multi-tone Modulation K.U.Leuven-ESAT/SISTA Driver Application: ADSL (VDSL) Modems Distance/bitrate trade-off (upstream) distance (km) bitrate (Mbits/sec) ADSL VDSL

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Postacademic Course on Telecommunications 11/5/00 p. 15 Module-3 Transmission Marc Moonen Lecture-7 Multi-tone Modulation K.U.Leuven-ESAT/SISTA 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 FEXTNEXT

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Postacademic Course on Telecommunications 11/5/00 p. 16 Module-3 Transmission Marc Moonen Lecture-7 Multi-tone Modulation K.U.Leuven-ESAT/SISTA Driver Application: ADSL (VDSL) Modems Communication Impairments :

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Postacademic Course on Telecommunications 11/5/00 p. 17 Module-3 Transmission Marc Moonen Lecture-7 Multi-tone Modulation K.U.Leuven-ESAT/SISTA 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. !

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Postacademic Course on Telecommunications 11/5/00 p. 18 Module-3 Transmission Marc Moonen Lecture-7 Multi-tone Modulation K.U.Leuven-ESAT/SISTA 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..

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Postacademic Course on Telecommunications 11/5/00 p. 19 Module-3 Transmission Marc Moonen Lecture-7 Multi-tone Modulation K.U.Leuven-ESAT/SISTA 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)

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Postacademic Course on Telecommunications 11/5/00 p. 20 Module-3 Transmission Marc Moonen Lecture-7 Multi-tone Modulation K.U.Leuven-ESAT/SISTA Driver Application: ADSL (VDSL) Modems ADSL (Preview) DAC S/PS/P FFT FEQ IFFT P/SP/S Tx clock Discrete equivalent channel Rx clock p(t) Tx filterChannelRx filter ch(t) r(t)ADC

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Postacademic Course on Telecommunications 11/5/00 p. 21 Module-3 Transmission Marc Moonen Lecture-7 Multi-tone Modulation K.U.Leuven-ESAT/SISTA DMT Principles: Preliminaries DMT `inspiration’ : see Lecture 2

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Postacademic Course on Telecommunications 11/5/00 p. 22 Module-3 Transmission Marc Moonen Lecture-7 Multi-tone Modulation K.U.Leuven-ESAT/SISTA DMT Principles : Preliminaries DMT `inspiration’ : see Lecture 2

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Postacademic Course on Telecommunications 11/5/00 p. 23 Module-3 Transmission Marc Moonen Lecture-7 Multi-tone Modulation K.U.Leuven-ESAT/SISTA DMT Principles : Preliminaries DMT `inspiration’ : see Lecture 3

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Postacademic Course on Telecommunications 11/5/00 p. 24 Module-3 Transmission Marc Moonen Lecture-7 Multi-tone Modulation K.U.Leuven-ESAT/SISTA 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’)

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Postacademic Course on Telecommunications 11/5/00 p. 25 Module-3 Transmission Marc Moonen Lecture-7 Multi-tone Modulation K.U.Leuven-ESAT/SISTA 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

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Postacademic Course on Telecommunications 11/5/00 p. 26 Module-3 Transmission Marc Moonen Lecture-7 Multi-tone Modulation K.U.Leuven-ESAT/SISTA 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)

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Postacademic Course on Telecommunications 11/5/00 p. 27 Module-3 Transmission Marc Moonen Lecture-7 Multi-tone Modulation K.U.Leuven-ESAT/SISTA DMT Principles: IFFT/FFT-based modulation DMT-transmission block scheme (revisited): DAC Tx clock S/PS/P FFT FEQ IFFT P/SP/S 0 Discrete equivalent channel Rx clock p(t) Tx filterChannelRx filter ch(t) r(t)ADC

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Postacademic Course on Telecommunications 11/5/00 p. 28 Module-3 Transmission Marc Moonen Lecture-7 Multi-tone Modulation K.U.Leuven-ESAT/SISTA 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 :

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Postacademic Course on Telecommunications 11/5/00 p. 29 Module-3 Transmission Marc Moonen Lecture-7 Multi-tone Modulation K.U.Leuven-ESAT/SISTA DMT Principles: The Magic Prefix Trick Prefix insertion :

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Postacademic Course on Telecommunications 11/5/00 p. 30 Module-3 Transmission Marc Moonen Lecture-7 Multi-tone Modulation K.U.Leuven-ESAT/SISTA DMT Principles: The Magic Prefix Trick Prefix insertion : in the receiver, the samples corresponding to the prefix are removed (=unused) : S/PS/P FFT FEQ IFFT P/SP/S 0 Discrete equivalent channel

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Postacademic Course on Telecommunications 11/5/00 p. 31 Module-3 Transmission Marc Moonen Lecture-7 Multi-tone Modulation K.U.Leuven-ESAT/SISTA 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-sideRx-side Tone 3 Tone 2 Tone 1 Tone 0 Tone 3 Tone 2 Tone 1 Tone 0 PrefixFrom IFFTGuardbandTo FFT * ch(t) r(t)s(t)

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Postacademic Course on Telecommunications 11/5/00 p. 32 Module-3 Transmission Marc Moonen Lecture-7 Multi-tone Modulation K.U.Leuven-ESAT/SISTA 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)

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Postacademic Course on Telecommunications 11/5/00 p. 33 Module-3 Transmission Marc Moonen Lecture-7 Multi-tone Modulation K.U.Leuven-ESAT/SISTA 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)

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Postacademic Course on Telecommunications 11/5/00 p. 34 Module-3 Transmission Marc Moonen Lecture-7 Multi-tone Modulation K.U.Leuven-ESAT/SISTA 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

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Postacademic Course on Telecommunications 11/5/00 p. 35 Module-3 Transmission Marc Moonen Lecture-7 Multi-tone Modulation K.U.Leuven-ESAT/SISTA DMT Principles: The Magic Prefix Trick Received samples for symbol m, after removing prefix :

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Postacademic Course on Telecommunications 11/5/00 p. 36 Module-3 Transmission Marc Moonen Lecture-7 Multi-tone Modulation K.U.Leuven-ESAT/SISTA DMT Principles: The Magic Prefix Trick...This is equivalent with :

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Postacademic Course on Telecommunications 11/5/00 p. 37 Module-3 Transmission Marc Moonen Lecture-7 Multi-tone Modulation K.U.Leuven-ESAT/SISTA 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) !

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Postacademic Course on Telecommunications 11/5/00 p. 38 Module-3 Transmission Marc Moonen Lecture-7 Multi-tone Modulation K.U.Leuven-ESAT/SISTA DMT Principles: The Magic Prefix Trick …By substituting this :

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Postacademic Course on Telecommunications 11/5/00 p. 39 Module-3 Transmission Marc Moonen Lecture-7 Multi-tone Modulation K.U.Leuven-ESAT/SISTA 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.

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Postacademic Course on Telecommunications 11/5/00 p. 40 Module-3 Transmission Marc Moonen Lecture-7 Multi-tone Modulation K.U.Leuven-ESAT/SISTA 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) S/PS/P FFT FEQ IFFT P/SP/S 0 Discrete equivalent channel

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