Module3 Transmission Lecture7 11500 Marc Moonen Dept E

Module-3 : Transmission Lecture-7 (11/5/00) Marc Moonen Dept. E. E. /ESAT, K. U. Leuven marc. moonen@esat. kuleuven. ac. be www. esat. kuleuven. ac. be/sista/~moonen/ Postacademic Course on Telecommunications Module-3 Transmission Lecture-7 Multi-tone Modulation Marc Moonen K. U. Leuven/ESAT-SISTA 11/5/00 p. 1

Lecture 7 -8 : Multi-tone Modulation Lecture 7 : Overview • Driver application : ADSL (VDSL) modems Modem technology : voice-band vs. x. DSL Communication impairments • DMT principles Preliminaries IFFT/FFT-based modulation/demodulation The magic `prefix’ trick Postacademic Course on Telecommunications Module-3 Transmission Lecture-7 Multi-tone Modulation Marc Moonen K. U. Leuven-ESAT/SISTA 11/5/00 p. 2

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

Acknowledgement Lecture partly adopted from Module T 2 `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) Postacademic Course on Telecommunications Module-3 Transmission Lecture-7 Multi-tone Modulation Marc Moonen K. U. Leuven-ESAT/SISTA 11/5/00 p. 4

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

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) • 1970 -1980 : Semiconductor technology (size & power reduction) • 1980 -1990 : Introduction of coding techniques (-> … 19. 2 kbits/sec) • 1990 -2000 : reaching Shannon limit (-> 33 kbits/sec, asymmetric 56 kbits/sec modems) • 1995 -… : ADSL (8 Mbits/sec downstream, 60 kbits/sec upstream) • 2000 -… : VDSL (52 Mbits/sec downstream, 6 Mbits/sec upstream), . . . Postacademic Course on Telecommunications Module-3 Transmission Lecture-7 Multi-tone Modulation Marc Moonen K. U. Leuven-ESAT/SISTA 11/5/00 p. 6

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

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’ up down frequency up down time • Full duplex with echo-cancellation (EC) up & down (see also Lecture-6/8) Postacademic Course on Telecommunications Module-3 Transmission Lecture-7 Multi-tone Modulation time & frequency Marc Moonen K. U. Leuven-ESAT/SISTA 11/5/00 p. 8

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

Driver Application: ADSL (VDSL) Modems Voice-band modems : Shannon capacity limit (Lecture-2) • In analog public switched telephone network SNR > 28 d. B (signal-to-noise ratio) BW > 2400 Hz (bandwidth). . . Hence capacity approx. 22. 4 kbits/sec • In digital public switched telephone network 100 Hz SNR > 34 d. B (signal-to-noise ratio) 3600 Hz BW > 3200 Hz (bandwidth). . . Hence capacity approx. 35 kbits/sec Postacademic Course on Telecommunications Module-3 Transmission Lecture-7 Multi-tone Modulation Marc Moonen K. U. Leuven-ESAT/SISTA 11/5/00 p. 10

Driver Application: ADSL (VDSL) Modems Digital Subscriber Line (DSL) Technologies: • HDSL : `High Speed Digital Subscriber Line’ … 2 Mbits/sec on 2 or 3 pairs • ADSL : `Asymmetric Digital Subscriber Line’ … 8 Mbits/sec down, 60 kbits/sec up on 1 pair uses frequency band up to approx. 1 MHz • SDSL : `High Speed Digital Subscriber Line’ … 2 Mbits/sec symmetrical on 1 pair • VDSL : `Very High Speed Digital Subscriber Line’ … 52 Mbits/sec down, 6 Mbits/sec up on 1 pair uses frequency band up to approx. 10 MHz Postacademic Course on Telecommunications Module-3 Transmission Lecture-7 Multi-tone Modulation Marc Moonen K. U. Leuven-ESAT/SISTA 11/5/00 p. 11

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. 1997 -. . . : ADSL deployment, reoriented to data applications, as telco’s reaction to cable operators offering highspeed internet access with cable modems. Postacademic Course on Telecommunications Module-3 Transmission Lecture-7 Multi-tone Modulation Marc Moonen K. U. Leuven-ESAT/SISTA 11/5/00 p. 12

Driver Application: ADSL (VDSL) Modems • ADSL : `Asymmetric Digital Subscriber Line’ Backbone Network Access Node max 3. 5… 5 km copper wire • VDSL : `Very High Speed Digital Subscriber Line’ Backbone Network Access Node cabinet (ONU) optical fiber copper wire max 0. 3… 1. 5 km Postacademic Course on Telecommunications Module-3 Transmission Lecture-7 Multi-tone Modulation Marc Moonen K. U. Leuven-ESAT/SISTA 11/5/00 p. 13

Driver Application: ADSL (VDSL) Modems • Distance/bitrate trade-off (upstream) bitrate (Mbits/sec) 40 VDSL 30 20 10 ADSL 1 Postacademic Course on Telecommunications 2 Module-3 Transmission Lecture-7 Multi-tone Modulation 3 4 distance (km) Marc Moonen K. U. Leuven-ESAT/SISTA 11/5/00 p. 14

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

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

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

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

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

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

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

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

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

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

DMT Principles: IFFT/FFT-based modulation Modulation is realized by means of 2 N-point Inverse Discrete Fourier Transform (I-DFT) : example N=4 real `*’ = complex conjugate Postacademic Course on Telecommunications Module-3 Transmission Lecture-7 Multi-tone Modulation Marc Moonen K. U. Leuven-ESAT/SISTA 11/5/00 p. 25

DMT Principles: IFFT/FFT-based modulation • I-DFT is implemented by means of 2 N-point (inverse) Fast Fourier Transform (I-FFT) - complexity is O(N. log. N) 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) Postacademic Course on Telecommunications Module-3 Transmission Lecture-7 Multi-tone Modulation Marc Moonen K. U. Leuven-ESAT/SISTA 11/5/00 p. 26

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

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

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

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

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

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

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

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

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

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

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

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

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

DMT Principles: The Magic Prefix Trick 0 IFFT P / S Discrete equivalent channel S / P FFT FEQ • PS : compare with transmitter & receiver transformation for MIMO-transmission (singular value decomposition of channel response matrix, etc. , see Lecture-2) Postacademic Course on Telecommunications Module-3 Transmission Lecture-7 Multi-tone Modulation Marc Moonen K. U. Leuven-ESAT/SISTA 11/5/00 p. 40