Introduction to ADSL Modems Prof. Brian L. Evans Dept. of Electrical and Comp. Eng. The University of Texas at Austin UT graduate students: Mr. Zukang Shen, Mr. Daifeng Wang, Mr. Ian Wong UT Ph.D. graduates: Dr. Güner Arslan (Silicon Labs), Dr. Biao Lu (Schlumberger), Dr. Ming Ding (Bandspeed), Dr. Milos Milosevic (Schlumberger) UT senior design students: Wade Berglund, Jerel Canales, David J. Love, Ketan Mandke, Scott Margo, Esther Resendiz, Jeff Wu Other collaborators: Dr. Lloyd D. Clark (Schlumberger), Prof. C. Richard Johnson, Jr. (Cornell), Prof. Sayfe Kiaei (ASU), Prof. Rick Martin (AFIT), Prof. Marc Moonen (KU Leuven), Dr. Lucio F. C. Pessoa (Motorola), Dr. Arthur J. Redfern (Texas Instruments) Last modified August 27, 2005

25-2 Outline Broadband Access –Applications –Digital Subscriber Line (DSL) Standards ADSL Modulation Methods –ADSL Transceiver Block Diagram –Quadrature Amplitude Modulation –Multicarrier Modulation ADSL Transceiver Design –Inter-symbol Interference –Time-Domain Equalization –Frequency-Domain Equalization Conclusion

25-3 Applications of Broadband Access

25-4 DSL Broadband Access Customer Premises downstream upstream Voice Switch Central Office DSLAM ADSL modem LPF PSTN Interne t

25-5 DSL Broadband Access Standards Courtesy of Mr. Shawn McCaslin (National Instruments, Austin, TX)

25-6 Spectral Compatibility of xDSL 10k100k1M10M100M POTS ISDN ADSL - USA ADSL - Europe HDSL/SHDSL HomePNA VDSL - FDD UpstreamDownstreamMixed Frequency (Hz) optional 1.1 MHz 12 MHz

25-7 P/S QAM demod decoder invert channel = frequency domain equalizer S/P quadrature amplitude modulation (QAM) encoder mirror data and N -IFFT add cyclic prefix P/S D/A + transmit filter N -FFT and remove mirrored data S/P remove cyclic prefix TRANSMITTER RECEIVER N/2 subchannelsN real samples N/2 subchannels time domain equalizer (FIR filter) receive filter + A/D channel ADSL Modem Bits 00110

25-8 Bit Manipulations Serial-to-parallel converter Example of one input bit stream and two output words Parallel-to-serial converter Example of two input words and one output bit stream S/P Bits Words S/P Words Bits

25-9 Amplitude Modulation by Cosine Function Multiplication in time is convolution in Fourier domain Sifting property of the Dirac delta functional Fourier transform property for modulation by a cosine

25-10 Amplitude Modulation by Cosine Function Example: y(t) = f(t) cos(  0 t) –f(t) is an ideal lowpass signal –Assume  1 <<  0 –Y(  ) is real-valued if F(  ) is real-valued Demodulation is modulation then lowpass filtering Similar derivation for modulation with sin(  0 t) 0 1  --  F()F()  0 ½ -   -   -   +       -     +    ½F    ½F    Y()Y()

25-11 Amplitude Modulation by Sine Function Multiplication in time is convolution in Fourier domain Sifting property of the Dirac delta functional Fourier transform property for modulation by a sine

25-12 Amplitude Modulation by Sine Function Example: y(t) = f(t) sin(  0 t) –f(t) is an ideal lowpass signal –Assume  1 <<  0 –Y(  ) is imaginary-valued if F(  ) is real-valued Demodulation is modulation then lowpass filtering 0 1  --  F()F()  j ½ -   -   -   +       -     +    -j ½F    j ½F    -j ½ Y()Y()

25-13 –One carrier –Single signal, occupying the whole available bandwidth –The symbol rate is the bandwidth of the signal being centered on carrier frequency Quadrature Amplitude Modulation (QAM) frequency channel magnitude fcfc Bits Constellation encoder Bandpass Lowpass filter I Q TX cos(2  f c t) sin(2  f c t) - Modulator I Q 00110

25-14 Multicarrier Modulation Divide broadband channel into narrowband subchannels Discrete Multitone (DMT) modulation –Based on fast Fourier transform (related to Fourier series) –Standardized for ADSL –Proposed for VDSL subchannel frequency magnitude carrier channel every subchannel behaves like QAM Subchannels are 4.3 kHz wide in ADSL

25-15 Multicarrier Modulation by Inverse FFT x x x + g(t)g(t) g(t)g(t) g(t)g(t) x x x + Discrete time g(t) : pulse shaping filter X i : i th symbol from encoder I Q

25-16 Multicarrier Modulation in ADSL N-point Inverse Fast Fourier Transform (IFFT) X1X1 X2X2 X1*X1* x0x0 x1x1 x2x2 x N-1 X2*X2* X N/2 X N/2-1 * X0X0 N time samples N/2 subchannels (carriers) QAM I Q

25-17 Multicarrier Modulation in ADSL CP: Cyclic Prefix N samplesv samples CP s y m b o l ( i ) s y m b o l ( i+1) copy D/A + transmit filter Inverse FFT

25-18 Multicarrier Demodulation in ADSL N-point Fast Fourier Transform (FFT) N time samples N/2 subchannels (carriers) S/P

25-19 Inter-symbol Interference (ISI) Ideal channel –Impulse response is an impulse –Frequency response is flat Non-ideal channel causes ISI –Channel memory –Magnitude and phase variation Received symbol is weighted sum of neighboring symbols –Weights are determined by channel impulse response Channel impulse response Received signal Threshold at zero Detected signal * = 1.7 1

25-20 Channel Impulse Response

25-21 Channel Impulse Response

25-22 Cyclic Prefix Helps in Fighting ISI Provide guard time between successive symbols –No ISI if channel length is shorter than +1 samples Choose guard time samples to be a copy of the beginning of the symbol – cyclic prefix –Cyclic prefix converts linear convolution into circular convolution –Need circular convolution so that symbol  channel  FFT(symbol) x FFT(channel) –Then division by the FFT(channel) can undo channel distortion N samplesv samples CP s y m b o l ( i ) s y m b o l ( i+1) copy

25-23 Cyclic Prefix Helps in Fighting ISI cyclic prefix equal to be removed Repeated symbol * =

25-24 Combat ISI with Time-Domain Equalizer Channel length is usually longer than cyclic prefix Use finite impulse response (FIR) filter called a time-domain equalizer to shorten channel impulse response to be no longer than cyclic prefix length channel Shortened channel

25-25 h[k]h[k] y[k]y[k]x[k]x[k] Represented by its impulse response h(t)h(t) y(t)y(t)x(t)x(t) Convolution Review Discrete-time convolution For every k, we compute a new summation Continuous-time convolution For every value of t, we compute a new integral

25-26 z -1 … … x[k]x[k]  y[k] h[0]h[1]h[2]h[N-1] Finite Impulse Response (FIR) Filter Assuming that h[k] is causal and has finite duration from k = 0, …, N-1 Block diagram of an implementation (called a finite impulse response filter)

25-27 z-z- h + w b - xkxk ykyk ekek zkzk rkrk nknk + Minimize mean squared error E{e k 2 } where e k =b k-  - h k *w k –Chose length of b k to shorten length of h k *w k Disadvantages –Does not consider channel capacity –Deep notches in equalizer frequency response Example Time-Domain Equalizer

25-28 Frequency Domain Equalizer in ADSL Problem: FFT coefficients (constellation points) have been distorted by the channel. Solution: Use Frequency-domain Equalizer (FEQ) to invert the channel. Implementation: N/2 single-tap filters with complex coefficients.

25-29 Frequency Domain Equalizer in ADSL Y N/2-1 Y1Y1 Y0Y0 N/2 subchannels (carriers) QAM decoder 0101 YiYi FEQ YiYi Q I

25-30 P/S QAM demod decoder invert channel = frequency domain equalizer S/P quadrature amplitude modulation (QAM) encoder mirror data and N -IFFT add cyclic prefix P/S D/A + transmit filter N -FFT and remove mirrored data S/P remove cyclic prefix TRANSMITTER RECEIVER N/2 subchannelsN real samples N/2 subchannels time domain equalizer (FIR filter) receive filter + A/D channel ADSL Modem Bits 00110

25-31 Crosstalk and Near-End Echo f ff TX RX Hcable H TX RX ff TX RX Hcable H TX RX f NEXT FEXT Near-End echo

25-32 ADSL vs. FEXT, NEXT, Near-end Echo ADSL with Freq. Division Multiplexing - FDM –Near-End Echo filtered out –Self-NEXT (NEXT from another ADSL) mostly filtered out –FEXT and NEXT (from another type of DSL) are problems ADSL with overlapped spectrum (Echo Cancelled) –Near-End Echo Eliminated using an echo canceller –FEXT, NEXT and self-NEXT are a problem –Larger Spectrum available for downstream – higher data rate US DS US ff FDMEC