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1 Introduction to ADSL Modems Original Lecture Notes developed by Prof. Brian L. Evans Dept. of Electrical and Comp. Eng. The University of Texas at Austin

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

3 Applications of Broadband Access Residential Application Downstream rate (kb/s) Upstream rate (kb/s) Willing to pay Demand Potential Database Access High Medium On-line directory; yellow pages Low High Video Phone 1,500 1,500 High Medium Home Shopping 1, Low Medium Video Games 1,500 1,500 Medium Medium Internet 3, High Medium Broadcast Video 6,000 0 Low High High definition TV 24,000 0 High Medium Business Application Downstream rate (kb/s) Upstream rate (kb/s) Willing to pay Demand Potential On-line directory; yellow pages Medium High Financial news 1,500 9 Medium Low Video phone 1,500 1,500 High Low Internet 3, High High Video conference 3,000 3,000 High Low Remote office 6,000 1,500 High Medium LAN interconnection 10,000 10,000 Medium Medium Supercomputing, CAD 45,000 45,000 High Low

4 Internet DSL Broadband Access DSLAM downstream Central ADSL ADSL Office modem modem Voice Switch PSTN upstream LPF LPF Customer Premises DSLAM - Digital Subscriber Line Access Multiplexer LPF Lowpass Filter (passes voiceband frequencies)

5 Spectral Compatibility of xdsl POTS 1.1 MHz optional ISDN ADSL - USA ADSL - Europe HDSL/SHDSL HomePNA VDSL - FDD 10k 100k 1M 10M 100M Frequency (Hz) 12 MHz Upstream Downstream Mixed

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

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

8 Bits Quadrature Amplitude Modulation Q i I Constellation encoder I Q (QAM) Modulator Lowpass filter Lowpass filter - cos(2πf c t) Bandpass sin(2πf c t) T magnitude f c channel frequency One carrier Single signal, occupying the whole available bandwidth The symbol rate is the bandwidth of the signal being centered on carrier frequency

9 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 Subchannels are 4.3 khz wide in ADSL every subchannel behaves like QAM magnitude channel carrier subchannel frequency

10 1 2 Multicarrier Modulation by Inverse g(t) g(t) j 2π f1t e x j2π f2t e x + Q FFT i I Discrete time 1 2 e e 1 j2π n N x 2 j2π n N x + j2π f N / 2t e e N / 2 j2π n N N / 2 g(t) x N / 2 x g(t) : pulse shaping filter i : i th symbol from encoder

11 00101 Multicarrier Modulation in ADSL QAM Q i I 0 N/2 subchannels (carriers) 1 2 N/2 * N/2-1 N-point Inverse Fast Fourier Transform (IFFT) x 0 x 1 x 2 N time samples 2 * x N-1 1 *

12 Multicarrier Modulation in ADSL Inverse FFT v samples N samples ADSL downstream upstream CP 32 4 N CP s y m b o l ( i ) CP s y m b o l ( i+1) copy copy D/A + transmit filter CP: Cyclic Prefix

13 Multicarrier Demodulation in ADSL S/P ~ 0 N/2 subchannels (carriers) ~ ~ N N ~ * N ~ * N-point Fast Fourier Transform (FFT) ~ x 0 ~ x 1 ~ x 2 ~ x N 1 N time samples

14 Inter-symbol Interference (ISI) * = Channel impulse response Threshold at zero.7 Received signal 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 Detected signal

15 Channel Impulse Response

16 Cyclic Prefix Helps in Fighting ISI Provide guard time between successive symbols No ISI if channel length is shorter than ν +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 v samples N samples CP s y m b o l ( i ) CP s y m b o l ( i+1) copy copy

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

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

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

20 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.

21 Frequency Domain Equalizer in ADSL Y 0 Y 1 Y N/2-1 Y i FEQ = c i ~ i ~ 0 ~ ~ 1 N 2 1 N/2 subchannels (carriers) Q ~ i FEQ Y i 0101 QAM Y i decoder I

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