ECE 4331, Fall, 2009 Zhu Han Department of Electrical and Computer Engineering Class 16 Oct. 20 th, 2007

EE 541/451 Fall 2007

Figure 4.24 (a) Near-end crosstalk (NEXT). (b) Far-end crosstalk (FEXT). Figure 4.25 Model of twisted-pair channel.

Line codes for the electrical representations of binary data. (a) Unipolar NRZ signaling. (b) Polar NRZ signaling. (c)Unipolar RZ signaling. (d) Bipolar RZ signaling. (e) Split-phase or Manchester code.  

Figure 4.18 Impulse response of the modified duobinary conversion filter. Output of a quaternary system. (a) Waveform. (b) Representation of the 4 possible dibits, based on Gray encoding.

Figure 4.26 (a) Illustrating the different band allocations for an FDM-based ADSL system. (b) Block diagram of splitter performing the function of multiplexer or demultiplexer. Note: both filters in the splitter are bidirectional filters. (DMT)

Today there are various DSL Technology Options FamilyITUNameRatifiedMaximum Speed capabilities ADSLG.992.1G.dmt19997 Mbps down, 800 kbps up ADSL2G.992.3G.dmt.bis20028 Mb/s down, 1 Mbps up ADSL2plusG.992.5ADSL2plus Mbps down, 1 Mbps up ADSL2-REG.992.3Reach Extended20038 Mbps down 1 Mbps up SHDSLG.991.2G.SHDSL Mbps up/down VDSLG.993.1Very-high-data-rate DSL Mbps down, 15 Mbps up VDSL2G.993.2Very-high-data-rate DSL Mbps up/down

Simple overview of ADSL in the phone network POTS- Plain Old Telephone Service

Residential Customer ADSL Modem or Gateway Customer Premises Equipment Central Office Building ADSL Rack of Line Cards Standard Telephone Lines ADSL Equipment

Reach of ADSL Typically ADSL can reach as far as 18 kft from the central office To extend the reach, service providers have a host of options, outlined in the white paper DSL Anywhere v.2

ADSL 1.5 to 8Mbit/s 9.6 to 640kbit/s Broadband Network Internet Video Servers Live Broadcast Telephone Network “Today’s Typical Network” : ADSL

ADSL Modem POTS Filter Mbit/s kbit/s ADSL Modem POTS Filter POTS Linecard Mbit/s kbit/s Line Exchange EndCustomer End In the home: ADSL Modems Keeping internet traffic from interfering with phone service

Equalizer When the channel is not ideal, or when signaling is not Nyquist, There is ISI at the receiver side. In time domain, equalizer removes ISR. In frequency domain, equalizer flat the overall responses. In practice, we equalize the channel response using an equalizer

Zero-Forcing Equalizer The overall response at the detector input must satisfy Nyquist’s criterion for no ISI: The noise variance at the output of the equalizer is: –If the channel has spectral nulls, there may be significant noise enhancement.

Transversal Transversal Zero-Forcing Equalizer If Ts<T, we have a fractionally-spaced equalizer For no ISI, let:

Zero-Forcing Equalizer continue Zero-forcing equalizer, Example: Consider a baud-rate sampled equalizer for a system for which Design a zero-forcing equalizer having 5 taps.

Figure 4.7 Baseband binary data transmission system.

MMSE Equalizer In the ISI channel model, we need to estimate data input sequence x k from the output sequence y k Minimize the mean square error.

EE 541/451 Fall 2007

EE 541/451 Fall 2007

EE 541/451 Fall 2007 Figure 4.29 Signal-flow graph representation of the LMS algorithm involving the kth tap weight.

Figure 4.30 Illustrating the two operating modes of an adaptive equalizer: For the training mode, the switch is in position 1; and for the tracking mode, it is moved to position 2.

EE 541/451 Fall 2007 Figure 4.31 Impulse response of a discrete-time channel, depicting the precursors and postcursors.

Decision Feedback Equalizer To use data decisions made on the basis of precursors to take care of postcursors Consists of feedforward, feedback, and decision sections (nonlinear) DFE outperforms the linear equalizer when the channel has severe amplitude distortion or shape out off. Try to cancel ISI from “old” symbols by feeding back previous detector outputs.

Different types of equalizers Zero-forcing equalizers ignore the additive noise and may significantly amplify noise for channels with spectral nulls Minimum-mean-square error (MMSE) equalizers minimize the mean- square error between the output of the equalizer and the transmitted symbol. They require knowledge of some auto and cross-correlation functions, which in practice can be estimated by transmitting a known signal over the channel Adaptive equalizers are needed for channels that are time-varying Decision-feedback equalizers (DFE’s) use tentative symbol decisions to eliminate ISI, nonlinear Blind equalizers are needed when no preamble/training sequence is allowed, nonlinear Turbo equalizers: iterative and nonlinear interleaving Ultimately, the optimum equalizer is a maximum-likelihood sequence estimator, nonlinear