EE29C Spring 211 Lecture 5: Equalization Techniques Elad Alon Dept. of EECS Link Channels Attenuation [db] -1-2 -3-4 -5 9" FR4, via stub 9" FR4 26" FR4-6 26" FR4, via stub 2 4 6 8 1 frequency [GHz] EE29C Lecture 5 2
Inter-Symbol Interference Channel is band-limited I.e., dispersive (low pass) Short TX pulses get spread out Low latency Also get reflections Z mismatches, connectors, etc. Longer latency pulse response 1.8.6.4.2 Tsymbol=16ps 1 2 3 ns EE29C Lecture 5 3 Why ISI Matters 1.8 Eye Diagram Amplitude.6.4.2 2 4 6 8 1 12 14 16 18 Symbol time First sample doesn t even reach RX threshold Suffers ISI from all previous zero bits Middle sample hardly different from first.2 trailing ISI (from previous symbol) and.1 leading ISI (from next symbol) EE29C Lecture 5 4
Equalization + = Basic goal is to flatten channel response I.e., in time domain, get back our nice clean pulse For low-pass channel, equalizer boosts high frequencies EE29C Lecture 5 5 History Equalization been around for a very long time What makes electrical interfaces unique: Performance Power and area constraints EE29C Lecture 5 6
Equalizer Types More alphabet soup CTLE, ZFE, DFE, RX FIR, MMSE, Three basic distinctions: Linear vs. Non-Linear Continuous Time vs. Discrete Time Minimize ISI vs. Minimize ISI + Noise EE29C Lecture 5 7 Continuous Time Linear Equalizer (CTLE) EE29C Lecture 5 8
CTLE Implementation, Limitations EE29C Lecture 5 9 Linear FIR EE29C Lecture 5 1
Transmitter FIR Example Tx Data Anticausal taps.7.5 Unequalized Equalization Pulse End of Line Voltage.3.1 Causal taps -.1 -.3..3.6.9 1.2 time (ns) EE29C Lecture 5 11 Setting the Coefficients Assume channel response is known for now See later how to estimate it Most basic approach: zero-forcing (ZFE) Single-bit Channel Response Equalized Response EE29C Lecture 5 12
ZFE Setting Formulation (Math ) EE29C Lecture 5 13 Zero-Forcing : Desired Response EE29C Lecture 5 14
Final Coefficients: Least Squares EE29C Lecture 5 15 Transmitter FIR Revisited Tx Data Anticausal taps.7.5 Unequalized Equalization Pulse End of Line Voltage.3.1 Causal taps -.1 -.3..3.6.9 1.2 time (ns) Can t generally use ZFE result directly TX has a peak swing constraint At same max. swing, RX amplitude reduced Is this a problem? EE29C Lecture 5 16
The Fundamental Issue: Noise Attenuation [db] -5-1 -15 equalized unequalized -2 frequency [GHz] -25.5 1 1.5 2 2.5 ZFE eliminates ISI But increases magnitude of noise relative to signal Noise enhancement Particularly bad on channels with notches TX/RX eq. needs large atten./gain EE29C Lecture 5 17 An Alternate Approach: MMSE Don t just cancel ISI Find optimal balance between noise and ISI Minimum Mean Squared Equalizer: EE29C Lecture 5 18
MMSE vs. ZFE, Limitations MMSE allows residual ISI But amplifies noise less Normalized Amplitide 1.8.6.4.2 Unequalized ZFE MMSE 1 2 3 4 5 6 7 8 9 1 11 Symbol Number Unfortunately, MMSE not so straightforward to apply in links Harder to adapt (more later) Noise may not be known EE29C Lecture 5 19 Good News: There Is Another Way Once you know which bit was transmitted You also know exactly what ISI that bit will cause Why not directly cancel the ISI you know is 2 4 6 8 1 12 14 coming? Symbol time 16 18 Amplitude 1.8.6.4.2 EE29C Lecture 5 2
Decision Feedback Equalization (DFE) RX_in Pulse response time FIR Filter Key advantage: no noise enhancement Feedback signal based on perfect digital bits ISI subtracted based on those bits EE29C Lecture 5 21 DFE Issues Only handles postcursors May still need linear (feedforward) filter for pre-cursors RX_in What happens when RX makes a mistake? EE29C Lecture 5 22
DFE Issues: Timing RX_in Need to do all of the following in at most 1UI: Resolve the (small) bit Scale the bit by the coefficient Sum the new analog value EE29C Lecture 5 23 Pulse Shape Interaction RX_in Ideal DFE would actually settle within.5ui Otherwise affects edge position FIR filter can have same issue Fixing it requires an over-sampled (fractional) equalizer EE29C Lecture 5 24
Fractional Equalization Normalized Amplitude 1.8.6.4.2 Symbol-spaced 2x Oversampled 1 2 3 4 5 6 7 8 9 1 Symbol Number EE29C Lecture 5 25