High Speed Serial Links
EE290C,Berkeley
Equalization Techniques
Prepared by: Eng. Muhammed Abdulmonsif, LinkedIn
Lecture 5
ISI ‘Inter-Symbol Interference’
o The main purpose of our system is to get the same bit you transmit , and one of the main
issues that violates this purpose is ISI.
o ISI reflects the effect of previous bits and the coming bit on the current bit.
o As the channel is bandlimited and has LPF response the high-speed transmitted pulses
spread out with small delay causing ISI.
o Another issue affects the received pulses shape is reflections due to impedance
discontinuities , connectors , vias ,etc.
Equalization
o The treatment of these issues such ISI and reflections is using
equalizers.
o The main idea is to theoretically get flatten response by adding equalizers
have high pass response with the low pass response of the channel.
o The previous behavior cancels ISI and there is another technique to
cancel reflections.
o Distinctions for different types of equalizers are linear vs non-linear
,continuous-time vs discrete-time and minimize ISI vs ISI + noise. 1
CTLE ‘ Continuous-Time Linear Equalizer’
o Assuming first order LPF channel response , we use a circuit
that inverts the response of the channel, but any real circuit is
bandwidth-limited and has dominant pole.
o CTLE provides high-frequency gain boost starting from a zero in
the same position of the channel dominant pole (this position
may vary so tuning zero position is required ) ,but the dominant
pole of the CTLE takes over.
o The most common implementation for CTLE is RC source-
degenerated differential pair which provides low gain at low
frequencies and increases with higher frequencies.
o The dominant pole of CTLE is related to the data rate
0.5~0.667 𝑑𝑎𝑡𝑎 𝑟𝑎𝑡𝑒 𝑤𝑖𝑡ℎ 𝑁𝑅𝑍 .
o The CTLE main issues:
➢ Limited to first-order compensation (two cascaded CTLE provide
+40db/decade but overall BW reduction and more power ).
➢ To cancel reflections, we need a circuit has a lot of poles and zeros
,CTLE can’t invert the actual channel response, another types of
equalizers used for that.
➢ Noise amplification. 2
Linear FIR ‘ Finite Impulse Response ’ Filter
o We switch from the continuous-time domain to work in the discrete-time
domain, the delayed samples of data is weighted by different coefficients
,then added together.
o Each tap coefficient refers to pre/post cursor in the pulse response.
o This circuit is more flexible in adaptation than CTLE as each tap has an
independent coefficient.
o This operation is done in Tx as the data is easily delayed by using flip-flops.
o Digital delay is easier than analog delay and is done by digital gates without
noise , but analog delay operation is painful.
ZFE ‘ Zero Forcing ’
o It’s one of the methods to set the coefficients of FIR filter.
o It forces the channel response to be single bit, forces ISI to be zero.
o The convolution operation between the input and LTI system can be done
as matrix multiplication between the input vector and the convolution
matrix of the system impulse response ,the convolution matrix shows the
memory characteristics of LTI system (ISI).
o Assume the channel pulse response as main cursor and two post-cursors.
o Assume the linear FIR equalizer has 3-taps. 3
ℎ0 0 0
ℎ1 ℎ0 0 𝑊0
𝐶ℎ𝑎𝑛𝑛𝑒𝑙 𝐶𝑜𝑛𝑣𝑜𝑙𝑢𝑎𝑡𝑖𝑜𝑛 𝑀𝑎𝑡𝑟𝑖𝑥 ≜ 𝐻𝐶𝐻 = ℎ2 ℎ1 ℎ0 𝐸𝑞𝑢𝑎𝑙𝑖𝑧𝑒𝑟 − 𝑡𝑎𝑝𝑠 𝐶𝑜𝑒𝑓𝑓𝑖𝑒𝑐𝑖𝑒𝑛𝑡𝑠 ≜ 𝑊𝑍𝐹𝐸 = 𝑊1
0 ℎ2 ℎ1 𝑊2
0 0 ℎ2
o The desired event, when single bit is at the input , single it appears at the output. 1
0
o Assume no channel delay & no pre-cursors so the desired output vector: 𝑌𝑑𝑒𝑠 = 0
o Ideally: 𝑌𝑑𝑒𝑠 = 𝐻𝐶𝐻 . 𝑊𝑍𝐹𝐸 0
o We try to solve 5 equations for 3 unknowns (desired taps coefficients ) so there is no exact solution for 0
these equations hence we should use least square method to find set of coefficients values that
minimizes the total error between the actual and estimated values.
𝑀𝑖𝑛𝑖𝑚𝑖𝑧𝑒 𝑌𝑑𝑒𝑠 − 𝐻𝐶𝐻 . 𝑊𝑍𝐹𝐸 2
o The result after optimization with least square fitting in linear algebra:
𝑊𝑍𝐹𝐸 = (𝐻𝐶𝐻 𝑇 . 𝐻𝐶𝐻 )−1 . 𝐻𝐶𝐻 𝑇 . 𝑌𝑑𝑒𝑠
o ZF tries to compensate all the channel loss, but Tx has a peak swing constraint, so the transmitted signal including
equalization must be within the acceptable swing , hence instead of emphasizing high-frequency stuff the Tx equalization
de-emphasizes low-frequency stuff.
o After this swing passes the channel the received amplitude at Rx is reduced so we faces low SNR issue.
4
Noise
o The small equalized signal feed to Rx relative to the noise will have
worse SNR.
o Linear equalization leads to noise Enhancement, linear equalization at
Tx applies attenuation to the signal and the linear equalization at Rx
applies gain to noise.
o There is a big issue with channels have notches as the equalizer tends
to make the signal level below the bottom of the notch level.
MMSE ‘ Minimum Mean Squared Error ’
o The minimum mean squared equalizer finds the optimal balance between noise and ISI.
o Not just cancel ISI it tends to minimize the overall mean squared error including noise.
−1
1
𝑊𝑀𝑀𝑆𝐸 = . 𝐼 + 𝐻𝐶𝐻 𝑇 . 𝐻𝐶𝐻 . 𝐻𝐶𝐻 𝑇 . 𝑌𝑑𝑒𝑠
𝑆𝑁𝑅
MMSE vs ZFE
o MMSE allows residual ISI ,but amplifies noise less ,but unfortunately, it’s very rarely used in
links and has difficulties: - Harder to adapt and - noise may not be known.
o Another good way to avoid noise enhancement is that once you know which bit was transmitted
(1 or 0 ) you subtract or add the residual ISI exists in the response. 5
DFE ‘ Decision Feedback Equalizer ’
o The main idea is to take the correct decision and subtract its
contribution in the coming bits to cancel ISI.
o DFE cancels the residual ISI without noise enhancement :
➢ The feedback signal is based on perfect digital bits.
➢ ISI is subtracted based on those bits.
o DFE only cancels post-cursors.
o If there is a mistake in the decision ,ISI is doubled ,hence you keep
making wrong decisions which called error propagation ,and it’s
not a big issue as BER is very low ~10−15
Timing
o All things must settle in one UI ‘unit interval’ :
➢ Resolve the small bit.
➢ Scale the bit by the coefficient.
➢ Sum the new analog value.
o The toughest path is the first one as it’s the critical path.
o But when we recover data and clock, we use edge sampling so actually we need all things to settle in 0.5UI.
6
Pulse Shape Interaction
o Ideal DFE would settle in 0.5UI otherwise affects the edge position.
o The amount of ISI at the left half a symbol time away is different from ISI at the full
symbol time away, so there will be different coefficients for the sample at half time and
the full time.
o We can fix that by oversampling using fractional equalizer.
Fractional Equalization
o The delay units in the FIR filter is doubled , but each one cause 0.5-bit delay and
each multiplied by different tap coefficient.
o Issues:
➢ It’s challenging to run the symbol rate hence it’s hard for half symbol rate.
➢ More area and power consumption.
