Optimal Linear Precoding with TheoreticalOptimal Linear Precoding with Theoretical and Practical Data Rates in High-Speed S i l Li k B k l C i iSerial-Link Backplane Communication

Vladimir Stojanovic1,2, Amir Amirkhany1, Mark Horowitz1

1Stanford University2R b I2Rambus Inc.

Backplane channel

0

dB]Loss is variable

-20

-10

enua

tion

[d 9" FR4Same backplaneDifferent lengthsDifferent stubs

50

-40

-30Atte

9" FR4, i t b

26" FR4

Attenuation is large

-60

-50 via stub

26" FR4,via stub

>30dB @ 3GHzBut is that bad?

0 2 4 6 8 10frequency [GHz]

Channel now a critical concernNeed communication techniques

2

Need communication techniques

Efficiency of communication

100000

1000000

1000

10000

ost p

er b

itG

b/s)

100

1000

Ene

rgy

com

W/(G

1

10

56Kb/ V 92 12 12Mb/ Gi bit 10Gb/

Gigabit Ethernet or ADSL for links?

56Kb/s V.92modem

12x12Mb/sADSL

modem

GigabitEthernet

10Gb/s High-speed

link

3

gHow do we get 50x improvement in efficiency?

Link modeling issues

No good link system and noise modelsHard to make performance/power tradeoffCannot predict the “right” architecture

Maximum achievable data rates – unknownLimited link communication system design

Peak power constraint in the transmitterNo solution for optimal transmit equalizationNo solution for automatic equalization

4

Outline

Create system level optimization for linksAddress the issues in link modeling

High-speed link modelingSystem level optimizationSystem level optimization

Energy-efficiency

5

A look at the system

High speed link chiplink chip

> 2 GHz signalsg

6

Now, the bandwidth limit is in wires

Previous system models

Borrowed from computer systemsWorst case analysis

Can be too pessimistic in links

Borrowed from data communicationsBorrowed from data communicationsGaussian distributions

Works well near mean Often way off at tails

ISI distribution is bounded

Need accurate modelsNeed accurate models To relate the power/complexity to performance

7

How bad is Gaussian model?

0

df]

Cumulative ISI distribution

-4

-2

roba

bilit

y [c

d

-8

-6log 10

pr

-1040mV error @ 10-10

25% of eye height

0 25 50 75 100re sidual ISI [m V ]

Gaussian model only good down to 10-3 probability

8

y g p yWay pessimistic for much lower probabilities

A new model

Use direct noise and interference statisticsUse direct noise and interference statistics

Main system impairmentsy pInterference

Voltage noise (thermal supply offsets quantization)Voltage noise (thermal, supply, offsets, quantization)

Timing noise – always looked at separatelyKey to integrate with voltage noise sourcesKey to integrate with voltage noise sourcesNeed to map from time to voltage

9

Effect of timing noise

Ideal sampling

Jittered sampling sampling sampling

Voltage noiseVoltage noise when receiver clock is offclock is off

The effect depends on the size of the jitter, the input sequence, and the channel

10

Need effective voltage noise distribution

Example: Effect of transmitter jitter

kbkb

1 TXb ε

ideal

kb

kT

TXkε

Tk )1( +

TXk 1+ε

kT Tk )1( +

TX+ kb

1

2

kkb 1+ε

TXkε

TXk 1+ε

kb−

2 ≈TXkkb ε−noisekb kk

Decompose output into ideal and noiseNoise are pulses at front and end of symbolNoise are pulses at front and end of symbol

Width of pulse is equal to jitter

Approximate with deltas on bandlimited channels

11

V. Stojanović, M. Horowitz, “Modeling and Analysis of High-Speed Links,” IEEE Custom Integrated Circuits Conference, September 2003. (invited)

Jitter Propagation Model

TXw )( jTpa kb

+ kxISIk

x kaprecoder

pulseresponse

idealw )( jTpka k +

jitTXx RXε

k

vddn

)(sHjit

PLL

TXkk 1, +ε

inn⎟⎠⎞

⎜⎝⎛ +

2TjTh

jk

x kε

impulse RX

noise

kk 1, + impulseresponse

∑ +=++sbE

RXISI jTpbkTx )()( φεφ ∑−=

− +=++sbSj

ijkki jTpbkTx )()( φεφ

( ) ( )∑ ⎥⎤

⎢⎡ −+−−−++=++

sbETXRXTXRXRXjitter TjThTjThbkTx )()()( εεφεεφεφ

12

( ) ( )∑−=

−+−− ⎥⎦⎢⎣+++=++

sbSjjkkijkkijkki jThjThbkTx 1)

2()

2()( εεφεεφεφ

Outline

Show system level optimization for linksCreate a framework to evaluate trade-offsCreate a framework to evaluate trade offs

High-speed link modelingg p gSystem level optimization

Limits – What is the capacity of these links?Limits What is the capacity of these links?Improving today’s baseband signaling

Energy-efficiencygy y

13

Baseline channels

20

0

n [d

B]

26" NELCO,t b

(b)

-60

-40

-20

Atte

nuat

ion no stub

-100

-80

-6026" FR4, via stub

0 5 10 15 20

100

frequency [GHz]

Legacy (FR4) - lots of reflectionsMicrowave engineered (NELCO)

14

Capacity calculation

Modified waterfilling

HEN12

⎟⎞

⎜⎛

⎟⎞

⎜⎛

Add phase noise

( )PARNENEEt

HE

HE

nEN

N

n nnnthermal

nn

N1log

21bmaximizelim

1

12222

⎟⎟⎟

⎠⎜⎜⎜

⎝⎟⎟

⎠

⎞

⎜⎜

⎝

⎛

+Γ+=

∑

∑

−

=∞→

θσσ

NnE

PARNENEEts

n

npeakavgn

,...,1,0

..1

1

=≥

==∑=

Concave problem

15

Capacity with link-specific noise

120

140

[Gb/

s]

thermal noiseNELCO120

140

y [G

b/s] FR4

60

80

100

Cap

acity

thermal noise and LC PLL phase noise

thermal noise and ring PLL phase noise

60

80

100

Cap

acity

thermal noise

20

40

60

20

40

60thermal noise and LC PLL phase noise

thermal noise and ring PLL phase noise

-25 -20 -15 -10 -5 00 log10(Clipping probability)

-25 -20 -15 -10 -5 00 log10(Clipping probability)

Given EpeakFind Eavg from PAR (desired clipping probability)

16

Capacity much higher than data rates in today’s links

Available bandwidth

9

10

Capacity with thermal noise

6

7

8

s/H

z

Capacity with thermal noise

Nelco 105Gb/sFR4 70Gb/s

3

4

5#bits

0

1

2

Up to 12GHz

0 5 10 150

frequency [GHz]

17

pNo need to build 40Gs/s transceivers

Uncoded Discrete-multitone

70

80

90

e [G

b/s] a) NELCO

thermal noiseNELCO70

80

90

e [G

b/s] b) FR4FR4

40

50

60

70

Data

rate

thermal noise and LC PLL phase noise

40

50

60

70

Data

rate

thermal noise

10

20

30 thermal noise and ring PLL phase noise

10

20

30 thermal noise and LC PLL phase noise

thermal noise and ring PLL phase noise

Modified Levin-Campello loading for phase noise

-25 -20 -15 -10 -5 00 log10(Clipping probability)

-25 -20 -15 -10 -5 00 log10(Clipping probability)

Modified Levin Campello loading for phase noiseGap is huge for BER=10-15

Too costly to use soft decoders

18

Still, data rates much better than in today’s baseband linksBaseband links ISI limited

Removing ISILinear transmit equalizer

SampledData

Deadband Feedback tapsTx Anticausal tapsData

TapSel

Data

Channel

Decision-feedback equalizer

Tap SelLogicCausal

taps

I

doutNoutP

d

Ω50Ω50

Transmit and Receive Equalization Ch i l f ISI

0eqI

Changes signal to correct for ISIOften easier to work at transmitter

DACs easier than ADCs

19

DACs easier than ADCs

J. Zerbe et al, "Design, Equalization and Clock Recovery for a 2.5-10Gb/s 2-PAM/4-PAM Backplane Transceiver Cell," IEEE Journal Solid-State Circuits, Dec. 2003.

Transmit equalization – headroom constraint

5

0

n [d

B]

unequalizedTx Anticausal tapsPeak power constraint

-15

-10

-5

Atte

nuat

ion

equalized

TxData

Channel

Peak power constraint

0 0.5 1 1.5 2 2.5-25

-20

frequency [GHz]

Amplitude of equalized signal

Causaltaps

Transmit DAC has limited voltage headroom

Amplitude of equalized signaldepends on the channel

Unknown target signal levelsHard to formulate error or objective function

Need to tune the equalizer and receive comparator levels

20

Need to tune the equalizer and receive comparator levels

Optimization example: Power constrained linear precoding

w P

power constraint

gka kake

precoder channelpulse response

g

noise ka

k

( )( ) 222121),( σgwwgwgEgwMSE TTTa ++−= Δ PPP

2)1(Δ E T P

Add i bl i t lif t k t t l l

2

2

)11)(11()1()(

σ+−−=

ΔΔΔΔ

ΔΔ

wwEwEwSINR

TTTTTa

Ta

unbiased PIIPP

Add variable gain to amplify to known target levelFormulate the objective function from error

SINR is not concave in w in general

21

SINR is not concave in w in generalChange objective to quasiconcave unbiasedSINR

Optimal linear precoding

Still, does this objective really relate to link performance? Need to look at noise and interference distributions

15.0ma imi e 1min −−Δ offsetwVwd PDpeak

T PIP

Need to look at noise and interference distributions

( )1..

)11)(11(maximize

1

2/12

1

≤

+−−−−=

ΔΔΔΔ

wtswwEw TT

PDT

PDTT

a

p

σγ

PIIIIP

Minimize BER

1

σ2=wTS0TXw+wTS0

RXw+σ2thermal

Residual dispersion into peak distortionReflections into mean distortion

Includes all link-specific noise sources

22

Includes all link specific noise sources

Multi-level: Offset and jitter are crucial

thermal noise + ff t

thermal noise + offset+ jittth l i offset jitter

25

30

e [G

b/s]

PAM8 25

30

[Gb/

s]

35

40

45

e [G

b/s]

thermal noise

15

20D

ata

rate

PAM16PAM4

PAM215

20

Dat

a ra

te

PAM2

PAM420

25

30

35

Dat

a ra

te

PAM4

PAM16

PAM8

0 2 4 6 8 10 12 14 16 18 200

5

10

0 2 4 6 8 10 12 14 16 18 200

5

10 PAM2

PAM8

0 2 4 6 8 10 12 14 16 18 200

5

10

15PAM2

To make better use of available bandwidth, need better circuits

0 2 4 6 8 10 12 14 16 18 20Symbol rate [Gs/s]

0 2 4 6 8 10 12 14 16 18 20Symbol rate [Gs/s]

0 2 4 6 8 10 12 14 16 18 20Symbol rate [Gs/s]

23

circuitsPAM2/PAM4 robust candidate for next generation links

Full ISI compensation too costly

thermal noisethermal noise + offset

thermal noise + offset+ jitter

14

16

18

20

rate

[Gb/

s]

14

16

18

20

a ra

te [G

b/s]

PAM414

16

18

20

rate

[Gb/

s]

6

8

10

12Dat

a

PAM16PAM4

PAM2PAM8

6

8

10

12Dat

a PAM8

PAM28

10

12Dat

a

PAM2

PAM4

PAM8

0 2 4 6 8 10 12 14 160

2

4

6

0 2 4 6 8 10 12 14 160

2

4

6 PAM2

0 2 4 6 8 10 12 14 160

2

4

6

0 2 4 6 8 10 12 14 16Symbol rate [Gs/s]

0 2 4 6 8 10 12 14 16Symbol rate [Gs/s]

0 2 4 6 8 10 12 14 16Symbol rate [Gs/s]

Today’s links cannot afford to compensate all ISI

24

Limits today’s maximum achievable data rates

Outline

Show system level optimization for linksCreate a framework to evaluate trade-offsCreate a framework to evaluate trade offs

High-speed link modelingg p gSystem level optimization

Limits – What is the capacity of these links?Limits What is the capacity of these links?Improving today’s baseband signaling

Energy-efficiencygy y

25

Energy efficiency of link components

120

140

W/G

b/s]

5.514

16

18

mW

/Gb/

s]

PAM4PAM2

60

80

100

PAM2 Tx5 Rx20PAM2 Tx5 Rx1+20PAM2 Tx50 Rx80PAM4 Tx5 Rx20 p

er b

it [m

115 9

4

6

8

10

12

ost p

er b

it [m

20

40

PAM4 Tx5 Rx20PAM4 Tx50 Rx80

nerg

y co

st

1 2.2

811

1.5

5.9

0.3

0.450

2

4

T T R T R S PLL CDR

Ener

gy c

o

Large chunk of energy on timing sub-system (PLL CDR)

0 2 4 6 8 10 12 14 16 18 200

Data rate [Gb/s]EnTxTap RxTap RxSamp PLL CDR

Large chunk of energy on timing sub-system (PLL, CDR)Different scaling for PAM2/PAM4

Energy scales linearly with technology

26

Likely to remain a key constraintCan’t count on very complex filters

Conclusions

Interfaces are challenging system designsGood space to explore system level optimization

Baseband links limited to PAM2,4Residual ISI biggest factorAl b ff t d jittAlso by offset and jitter

Still far from the capacity of these linksStill, far from the capacity of these linksLooking into multi-tone to mitigate ISIImproves energy efficiency

27

p gy y

BER sensitivity

-2

0

0(BER

) a) BER sensitivity to thermal noise-2

0

0(BER

) b) BER sensitivity to jitter

-8

-6

-4

log 10

-8

-6

-4

log 1

-12

-10 scaled ZFE precoder

optimized precoder-12

-10scaled ZFE precoder

-50 -40 -30 -20 -10 0 10 20 30

-14

Thermal noise attenuation from nominal [dB]-10 -5 0 5 10 15 20 25 30

-14 optimized precoder

Jitter attenuation from nominal [dB]

Optimized BER 2-3 orders better than ZFEThermal noise not critical

28

Thermal noise not criticalJitter is critical