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Analog Multi-Tone Signaling for
High-Speed
g
p
Backplane
p
Electrical
Links
A. Amirkhany1, A. Abbasfar2, V. Stojanovic3, and M. Horowitz1,2
1Stanford
St f d
University
U i
it
2Rambus
3Massachusetts
Inc
Institute of Technology
High-Speed
g
p
Link
0
Frequency Response
3" TOP
dB
-20
20
-40
-60
60 3" BUTTOM
-80
20" TOP
-100
0
5
10
GHz
15
20
• Multi Gb/sec chip
chip-to-chip
to chip
communication over PCB
traces
traces.
• Routers, XAUI, PCI express
7/2/2008
Slide 2
Channel
State of the Art Links
Rx
W1
W2
W3
W4
Line Driver
T
Tx
Wb1 Wb2
Wbk
• Baseband 2PAM or 4PAM
• 4-5 tap discrete linear transmit equalizer
p (predictive
(p
or partial
p
response)
p
) DFE
• 5-20 tap
• Designed for BER of 10-15
• No error detection/correction coding
7/2/2008
Slide 3
dB
Potential
ote t a o
of Multi-Tone
ut o e
S21 (dB)
• Better power allocation over channels
with a notch
f (GHz)
• Parallelized data stream in frequency
leading to implementation advantages
7/2/2008
Slide 4
Design
g Considerations
• Power efficiency is the main constraint
• Cannot afford high-resolution ADC
• Limits signal processing
• Rules out DMT techniques
• A customized MT architecture is
required
i d
• Few sub-channels can create close to
optimum transmit spectrum
7/2/2008
Slide 5
dB
Analog
g Multi-Tone ((AMT))
• A bank of parallel links on
different carrier frequencies
• Sub-channels not independent
• Inter-channel
I t
h
l interference
i t f
(ICI)
exists
7/2/2008
Slide 6
C
Conceptual
t l
Practical Architecture
• N-times over-sampled equalizers per sub-channel
• Tx power equal to a BB covering same BW
• Receive filters are integrators
• MIMO DFE in the receiver
• DFE power equal to a BB covering same BW
7/2/2008
Slide 7
Analysis
a ys s Framework
a e o (Co
(Convex
e - SOC
SOCP))
• Find Tx equalizer and Rx DFE taps that
• Minimize transmit voltage (power)
• Meet BER constraint per sub-channel
(
2 1− 2
−bk
)Q(
0.5d mink − offsetk
σ noise
) ≤ Pe
• offsetk: Receiver sampler dead-band (fixed)
• dmin: Minimum distance at Rx (linear)
•
σnoise: Sigma residual interf. and thermal (norm-2)
SOCP:
Minimize VPeak (Tx Peak Voltage)
Subject to :
BERk < Pe
VTxi _ Max < VPeak
7/2/2008
Slide 8
for k = 1, 2, ..., N
for i = 1, 2, ..., N
ZFE with BER Constrained Power Allocation
• Step 1: Independent sub-channel tap
optimization
ti i ti (ZFE)
• Minimize interference power from one transmitter
to all receivers (find WTx,k and WFB,km)
• Independent of sub-channel transmitter power
7/2/2008
Slide 9
ZFE with BER Constrained Power Allocation
• Step 2: Joint power allocation (BER
constrained)
• Assume Tx voltage of gk for each sub-channel
• Model interference as peak distortion
• BER constraint per sub-channel is linear in gk
• SOCP reduces to an LP in vector g
Minimize VPeak (Tx Peak Voltage)
Subject to :
Bg > b ( BER Const)
Ag < VPeak 1 (Peak Voltage Const)
7/2/2008
Slide 10
• A,B fixed since taps are
fixed
• Solution is g = B-1b
Closed From Jitter Modeling
g
Tx Jitter
xN-1
W(N-1)
CN-1
N1
(n)
y
Rx Jitter
s=[1 -1]
h
x1
W1
C1
x0
W0
C0
rN-1
r1
r0
Variance at kth Rx output
σ
N −1
2
TX _ jitterk
7/2/2008
= ∑ w S ( H H k • R Φ )Sw m σ
m =0
Slide 11
T
m
T
T
k
2
RX _ jitterk
⎛ N −1 T T T
⎞
= σ φk ⎜ ∑ w m S H k H k Sw m ⎟
⎝ m =0
⎠
2
Performance on a Channel with Notch
Sub-channel Response at Rx Output
Equalized Frequency Response
CHANNEL
-20
4PAM
2PAM
MT-2nd
MT-3rd
dB
B
-40
MT-1st
MT: 12Gbps
4PAM: 5Gbps
2PAM: 2.5Gbps
-60
-80
-100
100
7/2/2008
Slide 12
2
4
Frequency (GHz)
6
Performance on a Smooth Channel
Frequency Response
0
Peak
k Voltage (V
V)
2 PAM
5.0mV Deadband
dB
-20
-40
FR4
-60
-80
0
2
4
6
Frequency (GHz)
8
10
10
0
4 PAM
5.0mV
5
0mV Deadband
AMT (4P,2P,2P)
2.5mV Deadband
10
-1
6
8
10
12
Data Rate (Gbps)
14
• Comparable hardware complexity
• For same VPeak (transmit voltage)
• AMT can achieve higher rates
• Needs
N d better
b tt Rx
R precision
i i att lower
l
rates
t
• Possible since AMT samplers operate at half BB (4PAM) rate
7/2/2008
Slide 13
Conclusion
• Power efficiency in links requires customized
MT architectures
• The AMT architecture has comparable
y with BB
complexity
• AMT has
as c
clear
ea ad
advantage
a tage o
over
e c
channels
a e s with
t
a notch
• Comparable performance over smooth channels
7/2/2008
Slide 14