Part III

1
Part III Wireline Multiuser Basics
Prof. John M. Cioffi Dept of EE Stanford
University cioffi_at_stanford.edu
September 9, 2001
March 31, 2001
April 26 2001
2
Parts 3 and 4 Outline/Schedule

• 200-245 MU Theory
• 245-330 channels for wireline
• 330-400 Coffee
• 400-430 DSL and Ethernet arch
• 430-515 Multiuser improvements
• 515-530 Zeke

3
Part 3 Outline

• Levels of Coordination among Multi Users
• GDFE Theory
• Solutions
• MUD no coordination
• Iterative Waterfilling Interference Chan
• Vectoring
• Channels

4
Wireline Multiuser Basics
. . .

• Goal Best PHY signals for user sharing of
  channel
• Set spectra/signals, optimization via controller

5
Ultimate Goal use of Rate Regions
Rlong
Spectral pair 1
Spectral pair 2
Rshort

• Plot of all possible rates of users
• Any point in region is possible, but each with
  different spectra
• Varies for each channel

6
Wireline Coordination ?

• How much coordination among lines is allowed?
• None
• Spectra, all or some
• Signals
• Answer it depends on application (DSL, ethernet)
  and evolves with time

7
No Coordination
. . .
Controller ?

• Multiuser Detectors only (MUD)
• Different users could be competitive service
  providers (different DSLAMS, different
  modulation)
• Unbundled state of art

8
Coordinated Spectra (only)
Shared channel
User 1
User 1
User 2
User 2
. . .
User L
User L
Controller

• interference problem in Information Theory
• Good, but not optimum, solution known
• Iterative waterfilling

9
Coordinated 1-sided Signals
User 1
Shared channel
Router DSLAMS
User 2
. . .
User L
Controller

• Multiple access and Broadcast problems
• Monopoly Service Provider

10
Coordinated 2-sided Signals
Shared channel
Router DSLAMS
Router DSLAMS
Controller
Controller

• Full Vectoring Problem private networks (cat 5)
• Highest data rates

11
Part 3 Outline

• Coordination Levels
• GDFE Theory
• Solutions
• MUD no coordination
• Iterative Waterfilling Interference Chan
• Vectoring
• Channels

12
Block/Packet Transmission channel

• Assumes NO NEXT (FDM used to separate up/down
• X is input vector of
• One or up to L users data samples
• Coordinated or not, L users x mN dimensions
• Y is output vector of
• One or more receivers output packets
• Coordinated or not, L users x nN dimensions
• H is linear coupling, Noise vector is n

13
Generalized DFE

• W and B are matrix operations on the packets Y
  and X
• Traditional structures become matrices that do
  not necessarily correspond to convolution
• Applies to all single-user and multiple-user
  situations

14
Finding the Equivalent Channel
X
H
good part - gets through channel
Input components best are green
null space - blocked by channel
null space - zeroed by design
15
GDFE Solutions

• Always can be combined with good AWGN transmit
  codes and green signal optimization to get best
  performance
• bclog(1 SNRGDFE)
• Use good (turbo, LDPC) code on green components
• fundamental structure used to analyze (not
  implement)
• Useful one way or another in all the multiple
  user problems
• Introduced Cioffi/Forney, 1996 see 5

16
Part 3 Outline

• Coordination Levels
• GDFE Theory
• Solutions
• MUD no coordination
• Iterative Waterfilling Interference Chan
• Vectoring
• Channels

17
No coordination - MUD

• Similar to wireless case
• Various interference cancellation strategies
• Linear
• Decision-aided
• Each receiver learns or estimates channel from
  all users
• Each receiver attempts to reduce/eliminate
  signals from all other users while estimating the
  signal it wants
• Other signals may not be orthogonal for many
  reasons
• Intersymbol interference
• Interchannel interference (crosstalk)
• Wireline case differences (from wireless)
• Crosstalkers may be very large or very small, and
  still significant in all cases
• Channel is relatively stationary (usually)

18
MUD Channel Model

• yHx n H1 x1 H2 x2 n
• HH1 H2 HL

19
(L users) x (1N dimensions) Generalized DFE

• Tries to estimate all users, even if we dont
  want them all
• Helps estimate the user of interest in
  no-coordination problem
• Best that can be done, given any input spectra
• Error propagation can be enormous degradation

20
Error Prop Fix Iterative Decoding
h1,1
Channel output
Decoder 1 (prob of x1 symbol)
p1
Hard Decison
x1
User 1


x2
n
User 2
noise
h1,2
Hard Decison
Decoder 2 (prob of x2 symbol)
p2
(typically not implemented)

• Compute probabilities, rather than hard decisions
• when done iterating, then do hard decision
• Effectively achieves level of performance of
  no-error GDFE/capacity

21
Soft vs Hard Canceller 18
Soft symbols
Hard decisions
Soft or hard x3

• ci is average value of xi, computed from p.d.

22
3 step iteration

• Compute new soft output
• compute probability distribution from soft
  outputs for each output dimension
• compute new soft symbol and variance
• Do it again and again, cycling through estimates
  of all users signals x

23
Example for MUD HPNA into VDSL
CO
vdsl
hpna vdsl
telco
hpna
home

• No signal necessarily much larger than another
• Error propagation would destroy GDFE alone
• Iterative decoding with GDFE works at near
  optimum levels (I.e., as if there were no error
  prop.)

24
Optimum Detector
8 Mbps HLAN
26 Mbps VDSL

• 6 tones of 256 zeroed in 5-10 MHz band

25
Example DSL and HPNA

• VDSL and HPNA both share 5-10 MHz on twisted pair
• Use GDFE concept and soft-cancellation at rcvr
  for VDSL
• Works like HPNA wasnt there (mutliuser capacity
  on phone line is 200 Mbps vs 20 Mbps when other
  user is Gaussian noise)

26
Part 3 Outline

• Coordination Levels
• GDFE Theory
• Solutions
• MUD no coordination
• Iterative Waterfilling Interference Chan
• Vectoring
• Channels

27
Interference Channel Spectral Balancing

• No transmit or receive signal coordination
• Only spectra can be designed jointly
• Only cases for which opt. solution is known are
• 1N dimensions by L users - broadcast
• L by 1N multiple access
• 1N by 1N single user Water Filling
• General case, a good (not nec opt) solution is
  known as iterative waterfilling

28
Sub optimal Solution
GDFE 1
Shared channel
GDFE 1
GDFE 2
GDFE 2
. . .
GDFE 3
GDFE L
Controller

• GDFE on each receiver for all L users
• Best for any given spectra of all users
• Dont know best spectra for set of users
• Try to optimize anyway using iterative
  waterfilling

29
Waterfilling
NSR(f)
S(f)
?/g(f) ? N(f)/H(f)2

• Waterfilling is known optimum on single-user
  channel

30
Iterative Waterfilling 15,16

• Each channel considers all others to have fixed
  spectra
• Can start with flat on all
• Waterfilling executed for user 1
• New spectrum for user 1 replaces old
• Waterfilling executed for user 2 with new spectra
  for 1
• New spectra for user 2 replaces old
• user N
• Recycle a few times
• Converges close to optimum solution for
  Inteference channel nearly maximizes sum of all
  rates

31
Generation of Rate Regions
Rlong
Spectral pair 1
Spectral pair 2
Rshort

• Each user has power limit
• For each user
• Lower the power limit in IterWater and get
  increased rates on others
• Sketch N-dimensional rate region by running
  IterWater for many different power combinations
• Check if desired rate is in region

32
Part 3 Outline

• Coordination Levels
• GDFE Theory
• Solutions
• MUD no coordination
• Iterative Waterfilling Interference Chan
• Vectoring
• Channels

33
Multiple Access Up Link
User 1
Shared Channel H LN x LN
GDFE DSLAM
User 2
. . .
User L
Controller

• GDFE at one side with HH1 H2 HL
• Vector receiver, with synch-DMT, LxL GDFE
• Best Solution now known 15 Yu, Rhee, Cioffi
  (only FDM when there is only one receiver 14
  more complicated than that here)
• May have all L users on each tone
• GDFE separates them at DSLAM
• May have error propagation, so iterative decoding
  necessary

34
Input Spectra

• Can again be computed by iterative waterfilling
  across N tones
• known optimum in this multiple-access case
• Each tone is L x L GDFE receiver with DMT
  modulation on channel
• Can approximately compute a lower bound on rate
  region using iterative waterfilling and varying
  powers on each channel as in spectral balancing

35
Broadcast Downlink
simple 1
Shared Channel H LN x LN
Vector DSLAM Vector precoder
simple 2
. . .
simple L
Controller

• Optimum known (solved after 30 yrs in 2001)
• More complicated version of IterWater
• See Wei Yu recent work 17 , iterative solution
  of Ricatti eqn
• Achieves nearly same performance as multiple
  access for most wireline cases, but optimization
  occurs with precoder at transmit side to leave
  each receiver independent GDFE at each receiver
  is diagonal (no feedback) and is slicer for each
  user.

36
Ginis/Negi QR Simplification of Vectored GDFE
SNR
decision sequence for packet
WQ
X

Y
Z
BR

• ZF-GDFE close to MMSE-GDFE on wireline channels
  (max rate sum)
• FEXT from any source is less than on-line signal
  from that source
• HQR (orthogonal, triangular)
• Applies directly to Multiple Access Uplink
  Problem for each tone

37
Vectored Transmitter - downlink
X
x
Q

mod
X
I-R

• Vector version of Tomlinson precoder, done for
  each tone independently
• Prewarps transmitted signal to avert FEXT

38
Full Vectoring Solution SVD
Y
decision sequence for packet
X
WF
H
M
X

• HMLF (M,F orthogonal, L diagonal)
• Singular value decomposition
• Vectored VDSL or VDMT
• Always gets max rate-sum capacity
• QR is close on DSL channels, but not in all
  situations
• Easy to implement on per-tone basis
• MIMO Echo cancellation possible (so full band)

39
Part 3 Outline

• Coordination Levels
• GDFE Theory
• Solutions
• MUD no coordination
• Iterative Waterfilling Interference Chan
• Vectoring MA, Broadcast
• Full Vectoring solution
• Channels

40
ADSL Loops
d
d
3-5 mile loops
loops with bridge taps
41
Crosstalk
phone line 1
NEXT
FEXT
phone line 2
Dominant noises, increased coupling at
higher frequencies - must be mitigated in
design NEXT - 10-13 f1.5 FEXT - 10-19 d
H(f)2 f2
42
Other Noises

• Radio Noise, AM, HAM
• 1 mW differential into rcvr
• must reject HAM by 70-90 dB (VDSL) and AM by
  20-40 dB (ADSL)
• Impulse Noise
• 10s millivolts
• 100s microseconds
• narrowband (high amplitude)
• broadband (low amplitude)

43
Radio Emissions

• like crosstalk, except into radio receivers
• VDSL amateur (HAM) bands Public Safety bands
• transmit in discontinuous bands

44
MIMO Line Quantities 3

• Matrix Channel Xfer
• Individual lines ij
• Magnitude profiles (i.e., no phase information)
• Virtual Binder Group

(
)
)
(

f
H
f
H
ij


,...,
1

,...,
1
K
j
K
i
45
Noises 3,4

• Noises are unknown crosstalkers and
  thermal/radio
• Psd N(f)
• Frequency bandwidth of measurement
• Time interval for measurement
• Requisite accuracy

46
Source Information 3,5

• Clock offsets can be determined at various
  points for virtual binder lines
• Transmit power level needs reporting

47
Channel ID 1
nk

Size-N IFFT (with prefix)

pk

Xn
Size-N FFT


En

P
-
n

• Estimate gains at several frequencies
• Estimate noise variances at same freqs

48
Gain Estimation

• Divide/average channel-out by known in
• Need about L40 symbols of training to reduce
  gain estimation error to .1 dB

Y
L
1
å
ˆ

n
l
,
P
n
X
L

l
1
n
l
,
49
Noise Estimation

• Use Errors from Gain estimation
• Need L4000 for .1 dB error
• SNR is then gain-squared/noise estimate

L
1
å
2

s
2

ˆ
E
n
n
,
1
L

l
1
50
MIMO Complications

• Training may not be available
• Use actual data
• Different systems may not have same clock
• Interpolation problem

51
Basic MIMO crosstalk ID 4

• NEXTs and FEXTS
• Difference services (ADSL, HDSL ,)
• Different operators (unbundling)

52
Generic Crosstalk Model
noise n

• Mathematical model

Xmit 0
Channel h0

Rcvr 0 y
x0
Xmit 1
Crosstalk channel h1

• Objectives
• find hi(m)
• If each solely excited with training sequence,
  then previous method applies directly for each
• Rare if ever occurrence

x1
Crosstalk channel hk
Xmit K
xK
53
Step 1 Data Acquisition

• Network Maintenance Center (NMC)
• Acquire data during a pre-defined time period

Modem 0
Modem 0
Customer Premises
CO
Modem k
Modem k
SNMP
SNMP
NMC
54
Step 2 Resampling

• Different services
• Different sampling rate
• Time-varying crosstalk function
• Resample the transmitted input data
• Stationary crosstalk function

xc(t)
Tx Filter p(t)
xTalk hi(t)
Rcvr Filter hlp(t)
y
x(n)
1/T
1/T'
55
Timing difference

• Different modems ? Different time stamps
• Pre-defined periods do not align perfectly

Modem 0
DSLAM
NMC
Modem i
DSLAM
Modem k
56
Step 3 Timing Difference Estimation

• Example of timing difference
• Cross-correlation
• Calculate cross-correlation between xi and y,
  Rxiy(l)
• Detect the peak of Rxiy(l)

xi(0)
xi(di)
xi(Lt)
y(0)
y(Lt)
di
Lt1
time
30000
30100
57
Cross-correlation
58
Step 4 Crosstalk Functions Estimation

• Modified mathematical model

• Vector form

59
NEXTs and FEXTs
FEXTs
NEXTs
60
HDSL NEXT, time response
61
Estimation Error
62
MIMO Channel ID Method with training packets

• Correlate to rough timing alignment
• I/O packets stored around time stamp on lines and
  reported to maintenance center
• Determination of exact timing offset
• Interpolation of inputs to common timing phase
• Least-Squares fitting
• See JSAC or 4, C. Zeng for DSL

63
EM (Blind) Training
A block of received data can be collected to form
64
ML and EM Solutions

• Maximum Likelihood (complex)
• Matrix inversion for each possible sequence
• Expectation Maximization (easier)
• No training 1 matrix inversion

65
Block EM channel estimation
1. Compute
and invert.
2. Compute
using
3. Channel and noise variance estimate is given
by
66
Simulation Setup

• ADSL-DBM modem
• 1 NEXT (SSDSL) and
• 1 FEXT (ADSL)
• Initial condition acquired from sync symbol or
  from network maintenance center
• 500 m line FEXT source
• 10 ms of data (L40)

67
EM Simulation Results
68
Motivation

• Eliminates delay
• Reduces storage
• Track time-variant parameters or locally
  stationary processes in an adaptive manner
• Block stationary assumption no longer needed
• See 3

69
Parts 3 and 4 Outline/Schedule

• 200-245 MU Theory
• 245-330 channels for wireline
• 330-400 Coffee
• 400-430 DSL and Ethernet arch
• 430-515 Multiuser improvements