1 Multiuser Detection for CDMA Anders Høst-Madsen (with contributions from Yu Jaechon, Ph.D student) TRLabs & University of Calgary

1

Multiuser Detection for CDMA

Anders Høst-MadsenAnders Høst-Madsen(with contributions from Yu Jaechon, Ph.D student)(with contributions from Yu Jaechon, Ph.D student)

TRTRLabsLabs & University of Calgary & University of Calgary

Overview

Introduction Communications Signal Processing

CDMA 3G CDMA

Multiuser Detection (MUD) Basics Blind MUD Group-blind MUD Performance

Some Impression ofa Changing Korea

Compared with 2 years ago A lot has changed, fast

Internet 90% of subway ads about internet All ads have internet address

Cell phones Everyman’s Fashion item Small!

Even babies in Korea have mobile phones!

The Demands

“The future of the internet is wireless,” Steve Balmer, CEO Microsoft Now

Internet through telephone Wireless voice phones

Emerging High-speed internet (ADSL, cable, satellite, fixed wireless) Some wireless terminals (Nokia 9000, Palm VII, RIM Blackberry) Web on wireless phones

Future Wireless everything

– Internet terminals– LAN, home networks– Devices (Bluetooth)

Wireless video phones? More webphones than wired internet connections in 2004 (Ericsson, Nokia, Motorola) All wireless phones web enabled from 2001 (Nokia)

The Constraints

Limited spectrum Limited power Complex channels

Multipath, shading Interference: Other users, other electronics

Solutions

Efficient compression Coding Channel signal processing Efficient, cost-controlled

media access Software radio

New standards for mobile communications 3rd generation systems W-CDMA cdma2000

4th generation by year 2010

The Communication Channel

Com-pression

Transmitter ReceiverSpeech

Data

Video

UnknownUnknownchannelchannel

Sourcecoding

Sourcecoding Channel

coding

Channelcoding

Adaptivetransmission

Adaptivetransmission

Signalprocessing

Signalprocessing

Channel Dispersion (Low pass) filter effect (wireline

filters, frequency selective fading) Intersymbol Interference (ISI) Non-linear distortions (power

amplifiers)

Multipath Slow fading Time selective

fading Space-selective

fading

Interference External Interference (other

electronics, communications, cars)

Multiple Access Interference (MAI) (other users using the same channel)

Echo (line hybrids, room microphones, hands-free mobiles)

The Wireless Channel

Frequency-selective fading:ISI

Doppler spread:Time-varying channel

Space-selective fading:Beamforming

Path loss

DS/CDMA†

Applications US IS-95 standard Korean cellular system IMT-2000 (wide band (WB) CDMA) Part of future European Frames

standards

Principle Users share frequency and time Distinguished by unique code Separated by correlation with code

†Direct Sequence Code Division Multiple Access

3G CDMA

cdma2000 North America, Korea? Compatible with IS-95 Promoted by Qualcomm Long codes, synchronous

Wideband CDMA (WCDMA) Europe, Japan Compatible with GSM Promoted by Nokia, Ericsson Long/short codes, asynchronous FDD and TDD modes

Long versus Short Codes

Principle Code “infinite”

Applications IS-95 cdma2000

Advantages Interference averaged out

Disadvantages Limited signal processing options

Principle Code repeats on every symbol

Applications W-CDMA (FDD)? W-CDMA (TDD)

Advantages More signal processing options Higher capacity

Disadvantages Without advanced processing, high

interference

Long Codes Short Codes

Multi-user Detection

Multiple-Access Interference (MAI) Due to non-orthogonality of codes Caused by channel dispersion

Multiuser detection reduction of MAI through

interference cancellation 2-4 times capacity increase of

cellular systems Probably part of future wireless

systems (cellular, satellite, WLAN)– Included in WCDMA TDD standard– Several companies involved:

Siemens, Nokia, Nortel– Some field trials [Siemens]

History of Multi-user Detection

Optimum Multi-user Detector

Linear Multi-user Detector

Subtractive Interference Cancellation Detector

Decorrelating Detector

Parallel IC

Successive IC

Blind MMSE Detector

Blind Decorrelating Detector

Minimum Mean Squared Error (MMSE) Detector

Group-Blind MMSE

Synchronous CDMA

K users with no ISI. Sufficient to consider

signal in single symbol interval, i.e., [0,T]

Received signal

r t b A s t n t t Tk k kk

K

( ) ( ) ( ), [ , ]

1

0

where bk {-1,+1} is the k’th user’s transmitted bit.

Ak is the k’th user’s amplitude

sk(t) is the k’th user’s waveform (code or PN sequence)

n(t) is additive, white Gaussian noise.

Conventional detector

Matchedfilter bank

s1(t)

s2(t)

sK(t)

T

t = i T

t = i T

t = i T

y1

y2

yK

Decision

Decision

Decision

b1

......... .........

r(t) T

T

b1

bK

Detection of CDMA signals

The signal is processed by cross correlation (or matched filtering):

In the conventional detector, the estimate of the k’th bit is

If the MAI term is not small, the error probability will be large MAI can be kept small by

small cross correlation between codes ( small) Power control (all Ai same value)

y s t r t dt

A b s t s t dt A b s t s t dt s t n t dt

k k

T

k k k k

T

i i k i

T

i kk

T

( ) ( )

( ) ( ) ( ) ( ) ( ) ( )

0

0 0 0

sgn( )b yk k

Desired signal Multiple Access Interference (MAI) noise

s t s t dtk i

T( ) ( )

0

r t b A s t n t t Tk k kk

K

( ) ( ) ( ), [ , ]

1

0

Signals on Vector Form


dttrtsy

dttrtsy

T

T

0

22

0

11

)()(

)()(

)()()()( 222111 tntsAbtsAbtr

dttntsAbtsAbtsy

dttntsAbtsAbtsy

T

T

0

22211122

0

22211111

)()()()(

)()()()(



)()()()( 222111 tntsAbtsAbtr

dttntsAbtsAbtsy

dttntsAbtsAbtsy

T

T

0

11122222

0

22211111

)()()()(

)()()()(



dttstsAb

dttstsAb

T

T

0

2222

0

1111

)()(

)()(

dttntsAbtsAbtsy

dttntsAbtsAbtsy

T

T

0

11122222

0

22211111

)()()()(

)()()()(



dttstsAb

dttstsAb

T

T

0

2222

0

1111

)()(

)()(

dttstsAb

dttstsAb

T

T

0

1211

0

2122

)()(

)()(

dttnts

dttnts

T

T

0

2

0

1

)()(

)()(

dttstsAby

dttstsAby

T

T

0

22222

0

11111

)()(

)()(

dttstsAb

dttstsAb

T

T

0

1211

0

2122

)()(

)()(

dttnts

dttnts

T

T

0

2

0

1

)()(

)()(



=1

=1 =12

=12

=n1

=n2

2121122

1122211

2

1

nAbAb

nAbAb

y

y

2

1

221112

221211

n

n

AbAb

AbAb

2

1

22

11

12

12

1

1

n

n

Ab

Ab

2

1

2

1

2

1

12

12

0

0

1

1

n

n

b

b

A

A

R A b n

Detection of CDMA signals 2

The output y=[y1, y2,...,yK]T is sufficient statistic for b=[b1, b2,...,bK]T

y RAb n

y b

R R

A

nn R

[ , ,..., ] , [ , ,..., ]

( ) ( ) ,

[ ]

, ,

y y y b b b

s t s t dt

A

A

A

E

KT

KT

i j i j

T

i i

K

T

1 2 1 2

0

1

2

1

0 0

0 0

0 0

Optimum Multi-user Detector

Too complex : 2K Comparison Impractical

S. Verdú, Optimum multiuser signal detection, PhD thesis, University of Illinois at Urbana-Champaign, Aug. 1984.

)|(maxarg}1,1{

bbb

ypK

)(minarg}1,1{

kk bPbK

Viterbialgorithm ......

output correlator

correlator

correlator

)(tr

Linear Multi-User Detectors

Decorrelating detector

General linear detector

Linear MMSE detector Minimizes

Gives Lower bit error rate (BER) than decorrelating

y RAb n

R y Ab R n n nn R

b R y Ab b

1 11 1

1

1

A b A b EK KT T,..., ~, [~~ ]

sgn( ) sgn( )

no MAI

Ly LRAb Ln

b Ly

sgn( )

E Ly Ab2

2

L R A 2 2 1

Parallel Interference Canceller (PIC)

Received signal

Suppose b known:

Use initial estimate of b

Advantages works for long codes Each stage simple (no matrix inversion)

Problems If bit wrong, magnifies MAI Many stages needed

nRAby

nAbAbIRnRAbAbIRy )()(

)sgn(ˆ,ˆ)(

)sgn(ˆ,ˆ)(

)sgn(ˆ

)3()3()2()3(

)2()2()1()2(

)1(

ybbAIRyy

ybbAIRyy

yb

Blind Multiuser Detection

Traditional, non-blind MUD Codes of all users known Sufficient statistics

Blind MUD Only code of desired user known Similar to beam forming in antenna

arrays Works only for short codes Mobile station

M AInterference

Adaptive IC

M atchedFilter

Detector

Non-blindM ultiuserDetector

M AInterference

M AInterference

System Model - Synchroneous CDMA

Signal is sampled at chip rate (from matched filter)

Received signal on vector form

bk (1): transmitted bits

Ak: received amplitude

sk: code waveforms n: white, additive noise

nsr

K

kkkk Ab

1

Linear Detectors

Conventional detector

General linear detector:

noise

1

MAI

21

Desired

11111

1

0 111 ][][sgnsgnˆ

nsssssrs

rsrs

TK

kk

Tkk

TT

M

k

T

AbAb

kkb

sgnb

b A b A

T

T Tk k

Tk

k

KT

1 1

1 1 1 1 1 1

2

1

w r

w r w s w s w nDesired

MAI

noise

The Decorrelating Detector

Choose w1 so that

Detector:

sgnb

b A b A

b A

T

T Tk k

Tk

k

KT

T

1 1

1 1 1 1 1 1

0

2

1

1 1 1

w r

w r w s w s w n

w n

Desired

MAI

noise

Desired noise

w s

w s

1 1

1

1

0 2 3

T

Tk k K

, , ,...,

Choose w1 to satisfy

Solution

The MMSE Detector


2111

1

minarg rwww

TbE

11111 ][][21minarg1

wrrwrwww

TTT EbE

))(()(2minarg 111121

1

wrrwrww

TTT bbE

nsr

K

kkkk Ab

1

111111 ][21minarg

1

wrrwnswww

TTK

k kkkT EbAbE

The MMSE Detector


Solution

2111

1

minarg rwww

TbE ))(()(2minarg 111121

1

wrrwrww

TTT bbE

112 1111111 ][21minarg

1

wrrwnssww

TTK

k kkkT EbEAbbEAbbE

=1 =0 =0 11111 ][21minarg1

wrrwsww

TTT EA

111 111 ][21minarg

1

wrrwnsww

TTK

k kkkT EbEAbbE

The MMSE Detector


Solution

2111

1

minarg rwww

TbE

111111 ][21minarg1

wrrwswww

TTT EA

111111

][21 wrrwsww

0 TTT EA

))(()(2minarg 111121

1

wrrwrww

TTT bbE

112 sA 1][2 wrrTE

R111 Rws A 1

111 sRw A

The Blind MMSE Detector


Solution

))(()(2minargminarg 111121

2111

11

wrrwrwrwwww

TTTT bbEbE

11

11 sRw A

rwTb 11 sgnˆ

][ TE rrR

rRs 111sgn TA rRs 1

1sgn T

Bit 1 Bit 2 Bit 3 Bit 4 Bit 5 Bit 6 Bit ...

N

i

TiiN

1

1ˆ rrR

r1 r2 r3 r4 r5 r6 r...

Chip rate sampling

Subspace Methods

Correlation matrix of received data

The correlation matrix for CDMA has EVD

The MMSE detector is given by:

R rr SA S I S s s s E T TK[ ] , , ,...,2 2

1 2

R U U0

0 I

U

U

U S

s ns s

T

nT

s K i

2

12diag( ,..., ),

span( ) span( )s

)sgn(ˆ

1

rMs

UUM

A

A

Tii

Tsss

b

Subspace Tracking

Computation of Direct EVD

Estimate R:

Calculate EVD of R Find Us and s from K largest eigenvalues

Singular Value Decomposition Calculate SVD of [r0 r1 ... rn-1]

Find Us and s from K largest singular values

Subspace tracking Low complexity methods of dynamically updating EVD/SVD complexity O(MK2) (e.g., F2) or O(MK) (e.g., PASTd)

R r r

1

0

1

ni iT

i

n

Tsss UUMA

1

Group-Blind MUD

Multiple-Access Interference (MAI) Intra-cell interference: users in same

cell as desired user Inter-cell interference: users from

other cells Inter-cell interference 1/3 of total

interference

Intra-cell MAI

Inter-cell MAI

Blind Multi-User Detection

Non-Blind multi-user detection Codes of all users known Cancels only intracell interference

Blind multi-user detection Only code of desired user known Cancels both intra- and inter-cell

interference

Group-blind MUD

Codes of some, but not all, users known

Cancels both intra- and inter-cell interference

Uses all information available to receiver

Decreases estimation error Decreases BER

Potentially less computationally complex Only one adaptive IC common to all

users. Adaptive IC can have lower

complexity than pure blind IC

Group-Blind Hybrid Detector

Hybrid detector Decorrelating among known users MMSE with respect to unknown users Has convenient, simple expression

Algorithm Projection onto subspace of known codes Orthogonal Projection EVD

Detector

P S S S ST T1

P I P

P RP U U U

0 0

0 I 0

0 0 0

U

U

U

~ ~ ~

~ ~

~

~

~diag(

~,~

,...,~

),~

~

s n o

s sT

nT

oT

s K i

2

1 22

rUURISSSb Tsss

TT ~~~sgnˆ 11

Group-Blind Detector

Performance Simulations

K=7 users with known codes Variable number (4 or 10) of users with unknown codes Purely random codes of length M=31 SNR=20 dB Ensemble of 50 different random code assignments is generated Median signal to inference and noise ratio (SINR)

Over all code choices and known users total ensemble of 350

Simulation Results

50 100 150 200 250 300 350 400-2

0

2

4

6

8

10

12

14

16

18

20

SIN

R(d

B)

Bits

Full

Group-blind

Blind

Direct

Non-blind

Single user

1

2

7 Known users 4 Unknown users All same power

Simulation Results

7 Known users 10 Unknown users

4 Unknown users with power 0dB

6 unknown users with power -6dB

50 100 150 200 250 300 350 400-2

0

2

4

6

8

10

12

14

16

18

20

SIN

R(d

B)

Bits

Full

Group-blind

Blind

Direct

Non-blind

Single user

2

1

Simulation Results, BER

7 Known users 4 Unknown users Blocksize fixed at

200 20 different code

matrices Ensemble of 140

for each SNR value Upper curve: 90-

percentile Lower curve: median

0 2 4 6 8 10 12 14 16 18 2010

-6

10-5

10-4

10-3

10-2

10-1

100

SNR (dB)

BE

R

Group-blind

Blind

Non-blind

Summary

Multiuser Detection Gives considerably performance improvement Most useful for short codes PIC also useful for long codes

(Group) blind MUD For short code MUD More useful in real environments

Future Developments Further development of PIC Practical, real-time implementation of MUD Complexity reduction of (group-) blind MUD

Documents

1 Multiuser Detection for CDMA Anders Høst-Madsen (with contributions from Yu Jaechon, Ph.D student) TRLabs & University of Calgary