ICA-based Blind and Group-Blind Multiuser Detection

Independent Component Analysis(ICA)

What is Independence?

Independence is much stronger than Uncorrelated.

Uncorrelated

Independence

jiforyEyEyyE jiji ,0}{}{}{

jiforyfEygEyfygE jiji ,0)}({)}({)}()({

What is ICA ?

Independent Component Analysis (ICA) is an analysis techniquewhere the goal is to represent a set of random variables as a lineartransformation of statistically independent component variables.

jiforypypyyp jiji ),()()( Definition

Independent Component Analysis(ICA)

Asx NM

Unknown Random Vector:

Unknown Mixing Matrix:T

nssss ],,[ 21 ji ss ,

are assumed independent

ICA Model (Noise-free)

ICA Goal: Find a Matrix which recovers W Wxys

ICA Model (Noise)

nAsx Noise

ICA: Principles and Measures

Independence Nongaussian:

Want to be one independent component

Central Limit Theorem:

Measures of Nongaussian:

1. Kurtosis:

2. Negentropy and Approximation:

iy

szAswxwy TTi

Tii

224 })({3}{)( yEyEyKurt

23 )(48

1}{

12

1)()()( yKurtyEyHyHyJ gauss

iyMinimize Gaussianity of

js

dyyfyfyH )(log)()(

Differential entropy:

ICA: Principles and Measures

Measures of Nongaussian: (continued)

3. Mutual information

4. Kullback-Leibler divergence:

)()()...( ,2,1 yHyHyyyIi

im

WxHyHyyyIi

im detlog)()()...( ,2,1

Wxy

))(

)(log()()(

2

112,1 yf

yfyfff

Kullback-Leibler divergence can be considered as a kind of a distance between the two probability densities, though it is not a real distance measure because it is not symmetric

Factorized density

Real density      

Principle Component Analysis

Principle Component Analysis

1. Goal is to identify a few variables that explain all (or nearly all) of the total variance.

2. Intended to narrow number of variables down to only those that are of importance.

3. “Faithful” in the Mean-Square sense. Faithful Interesting!

Synchronous CDMA

Received signal

],0[),()()(1

TttntsAbtrK

kkkk

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

– hk is the k’th user’s channel coefficient

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

– n(t) is additive, white Gaussian noise.

Blind Multi-user Detection

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

What does “Blind” Mean?– Only the Interested user’s

Spreading code is Known to the receiver

– Channel is Unknown

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

users with known codes users with unknown codes Signal is sampled at chip rate

(from matched filter) Cancels both intra- and inter-

cell interference

KK

Synchronous Signal Model

],0[),()()()(11

TttvtsAbtsAbtrK

jjjj

K

k

kkk

Discrete Model

Uniform Received Model

chip1 chip2 chip3 …

Chip Matched Filter:

][][][][][][

][][][][

][11

iviHbiviSAbivibASbAS

ivsAibsAibir

i

K

jjjj

K

k

kkk

Synchronous!

vHbvbHbHr

Total Number of Users:

KKK

ksSpreading Gain of is N

Sub-space Concept

Auto-correlation Matrix of Received Data

IHHrrER HH 2)(

Auto-correlation Matrix (EVD)

)span()span(

),,...,diag(

s

21

22

HU

UUUUU

U

IUUUUR

iKs

Hnn

HsssH

n

Hss

nsH

0

0

FastICA & Challenges in CDMA

Ambiguities: Variance: Undetermined variances (energies) of the

independent components; Order: Undetermined order of the independent components.

Fixed-point algorithm for ICA (FastICA) Based on the Kurtosis minimization and maximization Two advantages:

1. Neural network learning rule into a simple fixed-point iteration;2. Fast convergence speed: CubicSee Handout for

Detail

ICA in CDMA:Hints

Hints:ICA Model:

rUy H2/1 Data whitening

IGGGGbbEyyE HHHH }{}{

vUHbUy HH 2/12/1

GIgnore noise

kICAk Gw 1 k

HICAk bGbw )( k

HICAk byw )(

Blind MMSE Solution

}){(minarg 2rwbEw Hkk

w

MMSEk

k

k

Hk

MMSEk HUUHRw 11 11

Two Questions

Question No.1

Question No.2 FastICA: Many Local local minima or maxima;

MMSE ICA: Near MMSE local minima or maxima Finding a tradeoff between two objective functions. Can we find a better local minima or maxima which

gives better performance by starting from other initial points?

vAsx ji ss ,

: are Independent.

vHbr ji bb ,

: Not only Independent; but also

+1or-1with with equal probability!

ICA-based Blind Detectors

Question No.1

Lemma: For a BPSK Synchronous DS-CDMA system,the maximization of Approximated Negentroy using high-order moments is same as the minimization of the Kurtosis.

See Handout for Proof

More Interesting Result?

ICA-based Blind Detectors

Question No.2

MMSEICA Detector:

rUy H2/1

kMMSEICAk HUw 12/1

Zero-Forcing ICA Detector:

rUy Hss

s 2/1

ksKsZFICAk HIUw 1)( 2/1

Performance of Blind Detector

Performance of Blind Detector

Summary for Blind Detectors

1. ICA-based blind detectors have better performance than the subspace detectors in high SNRs.

2. ZFICA Detector has better performance than MMSEICA Detector. Reduced complexity and robust to estimated length.

3. ICA-based blind detectors are free to BER floor.

4. When system is high loaded the performance of ZFICA is close the non-blind MMSE detector.

Advantages

Disadvantages

1. ZFICA Detector needs know K

2. ICA-based blind detectors:less flexibility to estimated length.

Group-blind MUD Detector

What is the Magic?

Make use of the signature waveforms of all known users suppress the intra-cell interference,while blindly suppressing the inter-cell interference.

Group-blind Zero-Forcing Detector

kHsss

Hsss

GZFk HUIUHHUIUw 1])([)( 11212

ICA-based group-blind detector

1. Non-blind MMSE (Partial MMSE) to eliminate the interference from the intra-cell users

2. Zero-Forcing ICA Detector based on output of Partial MMSE

HHPMMSE HIHHW 12 )(

Performance of Group-blind Detectors

6 7 8 9 10 11 12 13 14 15 1610

-3

10-2

10-1

100

GroupBlind-ICA Detectors with 100 Symbols (12 incell,8 outcell)

SNR Eb/No (dB)

BE

R

GroupBlind ZF Partial MMSE Blind ZFICA GroupBlindZFICA

Performance of Group-blind Detectors

6 7 8 9 10 11 12 13 14 15 1610

-4

10-3

10-2

10-1

100

GroupBlind-ICA Detectors with 200 Symbols (12 incell,8 outcell)

SNR Eb/No (dB)

BE

R

GroupBlind ZF Partial MMSE Blind ZFICA GroupBlindZFICA

Summary for Group-blind Detectors

1. Group-blind ZFICA detector has better performance than group- blind zero-forcing subspace detector.

2. Group-blind ZFICA detector Worse performance than the totally blind ZFICA method.

Partial MMSE Destroyed the Independence of desired random variables. Independent > Interference!!

References

[1] J.Joutsensal and T.Ristaniemi,”Blind Multi-User Detection by Fast Fixed Point Algorithm without Prior Knowledge of Symbol-Level Timing”, Proc. IEEE Signal Processing Workshop on Higher Order Statistics Ceasarea,Israel, June 1999,pp.305-308.

[2] T.Ristaniemi and J.Joutsensal, ”Advanced ICA-Based Receivers for DS-CDMA Systems”, Proc. 11th IEEE International Symposium on Personal, Indoor, and Mobile Radio Communications, London, September 18-21, 2000, pp.276-281.

[3] T.Ristaniemi,”Synchronization and blind signal processing in CDMA systems”,Doctoral Thesis,University of Jyv¨askyl¨a, Jyv¨askyl¨a Studies in Computing, August 2000.

[4] X.Wang and A.Høst-Madsen, ”Group-blind multiuser detection for uplink CDMA”, IEEE Journal on Selec. Areas in Commun, vol. 17, No. 11, Nov. 1999.

[5] X. Wang and H.V. Poor, ”Blind Equalization and Multiuser Detection in Dis-persive CDMA Channels”, IEEE Transactions on Communications, vol. 46, no. 1, pp. 91-103, January 1998.

[6] P. Comon, ”Independent Component Analysis, A new Concept?”, Signal processing, Vol.36, no.3, Special issue on High-Order Statistics, Apr. 1994.

Reference

Reference

References

[7] A.Hyv¨arinen and E.Oja, ”A Fast Fixed-Point Algorithm for Independent Component Analysis”, Neural Computation, 9:1483-1492, 1997.

[8] A.Hyv¨arinen, ”Fast and Robust Fixed-Point Algorithm for Independent Component Analysis”, IEEE Trans. on Neural Networks, 1999.

[9] A.Hyv¨arinen, ”Survey on Independent Component Analysis”, Neural Com-puting Systems, 2:94-128, 1999.

[10] S. Verdu, ”Multiuser Detection. Cambridge”, UK: Cambridge Univ. Press, 1998.