ica-based blind and group-blind multiuser detection
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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.
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