ICA-based Blind and Group-Blind Multiuser Detection

1. ICA-based Blind and Group-Blind Multiuser Detection

2. Independent Component Analysis(ICA) What is Independence? Independence is much stronger than Uncorrelated. Definition Uncorrelated Independence What isICA ? Independent Component Analysis (ICA) is an analysis technique where the goal is to represent a set of random variables as a linear transformation of statistically independent component variables.

3. Independent Component Analysis(ICA) ICA Model(Noise-free) Unknown Mixing Matrix: Unknown Random Vector: are assumed independent ICA Model(Noise) Noise ICA Goal:Find a Matrix which recovers HOW?

4. Minimize Gaussianity of ICA: Principles and Measures Independence Nongaussian: Want to be one independent component Central Limit Theorem: Differential entropy: Measures ofNongaussian: 1. Kurtosis: 2. Negentropy and Approximation:

5. ICA: Principles and Measures Measures ofNongaussian: (continued) 3. Mutual information 4. Kullback-Leibler divergence: Real density Factorized density 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

6. 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!

7. Received signal Synchronous CDMA where • bkÎ {-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.

8. Multiple Access Interference (MAI) Due to non-orthogonal of codes Caused by channel dispersion Blind Multi-user Detection What does “Blind” Mean? • Only the Interested user’s Spreading code is Known to the receiver • Channel is Unknown

9. 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 Group-Blind MUD

10. 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 Blind Multi-User Detection

11. users with known codes users with unknown codes Signal is sampled at chip rate (from matched filter) Cancels both intra- and inter-cell interference Group-blind MUD Wnated: Uniform Signal Model

12. Synchronous Signal Model Uniform Received Model Chip Matched Filter: … chip1 chip2 chip3 Discrete Model Spreading Gain of is N Synchronous! Total Number of Users:

13. Sub-space Concept Auto-correlation Matrix of Received Data Auto-correlation Matrix (EVD)

14. See Handout for Detail FastICA & Challenges in CDMA 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: Cubic Ambiguities: • Variance: Undetermined variances (energies) of the independent components; • Order: Undetermined order of the independent components.

15. ICA in CDMA:Hints Hints: ICA Model: Data whitening Ignore noise Blind MMSE Solution

16. Two Questions What we Know? ? Question No.1 : are Independent. : Not only Independent; but also +1or-1with with equal probability! ? 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?

17. See Handout for Proof More Interesting Result? 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. ? Further Work

18. ICA-based Blind Detectors Data Whitening Question No.2 MMSEICA Detector: Initial Point for FastICA Zero-Forcing ICA Detector:

19. Performance of Blind Detector

20. Performance of Blind Detector

21. Summary for Blind Detectors Advantages 1. ICA-based blind detectors have better performance than the subspace detectors in high SNRs. 2.ZFICA Detectorhas 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. Disadvantages 1.ZFICA Detectorneeds know K 2.ICA-based blind detectors:less flexibility to estimated length.

22. 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 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

23. Performance of Group-blind Detectors

24. Performance of Group-blind Detectors

25. 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!! End

26. Reference 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.

27. 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.