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ICA-based Blind and Group-Blind Multiuser Detection

Independent Component Analysis(ICA) What is Independence? Definition Independence is much stronger than Uncorrelated. Uncorrelated Independence What is ICA ? 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.

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

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

ICA: Principles and Measures of Nongaussian: (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

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 where – – bk Î {-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 l 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

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 l l users with known codes users with unknown codes Signal is sampled at chip rate (from matched filter) Cancels both intra- and inter-cell interference

Synchronous Signal Model Uniform Received Model Chip Matched Filter: chip 1 chip 2 chip 3 … Discrete Model Synchronous! Spreading Gain of is N Total Number of Users:

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

Fast. ICA & Challenges in CDMA Fixed-point algorithm for ICA (Fast. ICA) l Based on the Kurtosis minimization and maximization l Two advantages: 1. Neural network learning rule into a simple fixed-point iteration; 2. Fast convergence speed: Cubic See Handout for Detail Ambiguities: l Variance: Undetermined variances (energies) of the independent l components; Order: Undetermined order of the independent components.

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

Two Questions Question No. 1 : are Independent. : Not only Independent; but also +1 or-1 with equal probability! Question No. 2 l Fast. ICA: Many Local local minima or maxima; MMSE ICA: Near MMSE local minima or maxima l Finding a tradeoff between two objective functions. l Can we find a better local minima or maxima which gives better performance by starting from other initial points?

ICA-based Blind Detectors l 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: Zero-Forcing ICA Detector:

Performance of Blind Detector

Performance of Blind Detector

Summary for Blind Detectors Advantages 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. 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 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

Performance of Group-blind Detectors

Performance of Group-blind Detectors

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. 11 th 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.

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.