ICA Based Blind Adaptive MAI Suppression in DS-CDMA Systems

1. ICA Based Blind Adaptive MAI Suppression in DS-CDMA Systems Malay Gupta and Balu Santhanam SPCOM Laboratory Department of E.C.E. The University of New Mexico DSP-WKSP-2004

2. Motivation • Conventional detector ignores MAI and is near far sensitive. • Optimum detector requires complete knowledge of MAI and has exponential complexity. • Decorrelator requires complete knowledge of MAI. • MMSE detector requires training. • MOE detector requires knowledge about the desired user only. • ICA has been used in various source separation problems. DSP-WKSP-2004

3. Blind Multiuser Detection • Channel supports multiple users simultaneously. No separation between the users either in time or in frequency domain. • Receiver observers superposition of signal from all the active users in the channel. • Detection process needs to form a decision about the desired user (MISO model) or about all the active users (MIMO model), based only on the observed data. DSP-WKSP-2004

4. CDMA Signal Model • Composite signal at time t can be expressed as • User signature waveform is given as • Matrix formulation of the chip synchronous signal with AWGN is • b(i) is a bpsk signal DSP-WKSP-2004

5. Traditional Applications of ICA • Processing of biomedical signals, i.e. ECG, EEG, fMRI, and MEG. • Algorithms for reducing noise in natural images, e.g. Nonlinear Principal Component Analysis (NLPCA). • Finding hidden factors in financial data. • Separation and enhancement of speech or music (few of them were applied to deal with real environments). • Rotating machine vibration analysis, nuclear reactor monitoring and analyzing seismic signals. DSP-WKSP-2004

6. Independent Component Analysis • Mutual information between random vectors x and y is given as : • Mutual information in terms of Kullback-Leibler distance : • Kullback-Leibler distance of a random vector is defined as. DSP-WKSP-2004

7. ICA Algorithms • ICA algorithms minimize mutual information (or it’s approximation) to restore independence at the output. • ICA algorithms use SOS for preprocessing the data and HOS for independence. • Fixed Point ICA algorithm is the cost function to be minimized. G(.) is any non quadratic function. DSP-WKSP-2004

8. Interfering User subspace • Correlation matrix corresponding to the interfering users data, based on snapshots • Performing an eigen-decomposition on gives DSP-WKSP-2004

9. Projection Operators • Us=[u1, u2, …, uK-1] forms an orthonormal basis for the interfering users. • Us?denotes an orthogonal complement of Us • Projection of a vector x on Us?is given as DSP-WKSP-2004

10. Code Constrained ICA • Unconstrained ICA algorithms lead to extraction of one user but there is no control over which user is extracted. • Desired detector belongs to a subspace associated with the desired user’s code sequence. • Eigen-structure can be obtained only from the knowledge of the received data. • Indeterminacy can be removed by constraining the ICA detector to desired user’s subspace. DSP-WKSP-2004

11. Proposed Algorithm • Use the knowledge of the desired user’s code to estimated the interfering user signal subspace. • Use fixed point ICA algorithm to compute the separating vector. • Compute the projection of the separating vector onto the null space of the interfering user subspace. • Apply norm constraint to converge to the desired solution. DSP-WKSP-2004

12. Performance Metric • To demonstrate the efficacy of the present approach average symbol error probability measure is used. For binary modulation case this is given as :- • Effect of increasing correlation between the users is quantified by the signal to noise and interference ratio (SINR). DSP-WKSP-2004

13. Effect of Correlation • Eigen-spread quantifies the correlation between active users. • SINR is degrades when eigen-spread or correlation is high. • BER performance depends on the extent of correlation. DSP-WKSP-2004

14. Performance with two users • Performance of CC-ICA better than MOE detector. • Performance close to that of decorrelator. • Perfect power control is assumed. DSP-WKSP-2004

15. Performance with five users • Performance better than MOE. • Exhibits performance close to decorrelator. • Five equal energy user channel. DSP-WKSP-2004

16. No Power Control • Performance comparison in absence of power control. • Number of users in the channel is 5. insensitive to near far problem. • Performance again close to that of the decorrelator. DSP-WKSP-2004

17. Conclusions • Attempts to remove the inherent indeterminacy problem in ICA computations by constraining the ICA weight vector to lie in the null space of the interfering users. • The detector performance is near-far resistant. • Performance is close to that of decorrelator and better than MOE with significantly lesser side information. DSP-WKSP-2004