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-1- ICA Based Blind Adaptive MAI ICA Based Blind Adaptive MAI Suppression in DS-CDMA Systems 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

-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

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Page 1: -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

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ICA Based Blind Adaptive MAI ICA Based Blind Adaptive MAI Suppression in DS-CDMA Suppression in DS-CDMA

SystemsSystems

Malay Gupta and Balu SanthanamSPCOM Laboratory

Department of E.C.E.The University of New Mexico

DSP-WKSP-2004

Page 2: -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

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MotivationMotivation

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

Page 3: -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

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Blind Multiuser DetectionBlind 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

Page 4: -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

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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

CDMA Signal ModelCDMA Signal Model

DSP-WKSP-2004

Page 5: -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

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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.

Traditional Applications of ICATraditional Applications of ICA

DSP-WKSP-2004

Page 6: -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

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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.

Independent Component AnalysisIndependent Component Analysis

DSP-WKSP-2004

Page 7: -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

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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.

ICA AlgorithmsICA Algorithms

DSP-WKSP-2004

Page 8: -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

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Correlation matrix corresponding to the interfering users data, based on snapshots

Performing an eigen-decomposition on gives

Interfering User subspaceInterfering User subspace

DSP-WKSP-2004

Page 9: -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

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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

Projection OperatorsProjection Operators

DSP-WKSP-2004

Page 10: -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

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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.

Code Constrained ICACode Constrained ICA

DSP-WKSP-2004

Page 11: -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

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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.

Proposed AlgorithmProposed Algorithm

DSP-WKSP-2004

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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).

Performance Performance MetricMetric

DSP-WKSP-2004

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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.

Effect of Correlation Effect of Correlation

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Performance of CC-ICA better than MOE detector.

Performance close to that of decorrelator.

Perfect power control is assumed.

Performance with two usersPerformance with two users

DSP-WKSP-2004

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Performance better than MOE.

Exhibits performance close to decorrelator.

Five equal energy user channel.

Performance with five usersPerformance with five users

DSP-WKSP-2004

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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.

No Power ControlNo Power Control

DSP-WKSP-2004

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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.

ConclusionsConclusions

DSP-WKSP-2004