ICA Based Blind Adaptive MAI Suppression in DS-CDMA Systems

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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

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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.

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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.

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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

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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.

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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.

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ICA Algorithms

• ICA algorithms minimize mutual information (or
  its 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.

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Interfering User subspace

• Correlation matrix corresponding to the
  interfering users data, based on snapshots
  
• Performing an eigen-decomposition on gives

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Projection Operators

• Usu1, 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

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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 users 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 users subspace.

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Proposed Algorithm

• Use the knowledge of the desired users 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.

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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).

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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.

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Performance with two users

• Performance of CC-ICA better than MOE detector.
• Performance close to that of decorrelator.
• Perfect power control is assumed.

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Performance with five users

• Performance better than MOE.
• Exhibits performance close to decorrelator.
• Five equal energy user channel.

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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.

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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