Basis Selection Algorithms with Applications in Wireless Communication Systems

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Basis Selection Algorithms with Applications in
Wireless Communication Systems

• April 11, 2009
• EURASIP - Workshop on Sparsity and Compressive
  Sensing
• GÜNES KARABULUT KURT
• TURKCELL ILETISIM HIZMETLERI
• Applied Research Technologies (ART)

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Outline

• Introduction and objectives
• Basis selection problem
• Background on existing algorithms
• Applications in wireless communication systems
• Channel estimation
• Direction of arrival (DOA) detection
• Multi-user detection

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Introduction

• Sparse solutions for linear systems is a
  frequently encountered problem in communications
  and signal processing.
• The sparsest solution NP complete.
• Sub-optimal algorithms are proposed.
• Iterative algorithms
• Matching pursuit (MP)
• Orthogonal matching pursuit (OMP)
• Practical in most cases.
• Error propagation through iterations !

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Basis Selection Problem (1/2)

• Flexible signal decomposition.

Input
Overcomplete Signal Set
r components r lt n
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Basis Selection Problem (2/2)
Dictionary
Sparse vector (only r lt n nonzero components)
Selection of c Basis selection problem
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Matching Pursuit Algorithm

• MP
• An iterative greedy algorithm that chooses the
  dictionary element that best represents the
  residual part of the signal at each iteration.
• Each iteration optimization is performed over all
  vectors in the dictionary, it is possible to
  re-select a previously selected vector, slowing
  the convergence.

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Orthogonal Matching Pursuit Algorithm

• OMP
• An iterative greedy algorithm that chooses the
  dictionary element that best represents the
  residual part of the signal at each iteration (
  MP algorithm).
• It then projects this element onto those elements
  which have already been selected, which yields a
  new approximant signal.
• The re-selection problem is avoided with the
  stored dictionary.
• Error propagation problem still exists (!)

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Application Examples

• Channel Estimation
• Direction of Arrival (DOA) Detection
• Multi-User Detection

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Channel Estimation Problem Statement (1/2)

• Application of MP on sparse channel estimation
  problem is proposed in 2.

Transmitted symbols/ Training sequence
Channel impulse response
Received signal samples
AWGN
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Channel Estimation Problem Statement (2/2)

• In vector matrix notation

For a sparse h, a basis selection algorithm can
be applied to estimate h.
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Direction of Arrival Detection Problem Statement
Uniform Linear Array
For a small value of r, a basis selection
algorithm can be applied to estimate the arrival
angles.
Dictionary (N x M )
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Multi-User Detection Problem Statement
For a value of small value of M,number of
active users ( MltP ), a basis selection
algorithm can be applied to estimate b. Process
also includes joint channel estimation.
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Conclusions

• Sparse parameter estimation problems are
  frequently encountered in communication systems.
  
• Proposed solutions need to have
• High detection and approximation performance.
• Tolerable complexity.

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Thank you
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Direction of Arrival DetectionMedium Resolution
Results

• Assumptions
• Uniform linear array with 10 elements is
  considered.
• Actual angles 64.34o, 115.66o
• Uncorrelated signal from both directions.

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Direction of Arrival Detection Medium
Resolution Results

• Assumptions
• Uniform linear array with 10 elements is
  considered.
• Actual angles 64.34o, 115.66o
• 90 correlated signal from both directions.

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Direction of Arrival Detection High Resolution
Results

• Uncorrelated signal from both directions.