Sparse Equalizers

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Sparse Equalizers

• Jianzhong Huang
• Feb. 24th. 2009

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Outline

• Motivation
• Prior Methods
• My Thoughts

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Outline

• Motivation
• Prior Methods
• My Thoughts

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Typical Measured Channel Responses
Practical underwater acoustic channel
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Feedforward filter
Feedback filter
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Motivation

• Motivation
• Complexity reduction.
• Enable rapid adaptation of taps weights to
  changing channel conditions.
• Might outperform the optimal conventional
  equalizers

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Outline

• Motivations
• Prior Methods
• My Thoughts

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Prior Methods

• Tap selection methods for decision-feedback
  equalizer
• Threshold-based methods
• Iterative methods
• Pre-filtering methods (includes target impulse
  response)
• Trellis-based equalization methods
• Zero-pad channel (multiple parallel trellis)

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Threshold-based methods

• Idea A subset of taps is allocated according to
  a thresholding strategy.
• Advantages easy to implement, low complexity
• Disadvantages can not properly exploit the
  sparseness of the channel, especially for the
  decision-feedback equalizer performance loss.

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Iterative methods

• Idea a short feedforward filter a long
  feedback filter.
• Optimize the feedforward (FF) support only
• a. select significant arrivals by
  thresholding the CIR directly (M. Stojanovic
  1995).
• b. An ad hoc choice of contiguous taps
  around the central arrival (M. Stojanovic
  1997/1999).
• c.

How about the Feedback (FB) support?
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• Optimize the FF and FB supports jointly
  iteratively (M. J. Lopez Andrew C. Singer 2001)
• 1. Propose an exchange-type algorithm, which
  updates the FF and FB supports alternately.
• 2. Introduce the tap penalty when optimize
  the FF and FB supports.

Optimization criterion
L the number of selected FF taps
EMSE estimated mean-square error
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• Algorithm
• Ramp up Add initial FF and FB taps until some
  loosely-set noise margin is met.
• FB Place additional feedback taps where they
  will improve EMSE by at least an amount d.
• FF Increase L, until a minimum is found for the
  criterion.
• Repeat FB step.

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ISI from the combined channels and optimal FF
filters
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Pre-filtering methods

• Motivation DFE feedforward filter can spread out
  the channel postcursor response, i.e., the
  sparseness of the combined channel and FF filter
  fncn will be destroyed.
• ? ? ?
• The exploitation of the channel sparseness
  property in reducing the equalizer complexity
  should be done as much as possible prior to FF
  filtering.
• Partial Complete feedback equalizer (PFE
  CFE) partially/complete cancels the postcursor
  ISI before the feedforward filtering (M. P. Fitz
  1999).

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Effect of FF filtering on channel response
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Pre-filtering methods (PFE)
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Pre-filtering methods (target impulse response)

• Idea the channel is equalized to a chosen target
  impulse response (TIR), then, use other methods
  to further mitigate the controlled residual ISI
  (S. Roy, T. M. Duman 2009).

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BER Performance for Sparse PRE and DFE
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Trellis-based equalization methods

• Zero-pad channel (a special sparse channel)

Ex h h0 0 0 0 0 0 h1 0 h2
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My thoughts
Prior methods assume perfect channel estimation.
Advanced sparse channel estimation methods
appeared OMP, OOMP, L1-norm, etc.
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My thoughts

• Can we equalize the channel to a zero-pad target
  impulse response, then, use the trellis-based or
  the method proposed in S. Roy T. M. Duman 2009
  to future mitigate the controlled ISI?

How can we leverage advances in the theory of
compressive sensing to create a sparse equalizer?
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• Thank you

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Reference

• 1 M. Kocic, D. Brady and M. Stojanovic,
  Sparse equalization for real-time digital
  underwater acoustic communications", in Proc.
  Oceans 95, Oct. 1995, pp. 1417-1422.
• 2 L. Freitag, M. Johnson and M. Stojanovic,
  Efficient equalizer update algorithm for
  acoustic communication channels of varying
  complexity, in Proc. Oceans 97, pp. 580-585.
• 3 Ian J. Fevrier, S. B. Gelfand and M. P.
  Fitz, Reduced Complexity Decision Feedback
  Equalization for Multipath Channels with Large
  Delay Spreads, IEEE Trans, Commu., vol. 47, no.
  6, pp927-937, Jun 1999.
• 4 M. J. Lopez and A. C. Singer, "A DFE
  Coefficient Placement Algorithm for Sparse
  Reverberant Channes", IEEE Trans, Commu., vol.
  49, no. 8, pp1334-1338, Aug 2001.
• 5 J. Mietzner, S. Badri-Hoeher, I. Land and
  P. A. Hoeher, Trellis-Based Equalization for
  Sparse ISI Channels Revisited, available online.
• 6 S. Roy, T. M. Duman and V. McDonald, Error
  Rate Improvement in Underwater MIMO
  Communications Using Sparse Partial Response
  Equalization, JOE 2009.