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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. St

ojanovic 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:

LEMSE L: the number of selected FF taps

EMSE: “estimated” mean-square error

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Algorithm

i. Ramp up: Add initial FF and FB taps until some loosely-set noise margin is met.

ii. FB: Place additional feedback taps where they will improve EMSE by at least an amount δ.

iii. FF: Increase L, until a minimum is found for the criterion.

iv. 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 {fn*cn} 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.

Complexity of channel estimation

Training symbols needed

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Overall complexity

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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.