6
Motivation
Motivation Complexity reduction. Enable rapid adaptation of taps’ weights to changing
channel conditions. Might outperform the optimal conventional equalizers
8
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.
10
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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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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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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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
LS
MP
BP
Overall complexity
L
M
H
H
M
L
?
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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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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.