1. 1 Sparse Equalizers Jianzhong Huang Feb. 24 th. 2009

2. 2 Outline Motivation Prior Methods My Thoughts

3. 3 Outline Motivation Prior Methods My Thoughts

4. 4 Typical Measured Channel Responses Practical underwater acoustic channel

5. 5 Feedforward filter Feedback filter

6. 6 Motivation  Complexity reduction.  Enable rapid adaptation of taps’ weights to changing channel conditions.  Might outperform the optimal conventional equalizers

7. 7 Outline Motivations Prior Methods My Thoughts

8. 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)

9. 9 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. 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. 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?

11. 11  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

12. 12 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.

13. 13 ISI from the combined channels and optimal FF filters

14. 14 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 {f n *c n } 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 ).

15. 15 Effect of FF filtering on channel response

16. 16 Pre-filtering methods (PFE)

17. 17 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 ).

18. 18 BER Performance for Sparse PRE and DFE

19. 19 Trellis-based equalization methods Zero-pad channel (a special sparse channel) Ex: h = [ h 0 0 0 0 0 0 h 1 0 h 2 ]

20. 20 My thoughts Prior methods: assume perfect channel estimation. Advanced sparse channel estimation methods appeared: OMP, OOMP, L1-norm, etc.

21. 21 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?

22. 22 Thank you ~

23. 23 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.