comparison and analysis of equalization techniques for the time-varying underwater acoustic channel...
TRANSCRIPT
![Page 1: Comparison and Analysis of Equalization Techniques for the Time-Varying Underwater Acoustic Channel Ballard Blair bjblair@mit.edu PhD Candidate MIT/WHOI](https://reader031.vdocument.in/reader031/viewer/2022032206/56649ec45503460f94bcf348/html5/thumbnails/1.jpg)
1
Comparison and Analysis of Equalization Techniques for the
Time-Varying Underwater Acoustic Channel
Ballard [email protected] Candidate
MIT/WHOI Joint ProgramAdvisor: Jim Presisig
10/5/2009
![Page 2: Comparison and Analysis of Equalization Techniques for the Time-Varying Underwater Acoustic Channel Ballard Blair bjblair@mit.edu PhD Candidate MIT/WHOI](https://reader031.vdocument.in/reader031/viewer/2022032206/56649ec45503460f94bcf348/html5/thumbnails/2.jpg)
2
Outline
• Introduction: – Underwater Communication– Decision Feedback Equalization• Channel Estimate Based• Direct Adaptation
• Analysis of Equalization Behavior• Simulation Results• Summary and Conclusion• Future Directions
10/5/2009
![Page 3: Comparison and Analysis of Equalization Techniques for the Time-Varying Underwater Acoustic Channel Ballard Blair bjblair@mit.edu PhD Candidate MIT/WHOI](https://reader031.vdocument.in/reader031/viewer/2022032206/56649ec45503460f94bcf348/html5/thumbnails/3.jpg)
3
Underwater Communication
10/5/2009
![Page 4: Comparison and Analysis of Equalization Techniques for the Time-Varying Underwater Acoustic Channel Ballard Blair bjblair@mit.edu PhD Candidate MIT/WHOI](https://reader031.vdocument.in/reader031/viewer/2022032206/56649ec45503460f94bcf348/html5/thumbnails/4.jpg)
4
Time Varying Impulse Response
10/5/2009
![Page 5: Comparison and Analysis of Equalization Techniques for the Time-Varying Underwater Acoustic Channel Ballard Blair bjblair@mit.edu PhD Candidate MIT/WHOI](https://reader031.vdocument.in/reader031/viewer/2022032206/56649ec45503460f94bcf348/html5/thumbnails/5.jpg)
5
Channel Model
10/5/2009
Transmitted Data
Time-varying, linear baseband channel
Baseband noise
Baseband Received Data
+
![Page 6: Comparison and Analysis of Equalization Techniques for the Time-Varying Underwater Acoustic Channel Ballard Blair bjblair@mit.edu PhD Candidate MIT/WHOI](https://reader031.vdocument.in/reader031/viewer/2022032206/56649ec45503460f94bcf348/html5/thumbnails/6.jpg)
6
Channel Model (cont.)
10/5/2009
Vector-form:
+
Matrix Vector-form:
+
d[n-Nc+1]…
d[n]…
d[n+Na]
g*[n,-Nc+1] g*[n,Nc+2] … g*[n,0] … g*[n,Na]
u[n-Lc+1]…
u[n]…
u[n+La]
d[n-Lc-Nc+1]d[n-Lc-Nc+2]
…d[n]
…d[n+La+Na-1]d[n+La+Na]
g*[n-Lc+1,Nc-1] … g*[n-Lc+1,0] … g*[n-Lc+1,Na] 0 0 … 00 g*[n-Lc+2,Nc-1] … g*[n-Lc+2,0] … g*[n-Lc+2,Na] 0 … 0
…0 ..0 g*[n+La-1,Nc-1] … g*[n-La-1,0] … g*[n+La-1,Na] 00 ..0 0 0 0 0 g*[n+La,Nc-1] … g*[n-La,0] … g*[n+La,Na]
v[n-Lc+1]…
v[n]…
v[n+La]
![Page 7: Comparison and Analysis of Equalization Techniques for the Time-Varying Underwater Acoustic Channel Ballard Blair bjblair@mit.edu PhD Candidate MIT/WHOI](https://reader031.vdocument.in/reader031/viewer/2022032206/56649ec45503460f94bcf348/html5/thumbnails/7.jpg)
7
Equalization
10/5/2009
TX Data bit (linear) estimator:
LMMSE Optimization:
Solution:
Recursive Processing (lag 1):
Vector of RX data and TX data estimates
![Page 8: Comparison and Analysis of Equalization Techniques for the Time-Varying Underwater Acoustic Channel Ballard Blair bjblair@mit.edu PhD Candidate MIT/WHOI](https://reader031.vdocument.in/reader031/viewer/2022032206/56649ec45503460f94bcf348/html5/thumbnails/8.jpg)
8
Decision Feedback Equalizer (DFE)
• Two Parts:– (Linear) feed-forward filter (of RX data)– (Linear) feedback filter (of data estimates)
• Estimate using RX data and TX data estimates
• Split Channel convolution Matrix:– Received data becomes:
• Minimum Achievable Error: 10/5/2009
![Page 9: Comparison and Analysis of Equalization Techniques for the Time-Varying Underwater Acoustic Channel Ballard Blair bjblair@mit.edu PhD Candidate MIT/WHOI](https://reader031.vdocument.in/reader031/viewer/2022032206/56649ec45503460f94bcf348/html5/thumbnails/9.jpg)
9
DFE: Direct Adaptation
10/5/2009
![Page 10: Comparison and Analysis of Equalization Techniques for the Time-Varying Underwater Acoustic Channel Ballard Blair bjblair@mit.edu PhD Candidate MIT/WHOI](https://reader031.vdocument.in/reader031/viewer/2022032206/56649ec45503460f94bcf348/html5/thumbnails/10.jpg)
10
DFE: Channel Estimate
10/5/2009
![Page 11: Comparison and Analysis of Equalization Techniques for the Time-Varying Underwater Acoustic Channel Ballard Blair bjblair@mit.edu PhD Candidate MIT/WHOI](https://reader031.vdocument.in/reader031/viewer/2022032206/56649ec45503460f94bcf348/html5/thumbnails/11.jpg)
11
Assumptions
• Unit variance, white transmit data
• TX data and obs. noise are uncorrelated
– Obs. Noise variance:
• Perfect data estimation (for feedback)
• Equalizer Length = Estimated Channel Length Na + Nc = La + Lc
• MMSE Equalizer Coefficients have form:
10/5/2009
![Page 12: Comparison and Analysis of Equalization Techniques for the Time-Varying Underwater Acoustic Channel Ballard Blair bjblair@mit.edu PhD Candidate MIT/WHOI](https://reader031.vdocument.in/reader031/viewer/2022032206/56649ec45503460f94bcf348/html5/thumbnails/12.jpg)
12
Comparison between DA and CEB
• In the past, CEB methods empirically shown to have lower mean squared error at high SNR
• Reasons for difference varied:– Condition number of correlation matrix– Number of samples required to get good est.
• Analysis to follow: low and high SNR regimes
10/5/2009
![Page 13: Comparison and Analysis of Equalization Techniques for the Time-Varying Underwater Acoustic Channel Ballard Blair bjblair@mit.edu PhD Candidate MIT/WHOI](https://reader031.vdocument.in/reader031/viewer/2022032206/56649ec45503460f94bcf348/html5/thumbnails/13.jpg)
13
Comparison of DA and CEB on Rayleigh Fading Channel
10/5/2009
![Page 14: Comparison and Analysis of Equalization Techniques for the Time-Varying Underwater Acoustic Channel Ballard Blair bjblair@mit.edu PhD Candidate MIT/WHOI](https://reader031.vdocument.in/reader031/viewer/2022032206/56649ec45503460f94bcf348/html5/thumbnails/14.jpg)
14
Why the difference?
• Correlation time– DA equalizer taps have lower correlation time at
high SNR– At low SNR, two methods equivalent
• But how do we show this?– Combination of analysis and simulation
10/5/2009
![Page 15: Comparison and Analysis of Equalization Techniques for the Time-Varying Underwater Acoustic Channel Ballard Blair bjblair@mit.edu PhD Candidate MIT/WHOI](https://reader031.vdocument.in/reader031/viewer/2022032206/56649ec45503460f94bcf348/html5/thumbnails/15.jpg)
15
AR channel model
• Simple channel model to analyze• Similar to encountered situations
10/5/2009
![Page 16: Comparison and Analysis of Equalization Techniques for the Time-Varying Underwater Acoustic Channel Ballard Blair bjblair@mit.edu PhD Candidate MIT/WHOI](https://reader031.vdocument.in/reader031/viewer/2022032206/56649ec45503460f94bcf348/html5/thumbnails/16.jpg)
16
Low SNR
10/5/2009
![Page 17: Comparison and Analysis of Equalization Techniques for the Time-Varying Underwater Acoustic Channel Ballard Blair bjblair@mit.edu PhD Candidate MIT/WHOI](https://reader031.vdocument.in/reader031/viewer/2022032206/56649ec45503460f94bcf348/html5/thumbnails/17.jpg)
17
High SNR
10/5/2009
![Page 18: Comparison and Analysis of Equalization Techniques for the Time-Varying Underwater Acoustic Channel Ballard Blair bjblair@mit.edu PhD Candidate MIT/WHOI](https://reader031.vdocument.in/reader031/viewer/2022032206/56649ec45503460f94bcf348/html5/thumbnails/18.jpg)
1810/5/2009
![Page 19: Comparison and Analysis of Equalization Techniques for the Time-Varying Underwater Acoustic Channel Ballard Blair bjblair@mit.edu PhD Candidate MIT/WHOI](https://reader031.vdocument.in/reader031/viewer/2022032206/56649ec45503460f94bcf348/html5/thumbnails/19.jpg)
19
Correlation over SNR
10/5/2009
AR(1)model
Gaussian model
![Page 20: Comparison and Analysis of Equalization Techniques for the Time-Varying Underwater Acoustic Channel Ballard Blair bjblair@mit.edu PhD Candidate MIT/WHOI](https://reader031.vdocument.in/reader031/viewer/2022032206/56649ec45503460f94bcf348/html5/thumbnails/20.jpg)
2010/5/2009
Multi-tapAR(1)model
![Page 21: Comparison and Analysis of Equalization Techniques for the Time-Varying Underwater Acoustic Channel Ballard Blair bjblair@mit.edu PhD Candidate MIT/WHOI](https://reader031.vdocument.in/reader031/viewer/2022032206/56649ec45503460f94bcf348/html5/thumbnails/21.jpg)
21
Conclusions
• As SNR increases, correlation time of equalizer taps is reduced– CEB is tracking value correlated over longer time– DA should do worse
• Assumed noise statistics were stationary– Not always case in underwater
• Underwater communication is power limited– Operate in low SNR regime (<35dB)
10/5/2009
![Page 22: Comparison and Analysis of Equalization Techniques for the Time-Varying Underwater Acoustic Channel Ballard Blair bjblair@mit.edu PhD Candidate MIT/WHOI](https://reader031.vdocument.in/reader031/viewer/2022032206/56649ec45503460f94bcf348/html5/thumbnails/22.jpg)
22
Future Work
• Include channel state information into DA– Sparsity
• Reduce number of snapshots for channel model– Physical constraints?– Compressed sensing?
10/5/2009
![Page 23: Comparison and Analysis of Equalization Techniques for the Time-Varying Underwater Acoustic Channel Ballard Blair bjblair@mit.edu PhD Candidate MIT/WHOI](https://reader031.vdocument.in/reader031/viewer/2022032206/56649ec45503460f94bcf348/html5/thumbnails/23.jpg)
23
Questions?
10/5/2009