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THE UNIVERSITY OF TEXAS AT AUSTIN

Multi-Stage and Sparse Equalizer Design for Communications Systems in Reverberant

Underwater Channels

Karl Nieman, Kenneth Perrine, Terry Henderson, Keith Lent, Terry Brudner,and Brian Evans

Applied Research Laboratories: The University of Texas at Austin

2010 IEEE Workshop on Signal Processing SystemsOct. 8, 2010

APPLIED RESEARCH LABORATORIES

THE UNIVERSITY OF TEXAS AT AUSTIN

Communicator(s)

Receiver

UUVsSeafloor

Instruments

Buoys

Divers

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Reverberations are significant

-20 -10 0 10 20 30 40-70

-60

-50

-40

-30

-20

-10

0Representative Underwater Reverberation

Sample time (ms)

Sig

nal s

treng

th (d

B)

APPLIED RESEARCH LABORATORIES

THE UNIVERSITY OF TEXAS AT AUSTIN

APPLIED RESEARCH LABORATORIES

THE UNIVERSITY OF TEXAS AT AUSTIN

Doppler effects can be horrendous

???Toward Away

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Phase with no Doppler effects

0 50 100 150 200 250-pi

-pi/2

0

pi/2

piQPSK Ideal

Sample time (ms)

Pha

se

00

01

10

11

APPLIED RESEARCH LABORATORIES

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Uncompensated Doppler effects

0 50 100 150 200 250-pi

-pi/2

0

pi/2

pi

Sample time (ms)

Pha

se

APPLIED RESEARCH LABORATORIES

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After gross Doppler compensation

0 50 100 150 200 250-pi

-pi/2

0

pi/2

pi

Sample time (ms)

Pha

se

00

01

10

11

!!

APPLIED RESEARCH LABORATORIES

THE UNIVERSITY OF TEXAS AT AUSTIN

Doppler Detection: Carrier Recovery

t

f(t)

t

g(t) = f(t)2

Expected for

Zero-DopplerDoppler-inflicted

Observation

FFT

ω

|G(ω)| O(M ln M) for M samples

APPLIED RESEARCH LABORATORIES

THE UNIVERSITY OF TEXAS AT AUSTIN

Doppler Detection: Replica Bank

…

Δf = 3.6 Hz

Δf = 3.4 Hz

Δf = 3.2 Hz…

……O(cM ln M) for M samples and c replicas

c replicas

APPLIED RESEARCH LABORATORIES

THE UNIVERSITY OF TEXAS AT AUSTIN

Doppler Detection: Marker Distances

O(M ln M) for M samples

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THE UNIVERSITY OF TEXAS AT AUSTIN

Static Equalizer

ΣFeed-forward taps

Feedback taps

x[t] y[t]

Decision

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THE UNIVERSITY OF TEXAS AT AUSTIN

Sparse Equalizer

ΣFeed-forward taps

Feedback taps

x[t] y[t]

Decision

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THE UNIVERSITY OF TEXAS AT AUSTIN

Fully Adaptive Equalizer

ΣFeed-forward taps

x[t] y[t]

Decision

Update

Feedback taps

–

Update: O(N) per symbol(N = total # of taps)

APPLIED RESEARCH LABORATORIES

THE UNIVERSITY OF TEXAS AT AUSTIN

Single-Tap Adaptive Equalizer

ΣFeed-forward taps

x[t] y[t]

Decision

Update

Feedback taps

–

Update: O(1) per symbol

APPLIED RESEARCH LABORATORIES

THE UNIVERSITY OF TEXAS AT AUSTIN

Which is the best combination to use?

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- BPSK, 30 kHz carrier, 1 kHz symbol rate (1 kbit/sec)- QPSK, 25 kHz carrier, 32 kHz symbol rate (64 kbits/sec)

250 m

150 m

July, 2009

Start

APPLIED RESEARCH LABORATORIES

THE UNIVERSITY OF TEXAS AT AUSTIN

Results: Gross Doppler Detection

• Carrier recovery highest accuracy

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Results: BPSK (Narrowband) Packet

SNR at 150 m, Stationary SNR at 250 m, In Motion

# feedback taps1 4 8 16 32 64

# feedback taps1 4 8 16 32 64

Static EQSparse EQAdaptive (Single-Tap)Adaptive (Full)

APPLIED RESEARCH LABORATORIES

THE UNIVERSITY OF TEXAS AT AUSTIN

Results: QPSK Packet

SNR at 150 m, Stationary SNR at 250 m, In Motion

# feedback taps# feedback taps4 16 64 256 4 16 64 256

Static EQSparse EQAdaptive (Single-Tap)Adaptive (Full)

APPLIED RESEARCH LABORATORIES

THE UNIVERSITY OF TEXAS AT AUSTIN

Adaptation rate (8 feedforward and 32 feedback taps)

Out

put S

NR

(dB

)

BPSK, stationaryBPSK, in motionQPSK, stationaryQPSK, in motion

APPLIED RESEARCH LABORATORIES

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Conclusions

• No single choice for EQ parameters– EQ type– Number of adaptive taps– Adaptation rate

• Underwater channel changes quickly– Reverberation length– 150m to 250m– Underwater features– Thermocline

APPLIED RESEARCH LABORATORIES

THE UNIVERSITY OF TEXAS AT AUSTIN

Conclusions

• Fully adaptive equalizer:– Most sophisticated and most computationally expensive– Does not work in all cases

• Run multiple techniques and choose the best

APPLIED RESEARCH LABORATORIES

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Dataset

http://users.ece.utexas.edu/~bevans/projects/underwater/datasets/index.html

• 5-element underwater dataset available:– 5 simultaneous receiver elements– 62.5 kHz center frequency, up to 31.25 kHz bandwidth– MATLAB format