Adaptive Frequency-Domain equalization
for Underwater Acoustic Communications
Abdelhakim Youcef
Supervised by
Christophe Laot and Karine Amis
LabSticc seminary, Brest, February 9th , 2012
Introduction (1/2)
UWA channel

Multipath propagation (reflection at the surface and the bottom)

Doppler effect due to the movement of the platforms

Differential Doppler effect due to the movement on the sea

Compression/dilatation of the symbol duration

Why acoustic propagation?
- When the frequency increases:
» The transmission range decreases (signal is attenuated)
» The Doppler effect increases
» Radio and optical waves are strongly attenuated
- Speed of the sound
page 1
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Abdelhakim Youcef
Introduction (2/2)

Underwater acoustic (UWA) communication:
- Strong frequency selectivity (ISI)
- Time-variation
- Limited bandwidth (acoustic waves & transdictor )
CO
Théti
s
-Arrival of the cable from
port
-Signal input
50m
15m
30m
1.5km
page 2
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Abdelhakim Youcef
10m
Outline

Underwater acoustic (UWA) communication:

Digital receiver for UWA communication

Frequency-domain equalization (FDE)
- Cyclic-prefix adaptive FDE (CP-AFDE)
- Overlap-and-save adaptive FDE (OS-AFDE)
- Simulation results (CP-AFDE vs. OS-AFDE)

Joint OS-AFDE and phase synchronization
- Multiple input receiver
page 3

Experimental results

Conclusions and perspectives
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Abdelhakim Youcef
UWA communication system
Transmitter
Source:
•Image
•Speech
•Data
Channel Coding
Frame
fc: 35kHz
Bit rate: 10 kbps
QPSK
Modulation
Underwater Acoustic Channel
4 hydrophones
Receiver
Down conversion
Timing
recovery
Frequency
Domain
equalizer
Phase
synchronizer
Adaptive processing + PLL
page 4
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Abdelhakim Youcef
Channel
Decoding
Some applications on UWA
communications
•
•
•
•
•
•
•
•
page 5
The off-shore oil industry
Aquaculture and fishing industry
Pollution control
Climate recording
Ocean monitoring for prediction of natural disturbances
Detection of objects on the ocean floor
Scientific data collection
Security and military applications
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Abdelhakim Youcef
Frequency-domain Equalization (1/3)
Principle

Performance: equivalent to the time-domain equalization

The equalization is performed block by block

Fast Fourier Transform (FFT) ~ circular convolution
C0
Serial
I
C1
F
To
Parallel
.
.
.
Conversion
page 6
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F
T
Parallel
F
.
.
.
F
CN 1
Abdelhakim Youcef
T
.
.
.
To
Serial
Conversion
yk
Frequency-domain Equalization (1/3)
Computational complexity
page 7
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Abdelhakim Youcef
Frequency-domain Equalization (2/3)
Cyclic prefix based FDE (circular model)
N
N CP
Copy of the
last N CP
symbols
Block of N symbols
Transmitter

ck ,1

rk (1)
rn
FFT
S/P

rk (N )

ck , N

zk (1)
IFFT

zk (N )
Receiver
page 8
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Abdelhakim Youcef
P/S
yn
Frequency-domain Equalization (2/3)
Cyclic prefix based FDE (circular model)

Advantages and properties:
- CP length equal to the maximum channel delay spread in
terms of symbol duration
- Circular convolution in the channel
- Removes the inter block interference

Inconvenient:
- A loss in the spectral efficiency
- Additional treatment at the transmitter (CP insertion)
CP
N symbols
Copy of the Block of N symbols
last NCP symbols
page 9
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Ploss
N
 10 log10 (
) (dB)
N  N CP
Abdelhakim Youcef
Frequency-domain Equalization (3/3)
Overlap-and-save based FDE (linear model)
Sequence 1: incoming data blocks
Circular Convolution
between
the sequences 1 and 2
in the time-domain
Initiate N FF
zeros
N FF
N
N
N
N
N
Each equalizer input vector
contains N samples from the
current block and the last N FF
Samples from the previous one
Sequence 2: Equalizer vector
N FF
page 10
The last N samples
correspond to a linear
convolution result
The first N FF samples
correspond to a circular
convolution result
N zeros
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Abdelhakim Youcef
Frequency-domain Equalization (3/3)
Overlap-and-save (linear model)

Overlapping and sectioning methods (e.g. overlap and save)

The transmission of CP intervals is not necessary

Allows to perform linear convolution using FFT

The block/FFT size is selected at the receiver

Overlapping of 50% (block size equal to equalizer size)
Input data 2N
N
N
Equalizer vector
N
N
N
page 11
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...
Abdelhakim Youcef
N samples
Equalizer
Output
N zeros
Simulation results (1/2)
OS-AFDE vs. CP-AFDE
0
0
10
10
CP-FDE (Known channel)
MMSE TDE Theoretical bound
OS-AFDE
AWGN
CP-AFDE
-1
-1
10
Bit error rate
Bit error rate
10
-2
10
-3
CP-FDE (known channel)
MMSE TDE Theoretical bound
OS-AFDE
AWGN
CP-AFDE
-3
10
10
-4
10
-2
10
-4
2
4
6
8
10
12
Eb/N0 (dB)
16
10
2
4
6
8
10
12
14
Eb/N0 (dB)
(a) Porat channel model
Ploss
14
(b) Proakis B channel model
64
 10 log10 (
)  1dB
64  16
Bit error rate (Ber) vs. Eb/N0 calculated over 320 data blocks
N = 64, NCP = 16, number of blocks : 400, training sequence :80 data blocks
page 12
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Abdelhakim Youcef
16
Simulation results (2/2)
OS-AFDE vs. CP-AFDE
page 13
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Abdelhakim Youcef
Joint OS-AFDE and phase synchronization
Multiple input receiver
x(1) (t )

Adaptive processing is used to track the time-varying channel

Multiple input receiver
kTs
Low pass
Filter
Oversampling
Timing recovery
+
Sample rate
conversion
(1)
k
e
r
frequency-domain
equalizer
j n(1)
e j 2f c kTs
x( NR ) (t )
kTs
dˆn
Low pass
Filter
Oversampling
Timing recovery
+
Sample rate
conversion
( NR )
k
r
frequency-domain
equalizer
e j 2f c kTs
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Abdelhakim Youcef
e
j n( NR )
Adaptive
processing
The proposed multiple input equalizer
Joint optimization of the OS-AFDE and phase synchronization
rk(1)
Concatenate
two blocks
r
FFT
U k(1)
IFFT
(1)
k
C
r
yk(1)
..
T
(1)
k 1
Gradient Constraint
y
e
j k(1)
FFT
Discard
C
GC
Conjugate
U
(1) H
k
FFT
r
0
Delete last 
block
..
Ek(1)
IFFT
e  j k
rk( j )
( NR )
k
Delete last 
block
(1 )
Concatenate
two blocks
r
r
FFT
dˆk
U k( N R )
C
IFFT
( NR )
k
T
C
yk( N R )
..
y
e j k
( NR )
Discard
( NR )
k 1
GC
Ek( N R )
Conjugate
U k( N R )
H
FFT
e
page 15
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j k( N R )
0
e
Append
Abdelhakim Youcef
ek


Experimental results (1/2)
 fc = 35 kHz
 R =10 kbits/s
 N = 32
 Training period: 1 s
 Pe: 180 dB ref μ Pa
at 1m
CO
Thétis
-Arrival of the cable from port
-Signal input
Experiment B:
50m
15m
Experiment A:
•Sonar images
•v = 1.4 m/s
30m
1.5km
10m
page 16
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Abdelhakim Youcef
The transmitter is
submerged and fixed at
a buoy
Text sentences
v = 0.5 m/s
D= 500 m
Channel impulse response estimation
Experiment A
page 17
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Experiment B
Abdelhakim Youcef
Experimental results (2/2)
OS-AFDE vs. LMS-TDE
0
0
LMS-ATDE
OS-AFDE
Adaptive TDE
OS-AFDE
R=5747.1264Bauds
-4
Mean Square Error (dB)
Mean Square Error (dB)
R=4926.1084Bauds
-8
-12
-3
-6
-9
-16
0
1
2
3
4
5
6
7
8
9
0
1
Time in s


page 18
3
4
5
6
7
8
Time in s
Experiment A
D=1.5 Km

2
Experiment B
D=500 m
OS-AFDE: block by block equalization in the frequency-domain
LMS-TDE: symbol by symbol equalization in the time-domain
After channel decoding, the bit error rate is equal to zero
Telecom Bretagne
Abdelhakim Youcef
9
Conclusion & perspectives

Frequency-domain equalization: alternative to time-domain equalization
- Computational complexity gain
- Simple equalizer parameters setting

OS-AFDE vs. CP-AFDE: spectral efficiency and flexibility

Joint adaptive compensation of residual frequency offsets

Multiple input receiver

Influence of the block/FFT size on the performance of the OS-AFDE

Hybrid frequency-time domain decision Feedback equalization

SC-FDMA multiple access
page 19
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Abdelhakim Youcef
Questions?
page 20
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Abdelhakim Youcef
Backup
page 21
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Abdelhakim Youcef
The proposed multiple input equalizer
Joint optimization of the OS-AFDE and phase synchronization
rk(1)
Concatenate
two blocks
r
FFT
U k(1)
IFFT
(1)
k
C
r
yk(1)
..
T
(1)
k 1
Gradient Constraint
y
e
j k(1)
FFT
Discard
C
GC
Conjugate
U
(1) H
k
FFT
r
0
Delete last 
block
..
Ek(1)
IFFT
e  j k
rk( j )
( NR )
k
Delete last 
block
(1 )
Concatenate
two blocks
r
r
FFT
dˆk
U k( N R )
C
IFFT
( NR )
k
T
C
yk( N R )
..
y
e j k
( NR )
Discard
( NR )
k 1
GC
Ek( N R )
Conjugate
U k( N R )
H
FFT
e
page 22
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j k( N R )
0
e
Append
Abdelhakim Youcef
ek

