TELKOM
NIKA
, Vol.11, No
.3, March 2
0
1
3
, pp. 1173 ~ 1180
ISSN: 2302-4
046
1173
Re
cei
v
ed O
c
t
ober 2, 20
12;
Revi
se
d Ja
n
uary 6, 2013;
Acce
pt
ed Jan
uary 16, 201
3
Characteristics Analysis of HFM Signal over
Underwater Acoustic Channels
Yuan Fei, Wang We
n-J
u
n, Cheng En
*
Ke
y
Lab
orator
y of Under
w
a
t
e
r
Acoustic Com
m
unic
a
tion a
n
d
Marine Inform
ation
T
e
chnolog
y (
X
i
a
men U
n
ivers
i
ty),
Ministr
y
of Educati
on, P.R
.
C
*Corres
p
o
ndi
n
g
author, e-ma
i
l
: cheng
en@
xmu.edu.cn
A
b
st
r
a
ct
F
o
r puls
e
co
mpr
e
ssio
n
ch
aracteristics
a
nd n
o
t eas
ily
affected by
nois
e
, lin
ear f
r
equ
enc
y
mo
du
latio
n
sig
nal
are w
i
de
ly
used i
n
u
n
d
e
rw
ater acous
tic communic
a
tion. T
h
is p
a
p
e
r an
aly
z
e
s
t
h
e
character
i
stics
of hyper
bo
lic fr
equ
ency
modu
latio
n
si
g
n
a
l
o
v
er un
derw
a
ter
acoustic c
h
a
n
nels. C
o
mpar
e
d
w
i
th line
a
r freq
uency
modu
lat
i
on si
gn
al, hyp
e
rbo
lic
freq
uen
cy mo
dul
atio
n
has the s
a
me
perfor
m
a
n
ce o
f
strong anti-n
o
i
s
e and anti-
mult
ip
ath, w
hat
’
s
more, hyper
b
o
lic frequ
ency
mo
du
latio
n
sig
nal is better re
sist
the influ
enc
e o
f
doppl
er. And
discuss
ed the i
n
flue
nce of
d
o
ppl
er on si
gn
al
, simul
a
tio
n
res
u
lts show
that the
hyper
bol
ic freq
uency
mo
du
lati
on sig
n
a
l
dete
c
tion rate
is
be
tter than lin
ear
freque
ncy mo
dul
ation s
i
gn
al
i
n
the dop
pl
er en
viron
m
e
n
t.
Ke
y
w
ords
: LF
M, HF
M, Doppler, underw
a
ter
acoustic ch
an
n
e
ls
Copy
right
©
2013 Un
ive
r
sita
s Ah
mad
Dah
l
an
. All rig
h
t
s r
ese
rved
.
1. Introduc
tion
Ultra
s
ou
nd formed as hyp
e
rboli
c
modul
ation
freque
n
c
y (HFM
) is su
ccessfully use
d
in
ech
o
lo
cation
by some a
n
i
m
als. And
HFM sign
al
ha
d been
used
in many ap
plicatio
n su
ch as
synchro
n
ization, ech
o
location, medica
l enginee
rin
g
and so on [
1
-3]. In this paper, an
alysi
s
of
the LFM
wa
s given
as a
cont
ra
st to discu
ss
th
e cha
r
a
c
teri
stic
about
the
HFM sign
al over
unde
rwater a
c
ou
stic
cha
n
n
e
l.
2. HFM sign
al charac
teri
stics
HFM sig
nal is different from freque
ncy linear
chan
ge over time of LFM signal, it’s a
spe
c
ial
non
-li
near f
r
eq
uen
cy mod
u
latio
n
sig
nal
, freq
uen
cy modul
ation re
gula
r
i
t
y for hyperb
o
lic
function
s. HF
M signal
can
be expre
s
sed
as:
1
ln
(
1
/
)
()
c
o
s
[
2
]
kt
f
ct
k
(1)
Whe
r
e k is the signal sl
o
pe:
12
1
2
()
/
(
)
kf
f
T
f
f
,
1
f
is startin
g
frequen
cy,
2
f
is end
freque
ncy. If
12
f
f
, signal rep
r
e
s
ent
s HFM u
p
swe
ep si
gn
al, on the contrary, sign
al
is HFM
down swee
p sign
al. The si
gnal in
stanta
neou
s freq
ue
ncy is
1
1
()
1/
i
ft
kt
f
(2)
Instantan
eou
s frequ
en
cy is in the interv
al [
1
f
2
f
] over time to chang
e in the hyperb
o
li
c form.
HFM is
a do
ppler i
n
varia
n
t signal, a
s
sume th
e tra
n
sceiver
end
oppo
site sp
eed is v,
spe
ed of sou
nd is
c, the doppl
er fa
cto
r
is
1/
vc
. The inst
antane
ou
s freque
ncy of
HFM
sign
al be
com
e
s
Evaluation Warning : The document was created with Spire.PDF for Python.
ISSN: 2302-4
046
TELKOM
NIKA
Vol. 11, No
. 3, March 20
13 : 1173 – 1
180
1174
1
()
1
()
21
/
r
r
dt
ft
dt
k
t
f
(3)
The ph
ase
is
1
()
2
l
n
(
1
/
)
/
r
tk
t
f
k
,make delay
1
/(
)
tv
f
k
c
,s
o
()
(
)
ri
f
tt
f
t
.
This prove that while HFM
signal have frequ
en
cy shif
ted, there is a length of delay
t
, s
o
that
the freque
ncy
-
shifted
sign
a
l
with the origi
nal sig
nal ma
tching.
0
0.
05
0.
1
-1
0
1
Ti
m
e
(
s
)
A
m
plit
u
d
e
LF
M
0
0.
05
0.
1
-1
0
1
Ti
m
e
(
s
)
A
m
plit
ud
e
HF
M
0
0.
05
0.
1
0
500
1000
Ti
m
e
(
s
)
F
r
equ
enc
y
(
Hz
)
LF
M
0
0.
05
0.
1
0
500
1000
Ti
m
e
(
s
)
F
r
equ
enc
y
(
Hz
)
HF
M
Figure 1. Time domain of u
p
sweep
sign
al
3. The chara
c
teris
t
ics of
HFM signal i
n
under
w
a
t
e
r
acous
tic c
h
annels
3.1. White G
a
ussian nois
e
As we all kn
o
w
, LFM sign
a
l
has a stron
g
resi
stan
ce t
o
white Gau
s
sian noi
se, b
e
ca
use
of
it
s self
-
c
o
r
relat
i
on [
4
,
5]
cha
r
a
c
t
e
ri
st
i
cs.
A
nd
HFM
sign
al also h
a
ving a go
od
self-co
rrel
a
tion
cha
r
a
c
teri
stic. As can be seen from Fig
u
re 2,
the co
ntrast effect betwe
en HF
M signal and
LFM
sign
al is b
a
si
cally the sa
me, the self-correl
a
tion
p
eak of o
u
tput
matchin
g
si
gnal is
evide
n
t at
highe
r SNR,
and
side l
obe
is cl
ean. At l
o
w SNR,
sid
e
lobe
ene
rg
y beco
m
e la
rge, but the
si
gnal
self-co
rrel
a
tio
n
pea
k is
still evident. It shows that
wh
ite Gaussia
n
noise only influen
ce the si
de
lobe of the ou
tput matching
signal, self-correlation p
e
a
k
is still evide
n
t.
3.2. Multipath
The influe
nce
of multipath are very
seri
o
u
s
in u
nde
rwater a
c
ou
stic
comm
uni
cati
on [6], it
cau
s
e
s
ampl
itude attenu
ation and in
ter-symbol
i
n
terferen
ce. Signal whi
c
h
pass throu
gh
multipath ch
a
nnel may be
expre
s
sed a
s
[7]
1
0
1
()
()
(
)
N
ii
i
yt
a
c
t
a
c
t
(6)
The first com
pone
nt is the
signal
of first
arrive
at the
receiving en
d, the other
N-1
co
mpon
e
n
ts
that amplitud
e attenuation
i
a
, delay
i
.
Figure 3 sh
o
w
s u
nde
rwater acou
stic li
ne and im
p
u
l
s
e re
sp
on
se
of multipath simulation
cha
nnel, tran
smissio
n
sig
nal pass through si
m
u
lat
i
on cha
nnel
will become multipath del
ay
sign
als. Figu
re 4 sho
w
s wi
th the influen
ce of
multipa
t
h [8], the matchin
g
outpu
t effect of HFM
sign
al and LF
M signal is b
a
si
cally the same. T
herefo
r
e HFM
signa
l and LFM sig
nal have alm
o
st
the same anti-multipath
capability.
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TELKOM
NIKA
ISSN:
2302-4
046
Cha
r
a
c
teri
stics Analysi
s
of HFM Signal o
v
er
Und
e
rwat
er Aco
u
sti
c
Chann
els (Y
UAN Fei)
1175
0
500
10
00
150
0
2000
0
0.
2
0.
4
0.
6
0.
8
1
1.
2
LF
M
s
e
l
f
-c
orr
e
l
a
t
i
on pea
k
(
1
0dB
)
N
o
r
m
al
i
z
ed a
m
pl
i
t
ude
0
50
0
100
0
1
500
20
0
0
0
0.
2
0.
4
0.
6
0.
8
1
1.
2
H
F
M
s
e
l
f
-
c
o
r
r
e
l
a
t
i
on
pe
ak
(10d
B
)
N
o
r
m
al
i
z
ed a
m
pl
i
t
ude
0
500
10
00
150
0
2000
0
0.
2
0.
4
0.
6
0.
8
1
1.
2
L
F
M
s
e
l
f
-
c
or
rel
a
t
i
on peak
(
-
20d
B
)
N
o
r
m
al
i
z
ed am
pl
i
t
ude
0
50
0
100
0
1
500
20
0
0
0
0.
2
0.
4
0.
6
0.
8
1
1.
2
H
F
M
s
e
l
f
-c
orr
e
l
a
t
i
on
pea
k
(
-
2
0
d
B
)
N
o
r
m
al
i
z
ed am
pl
i
t
ude
Figure 2. The
influence of noise on self-correl
a
tion pe
ak
0
50
0
10
00
1
500
-1
2
0
-1
0
0
-80
-60
-40
-20
0
20
U
n
de
r
w
a
t
er
ac
o
u
s
t
i
c
l
i
n
e
di
s
t
anc
e (m
)
dept
h (
m
)
0
0.
01
0.
02
0.
03
0.
0
4
0.
05
0.
0
6
0
1
x 1
0
-4
Ti
m
e
(
s
)
A
m
pl
i
t
ud
e
I
m
pu
l
s
e res
p
ons
e
Figure 3. Und
e
rwater a
c
o
u
s
tic Lin
e
and i
m
pulse re
sp
o
n
se
3.3. Doppler
The influen
ce
of dopple
r
on signal is fre
quen
cy offset and time expan
sion/
com
p
re
ssi
on
[9], it change
s sign
al mod
u
lation frequ
ency rate an
d cau
s
e
s
sig
nal mismat
ch
with the local
correl
ation si
gnal. If doppler is small, the si
gn
al is a narrow-b
and ra
nge, time expan
sio
n
/
comp
re
ssion
has little in
fluence on
signal, do
pple
r
effect
s
sho
w
only th
e frequ
en
cy shi
ft.
Assu
me LFM
signal h
a
s a
freque
ncy offset
d
w
, the expression i
s
2
0
(
,
)
c
os[(
)
/
2]
/
2
/
2
dd
d
ct
w
w
w
t
u
t
T
t
T
(7)
Evaluation Warning : The document was created with Spire.PDF for Python.
ISSN: 2302-4
046
TELKOM
NIKA
Vol. 11, No
. 3, March 20
13 : 1173 – 1
180
1176
0
0.
0
2
0.
0
4
0.
06
0.
08
0
1
2
x 1
0
-4
R
e
l
a
ti
v
e
d
e
l
a
y(
s)
A
m
pl
i
t
ude
LF
M
0
0.
02
0.
0
4
0.
0
6
0.
0
8
0
1
2
x 1
0
-4
R
e
l
a
ti
v
e
d
e
l
a
y
(
s)
A
m
pl
i
t
ude
HF
M
Figure 4. The
influence of multipath on
self-co
rrel
a
tio
n
pea
k
After pass through the mat
c
he
d filt
er, the resulting si
gnal is
0
sin
2
2
co
s
2
d
d
d
wu
t
Tt
w
u
wt
T
t
T
wu
t
(8)
That
2
uM
, M for modulatio
n freque
ncy rate
of LFM sign
al
. The doppl
er freque
ncy sh
ift will
cau
s
e the match output sign
al’s lobe
s br
oa
den, the peak am
plitude attenuation and p
eak
loc
a
tion offs
et. If
s
e
t
/
d
wu
, frequen
cy offset cau
s
e the a
m
plitude of
match o
u
tput
peak
redu
ce
and the pea
k po
sit
i
on offset
T
.
If Doppler is
strong, it not only cause the fr
equency shift, as
well
as time expansion /
comp
re
ssion.
Assum
e
the Dopple
r
cau
s
e freq
uen
cy
shift of signal in transmi
ssi
on, that the
relative veloci
ty between sendin
g
and receivin
g end
is
v, speed of
soun
d is c, the dop
pler fa
ctor
for
1/
vc
. For LFM sign
al, unde
r the influence of freque
ncy shift and time com
p
ressed,
the insta
n
tan
eou
s fre
que
ncy be
co
me
0
()
'
d
f
tf
M
t
,
2
'
M
M
, s
y
mbol
time is
/
T
, and si
gnal
n
o
long
er m
a
tch with the
ori
g
inal
sign
al[10]. HFM si
gn
al is diffe
rent
from LFM
sign
al, according to formul
a (3), HFM si
gnal c
an effe
ctively resi
st the influen
ce
of dopple
r
.
As can be se
en from Figure5, delay time T1 and T2 of LFM signal
is not equal, and the
modulatio
n freque
ncy rate
chang
es si
g
n
ificantly, si
g
nal no longe
r match. Dela
y time T1 an
d T2
of HFM signa
l are equal that prove the modulatio
n freque
ncy rate doe
s not cha
nge, HFM sig
nal
can find a d
e
l
a
y time to match the origi
n
al sign
al.
Figure 6 sh
o
w
s
sign
al self
-co
r
relation p
eak h
a
ve different level of
amplitude
ch
ange a
nd
pea
k po
sition
offset, the modulatio
n fre
quen
cy
rate
of HFM si
gn
al doe
s not chang
e und
er
the
influen
ce of
doppl
er,
whil
e LFM
sig
nal
no lo
nge
r m
a
tch,
so the
self-co
rrel
a
tio
n
pea
k
of HFM
sign
al ch
ang
es smalle
r than LFM si
gna
l.
Evaluation Warning : The document was created with Spire.PDF for Python.
TELKOM
NIKA
ISSN:
2302-4
046
Cha
r
a
c
teri
stics Analysi
s
of HFM Signal o
v
er
Und
e
rwat
er Aco
u
sti
c
Chann
els (Y
UAN Fei)
1177
0
T/
D
T
fm
i
n
fm
i
n
*
D
fm
a
x
fm
a
x
*
D
T2
T1
LF
M
Ti
m
e
F
r
eq
uen
c
y
0
T/
D
T
fm
i
n
fm
i
n
*
D
fm
a
x
fm
a
x
*
D
T2
T1
HF
M
Ti
m
e
F
r
eq
uen
c
y
Figure 5. The
influence of Dop
p
ler o
n
m
odulatio
n freq
uen
cy rate
0
0.
005
0.
01
0.
01
5
0.
02
0
0.
1
0.
2
0.
3
0.
4
0.
5
0.
6
0.
7
0.
8
0.
9
1
R
e
l
a
ti
v
e
d
e
l
a
y
(
s
)
N
o
m
a
l
i
z
ed a
m
pl
i
t
ude
up-
L
F
M
dow
n
-
L
F
M
0
0.
005
0.
01
0.
015
0.
02
0
0.
1
0.
2
0.
3
0.
4
0.
5
0.
6
0.
7
0.
8
0.
9
1
R
e
l
a
t
i
v
e
del
ay
(
s
)
N
o
m
a
l
i
z
ed a
m
pl
i
t
ude
up
-HF
M
do
wn
-HF
M
Figure 6. The
influence of 30m/s relative velocity on self-co
rrel
a
tio
n
pea
k
Furthe
r study
the amplitude variation of the
self-co
r
relation pea
k unde
r the influen
ce of
Dop
p
ler, ana
lyze the ch
ange
s of se
lf-co
rrel
a
tion
peak by the influence of time-varying,
freque
ncy offset and both
cau
s
e
d
by Dopple
r
. Fi
gure7 sho
w
s HF
M signal is capabl
e of strong
resi
stan
ce to
the influence of Doppler.
Ev
en under the influence of strong dopple
r
, the peak
amplitude is
still large. Howeve
r, the peak
amplitude of LFM
decreased
rapi
dly with doppler
enha
nced, which
seri
ou
sly affect the sig
nal demo
dula
t
ion judgme
n
t.
Acco
rdi
ng to
formula (8
),
shorte
n sy
mbol time wi
ll redu
ce the
chan
ge of LFM self-
correl
ation
peak caused by
frequ
ency shift. For LFM si
gnal,
shor
ten symbol time effectively
resi
st the influen
ce of Do
ppler, and sh
orten symb
ol
time has almost no effect of resista
n
c
e to
Dop
p
ler fo
r H
F
M sign
al.
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ISSN: 2302-4
046
TELKOM
NIKA
Vol. 11, No
. 3, March 20
13 : 1173 – 1
180
1178
0
10
20
30
40
0.
6
0.
7
0.
8
0.
9
1
（）
R
e
l
a
ti
v
e
v
e
l
o
ci
t
y
m
/
s
N
o
r
m
a
l
i
z
ed
p
eak
am
pl
i
t
u
d
e
（）
L
F
M
B
=
5
kH
z,T
=
2
0
m
s
D
oppl
er
F
r
e
quenc
y
of
f
s
e
t
Ti
m
e
v
a
r
y
0
10
20
30
40
0.
9
0.
92
0.
94
0.
96
0.
98
1
（）
R
e
l
a
t
i
ve
ve
l
o
c
i
t
y
m
/
s
N
o
r
m
a
l
i
z
ed
p
eak
am
pl
i
t
u
d
e
（）
H
F
M
B
=
5
k
H
z
,
T
=
20m
s
D
oppl
er
F
r
eq
uenc
y
of
f
s
et
Ti
m
e
v
a
r
y
0
10
20
30
40
0.
8
0.
85
0.
9
0.
95
1
（）
R
e
l
a
ti
v
e
v
e
l
o
ci
t
y
m
/
s
N
o
r
m
al
i
z
ed peak
am
pl
i
t
ude
（）
L
F
M
B
=
5
kH
z,T
=
1
0
m
s
D
oppl
er
F
r
e
quenc
y
of
f
s
e
t
Ti
m
e
v
a
r
y
0
10
20
30
40
0.
9
0.
92
0.
94
0.
96
0.
98
1
（）
R
e
l
a
t
i
ve
ve
l
o
c
i
t
y
m
/
s
N
o
r
m
al
i
z
ed peak
am
pl
i
t
ude
（）
H
F
M
B
=
5
k
H
z
,
T
=
10m
s
D
oppl
er
F
r
eq
uenc
y
of
f
s
et
Ti
m
e
v
a
r
y
Figure 7. Amplitude of self
-co
r
relation p
eak
cha
nge
with frequ
en
cy offset
4. Simulation
The system para
m
eters
f
o
r
the simul
a
tion
are indi
cated in T
able
1
and
used t
he BOK
system, up
swee
p sig
nal repre
s
e
n
t the symbol "1
",
down sweep si
gnal
re
pres
en
t the symbol "0".
Table 1. System simul
a
tio
n
para
m
eters
Parameter
value
Signal sw
eep f
r
e
quenc
y
S
y
mbol time
band
w
i
dth
Sampling rate
Relative velocity
15kHz-20kHz
20ms
5kHz
40kHz
30m/s
Figure 8 sho
w
s the sim
u
l
a
tion re
sults
of det
ection
perfo
rman
ce
unde
r the influen
ce of
Dop
p
ler. Bet
w
ee
n -24
d
B to -10dB, the
HFM si
gnal d
e
tection
rate i
s
better tha
n
LFM sig
nal. T
h
e
detectio
n
rate of HF
M
signal
rea
c
he
s the maximu
m at -1
2dB, LFM
sign
al
backwa
r
d 2
d
B
comp
ared
with HFM
sig
nal
, reache
s the
maximum at
-10dB. It sh
o
w
s th
at HFM
sign
al dete
c
tion
rate is
supe
ri
or to LFM si
g
nal und
er the
influen
ce of Dopple
r
.
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TELKOM
NIKA
ISSN:
2302-4
046
Cha
r
a
c
teri
stics Analysi
s
of HFM Signal o
v
er
Und
e
rwat
er Aco
u
sti
c
Chann
els (Y
UAN Fei)
1179
-2
6
-2
4
-2
2
-2
0
-1
8
-16
-14
-1
2
-10
-8
0.
5
0.
55
0.
6
0.
65
0.
7
0.
75
0.
8
0.
85
0.
9
0.
95
1
S
NR/
d
B
D
e
t
e
c
t
i
on r
a
t
e
LF
M
-
doppl
er
H
F
M
-
doppl
er
Figure 8. Det
e
ction p
e
rfo
r
mance cu
rve
unde
r the influen
ce of Do
p
p
ler
Table2
sho
w
s that with the influen
ce of Dopple
r
, the minimum
value of SN
R while
detectio
n
rat
e
above 95%
. By compari
ng with LF
M
signal, the p
e
rform
a
n
c
e o
f
HFM sig
nal
is
better tha
n
LFM si
gnal,
with the in
cre
a
se of re
lative velocit
y
, the impro
v
ement of HFM
perfo
rman
ce i
s
more obvio
usly.
Table 2. The
minimum val
ue of SNR while dete
c
tion
rate above 9
5
%
Relative velocity
\ signal
HFM
LFM
10m/s
20m/s
30m/s
40m/s
-16dB
-15dB
-15dB
-14dB
-15dB
-14dB
-13dB
-11dB
5. Conclusio
n
In this pap
e
r
, by comp
a
r
isin
g the
chang
e of HFM sig
nal a
nd LFM
sig
nal over
unde
rwater a
c
ou
stic
simul
a
tion cha
nnel
, it s
hows tha
t
HFM signal
and LFM si
g
nal have stro
ng
anti-noi
se a
n
d
anti-multip
a
t
h capa
bility,
simulatio
n
prove that HF
M signal i
s
m
o
re effe
ctively to
resi
st the influen
ce of doppler. And
HFM sig
nal
is more
suit
able for und
erwater a
c
ou
stic
comm
uni
cati
on with mob
ile platform or und
erwat
e
r acou
stic
cha
nnel with
strong d
o
p
p
ler
influen
ce.
Ackn
o
w
l
e
dg
ement
This work was supp
orte
d by the National Natu
ral Scien
c
e
Found
ation
of China
(610
011
42, 6
1071
150, 61
0010
72, 612
7124
2), and i
n
part by Fundamental
Re
sea
r
ch Fund
s for
the Central Universitie
s
(2
0111
2105
0, 2
0121
2102
8).
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u
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