Carrier Frequency Modulation
2.9
2001/07/03
2004/03/17 17:02:22.313 US/Central
Behnaam
Aazhang
aaz@ece.rice.edu
Dinesh
Rajan
dinesh@ece.rice.edu
Mohammad
Jaber
Borran
mohammad@ece.rice.edu
Roy
Ha
rha@rice.edu
Shawn
Stewart
mrshawn@alumni.rice.edu
Behnaam
Aazhang
aaz@ece.rice.edu
frequency shift keying
FSK
frequency modulation
A method of carrier modulation in which signal information is carried in the carrier frequency of
the signal.
Frequency Shift Keying (FSK)
The data is impressed upon the carrier frequency. Therefore,
the M different signals are
s
m
t
A
P
T
t
2
f
c
t
2
m
1
Δ
f
t
θ
m
for
m
1
2
…
M
The M different signals have
M different carrier frequencies
with possibly different phase angles since the generators of
these carrier signals may be different. The carriers are
f
1
f
c
f
2
f
c
Δ
f
f
M
f
c
M
1
Δ
f
Thus, the M signals may be
designed to be orthogonal to each other.
s
m
s
n
t
0
T
A
2
2
f
c
t
2
m
1
Δ
f
t
θ
m
2
f
c
t
2
n
1
Δ
f
t
θ
n
A
2
2
t
0
T
4
f
c
t
2
n
m
2
Δ
f
t
θ
m
θ
n
A
2
2
t
0
T
2
m
n
Δ
f
t
θ
m
θ
n
A
2
2
4
f
c
T
2
n
m
2
Δ
f
T
θ
m
θ
n
θ
m
θ
n
4
f
c
2
n
m
2
Δ
f
A
2
2
2
m
n
Δ
f
T
θ
m
θ
n
2
m
n
Δ
f
θ
m
θ
n
2
m
n
Δ
f
If
2
f
c
T
n
m
2
Δ
f
T
is an integer, and if
m
n
Δ
f
T
is also an integer, then
S
m
S
n
0
if
Δ
f
T
is an integer,
then
s
m
s
n
0
when
f
c
is much larger than
1
T
.
In case
m
θ
m
0
s
m
s
n
A
2
T
2
sinc
2
m
n
Δ
f
T
Therefore, the frequency spacing could be as small as
Δ
f
1
2
T
since
sinc
x
0
if
x
±
1
or
±
2
.
If the signals are designed to be orthogonal then the average
probability of error for binary FSK with optimum receiver is
P
‐
e
Q
E
s
N
0
in AWGN.
Note that
sinc
x
takes its minimum value not at
x
±
1
but at
±
1.4
and the minimum value is -0.216.
Therefore if
Δ
f
0.7
T
then
P
‐
e
Q
1.216
E
s
N
0
which is a gain of
10
1.216
0.85
d
θ
over orthogonal FSK.