Journal of Signal and Information Processing, 2011, 2, 175-177
doi:10.4236/jsip.2011.23023 Published Online August 2011 (http://www.SciRP.org/journal/jsip)
175
Performance Evaluation of FM-COOK Chaotic
Communication System
Hikmat N. Abdullah1, Alejandro A. Valenzuela2
1Department of Electrical Engineering, Al-Mustansiryah University, Baghdad, Iraq; 2Department of Electrical Engineering, Mecha-
nical Engineering and Technical Journalism, University of Applied Sciences Bonn-Rhein-Sieg, Bonn, Germany.
Received May 3rd, 2011; revised May 30th, 2011; accepted June 7th, 2011.
ABSTRACT
In this paper, the performance evaluation of Frequency Modulated Chaotic On-Off Keying (FM-COOK) in AWGN,
Rayleigh and Rician fading channels is given. The simulation results show that an improvement in BER can be gained
by incorporating the FM modulation with COOK for SNR values less than 10 dB in AWGN case and less than 6 dB for
Rayleigh and Rician fading channels.
Keywords: Chaotic Transceiver, On-Off Keying, FM Modulation
1. Introduction
Chaotic signals are a relatively new field of interest in
communication systems. Motivations of this method de-
rived from the advantages offered by chaotic signals,
such as robustness in multipath environments and resis-
tance to jamming. Chaotic signals are non-periodic, broa-
dband, and difficult to predict and reconstruct. These are
properties which match with requirements for signals
used in communication systems [1].
Various types of modulation can be used in direct
chaotic communication systems like chaotic on-off key-
ing (COOK), differential chaotic shift keying (DCSK)
and additive chaos modulation (ACM), etc. Among all
chaotic modulation types, DCSK with orthonormal basis
functions of fers th e be st robustn ess ag ainst multip ath an d
channel imperfections [2]. Due to the length and non-
-periodicity of chaotic sample functions, the energy per
bit is not constant and varies from one sample function to
another. As a result, this varied energy per bit limits the
noise performance of modulation system.
In 1998, Kolumbán et al. [3] show that FM-DCSK
scheme generates an inherently wideband signal with
constant energy per bit, which enhances the noise per-
formance of DCSK. In 2001, Z. Galias and G. Maggio [4]
proposed QCSK (Quadrature Chaos Shift Keying) sche-
me which can transmit 2 bits in a sample function to im-
prove the speed of chaos shift keying. Then in 2006, Y.
Zhang [5] devised FM-QCSK which enhanced the noise
performance of QCSK by using frequency modulation,
because it can generate constant energy per bit and its
frequency spectrum. In 2009, J. Pan and H. Zhang [6]
proposed an advanced version of the previous scheme
named FM-QACSK (Frequency Modulated Quadrature
Amplitude chaos shift keying) where 256QAM modula-
tion is used to increase data rate also combined with the
use of FM modulation.
Although the performance of COOK chaotic modula-
tion lags behind the DCSK, the COOK have an advan-
tage of that it consumes less pow er since it sends chaotic
signal only in case of sending the data bit “1” while no
power is sent for case of data bit “0”. However, we don’t
find in the literature the performance evaluation of the
use of FM modulation with COOK to get constant en-
ergy per bit. So, this paper is an attempt to evaluate the
performance of FM-COOK modulation scheme.
2. FM-COOK Modulation
Figure 1 shows the block diagram of FM-COOK system.
Since the chaotic signal is nonperiodic and never re-
peated, the energy in each bit (for symbol “1”) would
vary from one bit to another. The variance of estimation
can be reduced by increasing the statistical bandwidth of
the transmitted chaotic signal or by increasing the bit
duration [7]. Alternatively, one may solve the problem
directly by modifying the generation of the basis func-
tions such that th e transmitted energy for each symbol is
kept constant by applying the chaotic signal to an FM

Performance Evaluation of FM-COOK Chaotic Communication System 176
modulator. Recall that the instantaneous power of an FM
signal does not depend on the modulation, provided that
the latter is slowly varying compared to the carrier.
Hence the transmitted FM-COOK is given by:
  

cosd when d1
0 when d0
ccf
AtKc t
st
t




 






(1)
where d( t) is the transmitted data, Ac is the carrier ampli-
tude, ωc is the carrier frequency, Kf is the modulation
constant in Hz/V and c(t) is the chaotic signal. Th e aver-
age energy per bit is 2
c
A
.
The upper limit on the noise performance of a modula-
tion scheme is determined by the separation of the mes-
sage points in the signal space; the greater the separation,
the better the noise performance. The distance between
the message points in FM-COOK is 2
c
A
. In principle,
the best noise performance in an AWGN channel can be
achieved by using a coherent receiver [7]. In practice, the
propagation cond itions may be so poor that it is difficult,
if not impossible, to regenerate the basis functions at the
receiver. Under these conditions, a noncoherent receiver
may offer better performance. The non-coherent detector
shown in Figure 1 is, in fact, a bit-energy estimator
whose output for the lth symbol is given by:






 

11
22
11
11
2
11
1d
2d
bb
bb
bb
bb
TT
blT lT
TT
lT lT
yTrtts ttd
d
s
tnt tnt t






(2)
where n(t) is the noise signal and r(t) is the received sig-
nal plus noise. In the absence of the noise signal n(t) , the
bit-energy estimator gives:





122
1cos d
when d1
0 when d0
b
b
Tt
ccf
lT
AtKc
st t
t
















(3)
The output is then passed to the threshold detector
with the threshold set to mid-value of
and zero, where


122
1cos d
b
b
Tt
ccf
lT
EA tKc 









E[.] denotes the expectation operator. The decoded sym-
bol is “1” if the estimated bit energy is larger than the
threshold, otherwise a “0” is recovered. In the presence
of noise (and fading), the threshold level needs to be
shifted in order to optimize the performance. Note that
Recovered
data
Chaotic
Generator FM
Modulato
r
Transmission Channel
COOK
Modulato
r
COOK Demodulato
Input data
Figure 1. The block diagram of FM-COOK system.
no FM demodulator is needed in the receiver because it
is only use to get constant energ y per bit.
3. Simulation Results
A simulation model has been implemented for FM-
COOK chaotic modulator. Hennon mapping given by:
n
2
11 nn
x
bx ax
  where a and b are constants and a =
–1.4 and b = 0.3 is used to generates the chaotic signal.
According to the article [8], we define the chip rate
equals 0.05 µs and Tb = 4 µsec. For FM modulator, Ac =
1V, fc = 36 MHz and then up conver ted to 433 MHz and
Kf = 7.8 MHz/v.
Figure 2 shows the noise performance of FM-COOK
as compared with COOK in AWGN channel. It is clear
from this figure that the performance of FM-COOK is
better than traditional COOK up to SNR = 10 dB and
after than the performance becomes similar. However,
this improvement is unfortunately lies in the region
where the error probability is less than 10–4. This is be-
cause the threshold detector can easily recognize the high
energy level for bit “1” as compared with bit “0” for high
values of SNR, so the use of FM modulation would not
add extra improvement. Figures 3 and 4 show the per-
formance in Rayleigh and Racian fading channels re-
spectively. In this case we used in our simulations two
paths, the second path delay was 75 ns with attenuation
of –3 dB which represents the specification of multipath
environment inside office buildings. Here the perform-
ance of FM-COOK is better than COOK up to SNR = 6
dB for both cases. The improvement region along the
performance curves here is much worse than that in
AWGN channel (BER less than 10–2).
However, these improvements can be increased rela-
tively as the ratio of bit duration to chip duration decrease
Figure 2. Performance of FM-COOK as compared with
COOK in AWGN channel.

Performance Evaluation of FM-COOK Chaotic Communication System 177
Figure 3. Performance of FM-COOK as compared with
COOK in Rayleigh Fading channel.
Figure 4. Performance of FM-COOK as compared with
COOK in Rician Fading channel.
because we would get more variance in the energy level
from one bit to another, so the use of FM would function
well. But from other hand this would make the chaotic
signal loss its characteristics as a spreading signal since
the process gain of spreading operation would be greatly
reduced which is not a practical case.
4. Conclusions
Although the FM-D CSK system offer the best noise per-
formance in noisy and fading channels, the FM-COOK
system offers the advantage of less power requirements
which is important for some applications. The use FM
modulation with COOK would provide constant energy
per bit which leads to improve the noise performance in
this system. Unfortunately, this improvement is achiev ed
at low values of BER, so we think that the disadvantage
of increasing the transmitter complexity by adding the
FM modulator to COOK transmitter is considered more
than the advantage gained in BER from practical point of
view.
5. Acknowledgements
The authors would like to thank IIE organization for fi-
nancing support to this work.
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