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Turk J Elec Eng & Comp Sci
(2020) 28: 606 – 620
© TÜBİTAK
doi:10.3906/elk-1904-186
Turkish Journal of Electrical Engineering & Computer Sciences
http://journals.tubitak.gov.tr/elektrik/
Researc h Article
A novel chaos-based modulation scheme: adaptive threshold level chaotic on–o
keying for increased BER performance
Kenan ALTUN1,∗, Enis GÜNAY2
1Department of Electronics and Automation, Sivas Vocational College, Sivas Cumhuriyet University, Sivas, Turkey
2Department of Electrical and Electronics Engineering, Faculty of Engineering, Erciyes University, Kayseri, Turkey
Received: 28.04.2019 • Accepted/Published Online: 04.10.2019 • Final Version: 28.03.2020
Abstract: A novel modulation scheme called adaptive threshold level-chaotic on–o keying (ATL-COOK) is proposed.
This scheme is applied to direct chaotic communication (DCC) systems where the chaotic signals are used as carrier
signals. The objective of the proposed adaptive method is to increase the low BER versus SNR performance caused by
the constant threshold voltage level. In the proposed method, the communication signal received by the receiver circuits
was dened as a Dirac delta function and a comparison signal was obtained from this signal. Then the BER versus SNR
performance was analyzed and compared with that of various chaotic generator structures by using an instantaneous
adaptive signal instead of a constant threshold voltage in the receiver circuit decision block. Both the simulation results
and the experiments show the eciency of the proposed method.
Key words: Direct chaotic communication system, eld programmable analogue arrays, bit error rate
1. Introduction
In the last century, chaos theory was applied in many dierent elds of science. It is noteworthy due to its
approaches in introducing system behavior and problem solving. Chaos theory studies, specically in medicine,
engineering, and mathematics, contribute to the introduction of novel techniques, models, and research areas
[1]. The chaotic signals generated by chaos-based generators stand out with their unpredictability despite their
deterministic structure and their high sensitivity to the initial values of system behavior.
Many of the chaotic systems are noise-like and they have a wideband spectrum. Wideband chaotic signals
bear the information signals in communication systems. Therefore, the use of chaotic signals in communication
systems has increased [2]. Direct chaotic communication (DCC) systems, where the chaotic signal is directly used
as an information carrier signal, can be categorized as coherent and noncoherent modulation techniques. The
most important problem in chaos-based communication systems is the necessity of recovering the carrier signals
in the receiver circuit. Furthermore, the high sensitivity to the initial conditions complicates the recovery and
synchronization of chaos signals in the receiver circuits. Therefore, digital noncoherent communication systems
that do not require continuous synchronization have begun to gain importance [3,4]. It is valid for systems
where both the chaotic and the periodic signals are used as carriers [5].
Noncoherent, instantly synchronized DCC systems that are used in digital information transmission
utilize techniques such as chaos shift keying (CSK) [6], chaotic on–o keying (COOK) [7], dierential chaos
shift keying (DCSK) [8,9], and quadrature chaos shift keying (QCSK) [10]. Digital communication systems
∗Correspondence: kaltun@cumhuriyet.edu.tr
This work is licensed under a Creative Commons Attribution 4.0 International License.
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ALTUN and GÜNAY/Turk J Elec Eng & Comp Sci
that are implemented using chaotic generators have become an alternative for conventional communication
systems due to their simple chaotic circuit structure, wideband carrier signals, and noise-like chaotic signals
[11]. The information signal is obtained through a decision block in the receiver circuits of these communication
systems. The decision is made with constant threshold voltage level at the comparator input of the decision
blocks. It complicates the recovery of the transmitted information signals at the receiver circuits. Therefore,
using a constant threshold voltage level, although the noise level at the transmission medium is variable, makes
the transmission of the information signal dicult and increases the bit error rate.
The proposed study aims to decrease the bit error rate by determining an adaptive threshold voltage level
in the decision blocks of the DCC systems’ receiver circuits. In the proposed chaotic communication system,
dierent chaotic generators were designed with a novel communication model that has an adaptive threshold
voltage level and simulation results were obtained. In Section 2, the novel model ATL-COOK is introduced. In
Section 3and Section 4, the simulation results and the experimental results that were obtained using dierent
chaotic signals are presented respectively. The nal section includes conclusions and discussions.
2. Proposed method ATL-COOK
In DCC systems, the information is transmitted by using the chaotic signals as carriers similar to conventional
communication systems. The carrier signals in the transmitter circuits must be recovered in the receiver circuits
to transmit the information signal. In DCC systems, the carrier signal is recovered in the receiver circuit
through instantaneous or continuous synchronization. The implementation of chaotic communication systems
that require continuous synchronization is dicult due to many reasons such as the sensitivity of the initial
conditions of the chaotic generators [12,13]. Therefore, it is much easier to use instantly synchronized DCC
systems in chaotic communication systems. In this section, the COOK modulation method, which is an instance
of a DCC system, will be explained briey before the introduction of the proposed ATL-COOK method.
The block schemes of the transmitter and receiver structures for COOK communication systems are
shown in Figure 1. The transmitted signal s(t) is generated by switching the chaos signal with the information
signal. The generated signal is expressed by Equation 1.
Chaotic Signal
Generator
c(t)
Binary
Data Signal Si(0,1)
S(t)
c
c.S(t)
(a) Transmitter block scheme
Threshold
Corelator Output
Tb
O(iTb)
r(t)=c.s(t)+n(t)
(b) Receiver block scheme
Figure 1. COOK block scheme.
s(t) = c(t),when symbol ”1” is transmitted
0,when symbol ”0” is transmitted (1)
The noise signal is added to the signal s(t) that comes from the digital modulator circuit, and then it is
transmitted to the receiver circuit along the transmission line. The signal r(t) at the receiver input is correlated
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with itself, transferred to the integrator, and sent to the threshold detector. The signal energy at the output
of the correlator in noisy situations is expressed by Equation 2. Moreover, the signal energy at the output of
the correlator in noiseless condition is expressed by Equation 3[14]. Since the second and third integrals of
Equation 2in the noiseless condition will be zero, the expression becomes Equation 3.
o(iTb) = ZiTb
(i−1)Tb
r2(t)dt =ZiTb
(i−1)Tb
[c.s(t) + n(t)]2dt
=ZiTb
(i−1)Tb
c2.s2(t)dt + 2 ZiTb
(i−1)Tb
c.s(t)n(t)dt +ZiTb
(i−1)Tb
n2(t)dt (2)
o(iTb) = (RiTb
(i−1)Tbc2(t)dt, ”1” is transmitted
0,”0” is transmitted (3)
Every symbol in the signal that is integrated in the threshold detector circuit is sampled with a detector
that has a zero threshold voltage level at the switching period Tb. Then the output becomes +1 if the signal is
positive and 0 otherwise.
The proposed ATL-COOK method has the same transmitter circuit with COOK. However, the constant
threshold voltage was replaced with an adaptive threshold voltage at the information signal decision block of
the receiver circuit. DCC communication systems with noncoherent modulation techniques such as DCSK,
CSK, COOK, and QCSK have a decision block at the output of the receiver circuit. The information signal at
the output of this decision block is obtained by comparing it with the constant threshold voltage. When the
modulation techniques used in noncoherent information transmission are examined, it can be seen that the most
important disadvantage of these techniques is the use of the constant threshold voltage level, which could always
change with the channel noise. When the adaptive threshold-COOK (AT-COOK) model that was proposed to
overcome this problem in the literature is examined [15–17], it is observed that the noise signal at the receiver
circuit is attempted to be obtained at the half period. In the structure given in Figure 2, the transmitter is
composed a binary information module, an ultrawideband (UWB) chaotic generator and a modulator. The
receiver is composed of two envelope detector (ED) modules, for estimating separately the chaotic radio pulse
(CRP) energy and the noise energy, a subtractor. It is also expressed with bit duration Tb, bit energy Eb,
noise energy N0, and estimated noise energy N,
0. This is similar to the modulation known as chaotic masking
in the literature. In the system of which the block scheme is given in Figure 2, the noise signal is obtained at
the receiver circuit at the half period of the switching. The information signal is obtained by extracting this
signal from the signal transmitted at the other half period. In the proposed method, the negative eect of the
instantaneous noise variations is ignored. In addition, it was observed that the AT-COOK method gives better
performance when compared to the proposed method in terms of performance. However, it has been observed
in previous studies [16–18] that the AT-COOK method decreases the performance in environments where the
ambient noise changes continuously, but gives a performance independent of noise in the proposed method. The
most important advantage of the proposed method is that it is independent of noise. Furthermore, if the BER
performance comparison is made with the AT-COOK [16] modulation technique, the proposed study performs
better, especially at low and negative noise levels. This aspect stands out as an important advantage compared
to all other models.
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The design of a decision block that could be used in all of the DCC systems was aimed with the proposed
ATL-COOK method. The decision block in the literature has two inputs. One of the inputs is constant threshold
voltage level. In the novel receiver circuit, the decision block also has two inputs. One of them is the adaptive
threshold voltage level. The information signal was simulated as a Dirac delta function in unit-impulse time.
The purpose of simulating the information signal as a Dirac delta function is the use of this function’s integral
as the comparison curve for signal processing purposes [19]. In the novel proposed communication system, the
signal that was squared at the input of the receiver circuit was used as the comparison signal at the decision
block. The comparison signal that was used in the other input of the decision block was obtained by integrating
the Dirac delta function. A second value was obtained for instantaneous comparison because the integral of the
Dirac delta function is the ramp function. Theoretically, it seems possible to decrease the BER versus SNR to
zero in the ideal operating conditions as shown in the mathematical expressions of the proposed system. When
the simulation results are examined, it is shown that the dependency of the proposed method on the noise level
was reduced. On the other hand, when these results are compared with the present DCC systems, it attracts
attention with the same level BER ratios at various noise levels. Therefore, it is also advantageous that the
model satises the system expectations with its predictable error rate in continuous operation.
Binary
Informat ion
UWB Chaotic
Generator
CRP Ener gy
ED
Noise Energy
ED
Tb
0
1
1
1
0
0
1
0
Tb/2 Tb/2
Figure 2. AT-COOK principle scheme [16].
As shown in Figure 3the signal r(t) at the input of the novel receiver circuit is the same as that in
the other DCC systems. Therefore, there is no dierence with the other systems in terms of communication
security. The fundamental improvement in the novel communication model is the reduction in the bit error rate
at the recovery of the information signal. As shown in Figure 4the decision mechanism of the receiver circuit
in the proposed communication system can be expressed mathematically as follows:
Output
r(t)=cs(t)+n(t)
e(t)
Adaptive
Threshold
Level
Correlator
Figure 3. A new chaotic communication model: receiver
circuit block.
Dec ision bloc k
Output
a
b
ḿ (t)
Figure 4. A new chaotic communication model receiver
decision block.
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In the ideal operating conditions (i.e. no noise)
r(t) = c.s(t)(4)
Here s(t) is the transmitted signal at the switching moment of the transmitter circuit and c is the antenna
gain of the transmitter circuit. For any time t, s(t) represents the direct delta function:
s(t) = δ(t)(5)
Thus, r(t)2= (c.δ(t))2=c2.δ(t). Therefore, the comparison signal when the switch equals ”1” is
c2.1 = c2(6)
When the switch transmits achaotic signal at the transmitter circuit, the input aof the decision block
becomes c2. When the switching signal is 0 at the transmitter circuit, the input aof the decision block becomes
0.
On the other hand, the signal at the other input of the decision block is
sZt
−∞
c.δ(t)dt =pc.u(t)(7)
Here u(t)(Equation 8) is the unit step function (in other terms Heaviside theta function).
u(t−a) = 0, t < a
1, t > a , f or a = 0, u(t) = 0, t < 0
1, t > 0(8)
When the unit step function (i.e. u(t)) is integrated, the result is the ramp function (i.e. ramp(t) =
Rt
−∞ u(t)dt) expressed in Equation 9. The ramp function is used as the comparison signal in the second input
of the decision block.
c.ramp(t) = cZt
−∞
u(t)dt =0, t < 0
c, t ≥0(9)
bm=1, a > b
0, a < b (10)
The information signal m is obtained at the receiver circuit with the decision function expressed in
Equation 10.
The red line in Figure 5shows the ideal ramp function with no noise. The blue line shows the ramp
function with the noise added in the simulation of the proposed communication system. Thus, the ramp
function obtained from the comparison signal was used instead of the constant threshold voltage in the other
digital communication systems. The results were obtained and interpreted using dierent chaotic generators for
the proposed communication system.
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050 100 150 2 00 250 300 350 400
5
40
35
30
25
20
15
10
45
t
V
Figure 5. Ramp function curve (V-t); noiseless (red line) and noise added (blue line).
3. Simulations, results, and discussion
Simulation of the proposed ATL-COOK method and COOK communication system was conducted using dif-
ferent chaotic generators. The simulation was realized using Rössler, Sproot h, and Sproot n chaos signals
with an AWGN noise between –6 dB and 15 dB. Simulation studies performed in agreement with the proposed
method are demonstrated using dierent chaotic generators. In the study, while the xed threshold value ”0”
is selected in the COOK communication system, the proposed system has created an adaptive threshold value.
The simulation study was performed in Matlab Simulink. When the obtained results are examined, an increase
of 90% in BER performance is observed with the proposed communication system. The results of the proposed
study with the novel communication model are given below:
First, the Rössler chaotic generator given with dynamic Equation 7was used. Rössler phase space and
communication signals are shown in Figure 6and Figure 7, respectively.
-12 -5 0510 1 5
-10
4
2
0
-2
-4
-6
-8
6
x
y
8
-10
Figure 6. Rössler chaotic attractor x, y plane.
-0.2
0
-0.5
-1
0.8
t
V
(a)
(b)
(c)
0 20
0.4
40 60 8 0 100 120 140 160 180 200
1.2
0
0.5
1
1.5
V
V
-0.5
0
0.5
1
1.5
t
t
Figure 7. Simulation results using the Rössler chaotic
generator: (a) transmitted data signal, (b) signal at the
receiving circuit input, (c) data signal obtained at the
receiver.
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˙x=−y−z
˙y=x+ay
˙z=zx −zc +b(11)
The analysis of the COOK communication system and the proposed ATL-COOK method was realized
at various noise rates. Table 1shows the number of errors and the error rate for dierent noise values. It can
be seen that the BER versus SNR of the proposed model is very small. It can also be understood from Figure 8
that the BER versus SNR performances increased greatly. Similar work was done for the Sprott h chaotic
generator. The dynamic system equations for the Sprott h chaotic generator are given by Equation 12.
Table 1. Communication system BER versus SNR rates with the Rössler chaotic generator.
Eb/No (db)
Rössler COOK
communication system
Proposed new communication
model with Rössler
Percentage decrease
in proposed new
communication
model with Rössler
Number of errors Error rate Number of errors Error rate % Percentage ratio
–6 736 0.18395401 65 0.01624594 91.17%
–5 627 0.15671082 53 0.01324669 91.55%
–4 536 0.13396651 44 0.01099725 91.79%
–3 455 0.11372157 32 0.00799800 92.97%
–2 387 0.09672582 27 0.00674831 93.02%
–1 311 0.07773057 24 0.00599850 92.28%
0 267 0.06673332 20 0.00499875 92.51%
1 244 0.06098475 18 0.00449888 92.62%
2 224 0.05598600 19 0.00474881 91.52%
3 216 0.05398650 16 0.00399900 92.59%
4 212 0.05298675 13 0.00324919 93.87%
5 211 0.05273682 13 0.00324919 93.84%
6 210 0.05248688 13 0.00324919 93.81%
7 210 0.05248688 12 0.00299925 94.29%
8 210 0.05248688 11 0.00274931 94.76%
9 210 0.05248688 10 0.00249938 95.24%
10 210 0.05248688 11 0.00274931 94.76%
11 210 0.05248688 11 0.00274931 94.76%
12 210 0.05248688 11 0.00274931 94.76%
13 210 0.05248688 11 0.00274931 94.76%
14 210 0.05248688 11 0.00274931 94.76%
15 210 0.05248688 11 0.00274931 94.76%
16 210 0.05248688 11 0.00274931 94.76%
17 210 0.05248688 11 0.00274931 94.76%
18 210 0.05248688 11 0.00274931 94.76%
The Sprott h chaotic generator given with dynamic Equation 7was used. Sprott h phase space and
communication signals are shown in Figures 9and 10, respectively.
˙x=−y+z2
˙y=x+ 0,5y
˙z=x−z(12)
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-3
-6
10
BER
-4 -2 0 2 4 6 8 10 12 14 16 18
10
10
10
-2
-1
0
Rossler COOK
Rossler COOK(New Model)
Eb/No [d B]
Figure 8. BER versus SNR performance comparison
studies using the Rössler chaos generator.
-0.5 -0.2 0 0.2 0.4
-0.4
0.2
0.1
0
-0.1
-0.2
-0.3
0.3
x
y
0.4
-0.4
Figure 9. Sprott h chaotic attractor x, y phase space.
-0.2
0
-200
-300
0.8
t
V
(a)
(b)
(c)
0 20
0.4
40 60 8 0 100 120 140 160 180 200
1.2
0
200
300
V
V
-0.5
0
0.5
1
1.5
t
t
100
-100
Figure 10. Simulation results using the Sprott h chaotic generator: (a) transmitted data signal, (b) signal at the
receiving circuit input, (c) data signal obtained at the receiver.
Table 2and Figure 11 show the results with the Sprott h chaos signal. It can be seen that the ATL-
COOK method shows better performance. However, when the BER performance of Sprott h chaos generators is
compared with that of other chaos generators, the switching times of the Sprott h chaos generators are long at
some points (80, 140 time duration in Figure 10). The change in information signals at these locations increases
the SNR rate. In other words, the Sprott h chaos generator has a dierent phase space representation, although
other space chaos generators are single lobed. Finally, the analysis was repeated with the Sprott n chaos signal.
Dynamic system equations are given by Equation 13. Furthermore, Sprott n phase space and communication
signals are shown in Figures 12 and 13, respectively.
˙x=−2y
˙y=x+z2
˙z= 1 −y−2z(13)
The results of the analysis with the Sprott n chaos signal are shown in Table 3and Figure 14. The entire
simulation results are shown in Figure 15. It can be seen that the error rates are high with the COOK model
and the performance decreases when the noise level increases. BER versus SNR of the proposed ATL-COOK
model is very small.
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Table 2. Communication system BER versus SNR rates with the Sprott h chaotic generator.
Eb/No (db)
Sprott h COOK
communication system
Proposed new communication
model with Sprott h
Percentage decrease
in proposed new
communication
model with Sprott h
Number of errors Error rate Number of errors Error rate % Percentage ratio
–6 756 0.188952762 135 0.033741565 82.14%
–5 651 0.162709323 110 0.027493127 83.10%
–4 560 0.139965009 94 0.023494126 83.21%
–3 480 0.119970007 89 0.022244439 81.46%
–2 406 0.101474631 84 0.020994751 79.31%
–1 342 0.08547863 80 0.019995001 76.61%
0 298 0.07448138 77 0.019245189 74.16%
1 277 0.069232692 79 0.019745064 71.48%
2 252 0.062984254 75 0.018745314 70.24%
3 235 0.058735316 74 0.018495376 68.51%
4 233 0.058235441 75 0.018745314 67.81%
5 226 0.056485879 73 0.018245439 67.70%
6 228 0.056985754 75 0.018745314 67.11%
7 242 0.060484879 77 0.019245189 68.18%
8 244 0.060984754 78 0.019495126 68.03%
9 245 0.061234691 75 0.018745314 69.39%
10 237 0.059235191 74 0.018495376 68.78%
11 233 0.058235441 78 0.019495126 66.52%
12 234 0.058485379 77 0.019245189 67.09%
13 238 0.059485129 76 0.018995251 68.07%
14 236 0.058985254 74 0.018495376 68.64%
15 236 0.058985254 69 0.017245689 70.76%
16 239 0.059735066 66 0.016495876 72.38%
17 241 0.060234941 61 0.015246188 74.69%
18 231 0.057735566 60 0.014996251 74.03%
-6
BER
-4 -2 0 2 4 6 8 10 12 14 1 6 18
10 0
Sproot h COOK
Sproot h (New Model)
Eb/No [d B]
10
-2
10-1
Figure 11. BER versus SNR performance comparison
using the Sprott h chaos generator.
-20 -25
0
-5
-10
-15
5
x
y
10
-30 -20 -15 -10 -5 0 5 10
Figure 12. Sprott n chaotic attractor x, y phase space.
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Table 3. Communication system BER versus SNR rates with the Sprott n chaotic generator.
Eb/No (db)
Sprott n COOK
communication system
Proposed new communication
model with Sprott n
Percentage decrease
in proposed new
communication
model with Sprott n
Number of errors Error rate Number of errors Error rate % Percentage ratio
–6 728 0.181954511 33 0.008247938 95.47%
–5 619 0.154711322 28 0.00699825 95.48%
–4 527 0.131717071 25 0.006248438 95.26%
–3 449 0.112221945 20 0.00499875 95.55%
–2 378 0.094476381 14 0.003499125 96.30%
–1 303 0.075731067 15 0.003749063 95.05%
0 260 0.064983754 13 0.003249188 95.00%
1 238 0.059485129 12 0.00299925 94.96%
2 216 0.053986503 12 0.00299925 94.44%
3 208 0.051987003 10 0.002499375 95.19%
4 205 0.051237191 11 0.002749313 94.63%
5 205 0.051237191 8 0.0019995 96.10%
6 203 0.050737316 7 0.001749563 96.55%
7 203 0.050737316 6 0.001499625 97.04%
8 204 0.050987253 6 0.001499625 97.06%
9 204 0.050987253 5 0.001249688 97.55%
10 204 0.050987253 6 0.001499625 97.06%
11 204 0.050987253 9 0.002249438 95.59%
12 205 0.051237191 7 0.001749563 96.59%
13 204 0.050987253 6 0.001499625 97.06%
14 204 0.050987253 7 0.001749563 96.57%
15 204 0.050987253 7 0.001749563 96.57%
16 204 0.050987253 7 0.001749563 96.57%
17 205 0.051237191 8 0.0019995 96.10%
18 204 0.050987253 6 0.001499625 97.06%
-0.2
0
-4000
-6000
0.8
t
V
(a)
(b)
(c)
0 20
0.4
40 60 8 0 1 00 120 140 1 60 180 200
1.2
0
2000
4000
V
V
-0.5
0
0.5
1
1.5
t
t
-2000
Figure 13. Simulation results using the Sprott n chaotic
generator: (a) transmitted data signal, (b) signal at the
receiving circuit input, (c) data signal obtained at the
receiver.
-6
BER
-4 -2 0 2 4 6 8 1 0 12 14 1 6 18
100
Sproot n COOK
Sproot n COOK (New Model)
Eb/No [d B]
10-2
10-1
10-3
Figure 14. BER versus SNR performance comparison
studies using the Sprott n chaos generator.
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-6
BER
-4 -2 0 2 4 6 8 10 12 14 1 6 18
10 0
Rossler CO OK
Rossler Ne w Model
Eb/No [d B]
10
-2
10-1
10
-3
Sproot n COOK
Sproot n New Model
Sproot h COOK
Sproot h New Model
Figure 15. BER versus SNR performance comparison studies using dierent continuous chaos generators in the COOK
communication system and the proposed communication system in Matlab Simulink.
4. Experimental realization of the proposed ATL-COOK on FPAA
The same simulation scenarios were repeated experimentally using eld programmable analogue arrays (FPAAs).
The chaos signal becomes periodic after a moment in the experiments done with digital hardware. The reliability
of the communication system decreases when the chaos signal is periodic. Therefore, the use of noncoherent
structures became much more important in analogue-based chaotic communication systems [20].
The ability to implement the ATL-COOK method in FPAA platforms is another advantage of the method.
Four FPAA blocks were used in the experimental study. The Rössler chaos signal was obtained in the FPAA1
block. The resulting chaos signal was transferred to the FPAA2 block. The FPAA2 block uses PERIODIC
WAVE BLOCK, where the information signal and ambient noise are modeled. In addition, in the FPAA2 block,
the GAINSWITCH block was used to switch the signal to the transmitted signal by adding ambient noise to the
transmitted signal. The signal switched on the AWGN signal and the GAINSWITCH block was transferred to
the FPAA3 block. These two signals from the FPAA2 block were collected using the SUMINVERTER BLOCK
and a transmission medium signal was obtained. In addition, in the FPAA3 block, the correlator operation at
the receiver circuit was performed using the TRANSFER FUNCTION and transferred to the FPAA4 block.
In the FPAA4 block, the rst signal at the comparator input was obtained from the signal INTEGRATOR in
the correlator output signal. The second signal at the comparator input was obtained using the TRANSFER
FUNCTION. The signal at the comparator output was transferred from the FPAA4 block to the output. The
FPAA realization scheme of the ATL-COOK communication system is shown in Figure 16. Table 4presents
the blocks and their purposes used in the FPAA realization scheme.
Figure 16. FPAA implementation of the proposed receiver circuit: (a) Rössler chaotic generator is presented in FPAA1,
(b) transmitting circuit and noise signal generator in FPAA2, (c) addition of AWGN with modulation signal in FPAA3,
(d) realization of the proposed system in FPAA4.
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The software was deployed in the FPAA development card after it was modeled in the interface. The
input and output information signals were measured experimentally using a digital oscilloscope via input/output
terminals of the FPAA development card.
The experimental implementation was performed with the Rössler chaos signal on FPAA1. Dynamic sys-
tem equations and phase space of the Rössler chaos signal are given by Equation 11 and Figure 17, respectively.
The information signal to be transmitted is shown in Figure 18. The information signal is used for switching
of the chaotic generator in the communication system. Switching with the information signal was realized with
the GAINSWITCH block in the experimental study.
Figure 19 shows the communication signal with added noise in the receiver circuit input. This received
signal was used in obtaining the decision block signals by correlating it in the receiver circuit.
Table 4. FPAA realization blocks used in the experimental study.
FPAA Realization Blocks
SUMFILTER BLOCK
SUMFILTER blocks work as an integrator by using Laplace transforms, and
are used to obtain state equations of the chaotic generator in FPAA1.
SumFilter1; Gain1=1, Gain2=1, Gain3=1, Corner Frequency=1.2 kHz.
SumFilter2; Gain1=1,Gain2=1.25, Corner Frequency=1.2 kHz.
SumFilter3; Gain1=1, Gain2=0.6, Gain3=2, Corner Frequency=1.2 kHz.
TRANSFER FUNCTION
TRANSFER FUNCTION in FPAA1 is used for implementation of PWL-based
output function of the system. On the other hand, TRANSFER FUNCTION in
FPAA3 and in FPAA4 performs the math function in the correlator blo ck.
GAINSWITCH BLOCK GAINSWITCH block is used to obtain switching and thresholding processes.
GAINSWITCH block in FPAA1 is used in the Rössler chaotic generator.
PERIODIC WAVE BLOCK
PERIODIC WAVE block is used in FPAA2 for generating the data signal,
which is a Bernoulli binary generator, in transmitter block, and also used for
additive white Gaussian noise in FPAA3.
SUMINVERTER BLOCK SUMINVERTER block is used for adding AWGN and modulation signal
in FPAA3.
DC VOLTAGE SOURCE BLOCK DC VOLTAGE SOURCE block provides constant values of Rössler
chaotic generator in FPAA1.
INTEGRATOR INTEGRATOR block works as an integrator in FPAA4.
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The information signal obtained at the output of the decision block is shown in Figure 20. The results
of the experimental study were obtained from the digital oscilloscope. The experimental results are shown in
Figure 21.
Figure 21 shows the BER versus SNR comparison for COOK and ATL-COOK. It can clearly be seen
that the BER versus SNR of the proposed model has better performance. The experimental results are similar
to the simulation results.
-1
-1.6
0
-0.4
-0.6
-0.8
1
x
y
-2 -1.2 -0.8 -0.4 0 0.4 0.8 1.2 2
1.6
-0.2
0.2
0.4
0.6
0.8
Figure 17. Rossler chaotic attractor x, y phase space.
t
0 20 40 60 80 100 120 1 40 1 60 180 200
V
-0.5
0
0.5
1
1.5
Figure 18. Transmitted data signal.
t
0 50 100 150 200 250 3 00 350 400
V
-60
-20
0
20
40
-40
Figure 19. Signal at the receiving circuit input.
t
0 20 40 60 80 100 120 1 40 1 60 180 200
V
-0.5
0
0.5
1
1.5
Figure 20. Data signal obtained at the receiver.
Figure 21. BER versus SNR performance comparison studies using the Rössler chaos generator in the COOK commu-
nication system and the proposed communication system in the FPAA platform.
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5. Conclusion
A novel decision block was proposed for distributed spectrum DCC systems with the present study. A decision
block with an adaptive threshold voltage level was realized for noncoherent structures with the proposed method.
The proposed method was called ATL-COOK because the threshold voltage level can change instantaneously.
The simulation of the proposed method was done using dierent chaos signals and it was veried that it has a
better error performance than the COOK system. As a result of the simulation and experimental studies, it is
observed that the proposed method increases the application areas of DCC systems in wireless communication
systems as it obviates the noise eect on chaotic communication systems. Furthermore, the method is also
important not just with its bit error rate but also its applicability to recongurable analogue systems. In future
work we will consider improving the bit error rate of DCC systems to be acceptable for reliable communication
systems.
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