# Experimental Study on FM-CSK Communication System for WSN

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Concept of the FM-CSK Communication System

_{1}, X

_{2}, X

_{3}); in turn, on the receiver side, the slave oscillator generates only two state variables (Y

_{1}, Y

_{3}) while one of the variables (Y

_{2}) is substituted by the transmitted signal from the master oscillator (X

_{2}). In such a scheme, the signal from the state variable (X

_{2}) of the master circuit is used as a synchronization signal. The other state variables (X

_{1}and X

_{3}) of the master circuit are used to transmit the information (Figure 1). All state variables are chaotic signals: voltages across and currents through the circuit elements in physically implemented chaos oscillators.

_{1}and X

_{3}. Bit “1” shifts to X

_{1}and bit “0” shifts to X

_{3}. Before an information-carrying signal is formed, X

_{1}and X

_{3}signals should be DC-cancelled, and their amplitudes must be matched. The DC component is suppressed in the synchronization signal as well. The formed information-carrying and synchronization signals are passed through the pre-emphasis filter. Then, both signals are used for frequency modulation and are transmitted in parallel (e.g., using different frequencies or polarization) through an additive white Gaussian noise (AWGN) channel.

_{1}and Y

_{3}from the slave circuit. If ${\beta}_{{X}_{1}}>{\beta}_{{X}_{3}}$, then data bit “1” is detected, otherwise—“0”. For precise bit detection, master and slave circuits’ signals must agree. Thus, chaotic synchronization between the two chaos oscillators is crucial for correct signal detection. Therefore, the properties of chaos oscillators are examined in the next section. Moreover, a bit error ratio (BER) estimation is performed in Section 4 to verify the obtained results and evaluate the communication system’s noise immunity.

## 3. Chaos Oscillators

#### 3.1. Description of Chaos Oscillators

#### 3.1.1. Two-Transistor RC Chaos Oscillator

_{2}. Two transistors are used as nonlinear active elements. The two-transistor RC chaos oscillator circuit is constructed with a standard single-supply self-biasing RC phase shift oscillator with an added subcircuit (outlined by the dashed line box) interacting with the RC ladder [24].

_{p}, v

_{1}, v

_{2}, v

_{BE}

_{1}, and v

_{BE}

_{2}are marked in Figure 2, i

_{C}

_{1}and i

_{C}

_{2}are transistors of Q

_{1}and Q

_{2}collector currents, i

_{B}

_{1}and i

_{B}

_{2}are transistors of Q

_{1}and Q

_{2}base currents.

_{B}

_{1}, i

_{B}

_{2}, i

_{C}

_{1}, and i

_{C}

_{2}are determined by the transistor model and are functions of the collector-emitter and base-emitter voltages v

_{CE}

_{1}, v

_{CE}

_{2}, v

_{BE}

_{1}, and v

_{BE}

_{2}[23].

#### 3.1.2. Vilnius Chaos Oscillator

_{C}is the voltage across capacitor C, V

_{C}

_{*}is the voltage across capacitor C*, I

_{L}is current through inductor L, k is OP AMP circuit gain, I

_{D}is the diode’s current described by the following expression:

_{D}is the voltage across the diode (due to parallel connection V

_{D}= V

_{C}

_{*}), I

_{S}is the saturation current, V

_{T}is the thermal voltage.

#### 3.1.3. Chua’s Chaos Oscillator

_{1}, C

_{2}, and the current through inductor L. The circuit diagram of Chua’s nonlinear resistor used as a nonlinear element [25] is shown in Figure 4b.

_{1}is the voltage across capacitor C

_{1}, v

_{2}is the voltage across capacitor C

_{2}, i

_{3}is current through inductor L. f(v

_{1}) is a nonlinear function defined by nonlinear Chua’s resistor N

_{R}properties. f(v

_{1}) is a current-voltage characteristic of the N

_{R}(Figure 5):

_{a}is a slope in the inner region, G

_{b}is a slope in the outer region, E is the voltage across the N

_{R}resistor. By choosing a slope in the inner region G

_{a}, a slope in the outer region G

_{b}, and the voltage E across resistor N

_{R}, any continuous three-segment odd-symmetric piecewise-linear current-voltage characteristic for Chua’s diode can be specified [25].

#### 3.2. Study on Performance of Chaos Oscillators

_{1}) is displayed on the x-axis and the other state variable (e.g., the voltage across capacitor C

_{2}) is shown on the y-axis. The acquired two-dimensional projection’s disposition corresponds to the two-dimensional projection in the original study, demonstrating that the model was successfully implemented and ready for further examination. The Analog Discovery 2 device was used to measure voltages in hardware experiments. Data from Analog Discovery 2 and LTspice simulations were processed and analyzed in MATLAB (Figure 6).

_{1}is taken to estimate correlation with Y

_{1}. The higher value of $\beta $ indicates better synchronization. Equation (13) was used for calculating the correlation coefficient between the given signals:

#### 3.3. Chaos Oscillator Performance Analysis

_{2}voltage in the master circuit is used to substitute C

_{2}voltage in the slave circuit). In this case, chaotic synchronization is obtained using OP-AMP in voltage follower mode [30,31]. When two chaos oscillators are synchronized in the master-slave system, the correlation coefficient between voltages across the same elements in the master and slave circuits approaches 1.

_{1}, Z

_{2}, and Z

_{3}correspond to C

_{1}, C

_{2}, and C

_{3}for the RC chaos oscillator; to C

_{1}, C

_{2}, and L

_{1}for Chua’s chaos oscillator. For Vilnius chaos, the oscillator results are presented in Table 2. The simulation results demonstrate that the correlation coefficient value was above 0.98, while the maximal possible value for the normalized correlation coefficient is 1, which means that the slave circuit signals precisely repeat the master circuit signals. In turn, during hardware experiments, correlation coefficient values were above 0.9. Thus, it has been proved that synchronization in the master-slave system was always present in both studies. Therefore, changing the nominal value of the reactive elements within ± 10% in the slave circuit did not affect the system’s dynamics.

## 4. Communication System’s Performance Analysis

_{1}and X

_{3}(Figure 1) are employed to map bit values “1” and “0”, respectively. Voltages across electrical circuit elements represent the state variables of the oscillator, which are summarized in Table 3 for the selected chaos oscillators.

_{1}and Y

_{3}. Decision-making for the received bit is based on the correlation coefficient β’s calculation: if ${\beta}_{{X}_{1}}>{\beta}_{{X}_{3}}$, then “1” is received, else “0” is received.

#### 4.1. FM-CSK System Parameter Selection for Different Chaos Oscillators

_{1}and X

_{2}is employed to set the bit length criterion. Figure 9 presents the cross-correlation function between V

_{1}and V

_{3}for RC two-transistor oscillator.

#### 4.2. Communication System’s Noise Immunity

_{b}/N

_{0}of 17 dB. For higher signal-to-noise ratio values, the curve shows nearly linear falling with 6.15 powers of ten per decade. In Figure 12, the red line denotes the BER curves for the communication system based on the Vilnius chaos oscillator. In the E

_{b}/N

_{0}ratio region from 20 dB to 27 dB, the curve linearly falls with a steepness of 14.2 powers of ten per decade. A further increase in the signal-to-noise ratio does not lead to a decrease in the error probability, which is explained by the structural features of the communication system, e.g., the operation of the synchronization system. The green curve in Figure 12 represents the FM-CSK communication system based on Chua’s chaos oscillator noise immunity estimation result. For E

_{b}/N

_{0}values from 31 dB to 36 dB, the BER value falls linearly with 20 powers of ten per decade. Note that the selection of parameters of communication systems is made to provide the same correlation properties of chaotic signals of different oscillators within one bit. Thus, the differences in the experimentally obtained BER curves are explained by the cross-correlation and spectral properties of signals generated by chaotic oscillators. Figure 12 shows that using the RC two-transistor oscillator provides the lowest error probability for a signal-to-noise ratio of less than 25 dB. A communication system based on Chua’s chaotic oscillator needs the highest signal-to-noise ratio to ensure the same error probability.

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

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**Figure 1.**Block diagram of the FM-CSK communication system, where X

_{1}, X

_{2}, and X

_{3}are master oscillator state variables, Y

_{1}, Y

_{2}, and Y

_{3}are slave oscillator state variables, b(t) is binary information signal, FM is frequency modulation, AWGN is additive white Gaussian noise channel, BPF is a bandpass filter, b’(t) is recovered binary information signal.

**Figure 2.**Simple two-transistor RC chaos oscillator circuit, where R = 10 kΩ, R

_{1}= 5.6 kΩ, R

_{2}= 15 kΩ, R

_{3}= 33 kΩ, R

_{4}= 47 kΩ, C = 1 nF, C

_{2}= 330 pF, V

_{p}= 5.6 V, NPN transistor 2N3904 is used as Q

_{1}and Q

_{2}.

**Figure 3.**Vilnius chaos oscillator circuit, where R

_{0}= 20 kΩ, R = 1 kΩ, R

_{1}= 10 kΩ, R

_{2}= 10 kΩ, C = 100 nF, C* = 15 nF, L = 100 mH, V

_{IN}= 3 V [21]. Silicon diode 1N4148 as D.

**Figure 4.**Chua’s chaos oscillator circuit (

**a**). Chua’s nonlinear resistor circuit (

**b**), where R = 1.6 kΩ, C

_{1}= 4.7 nF, C

_{2}= 47 nF, L = 8.5 mH, R

_{1}= 3.3 kΩ, R

_{2}= 3.3 kΩ, R

_{3}= 47 kΩ, R

_{4}= 47 kΩ, R

_{5}= 290 Ω, R

_{6}= 290 Ω, R

_{7}= 1.2 kΩ. Silicon diode 1N4148 as D

_{1}and D

_{2}and OP AMP LT1351 are used.

**Figure 7.**RC two-transistor chaos oscillator simulation (

**top row**) and hardware (

**bottom row**) two-dimensional projection.

**Figure 8.**Chua’s chaos oscillator simulation (

**top row**) and hardware (

**bottom row**) two−dimensional projections.

**Figure 10.**RC two-transistor oscillator synchronization (blue) and information-carrying (red) signal spectra.

**Figure 11.**Frequency-modulated synchronization (

**a**) and information-carrying (

**b**) signals’ spectra for RC two-transistor oscillator-based FM-CSK communication system. Blue and red lines denote the signals before and after bandpass filters (BPF).

**Figure 12.**BER curves of FM-CSK communication system based on Chua’s, Vilnius, and RC chaos oscillators in an AWGN channel.

**Figure 13.**Vilnius oscillator synchronization signal spectra (blue) and information-carrying signal spectra (red) (

**a**). Chua’s oscillator synchronization signal spectra (blue) and information-carrying signal spectra (red) (

**b**).

**Table 1.**Simulation and hardware experimental results of RC and Chua’s chaos oscillator dynamic estimation in the master circuit.

Element with Nominal Deviation | Z1TEST | |||||||
---|---|---|---|---|---|---|---|---|

Two-Transistor RC Chaos Oscillator | Chua’s Chaos Oscillator | |||||||

Simulation | Hardware | Simulation | Hardware | |||||

>0.7 | >0.8 | >0.7 | >0.8 | >0.7 | >0.8 | >0.7 | >0.8 | |

Z_{1} | 80.95% | 71.43% | 71.82% | 71.82% | 76.19% | 76.19% | 63.64% | 54.55% |

Z_{2} | 75.71% | 70.95% | 70.91% | 66.36% | 83.48% | 80.95% | 78.57% | 78.57% |

Z_{3} | 80.48% | 80.48% | 80.91% | 80.91% | 85.24% | 85.24% |

**Table 2.**Simulation and hardware results of Vilnius chaos oscillator dynamic estimation in master circuit [29].

Element with Nominal Deviation | Z1TEST | |||
---|---|---|---|---|

Simulation | Hardware | |||

>0.7 | >0.8 | >0.7 | >0.8 | |

C_{1} | 56.1% | 56.1% | 72.73% | 72.73% |

C_{2} | 87.1% | 87.1% | 74.19% | 70.97% |

L_{1} | 73.17% | 70.73% |

Chaos Oscillator | X_{1}, “1” | X_{3}, “0” | X_{2}, Synchronization |
---|---|---|---|

RC chaos oscillator | V_{C}_{1} | V_{C}_{3} | V_{C}_{2} |

Vilnius chaos oscillator | V_{C}_{1} | V_{R} | V_{C}_{2} |

Chua’s chaos oscillator | V_{C}_{2} | V_{OPAMP out} | V_{C}_{1} |

Chaos Oscillator | Bit Length | Information-Carrying Signal Bandwidth at −20 dB Level | Synchronization Signal Bandwidth at −20 dB Level | BPF Band for FM Information-Carrying Signal | BPF Band for FM Synchronization Signal |
---|---|---|---|---|---|

RC two-transistor oscillator | 110 µs | 90 kHz | 130 kHz | 80 kHz | 116 kHz |

Vilnius oscillator | 2 ms | 10 kHz | 8 kHz | 21 kHz | 19 kHz |

Chua’s oscillator | 20 ms | 9 kHz | 7 kHz | 21.5 kHz | 14.5 kHz |

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**MDPI and ACS Style**

Cirjulina, D.; Pikulins, D.; Babajans, R.; Zeltins, M.; Kolosovs, D.; Litvinenko, A.
Experimental Study on FM-CSK Communication System for WSN. *Electronics* **2022**, *11*, 1517.
https://doi.org/10.3390/electronics11101517

**AMA Style**

Cirjulina D, Pikulins D, Babajans R, Zeltins M, Kolosovs D, Litvinenko A.
Experimental Study on FM-CSK Communication System for WSN. *Electronics*. 2022; 11(10):1517.
https://doi.org/10.3390/electronics11101517

**Chicago/Turabian Style**

Cirjulina, Darja, Dmitrijs Pikulins, Ruslans Babajans, Maris Zeltins, Deniss Kolosovs, and Anna Litvinenko.
2022. "Experimental Study on FM-CSK Communication System for WSN" *Electronics* 11, no. 10: 1517.
https://doi.org/10.3390/electronics11101517