4. Experiment on information transmission by the method of spectral keying

The signal received from the communication channel feed the input of the ADC board. Further, digital representation of the received signal is recorded in the memory of a personal computer and processed according to an algorithm that includes the following software modules: two digital recursive filters of the first order operating in parallel; blocks of variance estimation; the comparator [38]. The algorithm for restoring the information sequence is as follows. During the information bit "0" a filter, in which the gain in the feedback circuit has a negative value, is matched with the signal spectrum. During the information bit "1" a filter with a positive coefficient in the feedback circuit is matched with the signal spectrum. By comparing signal variances at the filters outputs within a time interval T<sup>0</sup> corresponding to the number of samples M, an information sequence is extracted from the chaotic signal.

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Manchester coding of information bits produce sequence of rectangular pulses. It is used as a test information signal, representing binary word "11,001,110" for experimental evaluation of the system performance. Initial and reconstructed information sequences are shown in Figure 11.

As can be seen from the figure, the restored sequence of pulses at the output of the receiver module (red dashed line in Figure 11(b)) is identical to the initial information sequence arriving at the information input of the transmitter (Figure 11(a)); time lag between these two sequences has fixed value, which is determined by the length of the communication channel,

It should be noted that this method used for information transmission does not require chaotic synchronization. The necessary condition for high fidelity of transmitted message recovery is the exact coincidence of the delay time in the transmitter and the delay time in feedback circuit

There is a speed limitation in the proposed method for data transmission due to the existence of the minimum allowable time interval necessary for the receiver to correctly recognize the transmitted symbol after the transient processes that occurs due to change of one chaotic regime to another. This is inherent feature for all chaotic systems with mode switching. The accumulation time, necessary for the receiver to estimate the variance of the envelope of the elementary

of each of the comb filters used to reconstruct the information sequence at the receiver.

as well as internal delays in the transmitter and receiver modules.

Figure 11. Initial (a) and reconstructed (b) information sequences.

The scheme of the experiment on the transmission of a binary message based on the spectral keying of a broadband chaotic signal is shown in Figure 9. Designations on the picture as is following: F xð Þ ;<sup>s</sup> is a block of a nonlinear function, <sup>Z</sup>�<sup>M</sup> is a delay unit for <sup>M</sup> samples, AWG is an arbitrary waveform generator, ADC is an analog-to-digital converter, G1 and G2 are multipliers by a constant, D1 and D2 are blocks of variance estimation, C is a comparator. Functionally, it consists of a software module for calculating samples of a chaotic signal containing the information being transmitted, an AWG board, a communication channel, an ADC board, a software module for extracting the transmitted message from the received signal.

In the AWG module, the preloaded signal samples are extracted from the memory cells with the clock frequency of 4 GHz and feed the DAC input, at the output of which an analog signal is transmitted to the communication channel, which is a coaxial cable with a wave impedance of 50 Ω. An arbitrary waveform generator from Euvis company (California, USA), model AWG472 [37] (Figure 10) was used in experimental set-up.

Figure 9. Experimental set-up of communication system for data transmission based on the spectral manipulation of a broadband chaotic signal.

Figure 10. AWG472 board general appearance (a), AWG472 architecture (b).

The signal received from the communication channel feed the input of the ADC board. Further, digital representation of the received signal is recorded in the memory of a personal computer and processed according to an algorithm that includes the following software modules: two digital recursive filters of the first order operating in parallel; blocks of variance estimation; the comparator [38]. The algorithm for restoring the information sequence is as follows. During the information bit "0" a filter, in which the gain in the feedback circuit has a negative value, is matched with the signal spectrum. During the information bit "1" a filter with a positive coefficient in the feedback circuit is matched with the signal spectrum. By comparing signal variances at the filters outputs within a time interval T<sup>0</sup> corresponding to the number of samples M, an information sequence is extracted from the chaotic signal.

4. Experiment on information transmission by the method of spectral

software module for extracting the transmitted message from the received signal.

AWG472 [37] (Figure 10) was used in experimental set-up.

Figure 10. AWG472 board general appearance (a), AWG472 architecture (b).

The scheme of the experiment on the transmission of a binary message based on the spectral keying of a broadband chaotic signal is shown in Figure 9. Designations on the picture as is following: F xð Þ ;<sup>s</sup> is a block of a nonlinear function, <sup>Z</sup>�<sup>M</sup> is a delay unit for <sup>M</sup> samples, AWG is an arbitrary waveform generator, ADC is an analog-to-digital converter, G1 and G2 are multipliers by a constant, D1 and D2 are blocks of variance estimation, C is a comparator. Functionally, it consists of a software module for calculating samples of a chaotic signal containing the information being transmitted, an AWG board, a communication channel, an ADC board, a

In the AWG module, the preloaded signal samples are extracted from the memory cells with the clock frequency of 4 GHz and feed the DAC input, at the output of which an analog signal is transmitted to the communication channel, which is a coaxial cable with a wave impedance of 50 Ω. An arbitrary waveform generator from Euvis company (California, USA), model

Figure 9. Experimental set-up of communication system for data transmission based on the spectral manipulation of a

keying

74 Telecommunication Networks - Trends and Developments

broadband chaotic signal.

Manchester coding of information bits produce sequence of rectangular pulses. It is used as a test information signal, representing binary word "11,001,110" for experimental evaluation of the system performance. Initial and reconstructed information sequences are shown in Figure 11.

As can be seen from the figure, the restored sequence of pulses at the output of the receiver module (red dashed line in Figure 11(b)) is identical to the initial information sequence arriving at the information input of the transmitter (Figure 11(a)); time lag between these two sequences has fixed value, which is determined by the length of the communication channel, as well as internal delays in the transmitter and receiver modules.

It should be noted that this method used for information transmission does not require chaotic synchronization. The necessary condition for high fidelity of transmitted message recovery is the exact coincidence of the delay time in the transmitter and the delay time in feedback circuit of each of the comb filters used to reconstruct the information sequence at the receiver.

There is a speed limitation in the proposed method for data transmission due to the existence of the minimum allowable time interval necessary for the receiver to correctly recognize the transmitted symbol after the transient processes that occurs due to change of one chaotic regime to another. This is inherent feature for all chaotic systems with mode switching. The accumulation time, necessary for the receiver to estimate the variance of the envelope of the elementary

Figure 11. Initial (a) and reconstructed (b) information sequences.

fragments of the signal from which the information sequence is formed, is finite for the duration of one transmitted symbol. It determines the minimum duration of one information bit.

Author details

References

Oleg Zemlyaniy\* and Konstantin Lukin

Electronics. 2005;4(1):4-13

PhysRevLett.71.65

Raton, Florida, USA: CRC Press; 2000. 445 p

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\*Address all correspondence to: zolvas@ukr.net

Laboratory for Nonlinear Dynamics of Electronic Systems (LNDES), O.Ya. Usikov Institute for Radiophysics and Electronics, National Academy of Sciences of Ukraine, Kharkov, Ukraine

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The algorithm of the system operation can be constructed in such a way that at certain time intervals, the predetermined control code sequences will be analyzed by the receiver. If they are misidentified due to distortion during propagation through the channel, a decision will be made to slow down the transmission rate, which will allow the detectors to accumulate for a longer period of time. If necessary, it can be possible to periodically link the operation of the clock generators of the transmitter and the receiver to achieve their matched work by transferring the control code sequences.
