1. Introduction

There is significant interest in developing transmitter–receiver pairs of self-synchronized chaotic signal sources because of their potential application as masking carriers in secure communication systems. It was Pecora and Carroll who first proposed this in 1990 [1] and there have been numerous, subsequent proposals and demonstrations for analog, digital and optical communications systems based on chaos [2–10]. Argyris etal. have demonstrated high-speed long-distance communication based on chaos synchronization, using chaotic semiconductor lasers (two different systems), over a commercial fibre-optic channel in the metropolitan area network of Athens, Greece [11]. Transmission rates in the gigabit per second range were achieved, with bit-error rates below 10^-7. This high bandwidth of optical chaotic transmission is achievable because of the large dynamic bandwidth of the semiconductor lasers used for the chaotic transmitters and receivers. This can be potentially as high as ~40 GHz for the fastest semiconductor lasers available. The transmission can be either free space propagation, or, in optical fibre. The transmission bandwidth achievable in chaotic communication systems, based on nonlinear electronic circuits, is limited by the bandwidth of the electronics. Upper limits of order a few hundreds of megahertz are to be expected in this case and transmission from transmitter to synchronized receiver is via cable or radio/microwave wireless. Electronically-transformed optical (or opto-electronic) feedback systems, in which a signal that is non-linearly proportional to a laser output is detected, electronically transformed, and fed back to the laser [9,10], have similar bandwidth constraints as electronic systems. The more modest bandwidths of electronic or optoelectronic systems are sufficient for many communication applications such as point-to-point, direct sequence spread spectrum, and frequency hopping systems.

We have demonstrated a hybrid electronic/optical chaotic communication system where the chaotic source is an electronic circuit and the transmitter is a laser. The chaotic signal, v(t), is electronically injected onto an optical carrier for transmission by adding the current boosted chaotic signal to the dc injection current of a semiconductor laser. This generates an optical chaotic carrier (to which a message can also be added) that can be transmitted either in free space or in optical fibre. Free space propagation has been demonstrated here-in. The received signal is generated by a photodetector, and following gain and offset conditioning, is applied to a matched receiver electronic circuit. Chaos synchronization and successful message recovery are achieved with the system. The communication system has a transmission bandwidth associated with chaotic electronic circuits, that is, lower than achievable using chaotic semiconductor lasers. But, it has the advantage, compared to electronic chaotic communication systems, that the chaotic carrier plus message can be transmitted by line-of-sight, point-to-point, free space propagation of a laser beam, or via coupling to an optical fibre. Also, the level of chaotic modulation on the laser light can be independently controlled relative to the average optical power, which is not always possible with semiconductor laser chaotic sources. The latter are often operated close to laser threshold (and hence with very low output power) in order to generate the chaotic output.

2. The hybrid electronic/optical synchronized chaos communication system

The specific chaotic electronic circuit used in this proof-of-principle study is shown in the boxed transmitter and receiver sections of Fig. 1, and is described fully elsewhere [12,13]. The circuit is a delay differential feedback (DDF) chaotic system that uses a field programmable gate array (FPGA) to allow one of any number of different nonlinearities to be implemented in the feedback loop, and also to have the ability to vary and modulate the delay time, T. These are both features that increase security when the circuit is used in a communication system, as discussed in ref. [12]. The implementation of a DDF system produces high dimensional chaos, which also improves communication security [12]. In addition to the FPGA the electronic system also includes an analog-to-digital converter (ADC); a digital-to-analog converter (DAC); a gain element, indicated by β (or β’); and a low pass filter, indicated by τ (or τ’). Also shown are an electronic adder, indicated by Σ; and an input modulation message, indicated by m(t).

 

Fig. 1. Hybrid electronic/optical synchronized chaos communication system. The transmitter and receiver chaotic electronic circuits (boxed) consist of a delay differential feedback (DDF) chaotic system, as described in the text. The current boosted transmitter signal is added to a dc injection current and is the injection to a semiconductor laser. The optical signal is propagated in free-space and photodetected. The photodetector current is amplified and added to a dc offset before being applied to the receiver circuit which synchronizes with the transmitter. The synchronized receiver signal, v’(t), is subtracted from the optical signal to recover the message.

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The chaotic circuit also can be used for digital transmission when the transmitted carrier is taken from the node so labeled in Fig.1. Improvements in the synchronization of as much as 18 dB were observed in comparative studies of analog and digital transmission [13]. Analog transmission has been used in the study reported.

The chaotic carrier, either alone or with a masked message added, is current boosted using a purpose-designed circuit. This amplifies the chaotic carrier to give a depth of modulation of up to 11 mA. This chaotic current is added to a direct current from an ITC 510 constant current supply and is injected to a JDSU SDL5400 semiconductor laser, with an output wavelength of 852 nm. The threshold current of this laser is approximately 15 mA. The photodetected output power of the semiconductor laser clearly shows the chaotic variations following the chaotic carrier (with time delay). Cross correlation coefficients of up to 0.986 were obtained between the photodetected signal and the original electronic chaotic carrier. This was equivalent to that obtained in synchronizing a matched transmitter/receiver pair of similar circuits [12]. The photodetected signal was conditioned with a gain element and the addition of a dc voltage offset before input to the matched receiver. Matching in this context means the same DDF chaos circuit design, programmed with the same nonlinear function as the transmitter. The nonlinear function (such as a sine wave) is a key for increased security in the system. The bandwidth of the system, as implemented to date, is limited by the low-pass-filter in the transmitter and receiver circuits. It has an upper limit of 50kHz. This is not a fundamental limitation, and a bandwidth of hundreds of megahertz, or higher, should be readily achievable using standard electronic components.

Synchronization of the circuits was achieved by careful adjustment of the amplitude and dc offset of the signal being sent from the photodetector to the receiver circuit as shown in Fig. 1. It was also necessary, in some instances, to attenuate the laser power incident on the detector due to limitations in the amount of dc offset available from the current circuitry (which can be improved in future work).

3. Results

Figure 2 shows the output signal from the chaotic transmitter (Fig. 2(a)) and the synchronized receiver, after transmission via the optical carrier etc (Fig. 2(b)). A sinusoidal nonlinearity has been programmed into the FPGA in this case. The dimensionality of the chaos is much too high to be analysed using standard chaos data analysis techniques, as has been applied before to the synchronized outputs of semiconductor laser with optical feedback systems [14]. The output is hyperchaos, albeit of relatively low bandwidth. This high complexity is a further advantage in achieving secure communication. Figure 2(c) shows the synchronized chaotic receiver signal plotted against the chaotic transmitted signal. A line of slope 1 corresponds to perfect synchronization. Figure 2(d) shows the cross correlation coefficient (C³), calculated using Eq. (1) [15], as a function of the delay, Δ, calibrated in data points. P_tr,re are proportional to the optical power in the transmitter and receiver, respectively, and the expectation denoted 〈…〉 is evaluated via a time average. A C³ value of unity indicates the transmitter and receiver are identical in functional form, but not necessarily in magnitude. A C³ value of zero indicates unsynchronized outputs. The time interval between data points is 0.2 microseconds. A maximum value of 0.986 for C³ was achieved with the sinusoidal nonlinearity, with no message added.

Several different nonlinearities were programmed into the FPGA. These included a triangular, half-gain, and random nonlinearity, in addition to the sinusoid described above. With no added message to the transmitted signal, the receiver circuit was able to be synchronized such that the time series showed a maximum C³ value of 0.9895 using the triangular nonlinearity, while with the “half gain” nonlinearity the maximum achieved was 0.938. This latter value is consistent with previous experiments using analogue transmission of the chaos [12]. It was not possible to synchronize using the random nonlinearity. This was also the case in [12].

When a message signal is added to the chaotic modulation of the transmitter, the matched receiver circuit only synchronizes to the chaos, and suppresses the message. Thus, comparison of the input and output of the receiver allows recovery of the message, as has previously been demonstrated in both synchronized chaotic electronic circuits and synchronized chaotic lasers. It is a significant development that this suppression of the message in the synchronized receiver has here-in been demonstrated, for the first time, in a hybrid electronic/optical chaotic communication system.

 

Fig. 2 Chaotic signal and synchronized receiver. Fig. 2(a): the output from the chaotic transmitter; and Fig. 2(b): the synchronized receiver, after transmission via the optical carrier. A sinusoidal nonlinearity has been used to the FPGA. Fig. 2(c): the synchronized chaotic receiver signal plotted against the chaotic transmitted signal. Fig. 2(d): the cross correlation coefficient (C³) as a function of the delay (calibrated in data points).

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The amplitude of the added message must be small enough that it is well masked in the chaotic modulation for secure communication. Experimentally the message was introduced using an electronic adder at the output of the chaotic circuit, prior to the current boosting circuit, as indicated in Fig.1. A large amplitude 20 kHz sinusoidal message was added, and the size was gradually reduced until it was no longer visible in the frequency spectrum of the transmitted signal. A message amplitude of approximately 10% of the chaos modulation amplitude was found to be sufficiently small for the message to be well masked by the chaos. If the transmitter/receiver DDF chaos circuits (separated by the optical link) are synchronized before adding the message, then only very minor adjustments to the gain and dc offset are required to optimize the synchronization after the message is introduced.

Once the two circuits are synchronized message recovery can be seen in real-time by simply subtracting the output from the input of the receiver, as shown in Fig.1. In this experiment the time delay between the input and output was negligible compared to the inverse bandwidth of the chaotic variations, and so it was not necessary to evaluate the delay. If a larger delay occurs then the message can be retrieved by finding the delay time from that which gives the maximum C3 value, and then time shifting one of the signals by this amount before performing the subtraction.

Best message recovery was achieved using the nonlinearities that gave the largest chaotic modulations in amplitude – the sinusoidal and half gain nonlinearities. This meant that a message of larger amplitude could be masked in the chaos. Even with the message included, the transmitter and receiver could achieve a cross correlation coefficient of up to 0.97.

The graphs in Fig. 3 (a)–(c) show the transmitted and received signal time traces as well as the recovered message. The corresponding frequency spectra (Fig. 3 (d)–(f)) show no evidence of the message in either the transmitted or synchronized signals, while a sharp peak can be seen at the message frequency in that of the recovered signal.

A single frequency signal is used as a message in this proof-of-principle study, and so it is possible to detect the message by simply averaging the frequency spectrum of the observed time series. However, in real world applications the message would use the sophisticated signal processing techniques that are standard in communications to avoid this, and therefore it would not be possible to recover the message from the transmitted signal alone.

 

Fig. 3. Message masking and recovery. (a)-(c) show the transmitted, received and recovered message signal time traces. The corresponding frequency spectra (Fig. 3 (d)–(f)) show no evidence of the 20 kHz message in either the transmitted or synchronized signals, while a sharp peak can be seen at the message frequency in that of the recovered signal.

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4. Conclusion

We have demonstrated synchronization of two matched DDF circuits, which generate a hyperchaos electronic signal, and which are separated by an optical link to which the chaotic carrier has been electronically injected. When a message is added, the matched receiver DDF circuit only synchronizes with the chaotic transmitter. Thus, message recovery is achieved by subtraction of the output from the input to this receiver circuit. The system is limited to the communication bandwidth achieved by the electronic circuits. Secure communication is promoted by being able to use the nonlinearity programmed into the DDF circuits as a key; by having point-to-point transmission (either free-space, line-of-sight propagation or an optical fibre link) that avoids wireless broadcast; and independent control of the average power of the optical carrier relative to the depth of chaotic modulation and the message signal power. Further improvements in the bandwidth are to be expected with faster electronic circuitry. The principle of hybrid electronic/optical secure communication has been clearly demonstrated.