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Abstract
Physical layer encryption methods are emerging as effective, low-latency approaches to ensure data confidentiality in wireless networks. The use of chaotic signals for data masking is a potential solution to prevent a possible eavesdropper to distinguish between noise and sensitive data. In this work, we experimentally demonstrate the W-band wireless transmission of a 1 Gb/s chaotic signal over 2 m in a radio-over-fiber architecture. The chaos encoding scheme is based on the transition between different states of a Duffing oscillator system, digitally implemented. The bit error rate achieved in all cases was below the forward error correction limit for 7 % overhead. The presented results validate the proposed chaos-based physical layer encoding solution for gigabit data transmissions in hybrid millimeter-wave/photonic networks.
© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
As the next generation of wireless communications (5G) is getting closer, data transmission security challenges are gaining major importance and research focus. The broadcasting nature of wireless communications involves specific challenges which must be addressed to prevent potential eavesdroppers from intercepting sensitive messages [1,2]. An encryption algorithm must be employed to provide confidentiality between end users and base stations. Traditional end-to-end approaches rely on symmetric algorithms which require to share a common key to assure that a message which is ciphered by a transmitter can only be decoded by the intended receivers [3]. This key must be updated periodically, adding extra complexity and latency by key distribution algorithms. These algorithms are based on the computing limitations of current technology, so that a brute force attack is also unable to extract the secret information. However, the rapid improvement of computational technology and the development of efficient decryption algorithms compromise their safety [4,5].
Physical layer schemes have been proposed over the last years to further increase the security of wireless links. The main advantage of these algorithms is that they are protocol independent and transparent to the transported data, so they do not add extra latency due to the processing in the upper layers. This feature agrees with 5G key performance indicators (KPIs), which target a reduction of one order of magnitude in latency with respect 4G [6]. There are several ways to implement physical layer algorithms. First physical-layer works were derived from Shannon’s information theory, focusing on the study of secrecy capacity [7]. These ideas have been applied to Gaussian channels [8], multi-antennas channels [9, 10] and relay channels [11, 12], among others. Other approaches are based on using high-frequency and highly directional antennas for point-to-point transmission and the injection of artificial noise [13,14].
Although several physical layer encryption solutions have been proposed, their integration into hybrid millimeter-wave/optical systems for 5G has yet to be addressed. In this work, we describe a radio-over-fiber (RoF) architecture in which data confidentiality has been achieved by employing chaotic signals. The chaotic behavior is aperiodic and presents an erratic and irregular time evolution [15]. It is governed by a deterministic non-linear system and highly dependent on the initial conditions [15]. Therefore, a potential eavesdropper cannot distinguish between signal and noise. The scheme of the proposed chaos based security solution is shown in Fig. 1. The data to be transmitted from Alice is converted into a chaotic signal which is generated using a set of predefined parameters. The signal is transmitted through a RoF link to reach the intended recipient, Bob. Then, the signal can be decoded back. For this to be possible, knowledge of the encoding parameters is required as well as timing and phase recovery at the receiver. A key distribution scheme needs to be used to share the information required to decode the message between transmitter and receiver. The integration of the key distribution algorithm lies outside the scope of this work.
Fig. 1 Physical layer signal masking algorithm using chaotic signals over a radio-over-fiber architecture.
A Duffing oscillator system (DOS) has been successfully used both to codify binary signals in data transmission and as a receiver [16–19]. The parameters which define the oscillator system cause the output to change between chaotic and non-chaotic states. The experiments and results reported in this paper validate the wireless transmission of a chaotic signal based on the nonlinear second-order differential Duffing equation. First, a single Duffing stream achieving a bit rate of 1 Gb/s is successfully transmitted. Second, two different Duffing streams with different characteristics, one of them serving as a decoy, are I/Q multiplexed to make the whole signal chaotic. In both cases, the link distance is 2 m and the carrier frequency is fixed at W-band (75 – 110 GHz). The wireless distance is chosen for validation purposes and laboratory limitations, but W-band links can reach distances of hundreds of meters [20,21]. This work intends to serve as a first step towards a low latency encryption scheme for gigabit wireless links in radio-over-fiber architectures.
2. Duffing oscillator system encoding scheme
The Duffing oscillator system (DOS) can generate chaotic signals according to a second-order ordinary differential equation (ODE), which can be formulated as follows:
where δ represents the damping factor and γ cos(t) the driving signal. It has been widely studied in the literature how to switch the system from periodic states to chaotic ones by changing these parameters [16, 17]. If δ is fixed, as γ increases the system state changes from small periodic state (homoclinic orbits) to chaos and, finally, to large periodic state. Furthermore, the numerical algorithm used to solve the ODE and the step size, h, also influences on the threshold values for switching the state [16]. As an example, Eq. (1) was solved using the trapezoidal rule with a step size of 0.01. The damping factor δ is fixed to 0.5 and γ is swept between three values: 0.2, 0.6 and 1.1. Figure 2 shows the phase plane diagrams in the three cases, corresponding with the three aforementioned states: homoclinic orbit, chaos and large periodic state.Fig. 2 Phase plane diagrams of the three states of a Duffing Oscillator System: (a) homoclinic orbit (γ = 0.2), (b) chaos (γ = 0.6) and (c) large periodic state (γ = 1.1). The ODE (δ = 0.5) was solved using the trapezoidal rule and h = 0.01.
However, the described Duffing system is only valid for low frequency driving signals. To use the different states to encode high data rate signals (in the Gbit/s) wile maintaining a chaotic state, a change of variable is required to allow larger oscillation frequencies [16,17]. Defining t = ωdτ, we obtain:
leading to the new Duffing equation: where ωd is defined as the Duffing frequency. The new system described by Eq. (3) has no limitations in terms of ωd. Therefore, signals of several GHz can be used to drive the oscillator.This work proposes to use the output of a DOS, switching between chaos and homoclinic orbit states, to encode a binary sequence. The Duffing frequency ωd, the damping factor δ and the numerical method used to solve Eq. 3 are fixed, while γ is switched between two values to map ‘0’ and ‘1’ bits onto the two different states. The DOS is implemented by digital signal processing (DSP), and the electrical signal is generated by a 65 GSa/s arbitrary waveform generator (AWG). This technical specification fixes h to 1/65 · 10−9s. We present four different DOSs which will be used in the experimental demonstration. Table 1 shows the parameters used to define each system: Duffing frequency (ωd = 2π fd), damping factor (δ) and the driving signal amplitude to encode ‘0’ (γ0) and ‘1’ (γ1). In addition, we define the number of samples per symbol, which also determines the data rate. If the number of samples increases, the Duffing system oscillates during more time so it can be detected more easily. However, the data rate decreases. Conversely, if the number of samples decreases, the data rate increases but the system oscillates during less time. This effect is depicted in Fig. 3, which shows the phase plane diagrams of the symbols defined by the four DOSs. It can be seen that DOS1 and DOS2 have higher data rate (and less samples) than DOS3 and DOS4.
Table 1. Parameters of the four DOSs used in the experimental demonstration for data encoding. The ODE is solved using the trapezoidal rule and h = 1/65 · 10−9s.
Fig. 3 Phase plane diagrams of the four DOS used in the experimental demonstration for data encoding. The ODE is solved using the trapezoidal rule and h = 1/65 · 10−9s.
3. Experimental setup
Two experiments were conducted to validate the use of a Duffing oscillator system to transmit chaotic signals over a RoF architecture. In both cases, the photonic up-conversion technique was used to generate the W-band signal on a high-bandwidth photodiode [22]. First, a single DOS was used in an intensity modulation/envelope detection system to prove the feasibility of the proposed modulation scheme. Second, an optical I/Q modulation with intermediate frequency (IF) down-conversion system was used to enhance the data confidentiality by transmitting a continuously chaotic signal.
3.1. Intensity modulation with a single DOS and envelope detection
Figure 4 shows the first experimental demonstration used to encode the binary data using the different states of a DOS. A narrow linewidth external cavity laser (ECL) was used as a light source at 1550 nm with 13 dBm of power. The optical signal was modulated by a Mach-Zehnder modulator (MZM) biased at Vπ and driven by a sinusoid signal with half the frequency of the desired wireless carrier (40 GHz) for optical carrier suppressed (OCS) modulation [23]. Therefore, two spectral lines were generated with a spectral separation of 80 GHz. Afterwards, the signal was boosted by an erbium-doped fiber amplifier (EDFA) and the two tones were demultiplexed by an arrayed waveguide grating (AAWG). The first output was intensity modulated by a second MZM. The data signal was provided by a 25 GHz arbitrary waveform generator (AWG) at a sampling rate of 65 GSa/s.
Fig. 4 Experimental setup with a single DOS, based on intensity modulation and envelope detection. ECL: external cavity laser, PC: polarization controller, VSG: vector signal generator, RF: radiofrequency, MZM: mach-zehnder modulator, AAWG: arrayed waveguide grating, AWG: arbitrary waveform generator, EA: electrical amplifier, VOA: variable optical attenuator, EDFA: erbium-doped fiber amplifier, SMF: single mode fiber, PD: photodiode, MPA: medium power amplifier, LNA: low noise amplifier, ED: envelope detector. DSO: digital storage oscilloscope.
A DOS system, implemented by digital signal processing (DSP), generated chaotic states to encode ‘1’ bits and homoclinic orbits to encode ‘0’ bits. The encoded data is a pseudo-random bit sequence with a length of 211 − 1 bits. The power of the second AAWG output was controlled by a variable optical attenuator before it was coupled back with the modulated signal. The data was amplified by a second EDFA and launched into 10 km standard single mode fiber, representing an optical link to the remote antenna unit. A high-bandwidth photodiode, acting as heterodyne photomixer, converted the optical signal to radio frequency. The optical power incident on the photodiode was fixed at 3 dBm. This power was enough to reach the receiver without saturating the photodiode. A medium power amplifier was used to amplify the signal by 9 dB before it was wirelessly transmitted with a 24 dBi gain horn antenna. At the receiver side, situated 2 m away, a second horn antenna was used to recover the signal which was then amplified by a 40 dB low noise amplifier. Finally, a 3 GHz bandwidth envelope detector down-converted the signal to baseband and a digital storage oscilloscope (DSO) with a sampling rate of 80 GSa/s recorded the data for off-line processing.
3.2. Optical I/Q modulation with two DOSs and IF down-conversion
In the previous experimental setup (see Fig. 4), only one data stream was transmitted. This means that the wireless signals changed from periodic states to chaotic ones depending on the data bits. In the experimental setup shown in Fig. 5, the data confidentiality is increased by continuously transmitting a chaotic signal. The first modification with respect the previous approach was the wireless carrier. The first MZM was fed by a 44 GHz electrical signal to fix the wireless carrier at 88 GHz. This increment allowed us to select a higher intermediate frequency (IF) on the receiver side to exploit the available bandwidth. Second, the MZM used for data modulation was substituted by an optical in-phase(I)/quadrature(Q) modulator. A DOS was used to encode the data in one of the two dimensions, as it was done in the previous experiment. At the same time, the second dimension was modulated using a different DOS. This DOS, which has different parameters, different data rate and different data, is used to transmit a decoy signal to mask the actual data, adding an extra security layer. The receiver was modified to support the new scheme. A balanced mixer was used to down-convert the signal from the W-band to an IF of 12 GHz. A vector signal generator together with a passive double are used to drive the LO port of the mixer with a 76 GHz signal.
Fig. 5 Experimental setup with two DOSs, based on optical I/Q modulation and IF down-conversion. ECL: external cavity laser, PC: polarization controller, VSG: vector signal generator, RF: radiofrequency, MZM: mach-zehnder modulator, AAWG: arrayed waveguide grating, AWG: arbitrary waveform generator, I: in phase, Q: Quadrature, Mod.: modulator, VOA: variable optical attenuator, EDFA: erbium-doped fiber amplifier, SMF: single mode fiber, PD: photodiode, MPA: medium power amplifier, LNA: low noise amplifier, LO: local oscillator, IF: intermediate frequency, EA: electrical amplifier DSO: digital storage oscilloscope.
4. Results and discussion
In the two scenarios described previously, the data was captured by a DSO for off-line processing. This section presents the time and spectral analyses of the received signals as well as the bit error rate (BER) measurement.
4.1. Intensity modulation with a single DOS and envelope detection
Figure 6 (a) represents the captured signal in time when the DOS4 (see Fig. 3) was used to encode the transmitted data in the intensity modulation with envelope detection setup. It is possible to distinguish between the chaotic and non-chaotic states. During the chaotic transitions, the signal trajectory cannot be predicted and oscillates continuously around zero, in a similar way to noise. However, during the non-chaotic periods, the signal appears as a noisy DC component (positive or negative) according to the small periodic state. The spectrum (Fig. 6 (b)) shows a peak at 2 GHz, corresponding to the Duffing frequency (Tab. 1) and more spectral components at lower frequencies which contain the chaos information. Figure 6 (c) also shows the phase plane diagram, in which is possible to identify the non-chaotic states (homoclinic orbits) on both sides of the graph and the chaotic transitions in between, representing ‘0s’ and ‘1s’ respectively.
Fig. 6 Captured signal when DOS4 is transmitted in the intensity modulation/envelope detection experimental setup: (a) time, (b) spectrum and (c) phase plane diagram.
The received signal was demodulated using a statical decision approach after averaging its absolute value over the symbol periods. Figure 7 shows the histograms of that mean for the four transmitted DOSs (see Fig. 3). The symbol decision is done by setting the proper threshold value. The histograms are more open for the low data rate DOSs (Fig. 7 (c) and (d)) than the high data rate ones (Fig. 7 (a) and (b)). This is the expected behavior since low bit rate means more samples per symbol so the Duffing system oscillates during more time. Conversely, DOS1 and DOS2 use less samples so it is more difficult to distinguish between states. Therefore, there is a minimum number of samples per symbol needed to make the DOS settle in the corresponding state, which implies a maximum achievable data rate. The BER was computed in the four cases after processing 122880, 122880, 40960 and 20480 bit. The results for the 1Gb/s DOS are 3.9 · 10−4 and 9.8 · 10−4, lower than 3.8 · 10−3 which is the limit given by a forward error correction (FEC) scheme with 7% overhead. Error-free transmissions were achieved when the low bit rate DOSs were transmitted. Consequently, the feasibility of the Duffing encoding scheme is proven in the four cases.
Fig. 7 Histograms of the average signal intensity per symbol in the intensity modulation/envelope detection experimental setup.
4.2. Optical I/Q modulation with two DOSs and IF down-conversion
The optical I/Q modulation with intermediate frequency down-conversion experiment was done to make the signal continuously chaotic in time. A signal containing the actual data encoded by the output x(t) of a DOS was modulated onto the I component. At the same time, the derivative of a second DOS driven by a decoy data stream is modulated onto the Q component. The signal does not contain low-frequency information so the IF carrier frequency recovery is accomplished with more accuracy. Table 2 presents the two tested combinations. In both cases, the 1 Gb/s DOSs were used to transmit the desired data and the lower data rate DOS were used to mask the signal. The combination of the two DOS with different parameters makes the signal continuously chaotic, as it is shown in Fig. 8 (a) and (b), which represent the captured signal over the same period of time as in Fig. 6 (a). Figure 8 (c) and (d) show the respective spectra. There is a peak at 12 GHz in both cases, corresponding to the intermediate frequency, and two additional peaks on both sides corresponding to the two Duffing frequencies. In Fig. 8 (c), the Duffing frequencies are situated at 3.5 GHz and 5 GHz with respect IF, while in Fig. 8 (d) the peaks are at 2 GHz and 4 GHz with respect IF. These values agree with the predefined parameters in Tab. 1. The phase plane diagrams have also been included in Fig. 8 (e) and (f) to show the transitions between the chaotic/non-chaotic symbols. The small periodic states can be seen on both sides of the figure as well as the chaotic transitions.
Table 2. Measured BER for the two configurations in the optical I/Q modulation with IF down-conversion experimental setup.
Fig. 8 Captured signals in time and frequency and phase plane diagrams for the two configurations in the optical I/Q modulation with IF down-conversion experimental setup.
The data is demodulated by means of off-line DSP using a Costas loop for carrier recovery. Once the I/Q components are separated, the BER is calculated through statistical analysis as in the previous experiment, averaging each received symbol. The obtained histograms for the I/Q components in the two configurations are shown in Fig. 9. It is clear that the Q component in Fig. 9 (b) and (d) does not contain any useful information. However, the I component, can be demodulated by establishing a threshold value to distinguish between symbols. After analysis of 122880 bits in both cases, the measured BER is 3.5 · 10−4 (Fig. 9 (a)) and 2.6 10−3 (Fig. 9 (c)), respectively. These results are slightly worse than the BER obtained when transmitting a single DOS, but they are still below the FEC limit. Therefore, the feasibility of this scheme, where confidentiality is ensured through parallel transmission of a second decoy signal, is also proven.
Fig. 9 Histograms of the average signal intensity per symbol in the optical I/Q modulation with IF down-conversion experimental setup.
An important issue which should be further discussed is the scalability of the system to support higher data rates. The capacity of the Duffing encoded signal is limited by the internal Duffing frequency, the number of samples per symbol and the baud rate of the waveform generator. First, the Duffing oscillator frequency can be increased to make the system oscillate faster to allow a sufficient number of oscillations per symbol to achieve the chaotic/non-chaotic state. Second, the number of waveform samples per symbol can be reduced to increase the symbol rate. Finally, the sampling rate, which is a hardware limitation, can be increased by using a faster digital to analog converter to allow a sufficient number of waveform samples even at increased baud rates. It is important to note that there are minimum ratios between the internal Duffing frequency, waveform sampling rate and baud rate, i.e., the number of oscillations per symbol and the number of samples per symbol, respectively, to maintain the bit error rate below the pre-FEC limit required by the forward error correction techniques.
5. Conclusions
In summary, we have proposed the use of a Duffing oscillator system to encode data with chaotic signals and we have experimentally demonstrated the implementation of that scheme in two different radio-over-fiber architectures. The presented results show a successful wireless transmission, achieving data rates up to 1 Gb/s, using a single DOS in an intensity modulation with envelope detection scheme and two DOSs in an optical I/Q modulation with heterodyne down-conversion scheme. The BER achieved in all cases is below the limit set by FEC techniques using a 7% overhead. The obtained results validate the proposed solution for physical layer confidentiality based on chaotic Duffing transmission.
The current system architecture is based on DSP techniques to implement both the Duffing oscillator system and the Costas receiver. However, both algorithms consist of operations which can be implemented by hardware, meaning that a real-time implementation of the system is potentially feasible in the future. While the evaluated configurations require further improvement and extension to provide a full comprehensive security implementation in the physical layer, they serve as a proof of concept for confidential transmission based on chaotic Duffing signals and provide a basis for the development of low latency physical layer security schemes for radio-over-fiber transmission and 5th generation mobile network implementations.
Funding
European Union’s H2020-MSCA-ITN CELTA (675683).
Acknowledgments
Authors would like to thank the Technical University of Denmark (DTU) where the experiments were conducted.
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