## Abstract

This paper proposes and demonstrates an enhanced secure 4-D modulation optical generalized filter bank multi-carrier (GFBMC) system based on joint constellation and Stokes vector scrambling. The constellation and Stokes vectors are scrambled by using different scrambling parameters. A multi-scroll Chua’s circuit map is adopted as the chaotic model. Large secure key space can be obtained due to the multi-scroll attractors and independent operability of subcarriers. A 40.32Gb/s encrypted optical GFBMC signal with 128 parallel subcarriers is successfully demonstrated in the experiment. The results show good resistance against the illegal receiver and indicate a potential way for the future optical multi-carrier system.

© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

## 1. Introduction

The exponential growth on the Internet traffic spurs enormous transmission capacity demand on the underlying optical system [1–3]. The optical generalized filter bank multi-carrier (GFBMC) communication has considered as one of the most promising techniques for the future coherent optical multi-carrier system due to its high capacity, bandwidth efficiency and subcarrier flexibility [4–7]. In order to enable the system higher capacity, the information is usually to be encoded in the signal constellation space, namely amplitude and phase mappings. Moreover, the polarization modulation based on Stokes vectors space has brought larger freedom in the choice of modulation format and further increased the spectral efficiency [8–10]. It enables the optical GFBMC system fine granularity and large capacity by utilizing the constellation and Stokes spaces modulation.

With the help of constellation and Stokes space multiplexing, the optical multi-carrier system has attracted wide studies [10–12]. In the above works, the authors typically assumed that the physical link is secure since the optical wave is well restricted in the optical fiber. Typical security has been implemented at the upper layer via protocols, password protection and so on [13, 14]. However, as the flexibility and capacity increase, these schemes are deemed to be challenging in the optical multi-carrier system because of the computational difficulty and high-latency. Furthermore, it is a risky way to build security on top of an insecure foundation because the control information or headers are left to be unprotected. The physical layer security has emerged as an effective approach to provide defense against eavesdropper attacks, which ensures the security of the system [15, 16]. It offers the information a transparent secure pipe and can be easily incorporated with signal modulation thanks to the convenient digital signal processing. Recently, we have proposed a Stokes vector scrambling based physical layer encryption method for the coherent optical multi-carrier system [17]. It showed good resistance against the eavesdropper and provided an effective way through the Stokes vector scrambling. However, we only focused on the Stokes vectors but ignored the security of constellation space. Moreover, there wasn’t enough scrambling parameter for the constellation security due to the limited dimension of the chaotic function in the previous work.

In this paper, we propose an enhanced physical layer secure method for the four dimensional (4D) modulated optical GFBMC system. The physical layer encryption is executed by joint constellation and Stokes vector scrambling. A multi-scroll Chua’s circuit chaotic model is adopted for the secure key generation, which can realize combined scrambling for the constellation space and Stokes vectors. Utilizing the feature of parallel multi-carriers, the scrambling can be implemented both on each subcarrier and among different subcarriers. A 40.32 Gb/s encrypted optical GFBMC system with 4D modulation space is successfully demonstrated in the experiment.

## 2. Principle

Figure 1 illustrates the principle of the proposed method of 4D modulation space scrambling. The 4D modulation field can be represented by the state of polarization (SOP) in the Poincaré sphere. The six Stokes vectors named (SOP1, SOP2, SOP3, SOP4, SOP5, and SOP6) are orthogonal and each SOP has a complex IQ plane with four point mapping. The scrambling is executed both intra-subcarrier and among subcarriers. A multi-scroll Chua’s circuit chaotic map is adopted as the model to generate the scrambling vectors, which can be expressed as

*α*,

*β*,

*a*,

_{i}*b*and

_{i}*M*are constant parameters, and

*x*,

*y*,

*z*and

*t*are variable values. The multi-scroll Chua’s circuit model can be simply implemented by nonlinear electrical circuit in practical use but exhibit complex chaotic dynamics [18]. It exhibits hyper-chaotic behavior with multi-scroll attractors and increases the nonlinear complexity of the chaos map. Three chaotic sequences defined as {x; y; z} can be produced to generate the scrambling vectors. In our scheme, {x; y} are used for intra-subcarrier scrambling and {z} is used for inter-subcarrier scrambling. We assume that

*S*is the symbol of

_{k,n}*k*th Stokes vector on the

*n*th subcarrier. First, the constellation and Stokes vectors on the

*n*th subcarrier are scrambled, which is illustrated in Fig. 1(a). The scrambling process can be expressed as

*φ*and

_{k}*Г*are constellation and Stokes scrambling vectors respectively. The parameter

_{k,m}*φ*is represented as

_{k}*N*is the number of subcarriers and

*N*is a random integer. The elements of

_{p}*Г*are represented as

_{k,m}*sort()*indicates the generation of the order numbers according to the chaotic sequence of {

*y*}. In order to increase the randomicity of

*Г*, we use the decimal part of {

_{k,m}*y*} to generate the elements. Actually, the constellation scrambling is to disturb the original constellation distribution randomly and the constellation in the complex IQ plane can be a QAM constellation in general. The scrambling algorithm can be used in the majority of scenarios.

Then the Stokes vector scrambling is further performed among subcarriers, which is shown as Fig. 1(b). Because the scrambling process is executed on the six SOPs of different subcarriers, the scrambling vector can be written as

where*H*and

^{1}_{k,m}*H*are two matrices with size of 6 × 6 and N × N respectively. The values of the matrix elements can be derived with {z} as Eqs. (5) and (6). The encrypted signal can be expressed as

^{2}_{n,n}*f*is the central frequency of the

_{n}*n*th subcarrier and

*p(t)*is the prototype filter of filter bank expressed as

*Q*is the number of bins and

*a*is the filter coefficient. It can provide rapid decaying of signal side-lobe and get better spectrum confinement [19]. At the receiver, the secure key can be correctly regenerated by using the synchronized initial values and Eqs. (3)-(8). Because the PDM-QAM format can be seen as a form of Stokes vector modulation by using four Stokes vectors, the proposed scheme can also be modified to suitable for traditional PDM-QAM transmission.

_{q}## 3. Experiment and results

The experimental setup with single channel coherent optical system is shown in Fig. 2, where the Pol-QAM 6-4 modulation format is adopted for the multi-carriers. Compared with the PDM-QAM format, the Pol-QAM format utilizes two more Stokes vectors to carry the information [20], which could provide more flexible scrambling at the six orthogonal SOPs both on intra-subcarrier and among subcarriers due to the 4-D modulation space. At the transmitter, the original information is firstly sent for the Pol-QAM 6-4 modulation, where the intra-subcarrier scrambling is executed as well. During the modulation, nine bits are mapped into two symbols and the number of bit per symbol is 4.5. The 4th Runge-Kutta method is adopted to calculate the multi-scroll Chua’s circuit map during the scrambling vector generation. The inter-subcarrier scrambling is performed with subcarrier shaping. The number of subcarrier is 128 and the filter bank is consisting of 128 finite impulse filters, which are generated from the prototype filter. The frequency response of the prototype filter is shown in Fig. 3(a). Two aligned arbitrary waveform generators (AWGs) are used to produce the encrypted signal streams I_{x}, Q_{x}, I_{y} and Q_{y}, and the signal spectra of I_{x} and Q_{x} parts are shown in Fig. 3(b). Each subcarrier has a bandwidth of 35 MHz, which results in a bandwidth of 5.02 GHz including 0.12 exceed bandwidth. The total signal rate is 40.32 Gb/s with the 4D modulation. A CW laser at 1551.72 nm with an optical power of + 13 dBm is launched into the LiNbO_{3} waveguide based polarization division multiplexed (PDM) I/Q modulator for the optical signal modulation. The output of the PDM I/Q modulator is amplified by an erbium-doped fiber amplifier (EDFA) and then launched into a standard 80 km single mode fiber with an optical power of 0 dBm.

At the receiver, another CW laser with 100 kHz linewidth is employed as the local oscillator (LO). The received optical signal is detected by a coherent optical receiver, which consists of a polarization-diverse 90° optical hybrid and four balanced photo-detectors. After digitalized by a digital signal oscillator (DSO-X93204A) with 80 Gs/s sample rate, the signal is processed offline through digital signal processing. The training sequence is used to estimate the channel transform matrix and frequency offset. After filtered out with the matched filters, the scrambled symbols of different subcarriers are detected with maximum a posteriori detection. With correct secure key, the discrete constellation can be recovered in DSP domain. The scrambling will not bring any effect on the carrier phase recovery inside the coherent receiver. The SOP is decided by the maximum likelihood method by looking for the minimum squared distance between the received SOP and the six original SOPs.

Figures 3(c) and 3(d) compare the phase diagrams of the conventional Chua’s circuit map and multi-scroll Chua’s circuit map. Compared to the conventional Chua’s circuit map, five-scroll attractors are achieved in our scheme, which indicates more complicated chaotic kinetics behavior. The secure key of the system can be expressed as {*α, β, a _{i}, b_{i}, x, y, z, t, N, M*} (

*i*= 1,2,…,

*M*) and the initial values of intra-carrier scrambling can be different for the

*N*subcarriers. In the experiment, we have

*M*= 5 and the key space will be 4.39 × 10

^{158}if single-float value is used. The key space of our previous work in Ref [17]. is calculated to be 4.52 × 10

^{74}. Considering the different initial values of the

*N*subcarriers, the key space would further enlarge at an exponential rate as the number of subcarriers increases. The current fastest computing speed is 9.3 × 10

^{18}/s [21] and about 8.67 × 10

^{126}years will be spent to obtain the correct data via brute-force attack, which provides robust resistance to the illegal receiver.

The constellation phase distributions before and after scrambling are shown in Fig. 4, where normalized phase interval (−1, 1) is used. The phase distribution is averaged among the phase interval after scrambling and the probability of same phase is obviously reduced. It indicates that the original constellation information is totally disarranged by our proposed scrambling method.

Figure 5 illustrates the measured bit error ratio (BER) with and without correct key decryption after 80 km fiber transmission. For the regular receiver with correct key, the required optical signal-to-noise ratio (OSNR) at the BER of 1 × 10^{−3} is 16.3 and 16.6 dB before and after transmission. In contrast, the BER is ~0.5 for the illegal receiver without the correct key, indicating that the proposed method can provide secure transmission and resist eavesdropping from the illegal receiver. The constellation diagrams of the recovered signal are also shown as inset in Fig. 5. We have also tested the BER performance of subcarriers and the results are shown in Fig. 6, where the BER is measured every five subcarriers. Due to the spectrum confinement of prototype filter, it would introduce litter interference to the adjacent bands and high side-lobe suppression can be achieved. Thus the BER performance is concordant across the whole bandwidth.

We have also investigated the performance at the illegal receiver, where parts of the correct scrambling parameters are obtained. Figure 7 shows the measured BER results. The proposed method can keep BER values around 0.5 if the illegal receiver has wrong subcarrier or constellation scrambling vectors, which indicates a robust encryption for the information. The BER values is about 0.41 when the illegal receiver knows all the scrambling parameters except the Stokes scrambling vector. Due to the limited size of Stokes vector, the probability of recovering correct information is a little bigger than that of the other two cases.

Compared with Ref [17], the utilization of constellation scrambling can further increase the encryption strength. We have tested the encryption strength with and without constellation scrambling, and the results are shown in Fig. 8. When only Stokes vector scrambling is adopted, the BER at the illegal receiver is about 0.41 instead of maximum value of 0.5. With considering the constellation scrambling, the BER has get value of 0.5 due to the additional scrambling parameters of constellation. In order to verify the secure improvement of Stokes based 4-D modulation space, we have also compared the performance of Stokes vectors and QPSK modulation without constellation scrambling. The BER of QPSK modulation is around 0.37 while the BER of Pol-QAM 6-4 modulation is 0.41. It mainly attributes to the larger scrambling freedom of Stokes vectors.

## 4. Conclusion

We have proposed a novel secure transmission scheme to protect the confidential information in an optical coherent GFBMC system against the illegal receiver. The joint constellation and Stokes vector scrambling is adopted to enhance the security at different multi-carriers. The key space can obtain an exponential growth as the number of subcarriers increases. A 40.32 Gb/s encrypted optical signal is successfully demonstrated over 80 km fiber link. With the right scrambling vectors, a BER of 1 × 10^{−3} can be obtained under an OSNR of 16.6 dB after transmission. The BER is 0.5 with wrong scrambling vectors, which indicates an effective encryption. The results are demonstrated to prove the superiority of the proposed scheme in future secure optical multi-carrier system.

## Funding

Natural National Science Foundation of China (NSFC) (61522501, 61675004, 61425022 and 61475024); Program 863 (2015AA015501, 2015AA015502 and 2015AA015504).

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