Secure coherent optical multi-carrier system with four-dimensional modulation space and Stokes vector scrambling

Lijia Zhang; Bo Liu; Xiangjun Xin

doi:10.1364/OL.40.002858

The coherent optical system has witnessed an evolution to being large capacity and high-speed during the last years with the development of advanced modulation format [1,2]. The multi-carrier technologies such as Nyquist wavelength division multiplexing, orthogonal frequency division multiplexing (OFDM), and filter bank multicarrier can provide high capacity and flexibility for an optical network. In order to increase the spectral efficiency during transmission, the polarization diversity is usually adopted, which can be presented by the Jones vector. This diversity can be further extended by utilization of Stokes vectors, resulting in a four-dimensional (4D) signal space. The multi-state polarization modulation based on Stokes space has received wide attention [3 –5], including both digital and optical methods for the generation of Stokes vectors during modulation. It makes the system flexible with fine granularity and promises good power efficiency as well as high spectral efficiency.

Due to the significant growth in network capacity and the accessibility of the network, it is more and more desirable to establish a secure optical network. Several secure schemes have been proposed in the previous literatures [6 –8], such as employing the optical chaos lasers, exclusive or gate, and the higher layer security scheme. However, the stability and key distribution speed of optical chaotic laser is limited in practical use, and the exclusive or gate cannot support large key space. Although the higher layer security provides different encryption level settings for different services, it has rather complex key management and lacks the protection of header information or control data. The physical layer security offers transparent encryption for all the data including header information. It can be performed through uniformed physical layer interface, which is simpler to realize than higher layers. The physical layer security based on digital-signal processing (DSP) has potential of both improved security and convenient implementation [9]. Recently, we have proposed a secure optical system based on time and frequency-domain scrambling. Large key space and good system performance have been obtained in the former work [10].

In this Letter, we propose a novel Stokes vector-scrambling method for physical security in 4D-modulated multi-carrier system. The scrambling is executed through the six Stokes vectors both on each subcarrier and among different subcarriers, which is realized through the scrambling vectors. A multi-layer logistic map is proposed to increase the unpredictability of the chaotic kinetics characteristics. A 61.17-Gb/s encrypted coherent optical signal with 4D modulation space is successfully achieved in the experiment.

The 4D modulation field can be represented by the state of polarization (SOP) in the Poincaré sphere as shown in Fig. 1. The Stokes vectors SOP1 to SOP6 are orthogonal, and each SOP gets a complex constellation IQ plane with four points for 4-state quadrature amplitude-modulation (4QAM) mapping. It can be written as Pol-QAM 6-4 constellation, where 6 is the number of SOPs, and 4 is the number of 4QAM constellation points.

Fig. 1. Principle of 4D Stokes vector scrambling (a) intra-subcarrier; (b) among different subcarriers.

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The principle of the proposed encryption method is also illustrated in Fig. 1. The scrambling is realized both on each subcarrier and among different subcarriers. In the scheme, we adopt a multi-layer logistic map as the parameter function to generate the scrambling vectors, which can be expressed as

{\begin{cases} x_{n + 1}^{up} = μ x_{n}^{up} (1 - x_{n}^{up}) + (ζ x_{n}^{up}) \mod (0.016 μ) \\ x_{n + 1}^{down} = λ^{*} x_{n}^{down *} (1 - x_{n}^{down *}) \end{cases} .

Here

x_{n}^{up}

is the upper layer, which is 1D controlled logistic map, and

x_{n}^{down}

is the bottom layer subject to the upper layer. In Eq. (1),

μ

is the bifurcation parameter,

ζ

is a positive constant,

λ^{*}

and

x_{n}^{down *}

are two controlled parameters by upper layer, which is given by

{\begin{cases} λ^{*} = \frac{0.4 [x_{n}^{up} - ε_{1} μ^{2} (4 - μ)]}{0.25 μ - ε_{1} μ^{2} (4 - μ)} + ε_{2} \\ x_{n}^{down *} = {Mod}_{0.25 λ} (\frac{2}{3} | x_{n - 1}^{down *} - 0.9 x_{n}^{up} |) \end{cases} .

Here

ε_{1}

and

ε_{2}

are two constant values to ensure the chaotic nature of bifurcation parameters. For the multi-layer logistic map, parameters of

x_{0}^{up}

,

μ

,

ζ

,

x_{0}^{down}

,

ε_{1}

and

ε_{2}

correspond to the secure key. In the following experiment, we choose

ε_{1} = 1 / 16

and

ε_{2} = 3.35

. With the multi-layer map, the generated scrambling vectors will not belong to a fixed iteration orbit, but transition among a cluster of orbits, which would be difficult for the illegal receiver to detect the secure key. Two chaotic sequences defined as

{ψ_{a}}

and

{ψ_{b}}

are generated from the multi-layer map, which are used for scrambling on each subcarrier and among different subcarriers, respectively. In order to enhance the strength of the secure key, the update of chaotic sequences can be applied with a period of

P

, where

P

is a random integer value. The update is realized by the key controlling from the upper layer. When the data transmission is ready, the transmitter will randomly generate a key named KEY1 and send it to the receiver. After receiving KEY1, the receiver would send back the chaos information named KEY2, which is encrypted with KEY1. Then they will use KEY2 as the secure key.

There we assume that $S_{k, n}$ is the symbol of $k$ th Stokes vector on the $n$ th subcarrier, and the scrambling vectors are defined as $Ψ_{1}$ and $Ψ_{2}$ , respectively. First, the symbols on the $n$ th subcarrier are scrambled as Fig. 1(a) shows. The scrambling is applied in both Stokes vectors and constellation points. Considering 4QAM modulation for the six SOPs, we represent $S_{k, n}$ on $n$ th subcarriers with a size of $12 \times 2$ , which can be written as

S_{k, n} = [s_{j, 1}^{n}, s_{j, 2}^{n}], j = 1 to 12 .

Also,

Ψ_{1}

can be represented as

\begin{array}{l} Ψ_{1} = sort {ψ_{a}} \\ = sort {{[ψ_{1, j}, ψ_{2, j}]}^{T}} \end{array}, j = 1 to 12,

where the function

sort {}

means generation of the order numbers according to the values of chaotic sequence.

Ψ_{1}

indicates the new positions of the modulated data after scrambling. Because both the Stokes vectors and constellation points go through the scrambling, Eq. (4) would be executed by row and column, which results in a size of

12 \times 4

for

Ψ_{1}

. If we re-write

Ψ_{1}

as

{Ψ_{1,1 j}, Ψ_{1,2 j}, Ψ_{1,3 j}, Ψ_{1,4 j}}

(

j = 1

to 12), the symbols after scrambling can be expressed as

S_{k, n}^{'} = [s_{Ψ_{1,1 j}, Ψ_{1,3 j}}^{n}, s_{Ψ_{1,2 j}, Ψ_{1,4 j}}^{n}] .

To further enhance the security, the Stokes vector scrambling among subcarriers is performed after this, which is illustrated in Fig. 1(b). In this Letter, we take OFDM multi-carrier format to demonstrate the method. During the inter-subcarrier scrambling, we mainly consider the six SOPs. Assuming the number of data subcarriers is $N$ , the scrambling vector $Ψ_{2}$ can be further written as

Ψ_{2} = {Ψ_{2,1}, Ψ_{2,2}} = {{[φ_{1,1}, φ_{2,1}, \dots, φ_{6,1}]}^{T}, {[φ_{1,2}, φ_{2,2}, \dots, φ_{N, 2}]}^{T}},

where

Ψ_{2,1}

and

Ψ_{2,2}

are scrambling matrices with size of

6 \times 6

and

N \times N

, respectively. The elements

φ_{i, 1}

or

φ_{n, 2}

represent the scrambling position, and the values can be derived by the same method with

{ψ_{b}}

as Eq. (4). The final encrypted signal can be expressed as

s_{t}^{'} = \sum_{n = 1}^{N} (\sum_{k = 1}^{6} S_{k, n}^{'} \times Ψ_{2,1}) e^{j 2 π f_{n} \frac{(t - 1) T}{N}} \times Ψ_{2,2},

where

f_{n}

is the

n

th OFDM subcarrier. The receiver decrypts the correct information by applying the reverse operation with the right key. During transmission, the scrambling among different subcarriers can change the distribution of the original information and homogenize the information error caused by the burst noise.

In the experiment setup, we adopt a single-channel coherent Pol-QAM 6-4 OFDM system to investigate the Stokes vector scrambling-based secure approach. The experimental setup is shown in Fig. 2. The encrypted OFDM data stream is generated through DSP processing offline and then uploaded into the arbitrary waveform generators (AWG70002) to produce the signal. Two original pseudorandom binary-sequence (PRBS) bit streams with a word length of $2^{13} - 1$ are first mapped for Pol-QAM 6-4 modulation, where nine bits are mapped into two symbols. It has six states of polarization (SOP1, SOP2, SOP3, SOP4, SOP5, and SOP6) as shown in Fig. 1. The scrambling is executed during Pol-QAM 6-4 mapping and subcarrier modulation. The number of data subcarriers is $N = 256$ , and pilot tones are inserted every 32 subcarriers. The cyclic prefix and guard interval length are both 1/16 length of OFDM symbols. In order to provide enough output ports, we have used two AWGs with a total channel number of four, which are synchronized through RF cable. Four signal streams numbered as $I_{x}$ , $I_{y}$ , $Q_{x}$ , and $Q_{y}$ are generated from the AWGs. The signal spectra of $I_{x}$ and $Q_{x}$ parts are shown as inset in Fig. 2. The total signal rate is 61.17 Gb/s with 4D modulation. We use an optical transmitter consisting of a ${LiNbO}_{3}$ waveguide-based polarization division-multiplexed I/Q modulator plus laser source with linewidth less than 100 kHz. After amplified by an Er-doped fiber amplifier (EDFA), signal transmission is performed through a 80-km single-mode fiber (SMF). The fiber loss, dispersion, and dispersion slope are 0.22 dB/km, $17 ps / (nm \cdot km)$ , and $0.06 ps / ({nm}^{2} \cdot km)$ , respectively. The launched optical power is set to 0 dBm.

Fig. 2. Experimental setup for the secure multi-carrier system based on 4D Stokes vector scrambling (AWG, arbitrary waveform generator; SMF, single-mode fiber; LO, local oscillator; DSO, digital signal oscillator).

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At the receiver side, a DFB laser with 100-kHz linewidth is employed as the local oscillator (LO). The coherent optical receiver is consisting of a polarization-diverse 90° optical hybrid and four balanced photodetectors, recovering the I and Q branches in the X- and Y-polarization of the signal. The received signal is sampled and digitized by a digital signal oscillator (DSO-X93204A) with 80-GSa/s sample rate. During DSP processing, the channel transfer matrix and frequency offset are estimated by training symbols. The sampled signal streams can be viewed as a combination of PDM-QPSK and PS-QPSK in 4D Stokes space. The decision is performed for two consecutive Pol-QAM 6-4 symbols at once. The SOP is decided by maximum likelihood method looking for the minimum squared distance between the SOP of received signal and the six possible transmitted SOPs.

The phase diagrams of the multi-layer logistic map before and after update are illustrated in Figs. 3(a) and 3(b). They show a chaotic orbit rather than parabola curve compared with the conventional logistic map. The update would change the distribution of phase diagram, which enhances the unpredictability of the chaotic sequence. The secure key of the system is consisting of { $x_{0}^{up}$ , $μ$ , $ζ$ , $x_{0}^{down}$ , $ε_{1}$ , $ε_{2}$ , $N$ , $P$ }. We have tested the sensitivity of the chaotic sequences with tiny difference of keys, where the initial values are same except $x_{0}^{up}$ . The generated chaotic sequences with length of 128 are shown in Fig. 3(c). Then the sensitivity before and after update is also measured, and the results are presented in Fig. 3(d). It can be seen that both the two cases show total different iteration orbits, which indicates a high sensitivity for the multi-layer chaotic map.

Fig. 3. Phase diagrams of (a) original chaos; (b) after one update; the generated chaotic sequences (c) with slightly different keys (red line: $x_{0}^{up} = 0.565197469869506$ ; blue line: $x_{0}^{up} = 0.565197469869507$ ); (d) before and after one update.

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We first compare the performance of Pol-QAM 6-4 signal with PDM-QPSK signal under same bandwidth after 80-km transmission, where no encryption is applied for them. The measured result is shown in Fig. 4. It can be seen that Pol-QAM 6-4 signal maintains similar received sensitivity due to unchanged minimal Euclidean distance.

Figure 5 shows the measured bit error ratio (BER) with and without correct decryption. At the receiver, the optical signal-to-noise ratio (OSNR) can be adjusted by noise adding with variable optical attenuator and amplified spontaneous-emission (ASE) source. When the signal is corrected decrypted, the required OSNR for a BER under $1 \times 10^{- 3}$ is about 15.8 and 16.1 dB before and after transmission. It can be observed that signal without correct decryption gets a BER of 0.5, which ensures good security during transmission. The constellation diagrams of the recovered signal are also shown as inset in Fig. 5.

Fig. 4. Measured BER curves for Pol-QAM 6-4 and PDM-QPSK after 80 km transmission.

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Fig. 5. Measured BER curves with and without correct key (b2b, back to back; w/, with; w/o, without; OSNR resolution bandwidth: 0.1 nm).

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We have also investigated the performance at the illegal receiver with parts of the correct scrambling vectors, and the measured BER results are shown in Fig. 6(a). When the illegal receiver gets wrong $Ψ_{1}$ or $Ψ_{2},_{2}$ , both the BERs are about 0.5. However, the BER is around 0.41 when the illegal receiver gets incorrect $Ψ_{2},_{1}$ during measurement. It is mainly due to the limited scrambling size of $Ψ_{2},_{1}$ .

Fig. 6. Measured BER curves with (a) parts of the correct key at the illegal receiver; (b) different subcarrier lengths at the illegal receiver.

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We further study the decryption performance with different subcarrier lengths for the illegal receiver, and the BER curves are presented in Fig. 6(b). With the increasing of subcarrier length, the BER gradually achieves to a saturation value of 0.5. For different update periods of $P$ , the BER curves could reach the value of 0.5 when the subcarrier length is beyond 256.

In the proposed scheme, the utilization of Stokes vectors can produce 4D modulation space, which provides more flexible scrambling at the six orthogonal SOPs both on intra-subcarrier and among subcarriers. We further compare the strength of encryption with subcarrier scrambling, and the results are shown in Fig. 7, where Stokes vectors and QPSK modulation are adopted. When we only use subcarrier scrambling, the BER at the illegal receiver is around 0.4 instead of maximum value of 0.5. After adopting Stokes vectors, the BER gets value of 0.5 due to the flexibility and additional scrambling dimensions induced in 4D modulation space.

Fig. 7. Measured BER curves for different encryptions at the illegal receiver.

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In conclusion, we have proposed and experimentally demonstrated a secure, coherent optical-multi-carrier system using 4D modulation space and Stokes vector scrambling. The scrambling is implemented inter- and intra-subcarriers on six Stokes vectors and constellation points. The sensitivity and encryption performance are investigated in the experiment. It provides an efficient way for physical-layer confidential optical communication.

FUNDING INFORMATION

Beijing Nova Program (Z141101001814048); Fund of State Key Laboratory of IPOC (BUPT); National High Technology 863 Program of China (2013AA013403, 2015AA015501, 2015AA015502); National International Technology Cooperation (2012DFG12110); National Natural Science Foundation of China (NSFC) (61205066, 61275074, 613070864, 61425022, 61475024).

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Secure coherent optical multi-carrier system with four-dimensional modulation space and Stokes vector scrambling

Abstract

FUNDING INFORMATION

References

Cited By

Figures (7)

Equations (7)

Optics Letters