## Abstract

This paper proposes a novel 3D constellation-masked method to ensure the physical security in hierarchical optical orthogonal frequency division multiplexing access (OFDMA) system. The 3D constellation masking is executed on the two levels of hierarchical modulation and among different OFDM subcarriers, which is realized by the masking vectors. The Lorenz chaotic model is adopted for the generation of masking vectors in the proposed scheme. A 9.85 Gb/s encrypted hierarchical QAM OFDM signal is successfully demonstrated in the experiment. The performance of illegal optical network unit (ONU) with different masking vectors is also investigated. The proposed method is demonstrated to be secure and efficient against the commonly known attacks in the experiment.

©2013 Optical Society of America

## 1. Introduction

Nowadays, passive optical network (PON) has been a promising way to provide a future-proof broadband solution toward next-generation access systems [1–4]. Considering the cost and performance of system, it needs to be easily reconfigurable and maintain reasonable efficiency to remain attractive and practical for future PON. Optical orthogonal frequency division multiplexing access (OFDMA) has emerged as an attractive candidate for next generation PON due to its various merits such as dispersion tolerance, bandwidth flexibility and large capacity [5–8]. It is well known that high-order modulation format is an effective way to increase the capacity of OFDMA system, but the procedure for smooth upgrading and flexible allocation has to be considered for large capacity OFDMA system.

Due to the natural compatibility with digital signal processing (DSP), the hierarchical modulation based on OFDMA can realize a high spectral efficiency as well as flexible traffic, bandwidth or subcarrier allocation to different optical network units (ONU) [9, 10]. It allows more dynamic operations such as bandwidth allocation at physical layer and simplifies the protocol at media access control (MAC) layer. For example, the modulation adaption and margin assignment can be realized at physical layer without human intervention. Since the dependence on physical layer has greatly increased in hierarchical OFDMA system, it is necessary to improve the security at physical layer. However, most of the previous work is about security on the cryptographic protocols at higher layer and there has been little literature focusing on physical security of hierarchical OFDMA system before. Recently, we have concentrated on the physical layer security of OFDM access network and proposed secure scheme by employing chaos scrambling [11].

In this paper, to our best knowledge, we firstly propose a novel three dimensional (3D) constellation-masked method for physical security in hierarchical OFDMA system. The constellation masking is executed on the two levels of hierarchical modulation. Besides, the masking is also implemented among different OFDM subcarriers, which further enhance the system security. All the maskings are realized by the masking vectors, which are generated through Lorenz chaotic model. In the experiment, a 9.85 Gb/s encrypted hierarchical QAM OFDM access system is successfully demonstrated. The results suggest that it is a promising solution for physical security in hierarchical OFDMA system.

## 2. Principle

In OFDMA system, the hierarchical modulation can assign the ONUs with different spectral efficiencies according to their optical signal-to-noise ratio (OSNR) requirements. Figure 1 illustrates the principle of hierarchical modulation with 4QAM and 16QAM. Level 1 and level 2 have different Euclidean distances which are defined as d_{2} and d_{1} respectively. Generally, we have d_{2}<d_{1}. Each hierarchical symbol in the resulting constellation will be composed of 4 bits, where 2 bits for the case of level 2 and 2 bits for the case of level 1. When the channel gets good OSNR condition, information on both levels can be received at the ONU. In this case, the optical line terminal (OLT) can assign data or service to both levels, which results in a higher spectral efficiency. If the channel condition is worse, data or service can be modulated on level 2 of hierarchical symbol. Thus a flexible bandwidth allocation is realized according to different OSNR requirements of the services or ONUs.

The principle of 3D constellation masking for hierarchical OFDMA system is illustrated in Fig. 2, where the hierarchical modulation is with two levels as shown in Fig. 1. In this scheme, the constellation masking is realized by the masking vectors. We adopt a well-known Lorenz chaotic model [12] to generate the masking vectors, which can be represented as

_{1k}and δ

_{2k}respectively, the constellation masking can be expressed aswhere k is the index of OFDM subcarrier, N is the total number of OFDM subcarriers, S is the data symbol on k

^{th}subcarrier after i

^{th}masking, and δ

_{ik}(i = 1, 2) can be represented asHere the sequence {m

_{k}} equals {x

_{k}} for level 1 and {y

_{k}} for level 2. In order to enhance the irregularity of sequence values and incorporate Lorenz model into the constellation masking which operates on a finite precision, the values of x, y and z are mapped into the range of (-π, π]. With Eq. (2) and (3), the constellation symbols on the two hierarchical levels are masked with random phase angles. After this, the whole constellation map on k

^{th}subcarrier is further masked by another subcarrier numbered as μ, which is shown in Fig. 2(b). The masking vector δ

_{ik}(i = 3) for the k

^{th}subcarrier can be express asHere the index of subcarrier μ is determined by {z

_{k}}, and the relationship can be expressed asThe principle of inter-carrier masking also obeys Eq. (2) where we have i = 3. During the generation of sequences, we adopt the Runge-Kutta 4th-order method for the iteration of Lorenz ordinary differential equations. The proposed method cannot only mask the information at different levels, but also enhance the unpredictable nature of masking and improve the secure key space.

## 3. Experimental setup and results

The experimental setup of the proposed scheme is illustrated in Fig. 3, where offline DSP processing is adopted to generate the encrypted OFDM signal. In the experiment, the parameters a, b and c are same for the two regular ONUs. The step size t = 0.01 for ONU-1 and 0.02 for ONU-2. The number of total OFDM data subcarriers equals 256, and the pilots are inserted every 32 subcarriers. In OFDM modulation, the guard band interval is proposed to eliminate the crosstalk from harmonic waves of subcarriers, which is added before subcarrier modulation. The guard band interval is 1/16 length of OFDM symbol, which results in a total FFT size of 280. After subcarrier modulation, the cyclic prefix (CP) is attached and the CP length is also 1/16 of OFDM symbol. It is proposed to resolve the channel dispersion-induced inter-symbol interference of symbols. We adopt digital I/Q up-conversion for encrypted OFDM signal and the central frequency is 2 GHz. A 2.7 GHz-wide electrical encrypted OFDM signal is produced by the AWG7122B with sample rate of 10 Gs/s, and the electrical spectrum is shown as Fig. 4(a). The data rate of the encrypted OFDM signal is 9.85 Gb/s. Figure 4 also shows the 3D constellation-masked hierarchical signal at b2b case, where we have c = 28. It can be seen that the constellation map becomes chaotic and cannot be demodulated correctly without the right masking vectors. A CW light at 1552.52 nm plus a Mach-Zehnder modulator (MZM) with a half-wave voltage of 3.5 V acts as the optical transmitter for the encrypted signal.

At the ONU, a 25 GHz optical filter with insert loss of 3 dB is employed to suppress the ASE noise before signal detection. A 10 GHz photodiode (PD) and 20 Gs/s real-time digital oscilloscope (TDS) are adopted for O/E and A/D conversion respectively. The sampled signal is firstly digitally down-converted to baseband signal for further demodulation. Synchronization and frequency offset estimation are executed before subcarrier demodulation. Then inter-carrier unmasking and FFT operation are implemented in order to recover the correct symbols on each subcarrier. The two hierarchical level unmasking and QAM de-mapping are executed to recover the correct information at each subcarrier. In our proposed scheme, the synchronization can be realized by the signal itself with training symbols. Furthermore, the masking based on Lorenz model is executed on the phase of the signal, where the phase noise can be estimated by the pilots. It is robustness to the channel disturbance or noise during measurement.

In our proposed scheme, different time delay is adopted for ONU-1 and ONU-2 during the generation of sequences {x_{k}},{y_{k}} and {z_{k}}, and the 2D phase diagrams for x, y, z with different time delays are shown in Fig. 5. The phase diagram represents the obit of the Lorenz model. It can be seen that even the same parameters would lead to different phase diagrams for a little vary of time delay. The variation indicates that the obit is sensitive to the change of initial condition and can enhance the unpredictability of the masking. At present, the main attacks aimed at the physical encryption schemes are based on spectral and key space analysis. From Fig. 4(a), it can be seen that the constellation-masked method has not bring any change of the spectrum structure, which indicates a good resistance to spectral analysis. For an encrypted system, the key space needs to be large enough to resist the space analysis attack. During the attack, the illegal ONU needs to try certain analysis times to get the correct key. If assuming the time delay is Δτ, the secure key of the system can be written as (x, y, z, t, c, Δτ) and it can ensure a large key space for data encryption. The exhaustive number of analysis times would be 9.81 × 10^{55} if single-precision float value is used.

Figure 6 shows the measured bit rate error (BER) both for the two regular ONUs and illegal ONUs, where the two regular ONUs share same subcarriers but different time slots. For the two regular ONUs, the power penalties are 0.3 dB at BER of 1 × 10^{−3} before and after transmission. The BER performance and demodulated constellation of level 1 at illegal ONU is also shown in Fig. 6. The BER of illegal ONU is about 0.5 and it is obvious that the illegal ONU cannot get any information of the regular ONU without correct key.

In the experiment, we have also tested the performance of illegal ONU with different masking vectors and the measured BER curves are shown in Fig. 7. When the illegal ONU has totally wrong masking vectors of δ_{1k}, δ_{2k} and δ_{3k}, the BER is about 0.5, which indicates an excellent encryption for the data. When the illegal ONU gets the correct masking vector of δ_{3k}, the BER is still very close to 0.5. When the illegal ONU has correct masking vectors of δ_{2k} and δ_{3k}, the BER around 0.45 is obtained in our measurement. It is attributed to the insufficient dimension of constellation masking but it still cannot demodulate the useful data intended for the regular ONU.

## 4. Conclusion

We have proposed a novel 3D constellation-masked method to ensure the physical security of hierarchical OFDMA system. It provides constellation masking on the two levels of hierarchical modulation and OFDM subcarriers, and Lorenz chaotic model is employed to generate the masking vectors. It can be easily incorporated into the system due to the convenient DSP technology. A 9.85 Gb/s encrypted hierarchical QAM OFDM signal is successfully demonstrated in the experiment. The experimental results show a prospective solution against illegal ONU in hierarchical OFDMA system.

## Acknowledgment

The financial supports from National NSFC (grant no. 61205066), National High Technology 863 Program of China (grant no. 2012AA011301/04, 2013AA013403), National International Technology Cooperation (grant no. 2012DFG12110) and Beijing Excellent Ph.D. Thesis Guidance Foundation (grant no. 20121001302) are gratefully acknowledged. The project is also supported by Universities Ph.D. Special Research Funds of New Teacher (20120005120007).

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