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Optics Communications journal homepage: www.elsevier.com/locate/optcom

Secure Image Transmission over DFT-precoded OFDM-VLC systems based on Chebyshev Chaos scrambling

MARK

⁎

Zhongpeng Wanga,b, , Weiwei Qiua a b

School of Information and Electronic Engineering, Zhejiang University of Science and Technology, Hang Zhou 310023, China State Key Laboratory of Millimeter Waves, Southeast University, Nanjing 210096, China

A R T I C L E I N F O

A BS T RAC T

Keywords: Visible light communication OFDM Physical layer security Chebyshev chaos map Precoding

This paper proposes a physical layer image secure transmission scheme for discrete Fourier transform (DFT) precoded OFDM-based visible light communication systems by using Chebyshev chaos maps. In the proposed scheme, 256 subcarriers and QPSK modulation are employed. The transmitted digital signal of the image is encrypted with a Chebyshev chaos sequence. The encrypted signal is then transformed by a DFT precoding matrix to reduce the PAPR of the OFDM signal. After that, the encrypted and DFT-precoded OFDM are transmitted over a VLC channel. The simulation results show that the proposed image security transmission scheme can not only protect the DFT-precoded OFDM-based VLC from eavesdroppers but also improve BER performance.

1. Introduction Visible light communication (VLC) based on light-emitting diodes (LEDs) can provide both illumination and data transmission simultaneously. VLC has been applied in Internet-of-Things, ad hoc networks, and short-range wireless communication networks owing to its costeﬀective, electromagnetic-interference-free, license-free, and secure communication link. Owing to its high spectrum eﬃciency, orthogonal frequency division multiplexing (OFDM) has been applied to VLC systems [1,2]. The VLC technique can be a potential candidate solution for 5G networks [3]. However, in some public areas such as classrooms, hallways, and planes, a transmitted signal over a VLC link is susceptible to eavesdropping. In this case, the transmitted data can be easily eavesdropped by illegal users. Thus, some security measures can be considered for VLC links [4]. Secure data transmission in VLC links has become a main challenge in recent years. Typical security mechanisms are used in the application layer of communication networks. In recent years, the strategy of physical layer security based on chaos theory has attracted wide attention of scholars [5–8]. These security measures have been researched for passive optical networks (PON) and OFDMbased VLC access networks [9–17]. Chebyshev polynomials have been widely applied in control systems, signal processing, numerical computations, etc. In the past few years, encryption and decryption based on Chebyshev polynomials have been investigated [18–21].

⁎

In this work, we mainly research the physical layer secure strategy for OFDM-based VLC. Our goal is to enhance the security of the transmitted data while improving the BER performance of OFDMbased VLC systems. Owing to the advantage of precoding, this technique can be used to reduce the PAPR of OFDM signals while improving BER performance of OFDM systems. Common precoding methods such as DCT precoding, Hadamard precoding, and DFT precoding have been employed in optical OFDM systems [22–24]. Recently, a secure transmission scheme based on chaos scrambling was proposed for optical DFT-S-OFDM systems [25]. The advantage of the scheme is that secure data transmission has been enhanced while improving BER performance owing to the use of DFT precoding. In this paper, we use two Chebyshev scrambling sequences to enhance the security of image transmission for a DFT-precoded OFDM-based VLC system. The physical layer security can be enhanced by a Chebyshev chaos scrambling sequence, and the BER performance can be improved by DFT precoding. Our simulation results prove that this approach can provide a scalable, secure strategy with the improvement in the BER performance of systems. This paper is organized as follows. In Section 2, the principle of the proposed system is introduced. In Section 3, the system performance of the proposed DFT-precoded and encrypted OFDM-based VLC is evaluated by simulation. Finally, Section 4 concludes this paper.

Corresponding author. E-mail address: [email protected] (Z. Wang).

http://dx.doi.org/10.1016/j.optcom.2017.03.076 Received 19 January 2017; Received in revised form 18 February 2017; Accepted 13 March 2017 0030-4018/ © 2017 Elsevier B.V. All rights reserved.

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x (m + 1) = Tk (x (m )) = cos(k × arccos(x (m ))), y(m + 1) = Tl (y(m )) = cos(l × arccos(y(m ))),

2. System principle 2.1. DFT precoding

where (x (m ), y(m )) ∈ [−1, 1] and (k , l ) ∈ [2, ∞) are control parameters. When a sign function,sgn(⋅), is used on x (n ) and y(n ), the binary data can be expressed as

The DFT precoding technique is commonly used to reduce the PAPR of OFDM signals. In the transmitter, the DFT matrix multiplying operation is employed, while the inverse DFT matrix operation is employed in the receiver. When a data vector X in the transmitter is multiplied by DFT matrix P, the precoded data vector Y can be obtained. The new data vector can be expressed as below:

Y = PX = [Y0 Y1 ⋯ YM −1]T ,

a(m ) = sgn(x (m )), b(m ) = sgn(y(m )),

(4)

where a(m ) and b(m ) are the m-th elements of the generated chaotic sequences a, and b, respectively. Thus, two scrambling sequences can be obtained by Eqs. (3) and (4). In practical applications, some initial iterated values {x (m ), m = 1, 2, ... , Q} and {y(m ), m = 1, 2, ... , Q} are abandoned, where Q is the iteration step. In this scheme, the initial values x(0), y(0), iteration step Q , and parameters (k , l ) can be used as the keys. We assume that a and b are the generated scrambling sequences where a(m ), b(m ) ∈ {−1, 1}. In our proposed encrypted scheme, the real and imaginary parts of the frequency data are ﬁrst encrypted by scrambling sequences a and b, respectively. In the transmitter, the transmitted image data is converted into a QAM symbol sequence S = [ S (1) S (2) ⋯ S (M )]. The real part of the data vector S is encrypted by scrambling sequence a. The encrypted real part of the signal Z can be expressed as

(1)

where []T denotes the matrix transpose, and P states the DFT precoding matrix with an M × M dimension. Every element of matrix Y can be written as

⎛ 2πpm ⎞ ppm = exp⎜ ⎟ ⎝ M ⎠

(3)

(2)

where p = 0, 1, …, M − 1 ,m = 0, 1, …, M − 1 , and ppm denotes the p-th row and m-th column of the DFT precoding matrix. In the receiver, the inverse DFT precoding matrix is employed in the receiver to recover the original data symbols. Owing to the unitary DFT matrix, the inverse DFT precoding matrix can be calculated by P−1 = P*, where P* is the conjugate matrix of P.

rea(Z (m )) = real (S (m ))⋅a(m ),

(5)

where m = 1, 2, ... , M . Similarly, the imaginary part of the data signals is encrypted again by scrambling sequence b. The encrypted imaginary part of Z can be expressed as

2.2. Encryption and decryption principle of OFDM

imag(Z (m )) = imag(S (m ))⋅b(m )

A DFT-precoded OFDM-based visible light communications system with a Chebyshev scrambling sequence is shown in Fig. 1. In our proposed scheme, the real and imaginary parts of the frequency data of OFDM signals are encrypted using two scrambling sequences. The two scrambling sequence are produced from the two Chebyshev polynomials. In Fig. 1, the input image data are converted into m-QAM or mPSK data symbols and then undergo a serial-to-parallel (S/P) transformation. After that, the real and imaginary parts of the data signal are multiplied by a Chebyshev scrambling sequence to ensure image transmission. The legal receiver can recover the received signal because it can obtain suﬃcient information to generate identical chaotic scrambling sequences in the transmitter. Without knowledge of the secure key, the eavesdropper cannot recover the data information from the received signal. In addition, we employ a DFT-precoding technique to further improve the BER performance of an encrypted OFDM-based VLC system. In this section, the scrambling sequences based on Chebyshev polynomials are used to encrypt the transmitted image data. The scrambling sequences can be obtained by a pseudorandom bit generator based on two Chebyshev polynomials, as described by [19]

(6)

At the receiver, the real and imaginary parts of received signal Zˆ are decrypted using known keys. The decrypted real part of signal Sˆ can be written as follows:

real (Sˆ(m )) = real (Zˆ (m )⋅b(m )

(7)

The decrypted imaginary part can be expressed as

imag(Sˆ(m )) = iamg(Zˆ (m ))⋅a(m )

(8)

2.3. System model The proposed secure image transmission system based on Chebyshev scrambling is shown in Fig. 1. Image data are ﬁrst converted into a bit stream. The bits are then mapped into m-QAM data sequence S = [ S (1) S (2) ⋯ S (M )]T , where []T denotes the transpose matrix. Each obtained data block is ﬁrst encrypted by Chebyshev scrambling sequence a. The resulting encrypted sequence Z = [ Z (1) Z (2) ... Z (M )] is then transformed by a precoding matrix to generate the precoded data sequence Y = PZ = [Y (1) Y (2) ... Y (M )]. To guarantee the real-valued time domain OFDM signals, the frequency domain symbol vector X, which should satisfy Hermitian symmetry, can be expressed as

X = [ 0 Y (1) ... Y (M ) 0 Y *(M ) ... Y *(1)]

(9)

The data sequence is then passed through IFFT modulation to generate the corresponding discrete time x, which can be written as

x (n ) =

1 N

N −1

⎛ j 2πkn ⎞ ⎟ N ⎠

∑ X (k )exp⎜⎝ k =0

(10)

After a cyclic preﬁx (CP) is inserted into x, the OFDM signal with a DC bias is transmitted over the wireless optical channel. The time domain OFDM signal x (n ) is multiplied by scrambling sequence b to improve the security. On the receiver side, after the discrete received signal r (n ) is ﬁrst decrypted by scrambling sequence b, the decrypted signal r (n ) can be

Fig. 1. (a) Encryption principle of a DFT-precodedOFDM-based VLC system.

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written as (11)

r (n ) = h (n ) ⊗ x (n ) + w (n )

where ⊗ represents the convolution process, and w(n ) is the total noise. The received signal r (n ) can then be transformed into the frequency domain by the FFT unit after the CP is removed. The FFT output can be represented as

⎛ −j 2πkn ⎞ N −1 R(k ) = ∑n =0 r (n )exp⎜ ⎟, 0 ≤ k ≤ N − 1 ⎝ N ⎠ = H (k )Y (k ) + W (k ),

(12)

where Wk is the additive complex Gaussian noise with zero mean and unit variance, and H (k ) is the frequency domain channel impulse response of the optical wireless channel. The estimated signal vector Yˆ can be obtained after the Hermitian symmetric data of R and is transformed by inverse precoding matrix P H . Thus, the encrypted original signal can be recovered as

Sˆ = P H Yˆ

Fig. 2. Autocorrelation value of x0=0.329999999999998, and k=20.

(13)

Finally, the encrypted original data can be decrypted by scrambling sequence a. The resulting signal is converted into original image data.

sequence

for

the

initial

value

Owing to the sensitive dependence on the initial condition, the minor deviation of the original value will lead to the generation of a unique sequence. Fig. 2 shows the autocorrelation of a Chebyshev scrambling sequence. It can be see that the autocorrelation of the scrambling sequence is close to unit impulse function δ . When lag k ≠ 0 , the value of the autocorrelation function of the scrambling sequences is close to zero. Fig. 3 shows the cross-correlation of the two scrambling sequences. The values of cross-correlation functions are also approximately zero for all values of k . The results of autocorrelation and crosscorrelation mean that the Chebyshev scrambling sequences have very good random properties.

3. Simulation results and analysis In the following simulation setup, the IEEE 802.16–2004 standard [26] is adopted as the PHY protocol. The transmitted OFDM signal can be encrypted by the two chaos scrambling sequences into frequency domain and time domain data. The PAPR and BER performance of the proposed secure image transmission was evaluated by computer simulation. The main parameters are shown in Table 1. An OFDM frame with 256 subcarriers consists of 192 data symbols, 8 pilot symbols for channel estimation and equalization, and 56 zero symbols for the guard band. In practice, the eﬀective number of data symbols is 96 because the Hermitian symmetry of input data of IFFT should be satisﬁed to generate the real OFDM signal. The length of the scrambling sequence for a is 96. In our proposed encrypted scheme, the scrambling sequences can be generated based on a Chebyshev scrambling sequence according to Eq. (4).

3.2. PAPR performance The PAPR is deﬁned as the ratio of peak power and average power of OFDM signals. For a discrete OFDM signal, the PAPR can be expressed as follows:

max [ x (n ) 2 ] PAPR =

3.1. Property analysis of Chebyshev scrambling sequences

0≤ n ≤ N −1

E{ x (n ) 2 }

(15)

The complementary cumulative distribution function (CCDF) is usually used to evaluate the PAPR performance of OFDM signals. Fig. 4 shows the CCDF comparison for the QPSK OFDM signals. The PAPR of the DFT-precoded and encrypted QPSK OFDM can be reduced by approximately 1.5 dB compared to that of the encrypted OFDM at CCDF=10−3.

In our proposed scheme, the real and imaginary parts of data symbols are encrypted by the two Chebyshev scrambling sequences. The two scrambling sequences can be obtained from Eqs. (3) and (4). In our proposed scheme, the space of keys can be expressed as

Keys = {x (0), y(0), k , l, Q, Δ1 , Δ2 }

Chebyshev

(14)

where Δ1 and Δ2 state the changing step of initial values x(0) and y(0). An OFDM transmission block consists of 1024 OFDM frames. From an OFDM frame, the initial values increase by Δ1 and Δ2 , respectively. Table 1 Simulation Parameters. Bit rate

500 Mbits/s

Modulation FFT size Number of pilot data Length of CP Scrambling size H Initial value x(0) Initial value y(0) Bifurcation parameter k , l Changed Step of x(0) and y(0) Iteration step Q Original Lena image

QPSK 256 8 32 96 3.5 m 0.329999999999998 0.329999999999999 20 1×10−5 2000 256×256

Fig. 3. Cross-correlation value of Chebyshev sequence for the initial value x0=0.329999999999998, y0=0.329999999999999 and k=20.

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Table 2 PSNR, PAPR and BER performances at SNR=13 dB. Parameters Transmitted Signals

Peak Power

Average Power

PAPR (dB)

PSNR (dB)

BER

Original OFDM DFT precoded OFDM

16.2638

0.7778

13.2034

28.0973

2.1744e-004

10.4931

0.7777

11.3012

33.7013

3.6240e-005

hc(t ) = H (0)

6a 6 u(t ), (t + a ) 7

(16)

where H(0) and u(t ) are the channel DC gain and the step function. In addition, a = 2H / c , where H and c are the ceiling height above the transmitter and the velocity of light, respectively. The delay spread of a channel is a remarkably accurate predictor of ISI-induced signal-tonoise ratio (SNR) penalties and is independent of the particular time dependence of the impulse response of that channel. The discrete time impulse response h(n ) can be obtained by sampling the continuous impulse response of h(t ). This channel h(n ) was employed in the simulation. The main parameters of our simulation are shown in Table 1. To show the clear eﬀect of the proposed secure transmission scheme, we transmitted image data in our simulation experiment platform. Fig. 5 shows the BER performance comparison for the encrypted OFDM optical wireless system with and without DFT precoding. The original Lena image data after being transformed into a QPSK signal are propagated over a wireless optical channel. We can see that the BER performance of the proposed DFT-precoded and encrypted OFDM system can be improved by an approximately 1.2 dB gain compared with that of the OFDM system without DFT precoding at BER =10−3. Thus, the advantage of DFT precoding in an encrypted OFDM system can be demonstrated, which is consistent with the previously reported results [25]. From Fig. 5, we can see that the illegal receiver cannot recover the received signal without knowing the keys. The BER of the illegal receiver is almost 0.5. This indicates a secure communication at the physical layer.

Fig. 4. Comparison of the PAPRs of the precoded QPSK OFDM signals with encryption.

Fig. 5. Comparison of BER performance of the encrypted QPSK OFDM systems with and without DFT precoding.

3.4. Visual quality of image transmission For clarity and without loss of generality, at the same SNR condition, the recovery performance is evaluated using the standard objective measure PSNR (peak signal-to-noise ratio). The PSNR is usually adopted as the performance metric in a video transmission system. The higher the PSNR of the image, the better the video quality. PSNR is commonly deﬁned as

PSNR = 10log10

(2B − 1)2 MSE 1 mn

m −1 n −1 ∑i =0 ∑ j =0

(17) 2

I (i , j ) − K (i , j ) , and B states the bit where MSE = numbers per pixel. Fig. 6 shows the received image PSNR with encryption when transmitting the one test image. Our proposed secure transmission system can achieve a 2-dB gain improvement over the original secure image transmission with an SNR of 12 dB. Table 2 presents the relationship among PSNR, PAPR, and BER of OFDM signals for the SNR=13 dB case. The DFT-precoded and encrypted scheme can reduce the PAPR of OFDM signals and furthermore improve the quality of the transmitted image. Fig. 7(a) and (c) shows the visual quality of the original encrypted OFDM and the DFT-precoded and encrypted OFDM, respectively, with an SNR of 12 dB. The DFT-precoded and encrypted OFDM can produces better visual quality than the original encrypted OFDM.

Fig. 6. The eﬀect of channel quality on the image PSNR values.

3.3. BER performance The optical wireless channel model, which is called the ceilingbounce model developed by Caruthers and Kahn in Ref. [28], is adopted in our simulations. A single inﬁnite-plane reﬂector with Lambertian reﬂectance in the channel model is assumed. The continuous unit impulse response of an optical wireless link h(t ) can be written as follows [27]: 87

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Fig. 7. Received signal constellations and recovered images for SNR=12 dB case.

3.5. Security analysis

Fig. 7(b) and (d) shows the constellations of the original encrypted OFDM and the DFT-precoded and encrypted OFDM, respectively. It is observed that the received DFT-precoded encrypted signals shown in Fig. 7(d) are more densely distributed than the original encrypted signals shown in Fig. 7(b). Fig. 7(e) and (v) shows the received image and constellation of the illegal receiver, respectively. We can observe that the illegal receiver may obtain the correct constellation but cannot recover the original image because it has no keys.

3.5.1. Space key As mentioned above, the key of the proposed cryptosystem is expressed as {x (0), y(0), k , l , Q, Δ1 , Δ2 }. In the keys, the seven variables x (0), y(0), k , l , Δ1 , Δ2 , which are declared by Matlab type “long,” are in a scaled ﬁxed-point format with 15-digit precision for double precision. According to the IEEE ﬂoating point standard [28], the computational precision of the 64-bit double-precision number is approximately 1015.

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Fig. 8. Histogram of plain image and cipher image. (a) Plain image. (b) Cipher image. (c) Histogram of plain image. (d) Histogram of cipher image.

Therefore, the key space is approximately key=1015×6 ≈ 2300 , which is large enough to eﬃciently resist brute-force attacks.

Science Foundation of China under LY17F050005, by the Open Fund of the State Key Laboratory of Millimeter Waves (Southeast University, Ministry of Education, China) under K201214, and by the National Natural Science Foundation of China under 61505176.

3.5.2. Histogram analysis Histogram analysis of the cipher images is important is and usually used to evaluate the pixel distribution of the cipher images. The histogram of the plain image (Fig. 8(a)) is the transmitted original image. It is clearly shown that the original plain image has a highly tilted histogram. The histogram of the cipher image (Fig. 8(b)) is the received encrypted image after the optical wireless channel in the SNR=14 dB case. It is observable that the histogram of the cipher image becomes fairly fat. Thus, the proposed encrypted scheme is eﬀective.

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4. Conclusions We proposed a secure image transmission scheme for a DFTprecoded OFDM-based VLC system with a Chebyshev scrambling sequence. The physical layer encryption can eﬀectively enhance the security of image transmission. The simulation results verify that the Chebyshev scrambling sequence can lead to a successful secure image transmission in the physical. layer. In addition, in our scheme, DFT precoding was employed to reduce the PAPR and improve the BER performance of the system, which is conﬁrmed by simulation results. Thus, our proposed scheme can eﬀectively enhance the secure image transmission for OFDM-based VLC systems. Acknowledgments This work was supported in part by the Zhejiang Provincial Natural 89

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