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Abstract
Due to atmospheric turbulence, the reliability and security of free space optical (FSO) communication is seriously affected. In this paper, we propose a new FSO wiretap channel model based on a time-diversity scheme and optical code division multiple access (OCDMA). At the receiving end, the legitimate user employs time-diversity reception by matched optical decoders, while an eavesdropper uses a random optical decoder for eavesdropping. Using an avalanche photodiode (APD) photon counting model, bit error rate (BER) performances of legitimate and eavesdropping users are theoretically analyzed under different turbulence and diversity. Based on the binary asymmetric channel model, the physical layer security performance of the time-diversity FSO/CDMA wiretap channel is evaluated by using security capacity. With the increase of time-diversity order, the reliability and security performances of FSO/CDMA wiretap channel are improved. Simulation results show that the performances of the time-diversity FSO/CDMA wiretap channel are better than those of a non-diversity FSO/CDMA system.
© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Free space optical (FSO) communication has received much attention recently, thanks to its advantages of high data rates, unregulated bandwidth and high security [1]. However, FSO communications are highly susceptible to atmospheric turbulence, which occurs as a result of the variations in the refractive index due to inhomogeneities in temperature and pressure changes. These index inhomogeneities can cause fluctuations in both the intensity and the phase of the received signal [2,3], which limits the performance of FSO system.
Many methods have been proposed to overcome the effects of turbulence-induced fading. Diversity is an effective method to improve the data rate and the reliability of communications over fading channels [4]. Diversity techniques used in wireless communication include time-diversity, frequency diversity and spatial diversity. In [5,6], a spatial diversity reception with multiple receivers is proposed. It can reduce the influence of atmospheric turbulence effectively. However, the analysis is based on the condition that the receiver aperture diameter is smaller than the correlation length of intensity fluctuation. It is not suitable for most FSO communication system, so the results are limited. Although wavelength diversity technology can overcome the shortcomings of spatial diversity [7], it occupies too much bandwidth resources and lacks security. The adaptive optics which is based on the phase conjugation principle is another viable option. It has been used in FSO, as reported in [8,9], to reverse the wavefront deformation effect of atmospheric turbulence. However, the complexity and cost of its implementation are prohibitive. The time-diversity FSO communication system will cause a certain delay, but it can overcome the small aperture reception problem of spatial diversity, and the implementation cost is low [10].
On the other hand, the high directionality of laser beam can make FSO communications more secure than radio frequency (RF) ones. However, FSO communications can still suffer from optical tapping risks, especially when the main lobe of laser beam is considerably wider than the size of the receiver [11–14]. A plausible mechanism for interception arises when part of the beam radiation is reflected by small particles, and then is detected by an external observer not in the light-of-sight of both communication peers. An alternative scenario would have the eavesdropper blocking the laser beam in order to collect part of optical power. Since the laser beam experiences divergence duo to optical diffractions, one possibility for a successful eavesdropping is to locate Eve in the divergence region of the beam. For long distances FSO communication, Eve has a stronger chance for eavesdropping on the FSO link by collecting the power not captured by legitimate peers [15].The problem of information security in the FSO communication system is analyzed in [16], where the eavesdropper can obtain information from the non-sight scatter channel. The atmospheric turbulence, the radius and intensity of beam divergence will also affect the security of FSO communication system [17].
Compared to other network technologies, optical code division multiple access (OCDMA) can improve security performance by using optical encoding and decoding scheme [18]. However, most researches only consider the BER performance of FSO/CDMA system. Considering APD noise, thermal noise and multiple-access interference (MAI), the BER and capacity of on-off keying (OOK) OCDMA system are analyzed in [19]. BER performance of atmospheric one-dimensional OCDMA system is evaluated in [20], in presence of MAI, atmospheric turbulence, background light, shot noise and thermal noise. In this study, pulse position modulation and lognormal fading model are adopted. In [21], BER performance of one-dimensional OCDMA system is analyzed in different weather conditions (fog, rain, and snow) without considering turbulence as a random process, i.e., without any fading model. BER performances of one-dimensional and two-dimensional FSO/CDMA systems are discussed and compared in [2]. Effect of atmospheric turbulence on the BER performance of FSO/CDMA system employing multi-wavelength pulse position modulation is comprehensively analyzed in [22]. As reported in [23,24], BER of a single-user time diversity FSO/CDMA system is studied by considering random variation of cross-correlation value. However, it should be pointed out that in a single-user time diversity FSO/CDMA system, the relative delay of different diversity is fixed, so the code cross-correlation value is a fixed value of 1 or 0.
In this paper, the time-diversity FSO/CDMA wiretap channel model is proposed for the first time, and the BER performance and security performance of the system are analyzed theoretically. The rest of the paper is organized as follows. In section 2, the time-diversity FSO/CDMA wiretap channel model by considering various delays is described. In section 3, the legitimate user and eavesdropping user’s BER performances are evaluated. In section 4, the security performance of the system is analyzed. In section 5, numerical analysis and simulation results are described. Finally, the conclusions are given in section 6.
2. Time-diversity FSO/CDMA wiretap channel model
Figure 1 is a time-diversity FSO/CDMA wiretap channel model. At the transmitter (Alice), the data information is OOK modulated. Then, the modulated signal is divided into N (here, N = 2) identical streams of optical signals. Each optical signal is encoded by a different optical encoder, and two signals are transmitted at different times by optical delay line (ODL). FODL is a fixed optical delay line, and TODL is a tunable optical delay line. FODL guarantees that the relative delay of the two signals is greater than the coherent time of the atmospheric channel, so that the two signals are independent of each other as the atmospheric turbulence changes. By adjusting the delay value of TODL, the cross-correlation value of the two signals can be guaranteed to be 0, thus MAI between two encoded signals can be completely eliminated.
At the receiving end, the legitimate user (Bob) divides the received optical signal by optical splitter. The two parts are decoded by matched optical decoders respectively. Then, two decoded signals are aligned by FODL and TODL, and recombined into one signal. The optical signal is received by APD, and the legitimate user data is recovered. At the same time, there is an eavesdropper (Eve) at the receiving end. We assume that part of the power collected by the eavesdropper is ${{r}_{e}}$, and the power collected by the legitimate user is $1 - {{r}_{e}}$. Eve randomly selects optical address code and optical decoder for decoding, and also uses APD receiver to recover the legitimate user data.
We consider the independent time interval of atmospheric turbulence in 10−2s [1]. Therefore, the delay ${{\tau }_1}$ of FODL is an integer multiple of the bit duration and is larger than 10−2 s. Cross-correlation interference depends on the relative delay of two optical codes. Therefore, if the delay ${{\tau }_2}$ of TODL is adjusted properly, the MAI between diversity signals can be eliminated.
In this paper, we employ optical orthogonal code (OOC) (F, K, 1) where F is the code length, K is the code weight, and code cross-correlation limit is 1. For OOC (40,3,1), we employ {1000100000010000000000000000000000000000} and {1000000001001000000000000000000000000000}. The relationship between the cross-correlation value and the relative time delay is shown in Fig. 2. Here, ${T_c}$ is chip duration. It can be seen that, the cross-correlation value of two codes is changed with different delay of TODL. For example, ${{\tau }_2}=6{T_{c}}$, code cross-correlation value is 0, hence MAI can be eliminated. Code cross-correlation value is 1 if ${{\tau }_2}= 2{T_{c}}$, and MAI will exist in the system.
3. Analysis of BER performance
In FSO communication system, there are many fading models, such as Log-normal distribution, Gamma-Gamma distribution and negative exponential distribution. In this paper, we employ Log-normal to model the weak turbulence. The probability density function of the Log-normal distribution is defined as [25]
3.1 BER performance of legitimate users
3.1.1 Case A: no MAI between diversity signals
${P_{rw}}$ denotes the received power of chip “1” without turbulence and no Eve. In two time-diversity FSO/CDMA wiretap channel, received chip power of legitimate user can be expressed as
For data “1” and “0”, photon absorption rate can be represent as [26]
For bit data “1”, the mean and variance of the legitimate user output can be expressed as
For bit data “0”, the mean and variance of the legitimate user output can be expressed as
3.1.2 Case B: MAI between diversity signals
In this case, code cross-correlation value between legitimate user and Eve is always 1. Since legitimate user will send bit data “0” and “1” equally, the mean cross-correlation value is $\mu ={1 \mathord{\left/ {\vphantom {1 2}} \right.} 2}$.
For bit data “0”, the mean and variance of the legitimate user output can be expressed as
3.2 BER performance of Eve
Assuming Eve is close enough to the legitimate user, the atmospheric turbulence experienced by Eve's intercepted signal is exactly the same as that experienced by the legitimate user in weak turbulence. It is reasonably easy for the legitimated users to change the time factor ${{\tau }_1}$ and ${{\tau }_2}$. Hence, we assume that the time factor should not be available for eavesdropper. At this point, for Eve, only two signals can be detected, and it is not known that legitimate user is using time-diversity reception. Therefore, Eve can try to decode one signal (${X_1}$), which can be expressed as
In this case, another signal is regarded as interference signal ${P_{re}}({{X_2}} )={{{{r}_{e}}{X_2}{P_{rw}}} \mathord{\left/ {\vphantom {{{{r}_{e}}{X_2}{P_{rw}}} 2}} \right.} 2}$. Since Eve does not know the code of the legitimate user, the random code and optical decoder are used to decode optical signal. Because the code cross-correlation is related to relative delay, the influence of interference signals on Eve depends on the code chosen by Eve and the relative delay of the two signals. We consider the worst case of system security, that is, code cross-correlation value between legitimate user ${X_2}$ and Eve is 0.For bit data “1”, the mean and variance of Eve can be expressed as
For bit data “0”, the mean and variance of Eve can be expressed as
4. Security performance
In order to ensure the BER performance of legitimate user, we adopt the delay set in case A, where there is no MAI between diversity signals. When the optical code used by Eve is exactly the same as that of legitimate user (the code cross-correlation value is K), the BER performance is the best for Eve, and the security performance of legitimate user is the worst. On the contrary, when the cross-correlation between the code used by Eve and the code of legitimate user is 1, the BER performance of Eve is the worst, and the security performance of legitimate user is the best.
Figure 3 is the binary asymmetric channel model for legitimate channel and Eve channel respectively. X is the channel input of Alice, Z is the channel output of Bob, and Ze is the channel output of Eve. Channel capacity of main channel is
We assume Alice will send bit data “0” and “1” equally, hence $H(X) = 1$. Then, channel capacity can be calculated as
5. Numerical analysis and simulation
In this section, we investigate the performance of time-diversity FSO/CDMA system by numerical analysis and simulation. The system parameters and constants used in the analysis are shown in Table 1.
Table 1. Simulation parameters
Figure 4 is the relationship between the BER of legitimate user and the normalized threshold under different turbulence effects and different receiving power. Here, we consider case A in two time-diversity FSO/CDMA system, and employ OOC (40, 3, 1). Receiver threshold sets $T\textrm{h} = M{\mu _{b1}}$, where ${\mu _{b1}}$ is the average received photon number of data bit “1” without turbulence and M is the normalized threshold. It can be seen from Fig. 4 that, under different conditions, there is an optimal threshold to minimize the BER of legitimate user.
Fig. 4. Case A: Relationship between the BER of legitimate user and the normalized threshold in two time-diversity FSO/CDMA system
In time-diversity FSO/CDMA system, there are two kinds of BER performance in Case A and Case B, due to the different delay settings. Figure 5 shows the BER performance comparison under different turbulence conditions. For example, under turbulence variance 0.1 and received power −25 dBm, BER of Case A is 1E-12, while the BER of Case B is 1E-4. Therefore, if the relative delay of time-diversity FSO/CDMA is reasonably designed, the BER of legitimate user will be greatly reduced.
Fig. 5. Relationship between the BER of legitimate user and the received power in two time-diversity FSO/CDMA system
Figure 6 is the BER of legitimate user under different turbulence and different diversity order in Case A. Here, OOC (40,3,1) is employed. It can be seen from Fig. 6 that under the same turbulence effect and the same receiving power, the BER performance of three-diversity is better than that of two-diversity, and the BER performance of two-diversity is better than that of non-diversity. For example, if the turbulence variance is 0.1 and the BER is 1E-9, the received power of three-diversity needs −30 dBm, while the received power of non-diversity is −26dBm. Therefore, the more the diversity order is, the better the reliability of the system. However, due to the constraint of code capacity and system complex, we should choose a compromise scheme.
The BER of Eve is different with the random code and optical decoder. In the worst case of system security, Fig. 7 is the BER of Eve using matched decoder in two time-diversity FSO/CDMA system. Here, OOC (40, 3, 1) is used and power ratio is 1%. It can be seen from Fig. 7 that, with the increase of legitimate user power, the BER performance of Eve can be improved gradually, which will reduce the physical layer security.
Figure 8 is secrecy capacity in two time-diversity FSO/CDMA system, where three different turbulence effects and matched code are employed. We can see that with the increase of the receiving power, the capacity of the system increases first and then decreases. The reason is that, when the received power is small, with the increase of receiving power, the BER of legitimate user decreases faster than that of Eve. However, with the increase of receiving power, the BER of legitimate user tends to be stable, but the BER of Eve continues to decrease. Therefore, maximum security capacity can be achieved under different turbulence effects.
On the other hand, when the received power is high, the greater the turbulence effect, the larger the security capacity is. Conversely, when the received power is low, the larger the turbulence effect is, the smaller the secrecy capacity. The reason is that different turbulence and received power have different effects on the BER of legitimate user and Eve.
Figure 9 shows the BER of Eve under different diversity order when Eve uses a matched decoder. As can be seen from Fig. 9, the BER of Eve will increase with the diversity order. The reason is that Eve can only decode one signal, and other diversity signals are received as interference signals.
Figure 10 shows secrecy capacity under different diversity order, and Eve uses matched decoder. The wiretap channel has the largest secrecy capacity at three-diversity, but the worst security at non-diversity. For example, when the received power is −20 dBm, the non-diversity security capacity can only reach 0.15 bit/symbol, while the three-diversity can reach more than 0.45 bit/symbol, it increased by three times.
Based on all the above numerical analysis, it can be found that the security capacity is constrained by the BER of legitimate user and Eve under different power levels. For different turbulence, we can choose an appropriate power to ensure the BER performance and security performance of the system, even in the most favorable case for Eve.
Next, OptiSystem software is used to simulate two time-diversity FSO/CDMA system. Refractive index structure coefficient is $C_n^2 = 1E - 14{m^{ - {2 \mathord{\left/ {\vphantom {2 3}} \right.} 3}}}$, and atmospheric attenuation coefficient is 8. Optical delay lines are used to construct optical encoder/decoder, and two OOCs are consistent with the two codes in section 2.
Figure 11 and Fig. 12 are eye diagrams of legitimate user in case A and case B respectively. It can be seen that BER performance can be improved with appropriate delays, which is consistent with the theoretical analysis.
Figure 13 is the eye diagram of legitimate user in non-diversity FSO/CDMA system. It can be seen that BER performance of legitimate user in time-diversity FSO/CDMA system is better than that of non-diversity.
Figure 14 is the eye diagram of Eve in two time-diversity FSO/CDMA system. Here, the extraction ratio is 1%, and Eve also uses matched decoder (the worst security performance). As can be seen from Fig. 14, the eye diagram of Eve is very poor, which indicates that physical layer security can be improved in time-diversity FSO/CDMA system.
6. Conclusion
In this paper, a time-diversity FSO/CDMA wiretap channel model is proposed, and the BER performance and security performance are analyzed theoretically. The effects of atmospheric turbulence, APD noise, background light noise and different delay on the system are considered, and simulation results and discussions are given. The results show that the BER performance of time-diversity FSO/CDMA system can be improved effectively by setting appropriate delays.
With the increase of diversity order, the BER performance and security performance of FSO/ CDMA wiretap channel are improved. However, the complexity of the system will increase with diversity order, which requires a compromise in the design of system parameters. At the same time, with the increase of diversity order, the number of users will be limited. Therefore, a compromise between the diversity order and the number of users should be considered when designing a multi-user time-diversity FSO/CDMA system. In the future, we will study the reliability and security simultaneously in multi-user time-diversity FSO/CDMA systems.
Funding
National Natural Science Foundation of China (NSFC) (61671306); Fundamental Research Project of Shenzhen (JCYJ) (20160328145357990).
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