Privacy preserving with adaptive link selection for hybrid radio-frequency and free space optical networks

Dawei Wang; Woping Xu; Xingjie Fan; Julian Cheng

doi:10.1364/OE.27.003121

1. Introduction

Free space optical (FSO) communication is considered as a promising technique for next-generation wireless networks due to its high data rate and license-free operation [1]. Communicating through line-of-sight (LOS), the optical transmitter can directly transmit information to the optical receiver. Compared with radio-frequency (RF) communication, FSO communication has the advantage of inherent high security, flexibility, rapid deployment time and robustness [2]. The FSO communication has diverse applications such as front-haul of the cloud radio access network, building-to-building communications, communication restoration after a catastrophic event, tactic communication, etc,. However, the FSO link is susceptible to atmospheric turbulence and weather conditions that can degrade the channel quality and limit the FSO application in long-range communication [3].

RF/FSO communication is an alternative approach to overcome the above limitations by making the best of both the FSO and RF links. The RF/FSO communication has attracted much research attention in recent years. In [4], the authors studied the hybrid utilization of optical fibers and RF/FSO to minimize the cost of network backhaul. In addition, the networks adaptively select the optical fibers or RF/FSO link as the backhaul to satisfy the data rate, connectivity, and reliability constraints. In [5], the authors proposed an adaptive switching RF and FSO transmission scheme where the transmitter adaptively chooses to transmit through the FSO or RF link and provides the FSO link with higher priority. In [6], the authors studied the performance of the two-hop RF/FSO network where the first hop is the RF link and the second hop is the FSO link. In addition, the closed-form expressions of outage probability, bit-error rate, and the average capacity were derived. In [7], the authors discussed the outage probability and the average bit-error rate performance of the two-hop RF/FSO network with outdated channel state information for the RF link and the misalignment for the FSO link. In [8], the authors investigated adaptive combining for the hybrid RF/FSO system and derived the secrecy outage probability. In [9], the authors also investigated the performance of the two-hop RF/FSO networks with different modulation schemes, and closed-form expressions of the exact and asymptotic average symbol error rate were derived. In all the above works, the RF link can mitigate the shortcomings of the short-range and turbulence-induced fading in FSO transmission and the FSO link can improve the information rate and security.

The broadcasting nature of the wireless media makes the wireless networks susceptible to eavesdropping. Besides the upper-layer encryption methods, physical-layer security can utilize the intrinsic randomness of the transmission channel to protect the privacy information. According to the works in [10, 11], the privacy information is secure when the legitimate channel has advantages over the wiretap channel. Therefore, in order to protect the privacy information, we should improve the performance of the legitimate transmission and degrade the performance of the wiretap transmission. In [12–18], the authors utilized the cooperative relay to improve the legitimate transmission rate where techniques such as beamforming, relay selection, antenna selection were adopted to improve the secrecy performance. In [19–23], the authors designed the artificial noised assisted secure transmission schemes to interfere the eavesdroppers. For the RF/FSO networks, the FSO link can provide information security while the RF link is threatened by the eavesdroppers. To protect the privacy information, the authors in [24] analyzed the security and reliability trade-off for the two-hop RF/FSO networks while ignored the information security for the one-hop RF/FSO networks. In [24], the optimal RF transmitter was selected to transmit information through the RF link and securely forward through the FSO link. Following this idea, the authors in [25] considered the impact of cochannel interference during the RF secure transmission and derived the closed-form expression of the secrecy outage probability for the two-hop RF/FSO networks. However, the information security of the one-hop RF/FSO transmission is not considered in the above works. Therefore, in this paper, we study the information security of the one-hop RF/FSO hybrid network.

In this paper, we propose a secure hybrid RF/FSO transmission scheme by taking advantage of both the RF and FSO links to protect the privacy messages. In the proposed scheme, the transmitter adaptively selects the RF link or FSO link according to the secrecy performance and we name the proposed scheme as the FSO dominant secure (FDS) policy and the secrecy rate optimal (SRO) policy. In the FDS policy, we permit high priority for the FSO link due to its high security. The FDS policy can be summarized as follows: (i) when the FSO link is reliable, Alice utilizes the FSO link to transmit the privacy information; (ii) when the FSO link suffers outage but the RF link is secure, Alice transmits the privacy information through the RF link; (iii) when both the FSO and RF links cannot provide successful secure transmission, Alice stops her transmission. For this policy, we analyze the secrecy performance and derive the closed-form expression of the average secrecy rate. In the SRO policy, we optimally select the FSO or RF link according to the secrecy performance. The SRO policy can be summarized as follows: (i) when the FSO link can provide higher secrecy rate than the secrecy performance of the RF link, Alice utilizes the FSO link to transmit the privacy information; (ii) when the RF link can provide higher secrecy rate than the secrecy performance of the FSO link, Alice transmits the privacy information through the RF link; (iii) when both the FSO and RF links cannot provide successful secure transmission, Alice stops her transmission. For this policy, we also analyze the secrecy performance and derive a closed-form expression for the average secrecy rate. Numerical results demonstrate the performance improvement of the proposed policies when compared with the current RF or FSO secure schemes in terms of the average secrecy rate. Therefore, the contributions of this paper can be summarized as

We propose a secure hybrid RF/FSO transmission scheme that takes advantage of both the RF and FSO channels to protect the privacy messages;
Considering the priority of the FSO link, we propose two secure transmission policies: the FSO dominant secure (FDS) policy and the secrecy rate optimal (SRO) policy. In the FDS policy, we assign high priority to the FSO link due to its high secrecy performance. In the SRO policy, Alice optimally selects FSO link or RF link according to the secrecy rates of both the FSO and RF links in each time slot;
For both FDS and SRO policies, we analyze the secrecy performances and derive closed-form expressions for the average secrecy rate. Numerical results demonstrate the performance improvement of the proposed policies compared with the current RF or FSO secure schemes in terms of the average secrecy rate.

The rest of this paper is organized as follows. Section 2 describes the system model of the proposed secure scheme. In Section 3, we first interpret the secrecy rate of the RF and FSO links. Then, we propose two secure transmission policies for the hybrid RF/FSO network. We analyze the secrecy performance of the proposed secure policies in Section 4. Extensive simulation results are presented in Section 5, and Section 6 concludes the paper.

2. System model

We consider a hybrid RF/FSO network as shown in Fig. 1, where Alice securely transmits the privacy messages to Bob through the FSO or RF links. In addition, there is an eavesdropper who attempts to eavesdrop the privacy information. Alice has a photon-aperture transmitter and a radio frequency transmitter. Bob is equipped with a photon-aperture receiver and a radio frequency receiver. Alice and Bob can communicate through both RF and FSO links. Due to the collimated laser beam, it is challenging to eavesdrop the secrecy information without affecting the receiving power at the receiver. Therefore, the eavesdropper can be detected in the FSO receiver and we assume that the FSO link is secure while Eve only can eavesdrop the RF link. For the FSO link, it is sensitive to the atmospheric turbulence and weather conditions, and may experience transmission outage when the channel quality of FSO link is poor. The system will switch to the RF link when the FSO link fails to operate, especially in the presence of heavy fog and turbulence.

Fig. 1 The system model for the proposed link adaptation secure scheme.

Download Full Size | PDF

The upper layer data packets are divided into several equal frames and each frame consumes one time slot. All the noises in this network are assumed to follow zero-mean Gaussian random variables with unit variance. The FSO and RF channels from Alice to Bob are denoted as h_fso and h_rf, respectively. The channel power gain of the RF link is denoted as g_rf = |h_rf|² which follows the exponential distribution with parameter λ_rf. The FSO link is assumed to follow a Gamma-Gamma fading distribution with pointing error impairments. We consider coherent FSO with zero-boresight pointing error and adopt the heterodyne detection at Bob [26]. Therefore, the probability density function (PDF) of the received signal-to-noise ratio (SNR) of the FSO link is [27–29]

f_{h_{fso}} (γ) = \frac{ξ^{2}}{Γ (α) Γ (β) γ} G_{1, 3}^{3, 0} (\frac{ξ^{2} α β}{μ (ξ^{2} + 1)} γ | \begin{matrix} ξ^{2} + 1 \\ ξ^{2}, α, β \end{matrix})

where

G_{m, m}^{p, q} (\cdot)

is the Meijer’s G-function [30]; α and β are atmospheric turbulence parameters; σ denotes the ratio between the equivalent beam radius at the receiver and the pointing error displacement standard deviation (jitter) at the receiver given as

ξ = \frac{ω_{z_{eq}}}{2 σ_{s}^{2}}

, where

σ_{s}^{2}

is the jitter variance and ω_{z_eq} is the equivalent beam radius; μ is μ = 𝔼{h_fso} and where 𝔼{·} is the expectation operation. The cumulative distribution function of the received SNR for the FSO link is

F_{h_{fso}} (γ) = \frac{ξ^{2}}{Γ (α) Γ (β)} G_{2, 4}^{3, 1} (\frac{ξ^{2} α β}{μ (ξ^{2} + 1)} γ | \begin{matrix} 1, ξ^{2} + 1 \\ ξ^{2}, α, β, 0 \end{matrix}) .

Due to the broadcast nature of RF transmission, Eve will receive the privacy signal through the RF link. The RF link from Alice to Eve is denoted as h_e and its channel power gain is denoted as g_e = |h_e|² which follows the exponential distribution with parameter λ_e.

In order to protect the privacy messages, Alice adopts the wiretap coding in the RF transmission. In each time slot, Alice adopts the secrecy codebook of 𝒞 (2^nR_b, 2^nR_s, n) to forward the confidential messages, where R_b is the source target transmission rate; R_s is the intended secrecy rate; n is the length of the codeword; 2^nR_b is the size of the codebook and 2^nR_s is the number of confidential messages to be sent. The difference between R_b and R_s, denoted as R_e ≜ R_b − R_s, is the information redundancy against the eavesdropping. In each slot, a confidential message ω ∈ {1, · · · , 2^nR_s} is transmitted. Since the FSO transmission is secure [24,25,31–33], the FSO link’s information rate is also the secrecy rate for the FSO link. In the following, we will interpret the proposed scheme.

3. Hybrid RF/FSO secure transmission

In this section, we first investigate the secrecy rates of the FSO and RF links. Then, we propose two new hybrid RF/FSO secure transmission policies.

3.1. Secure transmissions for RF and FSO links

Since the FSO communicates through a collimated laser beam, it can provide high security. Therefore, in this work, we assume that the FSO link is secure and the FSO link’s information rate becomes the secure rate. When Alice transmits the privacy information through the FSO link with power p_a,f, the received signal at Bob is

y_{1} = \sqrt{p_{a, f}} h_{fso} x_{1} + n_{1}

where x₁ is the privacy message of the FSO link and it is normalized as 𝔼 {|x₁|²} = 1; n₁ is the received noise at the photon-aperture receiver of Bob. According to the above transmission, the instantaneous electrical signal-to-noise ratio (SNR) can be defined as

γ_{1} = \frac{p_{a, f} h_{fso}}{N_{0, f}}

where N_0,f is the received noise for the FSO link. Since the FSO link is secure, the transmission rate of the FSO link is the secure rate. When the privacy information is successfully decoded at Bob, the secrecy rate for the FSO link is

R_{1} = {log}_{2} (1 + \frac{p_{a, f} h_{fso}}{N_{0, f}}) .

When the RF link is utilized for the information transmission, the wiretap coding is adapted to encrypt the privacy information. Under this condition, the received signal at Bob is

y_{2} = \sqrt{p_{a, r}} h_{rf} x_{2} + n_{2}

where p_a,r is the transmit power for the RF link; x₂ is the privacy message of the RF link and it is normalized as 𝔼 {|x₂|²} = 1; n₂ is the received noise at the radio-frequency receiver of Bob. For the RF link, the instantaneous SNR is defined as

γ_{2} = \frac{p_{a, r} g_{rf}}{N_{0, r}}

where N_0,r is the received noise for the FSO link. The transmission rate of the privacy information is

R_{2} = {log}_{2} (1 + \frac{p_{a, r} g_{rf}}{N_{0, r}}) .

In addition, the eavesdropper also receives the privacy information through the RF link as

y_{e} = \sqrt{p_{a, r}} h_{e} x_{2} + n_{e}

where n_e is the received noise at Eve. The instantaneous SNR at Eve is

γ_{e} = \frac{p_{a, r} g_{e}}{N_{0, r}}

and the wiretap rate is derived as

R_{e} = {log}_{2} (1 + \frac{p_{a, r} g_{e}}{N_{0, r}}) .

According to the wiretap coding, the secrecy rate of the RF link is

R_{\sec} = {(R_{2} - R_{e})}^{+}

where (a)⁺ = max (0, a).

3.2. Secrecy transmission policy

For the FSO link, in order to successfully transmit the privacy information, the transmission rate should be larger than the target transmission rate R_b, i.e., R₁ ≥ R_b. Otherwise, the FSO transmission will experience transmission outage. Therefore, the SNR of the FSO link should satisfy

R_{1} = {log}_{2} (1 + γ_{1}) \geq R_{b} \Rightarrow γ_{1} \geq γ_{T} = 2^{R_{b}} - 1 .

For the RF link, there are two possible outage events: the connection outage and the secrecy outage. When the transmission rate R₂ is less than the target transmission rate R_b, the RF link will experience connection outage as

R_{2} = {log}_{2} (1 + γ_{2}) \geq R_{b} \Rightarrow γ_{2} \geq γ_{T} = 2^{R_{b}} - 1 .

According to the wiretap coding, when the secrecy rate R_sec is less than R_s, the RF link will experience secrecy outage with probability

\begin{array}{l} P_{\sec, o} & = Pr (R_{\sec} = {(R_{2} - R_{e})}^{+} < R_{s}) \\ = Pr ((R_{2} - R_{s}) < {log}_{2} (1 + \frac{p_{a, r} g_{e}}{N_{0, r}})) \\ = Pr (\frac{N_{0, r} (2^{(R_{2} - R_{s})} - 1)}{p_{a, r}} < g_{e}) \\ = exp (- \frac{N_{0, r} (2^{(R_{2} - R_{s})} - 1)}{p_{a, r} λ_{e}}) . \end{array}

Set the maximum secrecy outage probability as

P_{\sec, o}^{\max}

. Alice will transmit privacy messages only when g_rf ≥ τ as

P_{\sec, o} \leq P_{\sec, o}^{\max} \Rightarrow g_{rf} \geq τ = \frac{N_{0, r} (2^{(R_{s} + {log}_{2} (1 - \frac{p_{a, r} λ_{e} ln P_{\sec, o}^{\max}}{N_{0, r}}))} - 1)}{p_{a, r}} .

According to the above discussion, we propose two secure transmission policies: the FSO dominant secure (FDS) policy and the secrecy rate optimal (SRO) policy.

In the FDS policy, we take advantage of the inherent security in FSO transmission and assign high priority to the FSO transmission. Therefore, we can summarize the FSO policy as

When γ₁ ≥ γ_T, Alice transmits privacy messages through the FSO link;
When γ₁ < γ_T and $g_{rf} \geq max (\frac{N_{0, r} (2^{R_{b}} - 1)}{p_{a, r}}, τ)$ , Alice transmits the privacy messages through the RF link;
When γ₁ < γ_T and $g_{rf} < max (\frac{N_{0, r} (2^{R_{b}} - 1)}{p_{a, r}}, τ)$ , Alice stops the transmission.

In the SRO policy, Alice selects the optimal transmission link according to secrecy performances of both the FSO and RF links. We can summarize the SRO policy as

When γ₁ ≥ γ_T, $g_{rf} \geq max (\frac{N_{0, r} (2^{R_{b}} - 1)}{p_{a, r}}, τ)$ and R₁ ≥ (R_s − R̄_e), or when γ₁ ≥ γ_T and $g_{rf} < max (\frac{N_{0, r} (2^{R_{b}} - 1)}{p_{a, r}}, τ)$ , Alice transmits privacy messages through the FSO link;
When γ₁ ≥ γ_T, $g_{rf} \geq max (\frac{N_{0, r} (2^{R_{b}} - 1)}{p_{a, r}}, τ)$ and R₁ < (R_s − R̄_e), or when γ₁ < γ_T and $g_{rf} \geq max (\frac{N_{0, r} (2^{R_{b}} - 1)}{p_{a, r}}, τ)$ , Alice transmits privacy messages through the RF link;
When γ₁ < γ_T and $g_{rf} < max (\frac{N_{0, r} (2^{R_{b}} - 1)}{p_{a, r}}, τ)$ , Alice stops the transmission.

In the SRO policy, since the wiretap channel state information (CSI) can be acquired, we utilize the ergodic wiretap rate R̄_e to denote the instantaneous wiretap rate R̄_e as

\begin{array}{l} {\bar{R}}_{e} & = & 𝔼 {{log}_{2} (1 + \frac{p_{a, r} g_{e}}{N_{0, r}})} \\ \overset{(a)}{=} & - λ_{e} exp (\frac{N_{0, r}}{λ_{e} p_{a, r}}) E_{i} (- \frac{N_{0, r}}{λ_{e} p_{a, r}}) \end{array}

where the equality (a) is obtained according to E_i which is defined (8.211.1) at [30] and in (4.337.1) at [30].

For the proposed two secure transmission policies, the FDS assigns the FSO link with high priority and it can avoid frequent switching between the FSO link and RF link, and the FDS policy can be easily implemented. For the SRO policy, Alice selects the transmission link with high secrecy rate, which can improve the secrecy performance. However, the secrecy optimal selection in the SRO policy will lead to more channel switching compared with the FDS policy. Therefore, the FDS scheme can be utilized for the scenario with loose secrecy requirement, while the SRO policy is suitable for the applications with strict secrecy requirement.

4. Secrecy performances

In this section, we will analyze the secrecy performances of the proposed FDS and SRO policies. For both schemes, we will analyze the average secrecy rate which can give some insights about the performance superiority of the proposed scheme.

4.1. FDS policy

For the FDS policy, the privacy messages are transmitted through the FSO link with probability

\begin{array}{l} P_{fso}^{f} & = & Pr (R_{1} \geq R_{b}) \\ = & Pr (h_{fso} \geq \frac{N_{0, f} (2^{R_{b}} - 1)}{p_{a, f}}) \\ = & 1 - \frac{ξ^{2}}{Γ (α) Γ (β)} G_{2, 4}^{3, 1} [α β h (\frac{N_{0, f} (2^{R_{b}} - 1)}{μ p_{a, f}}) | \begin{matrix} 1, ξ^{2} + 1 \\ ξ^{2}, α, β, 0 \end{matrix}] \end{array}

where

h = \frac{ξ^{2}}{ξ^{2} + 1}

. In this case, the secrecy rate of the FSO link is R₁, since the FSO link can provide information security. When the FSO link cannot provide information security, Alice evaluates the channel quality of the RF link. Alice transmits the privacy through the RF link with probability

\begin{array}{l} P_{rf}^{f} & = & (1 - P_{fso}^{f}) Pr (g_{rf} \geq max (\frac{N_{0, r} (2^{R_{b}} - 1)}{p_{a, r}}, τ)) \\ = & \frac{ξ^{2}}{Γ (α) Γ (β)} G_{2, 4}^{3, 1} [α β h (\frac{N_{0, f} (2^{R_{b}} - 1)}{μ p_{a, f}}) | \begin{matrix} 1, ξ^{2} + 1 \\ ξ^{2}, α, β, 0 \end{matrix}] \\ = & \times exp (- \frac{1}{λ_{rf}} max (\frac{N_{0, r} (2^{R_{b}} - 1)}{p_{a, r}}, τ)) . \end{array}

For the RF link, the secrecy rate is

R_{\sec}^{rf} = {(R_{2} - {\bar{R}}_{e})}^{+} .

Therefore, for the FDS policy, the average secrecy rate is obtained as

\begin{array}{l} R_{\sec}^{f} & = & P_{fso}^{r} R_{1} + P_{rf}^{f} R_{\sec}^{rf} \\ = & (1 - \frac{ξ^{2}}{Γ (α) Γ (β)} G_{2, 4}^{3, 1} [α β h (\frac{N_{0, f} (2^{R_{b}} - 1)}{μ p_{a, f}}) | \begin{matrix} 1, ξ^{2} + 1 \\ ξ^{2}, α, β, 0 \end{matrix}]) {log}_{2} (1 + \frac{p_{a, f} h_{fso}}{N_{0, f}}) \\ + \frac{ξ^{2}}{Γ (α) Γ (β)} G_{2, 4}^{3, 1} [α β h \frac{N_{0, f} (2^{R_{b}} - 1)}{μ p_{a, f}} | \begin{matrix} 1, ξ^{2} + 1 \\ ξ^{2}, α, β, 0 \end{matrix}] \\ exp (- \frac{1}{λ_{rf}} max (\frac{N_{0, r} (2^{R_{b}} - 1)}{p_{a, r}}, τ)) ({log}_{2} (1 + \frac{p_{a, f} g_{rf}}{N_{0, f}}) \\ + λ_{e} exp (\frac{N_{0, f}}{λ_{e} p_{a, f}}) E_{i} (- \frac{N_{0, f}}{λ_{e} p_{a, f}})) . \end{array}

4.2. SRO policy

In the SRO policy, Alice optimally selects the transmission link from both FSO and RF links. For the FSO link, it will be selected when either of the following cases is satisfied:

The conditions γ₁ ≥ γ_T, $g_{rf} \geq max (\frac{N_{0, r} (2^{R_{b}} - 1)}{p_{a, r}}, τ)$ , and R₁ ≥ (R_s − R̄_e) indicate that both the FSO and RF links can preserve privacy and the secrecy performance of the FSO link is better than the secrecy performance of the RF link;
The conditions γ₁ ≥ γ_T and $g_{rf} < max (\frac{N_{0, r} (2^{R_{b}} - 1)}{p_{a, r}}, τ)$ indicate that only the FSO link can preserve privacy and the RF link experiences secrecy outage.

Therefore, Alice transmits through the FSO link with probability

\begin{array}{l} P_{fso}^{s} & = & Pr (γ_{1} \geq γ_{T}, g_{rf} \geq max (\frac{N_{0, r} (2^{R_{b}} - 1)}{p_{a, r}}, τ), R_{1} \geq (R_{2} - {\bar{R}}_{e})) \\ + Pr (γ_{1} \geq γ_{T}, g_{rf} < max (\frac{N_{0, r} (2^{R_{b}} - 1)}{p_{a, r}}, τ)) \\ = & \underset{I_{1}}{\underset{︸}{Pr (h_{fso} \geq \frac{g_{rf} 2^{- {\bar{R}}_{e}} p_{a, r} N_{0, f}}{p_{a, f} N_{0, r}} + \frac{N_{0, f} (2^{- {\bar{R}}_{e}} - 1)}{p_{a, f}}, h_{fso} \geq \frac{N_{0, f} (2^{R_{b}} - 1)}{p_{a, f} p_{a}}, g_{rf} \geq max (\frac{N_{0, r} (2^{R_{b}} - 1)}{p_{a, r}}, τ))}} \\ + \underset{I_{2}}{\underset{︸}{Pr (h_{fso} \geq \frac{N_{0, f} (2^{R_{b}} - 1)}{p_{a, f}}, g_{rf} < max (\frac{N_{0, r} (2^{R_{b}} - 1)}{p_{a, r}}, τ))}} . \end{array}

The term I₁ is derived as

\begin{array}{l} I_{1} & = & \int_{max (\frac{N_{0, r} (2^{R_{b}} - 1)}{p_{a, r}}, τ)}^{\infty} \frac{ξ^{2}}{Γ (α) Γ (β)} \frac{1}{λ_{rf}} exp (- \frac{x}{λ_{rf}}) \\ \times G_{2, 4}^{3, 1} [α β h (\frac{max (x \frac{2^{- {\bar{R}}_{e}} p_{a, r} N_{0, f}}{p_{a, f} N_{0, r}} + \frac{N_{0, f} (2^{- {\bar{R}}_{e}} - 1)}{p_{a, f}}, \frac{N_{0, f} (2^{R_{b}} - 1)}{p_{a, f} p_{a}})}{μ}) | \begin{matrix} 1, ξ^{2} + 1 \\ ξ^{2}, α, β, 0 \end{matrix}] d x \\ = & \frac{ξ^{2}}{Γ (α) Γ (β)} G_{2, 4}^{3, 1} [α β h (\frac{N_{0, f} (2^{R_{b}} - 1)}{p_{a, f} p_{a}}) | \begin{matrix} 1, ξ^{2} + 1 \\ ξ^{2}, α, β, 0 \end{matrix}] \\ \times (exp (- \frac{max (\frac{N_{0, r} (2^{R_{b}} - 1)}{p_{a, r}}, τ)}{λ_{rf}}) - exp (- \frac{\frac{N_{0, r} (2^{R_{b} + {\bar{R}}_{e}} - 1)}{p_{a, r}}}{λ_{rf}})) \\ + \int_{max (\frac{N_{0, r} (2^{R_{b} + {\bar{R}}_{e}} - 1)}{p_{a, r}}, τ)}^{\infty} G_{2, 4}^{3, 1} [α β h (\frac{x \frac{2^{- {\bar{R}}_{e}} p_{a, r} N_{0, f}}{p_{a, f} N_{0, r}} + \frac{N_{0, f} (2^{- {\bar{R}}_{e}} - 1)}{p_{a, f}}}{μ}) | \begin{matrix} 1, ξ^{2} + 1 \\ ξ^{2}, α, β, 0 \end{matrix}] \\ \times \frac{ξ^{2}}{Γ (α) Γ (β)} \frac{1}{λ_{rf}} exp (- \frac{x}{λ_{rf}}) d x \\ \frac{ξ^{2}}{Γ (α) Γ (β)} G_{2, 4}^{3, 1} [α β h (\frac{N_{0, f} (2^{R_{b}} - 1)}{p_{a, f} p_{a}}) | \begin{matrix} 1, ξ^{2} + 1 \\ ξ^{2}, α, β, 0 \end{matrix}] \\ \times (exp (- \frac{max (\frac{N_{0, r} (2^{R_{b}} - 1)}{p_{a, r}}, τ)}{λ_{rf}}) - exp (- \frac{\frac{N_{0, r} (2^{R_{b} + {\bar{R}}_{e}} - 1)}{p_{a, r}}}{λ_{rf}})) \\ + \frac{λ_{rf} ξ^{2}}{Γ (α) Γ (β)} exp (- \frac{1}{λ_{rf}} max (\frac{N_{0, r} (2^{R_{b} + {\bar{R}}_{e}} - 1)}{p_{a, r}}, τ)) \\ \times G_{4, 3}^{3, 2} [\frac{2^{- {\bar{R}}_{e}} α β h λ_{rf} p_{a, r} N_{0, f}}{μ p_{a, f} N_{0, r}} | \begin{matrix} 1, 0, ξ^{2} + 1 \\ ξ^{2}, α, β, 0 \end{matrix}] . \end{array}

For I₂, it can be derived as

\begin{array}{l} I_{2} & = & (1 - G_{2, 4}^{3, 1} [\frac{α β h N_{0, f} (2^{R_{b}} - 1)}{μ p_{a, f}} | \begin{matrix} 1, ξ^{2} + 1 \\ ξ^{2}, α, β, 0 \end{matrix}]) \\ \times (1 - exp (- \frac{max (\frac{N_{0, r} (2^{R_{b}} - 1)}{p_{a, r}}, τ)}{λ_{rf}})) . \end{array}

The RF link is selected for the secure transmission when either of the following cases is satisfied:

The conditions γ₁ ≥ γ_T, $g_{rf} \geq max (\frac{N_{0, r} (2^{R_{b}} - 1)}{p_{a, r}}, τ)$ , and R₁ < (R_s − R̄_e) indicate that both the FSO and RF links can preserve privacy and the secrecy performance of the RF link is better than the FSO link;
The conditions γ₁ < γ_T and $g_{rf} \geq max (\frac{N_{0, r} (2^{R_{b}} - 1)}{p_{a, r}}, τ)$ indicate that only the FSO link can preserve privacy and RF link experiences secrecy outage.

Therefore, Alice transmits through the RF link with probability

\begin{array}{l} P_{rf}^{s} & = & Pr (γ_{1} \geq γ_{T}, g_{rf} \geq max (\frac{N_{0, r} (2^{R_{b}} - 1)}{p_{a, r}}, τ), R_{1} < (R_{s} - {\bar{R}}_{e})) \\ + Pr (γ_{1} < γ_{T}, g_{rf} \geq max (\frac{N_{0, r} (2^{R_{b}} - 1)}{p_{a, r}}, τ)) \\ = & \underset{I_{3}}{\underset{︸}{Pr (\frac{N_{0, f} (2^{R_{b}} - 1)}{p_{a, f} p_{a}} \leq h_{fso} < \frac{g_{rf} 2^{- {\bar{R}}_{e}} p_{a, r} N_{0, f}}{p_{a, f} N_{0, r}} + \frac{N_{0, f} (2^{- {\bar{R}}_{e}} - 1)}{p_{a, f}}, g_{rf} \geq max (\frac{N_{0, r} (2^{{\bar{R}}_{b}} - 1)}{p_{a, r}}, τ))}} \\ + \underset{I_{4}}{\underset{︸}{Pr (h_{fso} < \frac{N_{0, f} (2^{R_{b}} - 1)}{p_{a, f} p_{a}}, g_{rf} \geq max (\frac{N_{0, r} (2^{R_{b}} - 1)}{p_{a, r}}, τ))}} . \end{array}

For I₃, it is derived as

\begin{array}{l} I_{3} & \times (1 - exp (- \frac{max (\frac{N_{0, r} (2^{R_{b}} - 1)}{p_{a, r}}, τ)}{λ_{rf}})) \\ = & \frac{ξ^{2}}{Γ (α) Γ (β)} G_{2, 4}^{3, 1} [α β h (\frac{N_{0, f} (2^{R_{b}} - 1)}{p_{a, f} p_{a}}) | \begin{matrix} 1, ξ^{2} + 1 \\ ξ^{2}, α, β, 0 \end{matrix}] \\ \times (exp (- \frac{max (\frac{N_{0, r} (2^{R_{b}} - 1)}{p_{a, r}}, τ)}{λ_{rf}}) - exp (- \frac{\frac{N_{0, r} (2^{R_{b} + {\bar{R}}_{e}} - 1)}{p_{a, r}}}{λ_{rf}})) \\ + \frac{λ_{rf} ξ^{2}}{Γ (α) Γ (β)} exp (- \frac{1}{λ_{rf}} max (\frac{N_{0, r} (2^{R_{b} + {\bar{R}}_{e}} - 1)}{p_{a, r}}, τ)) \\ \times G_{4, 3}^{3, 2} [\frac{2^{- {\bar{R}}_{e}} α β h λ_{rf} p_{a, r} N_{0, f}}{μ p_{a, f} N_{0, r}} | \begin{matrix} 1, 0, ξ^{2} + 1 \\ ξ^{2}, α, β, 0 \end{matrix}] \\ - G_{2, 4}^{3, 1} [α β h \frac{N_{0, f} (2^{R_{b}} - 1)}{p_{a, f} p_{a}} | \begin{matrix} 1, ξ^{2} + 1 \\ ξ^{2}, α, β, 0 \end{matrix}] \\ \times exp (- \frac{max (\frac{N_{0, r} (2^{R_{b}} - 1)}{p_{a, r}}, τ)}{λ_{rf}}) \frac{ξ^{2}}{Γ (α) Γ (β)} . \end{array}

For I₄, it can be derived as

\begin{array}{l} I_{4} & = & = (G_{2, 4}^{3, 1} [\frac{α β h N_{0, f} (2^{R_{b}} - 1)}{μ p_{a, f}} | \begin{matrix} 1, ξ^{2} + 1 \\ ξ^{2}, α, β, 0 \end{matrix}]) \\ \times (exp (- \frac{max (\frac{N_{0, r} (2^{R_{b}} - 1)}{p_{a, r}}, τ)}{λ_{rf}})) . \end{array}

When Alice transmits through the FSO link, the secrecy rate is R₁. When Alice transmits through the RF link, the secrecy rate is R₂ − R̄_e. Therefore, the secrecy rate of the SRO policy is

\begin{array}{l} R_{\sec}^{s} & = & P_{fso}^{s} R_{1} + P_{rf}^{s} R_{\sec}^{rf} \\ = & I_{1} I_{2} {log}_{2} (1 + \frac{p_{a, f} h_{fso}}{N_{0, f}}) + I_{3} I_{4} ({log}_{2} (1 + \frac{p_{a, r} g_{rf}}{N_{0, r}}) \\ + λ_{e} exp (\frac{N_{0, r}}{λ_{e} p_{a, r}}) E_{i} (- \frac{N_{0, r}}{λ_{e} p_{a, f}})) . \end{array}

5. Simulation results

In this section, we will present simulation results of the proposed policies with empirical parameters through Monte-Carlo method. For the FSO link, it consists of atmospheric turbulence, path loss and pointing errors [7]. The atmospheric turbulence is modeled as a Gamma-Gamma distribution with $α = {(exp (\frac{0.49 σ_{R}^{2}}{{(1 + 1.11 σ_{R}^{\frac{12}{5}})}^{\frac{7}{6}}}) - 1)}^{- 1}$ , $β = {(exp (\frac{0.51 σ_{R}^{2}}{{(1 + 0.69 σ_{R}^{\frac{6}{5}})}^{\frac{5}{6}}}) - 1)}^{- 1}$ where $σ_{R}^{2} = 1.23 C_{n}^{2} {(\frac{2 π}{λ})}^{\frac{7}{6}} L^{\frac{11}{6}}$ is the Rytov variance, $C_{n}^{2}$ denotes the refractive-index structure parameter, λ is the wavelength, and L is the transmission distance [34–37]. In the simulation, we consider the weak (α = 10.764, β = 9.247) and strong turbulence (α = 4.022, β = 1.566) conditions. For the RF link, we adopt the Rayleigh fading. The bandwidth of the RF link is set to 20MHz. In addition, the power consumption efficiency is assumed to be 1. We also simulate the secrecy performances of the RF transmission scenario and the FSO transmission scenario as reference systems.

In Fig. 2, we plot the secrecy outage probability versus Alice’s transmit power p_a,f. In this figure, we can observe that the secrecy outage probability is a decreasing function of p_a,f. The reason is that a large value of p_a indicates that there is more power for the secure transmission and the secrecy outage probability will decrease. Where p_a,f is small, the FSO link almost cannot successfully transmit the privacy information. Under this condition, the secrecy outage probability is higher than the RF link. However, when p_a,f is high, the privacy information can be successfully transmitted with high probability for the FSO link. Since the FSO link is secure, the secrecy outage probability of the FSO link will decrease with p_a,f. Since the proposed policies make the best use of the FSO and RF links, the secrecy outage probabilities are lower than both the RF and FSO schemes. In addition, the SRO policy selects the optimal link that can lower the secrecy outage probability.

Fig. 2 The secrecy outage probability versus Alice’s transmit power p_a,f.

Download Full Size | PDF

In Fig. 3, we plot the average secrecy rate versus Alice’s transmit power p_a,f. In this figure, we can observe that the simulation results agree with as the theoretical results in (21) and (28). In addition, we can also observe that the average secrecy rate is an increasing function of p_a,f. A large value of p_a,f indicates that there is more power for the secrecy transmission and the average secrecy rate increases. Since the proposed policies make the best use of the FSO and RF links, the average secrecy rate of the proposed policies is lower than that of either the RF or FSO scheme. In addition, the SRO policy selects the optimal link that leads to the increase of the average secrecy rate.

Fig. 3 The average secrecy rate versus Alice’s transmit power p_a,f.

Download Full Size | PDF

In Fig. 4, we plot the secrecy outage probability versus the target transmission rate R_b. In this figure, we can observe that the secrecy outage probability is an increasing function of the target transmission rate R_b. When R_b is increased, it is challenging to successfully decode the privacy information and the secrecy outage probability will increase. In the proposed policies, we take advantage of both the RF and FSO links. Therefore, the secrecy outage probabilities of the proposed policies are higher than those of the RF and FSO schemes. In addition, the SRO policy selects the optimal link that lowers the secrecy outage probability.

Fig. 4 The secrecy outage probability versus the target transmission rate R_b.

Download Full Size | PDF

In Fig. 5, we plot the average secrecy rate versus the target transmission rate R_b. In this figure, we can observe that the average secrecy rate is a decreasing function of the target transmission rate R_b. A small value of R_b indicates there are more secure transmission opportunities and the average secure rate will increase when R_b is decreased. In the proposed policies, we take advantage of both the RF and FSO links. Therefore, the average secrecy rates of the proposed policies are higher than the RF and FSO schemes. In addition, the SRO policy selects the optimal link that can achieve higher average secrecy rate.

Fig. 5 The average secrecy rate versus the target transmission rate R_b.

Download Full Size | PDF

6. Conclusion

In this paper, we proposed a secure transmission scheme to protect the privacy information in a hybrid RF/FSO network. In the proposed scheme, we made the best use of both the RF/FSO links to securely transmit the privacy information and proposed two secure transmission policies: the FDS policy and the SRO policy. In the FDS policy, we assign high priority for the FSO link that allows Alice to transmit the privacy information through the FSO link when the FSO link is reliable. When the FSO link cannot provide successful transmission, Alice will consider the secure RF transmission. In the SRO policy, Alice optimally selects the FSO link or RF link according to the secrecy rates of both the FSO and RF links in each time slot. For both the FDS and SRO policies, we analyzed the secrecy performances and derived the closed-form expressions of the average secrecy rate. Numerical results are demonstrated to prove the performance superiority of the proposed policies in terms of the secrecy performance.

References

1. M. Alzenad, M. Z. Shakir, H. Yanikomeroglu, and M.-S. Alouini, “Optical wireless: The story so far,” IEEE Commun. Mag. 36(12), 72–74 (1988).

2. B. Epple and H. Henniger, “Discussion on design aspects for free-space optical communication terminals,” IEEE Commun. Mag. 42(10), 62–69 (2007). [CrossRef]

3. H. Dahrouj, A. Douik, F. Rayal, T. Y. Al-Naffouri, and M.-S. Alouini, “Cost-effective hybrid RF/FSO backhaul solution for next generation wireless systems,” IEEE Wirel. Commun. 22(5), 98–104 (2015). [CrossRef]

4. A. Douik, H. Dahrouj, T. Y. Al-Naffouri, and M.-S. Alouini, “Hybrid radio/free-space optical design for next generation backhaul systems,” IEEE Trans. Commun. 64(6), 2563–2577 (2016). [CrossRef]

5. M. Usman, H. Yang, and M.-S. Alouini, “Practical switching-based hybrid FSO/RF transmission and its performance analysis,” IEEE Photonics J. 6(5), 1–14 (2014). [CrossRef]

6. Y. Liang, H. O. Mazen, and X. Gao, “Performance of mixed RF/FSO with variable gain over generalized atmospheric turbulence channels,” IEEE J. Sel. Areas Commun. , 33(9), 1913–1924 (2015). [CrossRef]

7. T. D. Goran, I. P. Milica, M. C. Aleksandra, and G. K. Karagiannidis, “Mixed RF/FSO relaying with outdated channel state information,” IEEE J. Sel. Areas Commun. , 33(9), 1935–1948 (2015). [CrossRef]

8. T. Rakia, H. Yang, M.-S. Alouini, and F. Gebali, “Outage analysis of practical FSO/RF hybrid system with adaptive combining,” IEEE Commun. Lett. , 19(8), 1366–1369 (2015). [CrossRef]

9. L. Kong, W. Xu, L. Hanzo, H. Zhang, and C. Zhao, “Performance of a free-space-optical relay-assisted hybrid RF/FSO system in generalized M-distributed channels,” IEEE Photonics J. 7(5), 1–20 (2015). [CrossRef]

10. A. D. Wyner, “The wire-tap channel, ” Bell Syst. Tech. J. , 54(8), 1335–1387 (1975). [CrossRef]

11. D. Wang, P. Ren, J. Cheng, and Y. Wang, “Achieving full secrecy rate with energy-efficient transmission control,” IEEE Trans. Commun. 65(12), 5386–5400 (2017). [CrossRef]

12. H. Liu, K. J. Kim, T. A. Tsiftsis, K. S. Kwak, and H. V. Poor, “Secrecy performance of finite-sized cooperative full-duplex relay systems with unreliable backhauls,” IEEE Trans. Signal Process. 65(23), 6185–6200 (2017). [CrossRef]

13. X. Tang, Y. Cai, Y. Huang, T. Q. Duong, W. Yang, and W. Yang, “Secrecy outage analysis of buffer-aided cooperative MIMO relaying systems,” IEEE Trans. Veh. Tech. 67(3), 2035–2048 (2018).

14. L. Fan, X. Lei, N. Yang, T. Q. Duong, and G. K. Karagiannidis, “Secrecy cooperative networks with outdated relay selection over correlated fading channels,” IEEE Trans. Veh. Tech. 66(8), 7599–7603 (2017). [CrossRef]

15. T. Mekkawy, R. Yao, T. A. Tsiftsis, F. Xu, and Y. Lu, “Joint beamforming alignment with suboptimal power allocation for a two way untrusted relay network,” IEEE Trans. Inf. Forensics Secur. 13(10), 2464–2474 (2018).

16. A. Mabrouk, A. E. Shafie, K. Tourki, and N. Al-Dhahir, “Adaptive secure transmission for RF-EH untrusted relaying with alien eavesdropping,” IEEE Commun. Lett. 21(11), 2516–2519 (2017). [CrossRef]

17. D. Wang, P. Ren, and J. Cheng, “Cooperative secure communication in two-hop buffer-aided networks,” IEEE Trans. Commun. 66(3), 972–2985 (2018). [CrossRef]

18. T. M. Hoang, T. Q. Duong, H. D. Tuan, and H. V. Poor, “Secure massive MIMO relaying systems in a poisson field of eavesdroppers,” IEEE Trans. Commun. 675(11), 4857–24870 (2017). [CrossRef]

19. J. Choi, “Physical layer security for channel-aware random access with opportunistic jammings,” IEEE Trans. Inf. Forensics Secur. 12(11), 2699–2711 (2017). [CrossRef]

20. L. Hu, H. Wen, B. Wu, J. Tang, F. Pan, and R. Liao, “Cooperative-jamming-aided secrecy enhancement in wireless networks with passive eavesdroppers,” IEEE Trans. Veh. Tech. 167(7), 2108–2117 (2018). [CrossRef]

21. H. Xing, K. Wong, A. Nallanathan, and R. Zhang, “Wireless powered cooperative jamming for secrecy multi-AF relaying networks,” IEEE Trans. Wireless Commun. 15(12), 7971–7984 (2016). [CrossRef]

22. D. Wang, P. Ren, Q. Du, L. Sun, and Y. Wang, “Security provisioning for MISO vehicular relay networks via cooperative jamming and signal superposition,” IEEE Trans. Veh. Tech. 66(12), 10732–10747 (2017). [CrossRef]

23. R. Zhao, Y. Huang, W. Wang, and V. K. N. Lau, “Ergodic achievable secrecy rate of multiple-antenna relay systems with cooperative jamming,” IEEE Trans. Wireless Commun. 15(4), 26537–2551 (2016). [CrossRef]

24. A. H. A. El-Malek, A. M. Salhab, S. A. Zummo, and M.-S. Alouini, “Security-reliability trade-off analysis for multiuser SIMO mixed RF/FSO relay networks with opportunistic user scheduling,” IEEE Trans. Wireless Commun. 15(9), 5904–5918 (2016). [CrossRef]

25. A. H. A. El-Malek, A. M. Salhab, S. A. Zummo, and M.-S. Alouini, “Effect of RF interference on the security-reliability tradeoff analysis of multiuser mixed RF/FSO relay networks with power allocation,” J. Lightwave Technol. 35(9), 1490–1505 (2017). [CrossRef]

26. I. S. Ansari, M.-S. Alouini, and J. Cheng, “Ergodic capacity analysis of free-space optical links with nonzero boresight pointing errors, ” IEEE Trans. Wireless Commun. , 14(8), 4248–4264 (2015). [CrossRef]

27. E. Zedini, H. Soury, and M.-S. Alouini, “On the performance analysis of dual-hop mixed FSO/RF systems,” IEEE Trans. Wireless Commun. 15(5), 3679–3689 (2016). [CrossRef]

28. A. Farid and S. Hranilovic, “Outage capacity optimization for free-space optical links with pointing errors,” J. Lightw. Technol. , 25(7), 1702–1710 (2007). [CrossRef]

29. D. Zhai, R. Zhang, L. Cai, B Li, and Y. Jiang, “Energy-efficient user scheduling and power allocation for NOMA based wireless networks with massive IoT devices,” IEEE Int. Things , 5(3), 1857–1868 (2018). [CrossRef]

30. I. S. Gradshteyn and I. M. Ryzhik, Table of Integrals, Series and Products, 7th ed., (Academic, 2007).

31. H. Lei, Z. Dai, I. Shaflque, K. -H. Park, G. Pan, and M.-S. Alouini, “On secrecy performance of mixed RF-FSO systems,” IEEE Photonics J. 9(4), 1–15 (2017). [CrossRef]

32. H. Lei, H. Luo, K. -H. Park, Z. Ren, G. Pan, and M.-S. Alouini, “Secrecy outage analysis of mixed RF-FSO systems with channel imperfection,” IEEE Photonics J. 10(3), 1–14 (2018). [CrossRef]

33. Y.-S. Shiu, S. Y. Chang, H.-C. Wu, S. C.-H. Huang, and H.-H. Chen, “Physical layer security in wireless networks: A tutorial,” IEEE Wireless Commun. , 18(2), 66–74 (2011). [CrossRef]

34. G. Marsaglia and W. W. Tsang, “A simple method for generating gamma variables,” ACM T. Math. Software (TOMS) , 26(3), 363–372 (2000). [CrossRef]

35. D. Kundu and R. D. Gupta, “A convenient way of generating gamma random variables using generalized exponential distribution,” Comput. Stat. Data Anal. , 51(6), 2796–72802 (2007). [CrossRef]

36. D. A. Luong, T. C. Thang, and A. T. Pham, “FEffect of avalanche photodiode and thermal noises on the performance of binary phase-shift keying-subcarrier-intensity modulation/free-space optical systems over turbulence channels,” IET Commun. , 7(8), 738–744 (2013). [CrossRef]

37. B. He and R. Schober, “Bit-interleaved coded modulation for hybrid RF/FSO systems,” IEEE Trans. Commun. , 62(2), 713–725 (2014).

Privacy preserving with adaptive link selection for hybrid radio-frequency and free space optical networks

Abstract

1. Introduction

2. System model

3. Hybrid RF/FSO secure transmission

3.1. Secure transmissions for RF and FSO links

3.2. Secrecy transmission policy

4. Secrecy performances

4.1. FDS policy

4.2. SRO policy

5. Simulation results

6. Conclusion

References

Cited By

Figures (5)

Equations (28)

Optics Express