Secure transmission for mixed FSO-RF relay networks with physical-layer key encryption and wiretap coding

Dawei Wang; Pinyi Ren; Julian Cheng; Qinghe Du; Yichen Wang; Li Sun

doi:10.1364/OE.25.010078

1. Introduction

Free space optical (FSO) communication is considered as a promising technique for developing the next generation networks due to its desirable features of license free operation, flexibility, rapid deployment time, low-cost and so on [1]. FSO communication has been proposed in front-haul of the cloud radio access network, building communications, emergency situation recovery, military applications [2], and it is regarded as a complementary technology for the radio frequency (RF) communication. However, FSO communication depends on the line-of-sight channel quality of the FSO link, which limits its applications. To overcome this limitation, the mixed FSO-RF relay scheme, which utilizes RF communication to replace FSO for the scenarios when FSO links cannot be utilized, has attracted much recent research attention [3,4].

In the FSO-RF relay network, the messages are transmitted in two-hop (FSO and RF). The performance superiority of the FSO-RF relay network in terms of outage probability, bit-error rate, ergodic capacity, has been established in [5–9]. In addition, the user schedule [10, 11], relay selection method [12], and information combining technique [13] are exploited to further improve the performance of the FSO-RF relay network. In the above works, the authors typically assumed that the FSO link is secure. However, when the main lobe of the laser beam is considerably wider than the receiver aperture size and/or there is a pointing error, the FSO-RF relay network still faces the eavesdropping threat from one or more malicious eavesdroppers. Moreover, due to the broadcast nature of the wireless media, the RF link can also be threatened by malicious eavesdropping. Traditionally, the upper-layer cryptographic algorithms, which assume limited computational capability at the eavesdropper, are sufficient to protect the confidential messages. Due to the complexity in key generation and allocation as well as the current advanced hardware at the eavesdropper, these cryptographic algorithms cannot satisfy secure requirements in future wireless networks. Besides these upper-layer algorithms, physical-layer key generation and encryption method (which exploits the channel reciprocity to generate key packets [14]) and physical-layer wiretap coding (which exploits the channel quality difference between the channels from the transmitter to the receiver and from the transmitter to the eavesdropper to protect the confidential messages [15, 16]) can be utilized to protect the confidential messages in the FSO-RF relay network.

The information security in the FSO-RF relay network was first studied in [17] where the physical-layer security method of cooperative jamming was utilized to secure the RF link. Also, the reliability and security tradeoff of the proposed scheme was investigated. However, the FSO link in [17] was assumed to be perfectly secure and the authors did not study the security issues associated with the FSO link. For the security of the FSO link, the authors in [18] first proposed a physical-layer key generation and sharing scheme to encrypt the confidential messages. But the pointing error that will affect the key generation rate was not considered in [18]. Besides the physical-layer key encryption scheme, the authors in [19] investigated the secrecy performance with a physical-layer security method. Since the FSO requires line-of-sight transmission, those physical layer security methods designed for RF communication cannot be utilized to protect the confidential messages. For example, the eavesdropper is a passive user and the cooperative jammer cannot find the eavesdropper to jam. Therefore, in this paper, we propose a new secure transmission scheme by utilizing the physical-layer key encryption and wiretap coding to protect the confidential messages for a mixed FSO-RF relay network where both the FSO and RF links are protected. To the best of the authors’ knowledge, this is the first work that considers secure transmission for both FSO and RF links.

In this paper, we propose a secure transmission scheme to protect an FSO-RF relay network against a malicious eavesdropper. In the proposed scheme, the physical-layer key encryption method and the physical-layer wiretap coding are utilized to protect both FSO and RF links. Specifically, for the FSO link, we utilize the channel reciprocity of the FSO link to generate key packets and these key packets will encrypt the confidential messages in the following transmission. By taking into account of the pointing error, the key generation rate can be obtained from our analysis. For the RF link, the physical-layer wiretap coding is adopted to protect the confidential messages. In the proposed scheme, we analyze the connection outage probability (COP) and the secrecy outage probability (SOP), and optimally design the target transmission rate and the secrecy rate under the constraint of the maximum permitted COP such that the average secrecy rate is maximized. Since we take advantages of both the FSO and RF links, the confidential messages can be efficiently and securely transmitted. Numerical results are presented to demonstrate the performance superiority of the proposed scheme 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 scheme. In Section 3, we demonstrate the key generation process and study the key generation rate. We interpret the information transmission process and formulate the optimization problem in Section 4. Extensive simulation results are presented in Section 5, and Section 6 concludes the paper.

2. System model

We consider a mixed FSO-RF network shown in Fig. 1 in which Alice wants to securely transmit the confidential messages to Bob, and her transmission is assisted by a relay node, which is called Relay. There is no direct link between Alice and Bob, and Relay adopts the decode-and-forward (DF) relay protocol to forward the confidential messages. Alice is equipped with a single photon-aperture transmitter; Relay is equipped with a single photon-aperture receiver from one side and a single antenna transmitter from the other side; Bob is equipped with a single antenna receiver. Therefore, Alice will transmit her confidential messages to Relay through the FSO link and Relay will forward these messages to Bob over the RF link. In addition, there is an eavesdropper (Eve) who can eavesdrop Alice’s confidential messages. For the FSO link, when there is a broad laser beam at Relay or when there is pointing error, the FSO link can be eavesdropped. For the RF link, due to the broadcast nature of the wireless media, Eve can receive the confidential messages. Thus, both the FSO and RF links require to be protected. This communication scenario can capture, for example, an unmanned aerial vehicle (UAV) based cloud radio access network where Alice contains the baseband units (BBUs) that are being housed on a UAV plane, Relay is the remote radio head (RRH) and the FSO fronthaul link will provide reliable and secure communication between Alice and Relay.

Fig. 1 The mixed FSO-RF relay system model.

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The upper layer data packets are divided into equal frame. In each frame, a packet will be transmitted from Alice to Bob assisted by Relay. The channel variables of Alice → Relay, Alice → Eve, Relay → Bob and Relay → Eve are denoted as h_ar, h_ae, h_rb and h_re, respectively. h_ar denotes the FSO link that consists of path loss, atmospheric turbulence, and pointing errors [5], i.e., $h_{ar} = h_{ar}^{l} h_{ar}^{a} h_{ar}^{e}$ where $h_{ar}^{l}$ denotes the path loss; $h_{ar}^{a}$ denotes the atmospheric turbulence attenuation modeled by a Gamma-Gamma distribution; $h_{ar}^{e}$ denotes the pointing error. Utilizing the Beer-Lambert law, $h_{ar}^{l}$ can be derived as [20]

h_{ar}^{l} = exp (- λ L)

where λ is the atmospheric attenuation coefficient and L is the distance between Alice and Relay. Then, by applying the coherent modulation technique and the pointing error model in [21], the probability density function (PDF) of h_ar is given by [5]

f_{h_{ar}} (x) = \frac{ξ^{2} α β}{A_{0} h_{ar}^{l} Γ (α) Γ (β)} G_{1, 3}^{3, 0} (\frac{α β}{A_{0} h_{ar}^{l}} x | \begin{matrix} ξ^{2} \\ ξ^{2} - 1, α - 1, β - 1 \end{matrix})

where

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

is the Meijer’s G-function [22]; α and β are atmospheric turbulence parameters [20]; A₀ and ξ represent the parameters relating the pointing error and they are defined in [21]. For the RF links, we assume that each frame experiences stationary, ergodic, independent, and flat Rayleigh fading. Therefore, the channel power gains g_rb = |h_rb|² and g_re = |h_re|² follow the exponential distribution with parameters

σ_{rb}^{2}

and

σ_{re}^{2}

, respectively. Moreover, we assume that all noise variables in the RF link are zero-mean circularly-symmetric Gaussian random variables with variance N₀, and all noise in the FOS link are shot-noise that can be modeled as additive white Gaussian noise (AWGN) with variance N_f = 2qRp_loΔf, where q is electronic charge, R is the responsibility, p_lo is the local oscillator power, and Δf is the noise equivalent bandwidth of the photoelectric [25,26]. The transmit powers of Alice and Relay are denoted as p_a and p_r, respectively.

In the proposed scheme, each frame, denoted as T, is equally divided into two slots as T₁ and T₂ with T₁ + T₂ = T shown in Fig. 2. In the first time slot, Alice and Relay will generate key packets to encrypt the confidential messages. In the second time slot, Alice first transmits her confidential messages to Relay encrypted by the key encryption, and then Relay will forward these confidential messages to Bob by utilizing the wiretap coding. For the wiretap coding, the target transmission rate R_b and secrecy rate R_s are selected, and the difference between R_b and R_s, denoted as R_e = R_b − R_s, is the information redundancy against eavesdropping. In the following, we will describe in details the key generation and information transmission processes.

Fig. 2 Two time slots required to transmit one data packet from Alice to Bob via Relay.

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3. Key generation

In this section, we first interpret the key generation process. Then, we will investigate the key generation rate.

3.1. Key generation process

The key generation process is divided into two stages. During the first stage with duration $\frac{T_{1}}{2}$ , Alice sends a known sequence S_A with $\frac{T_{1}}{2}$ symbols to Relay.. We select the integer that is nearest to $\frac{T_{1}}{2}$ and less than $\frac{T_{1}}{2}$ . The received signal at Relay is

Y_{R} = \sqrt{p_{a}} h_{ar} S_{A} + n_{R}

where n_R is the noise sequence at Relay with each element being a shot-noise variable [25, 26]. In the second stage, Relay transmits a known sequence S_R with

\frac{T_{1}}{2}

symbols to Alice. The received signal at Alice is

Y_{A} = \sqrt{p_{r}} h_{ar} S_{R} + n_{A}

where n_A is the noise sequence at Alice with each element being a shot-noise variable [25, 26]. From Eqs. (3) and (4), Alice and Relay can estimate the FSO channel h_ar as [18]

Y_{R} = \sqrt{p_{a}} h_{ar} S_{A} + n_{R} \to {\tilde{h}}_{ar, r} = \frac{S_{A}^{T}}{\sqrt{p_{a}} | S_{A} |} Y_{R} = h_{ar} + N_{R}

and

Y_{A} = \sqrt{p_{r}} h_{ar} S_{R} + n_{A} \to {\tilde{h}}_{ar, a} = \frac{S_{R}^{T}}{\sqrt{p_{a}} | S_{R} |} Y_{A} = h_{ar} + N_{A}

where

N_{R} = \frac{S_{A}^{T}}{\sqrt{p_{a}} | S_{A} |} n_{R}

with

| S_{A} | = \sqrt{\frac{p_{a} T_{1}}{2}}

;

N_{A} = \frac{S_{R}^{T}}{\sqrt{p_{r}} | S_{R} |} n_{A}

with

| S_{R} | = \sqrt{\frac{p_{r} T_{1}}{2}}

. In addition, Eve also receives S_R and S_A that are given by

Y_{E 1} = \sqrt{p_{a}} h_{ae} S_{A} + n_{E 1}

and

Y_{E 2} = \sqrt{p_{r}} h_{re} S_{R} + n_{E 2}

where n_E1 and n_E2 are, respectively, the noise variables at the first and second stages. Since h_ar is independent of h_ae and h_re, Y_E1 and Y_E2 are independent of h̃_ar,r and h̃_ar,a. Therefore, the generated key packets cannot be decoded by Eve. After the channel estimation, Alice and Relay will agree with a common random key based on their estimation of the channel gain by employing Slepian-Wolf source coding [14].

3.2. Key generation rate

According to Eq. (5), the PDF of h̃_ar is derived as

f_{{\tilde{h}}_{ar}} (x) = f_{h_{ar}} (x) * f_{N_{R}} (x)

where “ * “ denotes the convolution operation. The PDF of N_R is

f_{N_{R}} (x) = \frac{1}{\sqrt{2 π} σ_{N_{R}}} exp (- \frac{x^{2}}{2 σ_{N_{R}}^{2}})

with

σ_{N_{R}}^{2} = \frac{N_{0}}{p_{a}}

. Substituting Eq. (2) into Eq. (9), f_{h̃_ar} (x) is derived as

\begin{array}{l} f_{{\tilde{h}}_{ar}} (x) & = \frac{ξ^{2} α β}{A_{0} h_{ar}^{l} Γ (α) Γ (β)} G_{1, 3}^{3, 0} (\frac{α β}{A_{0} h_{ar}^{l}} x | \begin{matrix} ξ^{2} \\ ξ^{2} - 1, α - 1, β - 1 \end{matrix}) \\ * \frac{1}{\sqrt{2 π} σ_{N_{R}}} exp (- \frac{x^{2}}{2 σ_{N_{R}}^{2}}) \\ = \frac{ξ^{2} α β}{\sqrt{2 π} σ_{N_{R}} A_{0} h_{ar}^{l} Γ (α) Γ (β)} \int_{0}^{\infty} G_{1, 3}^{3, 0} (\frac{α β}{A_{0} h_{ar}^{l}} t | \begin{matrix} ξ^{2} \\ ξ^{2} - 1, α - 1, β - 1 \end{matrix}) \\ \times exp (- \frac{{(x - t)}^{2}}{2 σ_{N_{R}}^{2}}) d t \\ = \frac{ξ^{2} α β}{A_{0} h_{sr}^{l} Γ (α) Γ (β)} \int_{0}^{\infty} \int_{0}^{\infty} \frac{Γ (ξ^{2} - 1 - s) Γ (α - 1 - s) Γ (β - 1 - s)}{\sqrt{2 π} i Γ (ξ^{2} - s)} \\ \times {(\frac{α β}{A_{0} h_{sr}^{l}} t)}^{s} exp (- \frac{x^{2} - 2 x t + t^{2}}{2 σ_{N_{a}}^{2}}) d s d t \\ \overset{(a)}{=} \frac{ξ^{2} α β}{A_{0} h_{sr}^{l} Γ (α) Γ (β)} \int_{0}^{\infty} \frac{Γ (ξ^{2} - 1 - s) Γ (α - 1 - s) Γ (β - 1 - s)}{\sqrt{2 π} i Γ (ξ^{2} - s)} \\ \times {(\frac{α β}{A_{0} h_{sr}^{l}})}^{s} {(\frac{1}{σ_{N_{a}}^{2}})}^{- \frac{s + 1}{2}} Γ (s + 1) exp (\frac{x^{2}}{4 σ_{N_{a}}^{2}}) D_{- (s + 1)} (- \frac{x}{σ_{N_{a}}}) d s \end{array}

where (a) is derived according to Eq. (3.462.1) in [29] and

\begin{array}{l} D_{- (s + 1)} (- \frac{x}{σ_{N_{a}}}) = & 2^{- \frac{s + 1}{2}} exp (- \frac{x^{2}}{4 σ_{N_{a}}^{2}}) (\frac{\sqrt{π}}{Γ (\frac{s + 2}{2})} Φ (\frac{s + 1}{2}, \frac{1}{2}; \frac{x^{2}}{2 σ_{N_{a}}^{2}}) \\ + \frac{\sqrt{2 π} x}{σ_{N_{a}} Γ (\frac{s + 1}{2})} Φ (\frac{s + 2}{2}, \frac{3}{2}; \frac{x^{2}}{2 σ_{N_{a}}^{2}})) \end{array}

which is defined in Eq. (9.240) in [29] and Φ (·, ·; ·) is the confluent hypergeometric function [29]. Therefore, f_{h̃_ar} (x) is derived as

\begin{array}{l} f_{{\tilde{h}}_{{\tilde{h}}_{ar}}} (x) & = \frac{σ_{N_{a}} ξ^{2} α β}{\sqrt{2} A_{0} h_{sr}^{l} Γ (α) Γ (β)} \int_{0}^{\infty} G_{1, 3}^{3, 0} (\frac{α β}{A_{0} h_{sr}^{l}} t | \begin{matrix} ξ^{2} \\ ξ^{2} - 1, α - 1, β - 1 \end{matrix}) \\ \times (\frac{\sqrt{π}}{Γ (\frac{s + 2}{2})} Φ (\frac{s + 1}{2}, \frac{1}{2}; \frac{x^{2}}{2 σ_{N_{a}}^{2}}) + \frac{\sqrt{2 π} x}{σ_{N_{a}} Γ (\frac{s + 1}{2})} Φ (\frac{s + 2}{2}, \frac{3}{2}; \frac{x^{2}}{2 σ_{N_{a}}^{2}})) d s . \end{array}

According to the common channel state information between Alice and Relay, the key generation rate is derived as [18]

\begin{array}{l} R_{k} & = \frac{T_{1}}{T} I ({\tilde{h}}_{ar}, {\tilde{h}}_{ra}) \\ = \frac{T_{1}}{T} (H ({\tilde{h}}_{ar}) - H ({\tilde{h}}_{ra} | {\tilde{h}}_{ra})) \\ = \frac{T_{1}}{T} (H ({\tilde{h}}_{ar}) - H ({\tilde{h}}_{ra} - \frac{S_{R}^{T}}{| S_{R} |} n_{A} + \frac{S_{A}^{T}}{| S_{A} |} n_{R} | {\tilde{h}}_{ra})) . \end{array}

Since h̃_ra, S_R, S_A, n_R and n_A are independent of each other, the key generation rate is derived as

\begin{array}{l} R_{k} & = \frac{T_{1}}{T} (H ({\tilde{h}}_{ar}) - H ({\tilde{h}}_{ra} | {\tilde{h}}_{ra}) - H (- \frac{S_{R}^{T}}{| S_{R} |} n_{A} | {\tilde{h}}_{ra}) - H (\frac{S_{A}^{T}}{| S_{A} |} n_{R} | {\tilde{h}}_{ra})) \\ = \frac{T_{1}}{T} (H ({\tilde{h}}_{ar}) - H (\frac{S_{R}^{T}}{| S_{R} |} n_{A}) - H (\frac{S_{A}^{T}}{| S_{A} |} n_{R})) \\ = \frac{T_{1}}{T} (H ({\tilde{h}}_{ar}) - H (\frac{S_{R}^{T}}{| S_{R} |} n_{A} + \frac{S_{A}^{T}}{| S_{A} |} n_{R})) \end{array}

where H (h̃_ar) is derived as

H ({\tilde{h}}_{ar}) = \int f_{{\tilde{h}}_{ar}} (x) {log}_{2} f_{{\tilde{h}}_{ar}} (x) d x

and

H (\frac{S_{R}^{T}}{| S_{R} |} n_{A} + \frac{S_{A}^{T}}{| S_{A} |} n_{R}) = \frac{1}{2} {log}_{2} (2 π e σ_{N_{A}}^{2} N_{f} + 2 π e σ_{N_{R}}^{2} N_{f})

with

σ_{N_{A}}^{2} = \frac{N_{0}}{p_{r}}

. Therefore, substituting Eqs. (13), (16) and (17) into Eq. (15), the key generation rate is obtained.

4. Secure transmission

After the generation of the key packets, Alice will securely transmit the confidential messages to Bob over two phases. In the first phase with duration $\frac{T_{2}}{2}$ , Alice transmits the confidential messages to Relay encrypted by the key packets. Then, in the second phase with duration $\frac{T_{2}}{2}$ , Relay will forward the confidential messages to Bob protected by the physical-layer wiretap coding.

4.1. Information transmission

In the first phase, the confidential messages are encrypted by the key packets through the XOR operation. In this paper, we adopt the coherent optical receiver to process the received signal and, the information rate at Relay is derived as [23, 24, 26]

R_{ar} \approx \frac{T_{2}}{2 T} {log}_{2} (1 + \frac{p_{a} RA h_{ar}}{q Δ f})

where A denotes the detector area. Since Alice utilizes the key packets to encrypt the confidential messages, the following condition must satisfy R_ar ≤ R_k. Since Eve does not know the key packets, she cannot decode the confidential message. Therefore, the information rate R_ar is the secrecy rate.

In the second phase, Relay will decode the encrypted message and re-encode the confidential messages through physical-layer security wiretap coding. Then, the information rate at Bob is given by

R_{rb} = \frac{T_{2}}{2 T} {log}_{2} (1 + \frac{p_{r} g_{rb}}{N_{0}}) .

In addition, Eve also eavesdrops the confidential messages with rate

R_{re} = \frac{T_{2}}{2 T} {log}_{2} (1 + \frac{p_{r} g_{re}}{N_{0}}) .

In the first phase, the confidential messages are encrypted by the key packets and the secrecy rate is R_ar. In the second phase, according to the wiretap coding, the secrecy rate is

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

where (a)⁺ = max (0, a). According to Eqs. (18), (19) and (20), the secrecy rate of the proposed scheme is derived as

R_{\sec} = min (R_{ar}, {(R_{rb} - R_{re})}^{+}) .

Since the channel state information (CSI) associated with Eve is always difficult to acquire, in the following, we will analyze the outage performance and optimal the target transmission rate and secrecy rate.

Remark: For the proposed scheme, since the confidential messages are encrypted by the key packets in the FSO link, the transmission link for the FSO link R_ar should not be larger than the key generation rate R_k. According to Eq. (22), R_sec ≤ R_k. From Eq. (15), we observe that R_k is a monotonically increasing function of T₁. Therefore, we should increase T₁ to increase the key generation rate. However, since from Eq. (21), we can observe that R_sec2 is a monotonically increasing function of T₂ and T₁ + T₂ = T; therefore, there is a trade-off between the maximum secrecy rate and the time allocation. Since R_k in Eq. (15) is too complex to analyze, it is challenging to derive the optimal time allocation, and we will study this problem in our future work.

Remark: For the proposed scheme, in this first slot, Relay will first generate key packets and consume an energy of $\frac{p_{r} T_{1}}{2}$ for transmitting the known signal sequences. during the channel estimation and key generation processes, Alice and Relay will consume some time and energy for processing the channel estimation and key generation. In the second slot, Relay first processes the decoding and re-encoding of the confidential messages and then, consumes an energy of $\frac{p_{r} T_{2}}{2}$ for relaying. This consumption of time and energy will guarantee the security of the confidential messages. In addition, for the slow fading channel scenarios, the generated key packets can be utilized for a long period of time until the channel changes.

4.2. The optimal transmission scheme

In the proposed scheme, when the transmission rate is less than R_b, the confidential messages will experience connection outage; when the eavesdropping rate is larger than R_e = R_b − R_s, the confidential messages will experience secrecy outage. In order to securely and reliably transmit the confidential messages, we first investigate the performances of COP and SOP, and then optimally design the target transmission rate and secrecy rate to maximize the average secrecy rate.

4.2.1. COP and SOP

In the first phase, the transmission will experience connection outage when R_ar < R_b. There fore, the COP for the FSO link is

\begin{array}{l} P_{cop, ar} & = & Pr (R_{ar} < R_{b}) \\ = & \frac{ξ^{2}}{Γ (α) Γ (β)} G_{2, 4}^{3, 1} (\frac{ξ^{2} α β}{ξ^{2} + 1} \sqrt{\frac{{\hat{R}}_{b}}{μ}} | \begin{matrix} 1, ξ^{2} + 1 \\ ξ^{2}, α, β, 0 \end{matrix}) \end{array}

where

{\hat{R}}_{b} = \frac{q Δ f}{p_{a} RA} (\frac{2 {TR}_{b}}{T_{2}} - 1)

and

μ = \frac{ξ^{2} (ξ^{2} + 2) A_{0}^{2} h_{l}^{2} α β}{(α + 1) (β + 1) {(ξ^{2} + 1)}^{2}}

. In the second phase, the transmission will experience connection outage when R_rb < R_b. Therefore, the COP for the RF link is

P_{cop, rb} = Pr (R_{rb} < R_{b}) = 1 - exp (- \frac{{\overset{ˇ}{R}}_{b}}{P_{r} σ_{rb}^{2}})

where

{\overset{ˇ}{R}}_{b} = \frac{N_{0}}{p_{r}} (\frac{2 {TR}_{b}}{T_{2}} - 1)

. Therefore, the COP for the proposed scheme is

P_{cop} = 1 - (1 - P_{cop, ar}) (1 - P_{cop, rb}) .

In the FSO link, since the confidential messages are encrypted by the key packets, Eve cannot decode the confidential messages. In the RF link, when the eavesdropper rate is greater than R_e, the secrecy outage will occur with probability

P_{sop} = Pr (R_{re} \geq R_{e}) = exp (- \frac{{\hat{R}}_{e}}{P_{r} σ_{re}^{2}})

where

{\hat{R}}_{e} = \frac{N_{0}}{p_{r}} (\frac{2 T (R_{b} - R_{s})}{T_{2}} - 1)

. Then, the average secrecy rate is R_s (1 − P_sop).

4.2.2. Optimal transmission design

In order to maximize the average secrecy rate, we formulate the optimization problem as

\begin{array}{l} P 1 : & max_{R_{b}, R_{s}} & R_{s} (1 - P_{sop}) \\ s . t . & P_{cop} < P_{upper}, \\ R_{s} \leq min {R_{b}, R_{ar}} \leq R_{k} \end{array}

where the first constraint is the reliability requirement; the second constraint indicates that the target secrecy rate should be less than the information rates in both the FSO and RF links.

To solve P1, we first set a target secrecy rate R_s. Then, P1 can be rewritten as

\begin{array}{l} P 2 : & min_{R_{b}} & P_{sop} \\ s . t . & P_{cop} < P_{upper}, \\ R_{s} \leq min {R_{b}, R_{ar}} \leq R_{k} . \end{array}

According to Eqs. (23) and (24), we can easily verify that P_cop,ar and P_cop,rb are monotonically increasing functions of R_b. From Eq. (25), we can show that P_cop is an increasing function of R_b. Therefore, we can acquire the optimal

R_{b}^{max}

that satisfies P_cop = P_upper. Substituting the optimal

R_{b}^{max}

into P2, this problem can be rewritten as

\begin{array}{l} P 3 : & min_{R_{s}} & R_{s} (1 - P_{sop}) \\ s . t . & R_{s} \leq min {R_{b}^{max}, R_{ar}} \leq R_{k} . \end{array}

Set F = R_s (1 − P_sop). The first-order and second-order derivatives of F with respect to R_s are derived as

{\begin{cases} \frac{d F}{d R_{s}} = 1 - (1 + \frac{R_{s}}{p_{r} σ_{re}^{2}}) exp (- \frac{R_{b}^{max} - R_{s}}{P_{r} σ_{re}^{2}}), \\ \frac{d^{2} F}{d R_{s}^{2}} = - (\frac{2 R_{s}}{p_{r} σ_{re}^{2}} + \frac{R_{s}}{p_{r}^{2} σ_{re}^{4}}) exp (- \frac{R_{b}^{max} - R_{s}}{P_{r} σ_{re}^{2}}) . \end{cases}

Since

\frac{d^{2} F}{d R_{s}^{2}} < 0

, F is convex with respect to R_s. We can solve P3 through the traditional convex optimization methods. Therefore, we can derive the optimal target transmission rate and secrecy rate.

5. Simulation results

In this section, we will simulate the proposed scheme with empirical parameters. For the FSO link, we consider the air-to-ground communication scenario over the atmospheric turbulence channel by considering the pointing error. In addition, according to the plane wave propagation in the absence of inner scale, the parameters of α and β are respectively derived as $α = {(exp (\frac{0.49 σ_{R}^{2}}{{(1 + 1.11 σ_{R}^{\frac{12}{5}})}^{\frac{7}{6}}}) - 1)}^{- 1}$ and $β = {(exp (\frac{0.51 σ_{R}^{2}}{{(1 + 0.69 σ_{R}^{\frac{6}{5}})}^{\frac{5}{6}}}) - 1)}^{- 1}$ , 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 [5, 20]. In our simulation, λ is set to 1550 nm [27, 28]; $C_{n}^{2}$ is set to $2 \times 10^{- 14} m^{- \frac{2}{3}}$ for the moderate turbulence case and $5 \times 10^{- 14} m^{- \frac{2}{3}}$ for the strong turbulence case [18, 20, 29, 30]. For the RF link, we adopt the Rayleigh fading scenario. In addition, we also simulate the average secrecy rate in [17] and the key generation rate in [18] for comparison.

In Fig. 3, we plot the key generation rate versus Alice’s transmit power p_a under different turbulence conditions. In Fig. 3, we can observe that the key generation rate is an increasing function of p_a. The reason is that when more power is allocated for the training sequence, Alice and Relay can estimate the common channel state information with high precision. Therefore, the key generation rate will increase. In addition, since the moderate turbulence has less effect on the channel estimation, the key generation rate under moderate turbulence will be larger than the key generation rate under strong turbulence condition. Moreover, we also simulate the key generation rate in [18]. Since the pointing error is not considered in [18], the key generation rate in the contrast key generation scheme is slightly larger than the proposed scheme. Furthermore, the performance trends of the proposed scheme and the comparison scheme are the same.

Fig. 3 The key generation rate of the proposed scheme is a function of Alice’s transmit power p_a.

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In Fig. 4, we plot the average secrecy rate versus Relay’s transmit power p_r under different turbulence conditions. In this figure, we can observe that the average secrecy rate is a monotonically increasing function of p_r. The reason is that a large value of p_r indicates that more power is allocated for the reliable and secure transmission. Therefore, the average secrecy rate will increase. However, since the SOP is an increasing function of p_r, the average secrecy rate will increase slowly under a large value of p_r. In addition, under the moderate turbulence condition, the key generation rate will increase, resulting in an increase of the average secrecy rate. Moreover, we also simulate the average secrecy rate in [17] for comparison. Since the comparison scheme has not considered the information security in the FSO link, its average secrecy rate is lower than the proposed scheme.

Fig. 4 The average secrecy rate of the proposed scheme is a function of Relay’s transmit power p_r.

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In Fig. 5, we plot the average secrecy rate versus the maximum permitted COP P_upper under different turbulence conditions. In this figure, we can observe that the average secrecy rate is an increasing function of P_upper. The reason is that under the constraint of strict COP requirement, the reliability requirements of both the FSO and RF links limit the increase of the average secrecy rate. On the contrary, under a large value of P_upper, the SOP will limit the increase of the average secrecy rate. Similarly, under the moderate turbulence condition, the key generation rate will increase, resulting in an increase of the average secrecy rate. Since the comparison scheme in [17] has not considered the information security in the FSO link, the average secrecy rate of the contrast scheme is lower than that of the proposed scheme.

Fig. 5 The average secrecy rate of the proposed scheme is a function of the maximum permitted COP.

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6. Conclusion

In this paper, we proposed a secure transmission scheme to protect the confidential messages in a mixed FSO-RF relay network against malicious eavesdroppers. In the proposed scheme, the physical-layer key encryption and wiretap coding techniques were utilized to protect the FSO and RF links. By taking into account of the pointing error, we derived the key generation rate. In addition, we investigated the COP and SOP performances, and optimally designed the target transmission rate and secrecy rate such that the average secrecy rate is maximized. Since we take advantages of both the FSO and RF links, the confidential messages can be efficiently and securely transmitted. Numerical results are demonstrated to prove the performance superiority of the proposed scheme in terms of the average secrecy rate.

Funding

National Natural Science Foundation of China (61431011); Key Laboratory of Wireless Sensor Network and Communication, Chinese Academy of Sciences (NO. 2015003); and the Fundamental Research Funds for the Central Universities.

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Secure transmission for mixed FSO-RF relay networks with physical-layer key encryption and wiretap coding

Abstract

1. Introduction

2. System model

3. Key generation

3.1. Key generation process

3.2. Key generation rate

4. Secure transmission

4.1. Information transmission

4.2. The optimal transmission scheme

4.2.1. COP and SOP

4.2.2. Optimal transmission design

5. Simulation results

6. Conclusion

Funding

References and links

Cited By

Figures (5)

Equations (30)

Optics Express