An Anti-Eavesdropping Interference Alignment Scheme ... - IEEE Xplore

An Anti-Eavesdropping Interference Alignment Scheme with Wireless Power Transfer †

Yang Cao† , Nan Zhao† , F. Richard Yu∗ , Yunfei Chen‡ , Xin Liu† , and Victor C.M. Leung§

School of Information and Communication Engineering, Dalian University of Technology, Dalian, China Department of Systems and Computer Engineering, Carleton University, Ottawa, ON, K1S 5B6, Canada ‡ School of Engineering, University of Warwick, Coventry CV4 7AL, U.K. § Department of Electrical and Computer Engineering, the University of British Columbia, Vancouver, BC V6T 1Z4 Canada Email: {zhaonan, liuxinstar1984}@dlut.edu.cn; [email protected]; [email protected]; [email protected] ∗

Abstract—Passive eavesdropping is a main threat for the security of interference alignment (IA) networks. To solve this problem, artificial noise (AN) can be utilized in IA networks. In addition, AN can be exploited as an energy source through wireless power transfer (WPT). In this paper, we propose an ANassisted IA scheme with WPT. In the scheme, AN is transmitted by each IA transmitter to disrupt the eavesdroppers, with energy harvesting implemented by the power-splitting (PS) method. To enhance the capability of anti-eavesdropping and WPT, the total transmit power of AN is maximized to disrupt the eavesdropper by jointly optimizing the transmit power of legitimate signal and the PS coefficients, with both of the required SINR and harvested energy constrained. Extensive simulation results are presented to validate the effectiveness of the proposed scheme. Index Terms—Anti-eavesdropping, artificial noise, interference alignment, physical layer security, wireless power transfer.

I. I NTRODUCTION Interference management (IM) has been a critical issue in the modern wireless communication for decades. Recently, interference alignment (IA), as a revolutionary technique for IM, was proposed in [1], which has drawn great attentions due to its remarkable capability [2]. The closed-form solution of IA is much more difficult to derive when the number of users increases. Consequently, researchers focused on developing iterative IA algorithms to solve this problem with low computational complexity [3]. The feasibility conditions were analyzed in [4], which determine the relationship between the number of antennas, users and data streams when the interferences can be perfectly eliminated. On the other hand, due to the openness and broadcast nature of wireless transmission, secure information transfer becomes a challenging subject [5]–[7]. In this paper, we mainly focus on the aspect of external eavesdropping. To fight against the eavesdroppers and maintain the secure transmission, considerable research efforts have been dedicated to the This work was supported in part by the Xinghai Scholars Program, the National Natural Science Foundation of China (NSFC) under Grant 61601221, and the Fundamental Research Funds for the Central Universities under DUT16RC(3)045. Xin Liu is the corresponding author.

development of anti-eavesdropping techniques over the past decade, a large group of which were based on artificial noise (AN) [8], [9]. In addition, AN can be employed to enhance security communication in IA wireless networks. In [10], an AN scheme for anti-eavesdropping in IA wireless networks was presented. In the above research on AN methods, most of the transmit power is usually allocated as AN to boost the performance of anti-eavesdropping, which is a waste of energy. Fortunately, wireless power transfer (WPT) can be leveraged to collect the redundant energy in wireless networks to supply the lowpower applications, and simultaneous wireless information and power transfer (SWIPT) becomes a promising technique for energy harvesting and attracts plenty of attention [11]– [13]. Besides, the performance of wireless energy harvesting and SWIPT was also investigated in IA networks [12], [14]. In our previous work, an AN scheme was proposed to enhance the security of IA networks, and we can conclude that the eavesdropping rate will be decreased when the transmit power of AN increases [15], [16]. In this paper, we further investigate the influence of the transmit power of AN on the eavesdropping rate with optimal power allocation of each transmitter. Moreover, because the redundant energy generated by AN streams and interferences can serve as a new energy source, WPT technique is employed at the receivers in the proposed scheme. Notation: IN represents the N × N identity matrix. A† is the Hermitian transpose of matrix A. a is the Euclidean norm of vector a and A means the norm of matrix A, and CM ×N is the space of complex M × N matrices. CN (a, A) is the complex Gaussian distribution with mean a and covariance matrix A. 0M ×N denotes an M × N zero matrix. E(·) stands for expectation. II. S YSTEM D ESCRIPTION A. IA Wireless Networks Consider a K-user IA-based wireless network, we assume that M[k] and N[k] antennas are equipped at the kth transmitter and receiver, respectively, and d[k] independent data streams

978-1-5090-3423-9/16/$31.00 ©2016 IEEE

are emitted by the kth transmitter. The recovered signal of the kth receiver can be expressed as [k]†

[k]

y =U

[kk]

H

K  V x + U[k]† H[kj] V[j] x[j]+U[k]† n[k], (1) [k] [k]

j=1,j=k M [k] ×d[k]

[k]

[k]

[k]

where V ∈ C and U[k] ∈ CN ×d are the precoding and decoding matrices of the kth user, respectively. [k] [j] H[kj] ∈ CN ×M denotes the channel coefficient matrix from the jth transmitter to the kth receiver, each entity of [k] which is i.i.d., following CN (0, 1). n[k] ∈ CN ×1 represents the additive white Gaussian noise (AWGN) vector satisfying distribution CN (0, σ 2 IN [k] ) at the kth receiver. x[k] denotes by the signal vector including d[k] data streams  transmitted   [k] [k] [k] 2  = Pt . the kth transmitter with power Pt , i.e., E x To accurately retrieve the desired signal at the kth receiver, interferences should be aligned into the same subspace and perfectly eliminated with the following conditions satisfied. U[k]† H[kj] V[j] = 0d[k] ×d[j] , ∀j = k,   rank U[k]† H[kj] V[j] = d[k] , k = 1, 2, · · · , K.

(2) (3)

When (2) and (3) are met, the recovered signal at the kth receiver can be simplified as y[k]=U[k]† H[kk] V[k] x[k] +U[k]† n[k] .

(4)

The transmission rate of the kth user can also be denoted as   [k] Pt [kk] [kk]† [k] , (5) Rt = log2 det Id[k] + [k] 2 H H d σ where

[kk]

H

 U[k]† H[kk] V[k] .

(6)

B. AN-Assisted IA Networks The existence of MIMO eavesdroppers threatens the secure transmission of IA networks. In our previous work [10], an AN scheme was proposed to fight against the external eavesdroppers of the IA network. In the AN-assisted IA networks, AN is generated by each transmitter, and the retrieved signal at the kth receiver can be denoted as y

[k]

[k]†

= U

[kk]

H

[k] [k]

V x

+

K 

U

[k]†

[kj]

H

[j] [j]

V x

j=1,j=k

+

K 

U[k]† H[kj] W[j] s[j] + U[k]† n[k] ,

(7)

j=1 [j]

[j]

where W[j] ∈ CM ×dan is the unitary precoding matrix for [j] AN of the jth user, and s[j] is the vector that consists of dan streams of AN by the jth transmitter with power  emitted 2  [j] [j] Pan , i.e., E s[j]  = Pan . For simplicity, we assume that [k]

M [k] = M , N [k] = N , d[k] = d, dan = dan for all IA users. To eliminate the AN from all the users, the following condition should also be satisfied. U[k]† H[kj] W[j] = 0d×dan , ∀j, k = 1, 2, · · · , K.

(8)

When the conditions (2) and (8) are solvable at the same time, both AN and interferences at the receivers can be entirely removed, and thus AN won’t impact the legitimate transmission. Besides, the feasibility condition for AN-assisted IA networks is derived in our prior literature whereby the relationship between the number of equations and variables of conditions (2) and (8) [10], which is reviewed as dM + dN + dan M ≥ d2 + d2an + d2 K + ddan K M ≥ d, N ≥ d.

(9)

III. AN-A SSISTED IA S CHEME WITH WPT A. Wireless Power Transfer WPT is a remarkable technique to replenish energy for low-power applications. In MIMO wireless networks, due to the fact that the RF signal carries information as well as energy simultaneously, the RF signal triggered WPT is becoming a main approach for energy harvesting (EH). There are two main types of receiver designs that can be utilized to harvest energy from ambient RF signals, time switching and power splitting (PS) [11]. In this paper, we take the PS technique in the IA receiver design. After receiving the RF signal by the antenna, the PS method divides the received power into two portions whereby the coefficient of power splitting ρ ∈ (0, 1), i.e., the ρ portion of the received power at the receiver is assigned for ID terminal and 1 − ρ portion is assigned for EH terminal, respectively. In addition, n and z denote the antenna noise and ID noise of the receiver, respectively. Providing that the received signal at the receiver with single antenna can be given by y, and then the received signal for ID can be expressed as √ yID = ρ (y + n) + z. (10) Besides, the received signal for EH can be denoted as

yEH = 1 − ρ (y + n) . (11) Thus the harvested energy at the receiver is equal to 2

2

E = ζEyEH  ≈ ζ (1 − ρ) y ,

(12)

where ζ ∈ (0, 1) is the power convention efficiency. The antenna noise power is so tiny that can be ignored in (12). Furthermore, In IA-based MIMO networks, the receiver equipped with multi-antennas can be considered to comprise of the same number of single antenna, and then we employ PS method at each antenna with identical coefficient of PS. B. AN-Assisted IA Scheme with WPT In the AN-assisted IA networks, the eavesdropping rate is decreasing over the increasing transmit power of AN, while the transmission rate will not be impacted, which have been demonstrated in our previous work [10]. However, eliminating the AN signals directly in IA networks will cause a waste of energy, thus the abovementioned WPT technique should also be leveraged in our scheme to gather the surplus energy at the receivers. Consider that an external eavesdropper exists

[k] yID

⎛

= ρ[k] ⎝U[k]† H[kk] V[k] x[k] +

K 

U[k]† H[kj] V[j] x[j] +

j=1,j=k

The transmission rate in the IA network with WPT can be modified as   [k] ρ[k] Pt [kk] [kk]† [k] Rt = log2 det Id + . (15) H H d(ρ[k] σ 2 + δ 2 ) Besides, the received SINR for ID at the kth receiver can be presented as  2  [k]  ρ[k] Pt U[k]† H[kk] V[k]  [k] SIN R = . (16) ρ[k] σ 2 + δ 2 On the other hand, the received signal for EH of the kth receiver can be given by ⎛ ⎞ K K

  [k] H[kj] V[j] s[j]+n[k]⎠. yEH = 1−ρ[k]⎝ H[kj] V[j] x[j]+ j=1

(17) According to (17), the harvested power for EH at the kth receiver can be denoted as (18) (on the next page). Based on the above analysis, we present the objective function of the proposed AN-assisted IA scheme as max

[k]

ρ[k] ,Pt

K 

[k] Pan

k=1

s.t. SINR[k] ≥ γ [k] , E [k] ≥ e[k] , [k] Pan [k] Pan

[k] + Pt = [k] ≥ P¯an , [k]

0 1. Proof: From (21), the transmit power of legitimate signal [k] 2 2 [k] can be expressed as Pt ≥ γ[k]† (σ[kk]+δ[k]) 2 . For the purpose U H V  [k] γ [k] (σ 2 +δ 2 ) of convenient computation, define Pt = 2 U[k]† H[kk] V[k]  [k] and make an auxiliary variable β (β ≥ 1) scale up the Pt . [k] [k] [k] Then the solution for Pt can be expressed as Pt = β Pt . Besides, it’s noticeable that the SINR constraints in (21) hold with equality when β = 1 and ρ[k] = 1. Nonetheless, it is required that 0 < ρ[k] < 1 in the primal problem (19) with additional EH constraints satisfied. Consequently, β > 1





⎛

E [k] = ζ 1 − ρ[k] ⎝

K 

⎞ K  2   2   [j]  [j]  [kj] Pt H[kj] V[j]  + Pan H W[j]  ⎠ .

j=1

is required to meet both the SINR and EH constraints in problem (19). In conclusion, Lemma 1 is proved. According to Lemma 1, problem (19) can be reformulated as follows.  K   [k] [k]  Psum − β Pt max ρ[k] ,β

s.t.

k=1

ρ[k] β Pt

[k]

   [k]† [kk] [k] 2 U H V 

ρ[k] σ 2

δ2

+ [k] [k]  [k] ≥ e[k] , Pan E ≥ P¯an , 0 < ρ[k] < 1, β > 1,

≥ γ [k] ,

(22)

∀k.

 [k] is given by (23) (on the next In (22), the expression for E page). Then a proposition is proposed for the solution of (22). Proposition 1: Define the following variables [k] U[k]† H[kk] V[k] 2 P t , γ [k]   K  [j]  [kj] [j] 2 Psum H W  j=1

A[k] = B [k] = C

[k]

(24) ,

j=1

For the following quadratic equation, set βk2 as the largest real root of the following kth equation. e[k] δ2 − 1 = 0. + ζ(βC [k] + B [k] ) βA[k] − σ 2

k=1

δ2 , − σ2 e[k] 1 − ρ[k] ≥ , ζ(βC [k] + B [k] ) [k] [k] 0 < ρ[k] < 1, Pan ≥ P¯an , ρ[k] ≥

βA[k]

(27)

∀k.

β > 1,

Apparently, problem (27) can be equally rewritten as min β

s.t.

β

fk (β) ≤ 0, β > 1,

2

[k]∗

Pt

= β ∗ Pt

[k]

γ [k] (σ 2 + δ 2 ) = β∗   , ∀k.  [k]† [kk] [k] 2 U H V 

(28)

(29)

Furthermore, the solution of the transmit power for AN can be expressed as [k]∗

[k]∗ [k] = Psum −Pt Pan

γ [k] (σ 2 + δ 2 ) [k] = Psum −β ∗   . (30)  [k]† [kk] [k] 2 U H V  [k]∗

Then the optimal solution to problem (22) can be obtained [k] as β ∗ = max1≤k≤K βk2 and ρ[k]∗ = 1 − ζ(β ∗ Ce[k] +B [k] ) , ∀k. Proof: It’s obvious that the maximum of the transmit power for AN is corresponding to the minimum of the factor β according to problem (22). In addition, with the defined variables in Proposition 1 and the term βA[k] − σ 2 > 0 with β > 1, (22) can be equivalent to the following expression.  K   [k] [k] min Psum − β Pt s.t.

[k]

e δ + βA[k] − 1. where fk (β) = ζ(βC [k] +B [k] ) −σ 2 From problem (28), we can see that fk (β) = 0 is a quadratic equation with an unknown variable β. Assume that βk1 and βk2 , where βk1 < βk2 , are the two roots for the solution of the equation. Owing to the term ζA[k] C [k] > 0, the solution of the inequality fk (β) ≤ 0 can be denoted as either β ≤ βk1 or β ≥ βk2 . Besides, it’s worth noting that the graph of the function fk (β) is a downward parabola and we can easily observed that fk (β) > 0 with β = 1. Thus it must have βk1 < 1 < βk2 . Then we can conclude that the optimal solution of problem (28) can be expressed as β ∗ = max1≤k≤K βk2 . Thus the optimal solution to problem (22) can be expressed as β ∗ = max1≤k≤K βk2 and [k] ρ[k]∗ = 1 − ζ(β ∗ Ce[k] +B [k] ) When the optimal solution β ∗ is obtained from Proposition [k] 1, the corresponding solution of Pt can be given by

(25)

     K  [j]  [kj] [j] 2  kj [j] 2  Pt = H V  − H W  . (26)

ρ[k] ,β

(18)

j=1

At the end, the value of Pan should be [k] [k] condition Pan ≥ P¯an . If the condition successfully get the suboptimal solution otherwise, the result should be regarded as abandoned.

verified with the is met, we will of the problem, unreasonable and

V. S IMULATION R ESULTS In this section, we provide extensive results to evaluate the performance of the proposed AN-assisted IA scheme with WPT. In the simulations, we assume that K = 5, d = 2, dan = 1, M = 9, N = 5, Ne = 14, σ 2 = −70dBmW, δ 2 = −50dBmW, and ζ = 0.5. For simplify, some of the constraints and parameters are set to be equal for all the [k] [k] receivers, i.e., γ [k] = γ, e[k] = e, P¯an = P¯an , Psum = Psum , ∀k. Based on the above settings, we compare the average transmission rate and average eavesdropping rate of the proposed scheme with different SINR constraints in Fig. 1 and Fig. 2. In the simulation, P¯an = 5mW, Psum = 10mW, and three different EH thresholds are considered, i.e., e = 0.1mW, e = 0.5mW and e = 1mW. From Fig. 1, it’s obvious that the average transmission rate of each user is increased with the growth of SINR thresholds and mostly won’t be changed with the increasing EH constraints. In Fig. 2, we can see that the eavesdropping rate becomes larger with both the increasing



 [k] = ζ 1 − ρ[k] E



⎞ ⎛ K K    2   [j]  [kj] [j] 2 [j]   [j] ⎝ β Pt H V  + (Psum − β Pt ) H[kj] W[j]  ⎠ . j=1

Average Transmission Rate (Bits\s\Hz)

10

eavesdropper while guaranteeing the information transmission and power transfer. Due to the non-convex nature of the problem, a suboptimal algorithm was further derived with much lower complexity. Extensive simulation results were presented to show the effectiveness of the proposed scheme. Future work is in progress to consider wireless network virtualization in the proposed framework.

e=0.1mw e=0.5mw e=1mw

9 8 7 6

R EFERENCES

5 4 3 2 10

15

20 SINR threshold (dB)

25

30

Fig. 1. Comparison of the average transmission rate versus SINR constraints in the proposed scheme with e = 0.1mW, e = 0.5mW and e = 1mW. 0.03 Average Eversdropping Rate (Bits\s\Hz)

(23)

j=1

0.025

e=0.1mw e=0.5mw e=1mw

0.02

0.015

0.01

0.005

0 10

15

20 SINR threshold (dB)

25

30

Fig. 2. Comparison of the average eavesdropping rate versus SINR constraints in the proposed scheme with e = 0.1mW, e = 0.5mW and e = 1mW.

of SINR and EH constraints. This is due to the fact that the transmit power of AN will be decreased as either the SINR constraint or the EH constraint becomes larger. VI. C ONCLUSIONS AND F UTURE W ORK In this paper, we proposed a novel AN-assisted IA scheme with WPT when external eavesdroppers exist. In the scheme, we aimed to maximize the transmit power of AN to enhance the security of the network and adopted WPT technique to avoid energy wasting. Thus the transmitted power and PS coefficients were jointly optimized to efficiently oppose the

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