Cooperative Jamming Aided Robust Secure ... - Semantic Scholar
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IEEE TRANSACTIONS ON COMMUNICATIONS, VOL. 63, NO. 3, MARCH 2015
Cooperative Jamming Aided Robust Secure Transmission for Wireless Information and Power Transfer in MISO Channels Qi Zhang, Member, IEEE, Xiaobin Huang, Quanzhong Li, and Jiayin Qin
Abstract—Considering simultaneous wireless information and power transfer (SWIPT), we investigate cooperative-jamming (CJ) aided robust secure transmission design in multiple-inputsingle-output channels, where a cooperative jammer introduces jamming interferences and assists a source to supply wireless power for both an energy receiver and a legitimate destination. The destination employs a power splitting (PS) scheme to split the received signals for both information decoding and energy harvesting (EH). Compared with conventional transmission without SWIPT, the transmission with SWIPT should satisfy additional worst-case EH constraints. Furthermore, the PS scheme introduces an additional multiplicative optimization variable, i.e., the PS factor. Our objective is to maximize worst-case secrecy rate under transmit power constraints and worst-case EH constraints. We propose to decouple the problem into three optimization problems and employ alternating optimization algorithm to obtain the locally optimal solution. For the optimization of transmit covariance matrices and PS factor, we propose to employ the S-procedure and its extension to reformulate it as a convex semidefinite programming. It is shown through the simulation results that our proposed CJ aided robust secure transmission scheme outperforms the robust direct transmission scheme without CJ and the CJ aided non-robust scheme. Index Terms—Cooperative jamming (CJ), energy harvesting (EH), multiple-input-single-output (MISO), power splitting (PS), security, simultaneous wireless information and power transfer (SWIPT).
I. I NTRODUCTION
S
IMULTANEOUS wireless information and power transfer (SWIPT), which belongs to energy harvesting (EH) techniques, is promising to solve energy scarcity problem in energyconstrained wireless networks [1], [2]. The SWIPT scheme for single-input-single-output (SISO) channel was investigated in [1], [2]. Motivated by benefits of multi-antenna techniques, the SWIPT schemes for multiple-input-single-output (MISO) and multiple-input-multiple-output (MIMO) channels were studied Manuscript received December 20, 2014; accepted February 9, 2015. Date of publication February 20, 2015; date of current version March 13, 2015. This work was supported in part by the National Natural Science Foundation of China under Grant 61472458, Grant 61202498, and Grant 61173148 and in part by the Fundamental Research Funds for the Central Universities under Grant 15lgzd10 and Grant 15lgpy15. The associate editor coordinating the review of this paper and approving it for publication was M. Tao. Q. Zhang, X. Huang, and J. Qin are with the School of Information Science and Technology, Sun Yat-Sen University, Guangzhou 510006, China (e-mail: [email protected]; [email protected]; issqjy@ mail.sysu.edu.cn). Q. Li is with the School of Advanced Computing, Sun Yat-Sen University, Guangzhou 510006, China (e-mail: [email protected]). Digital Object Identifier 10.1109/TCOMM.2015.2405063
in [3]–[5]. The SWIPT scheme for MIMO relay networks was investigated in [6], [7]. For co-located information decoding (ID) and EH receivers, two practical receiver designs were proposed for SWIPT, namely, time switching (TS) and power splitting (PS) [3]. With TS, the receiver switches over time between ID and EH, while with PS, the receiver splits the received signal into two streams of different powers for ID and EH separately. It is worth noting that TS can be regarded as a special form of PS with only binary PS ratios and thus in general PS achieves better rate-energy transmission tradeoff than TS [3]. Because of broadcast nature of radio propagation and inherent randomness of wireless channel, radio transmission is vulnerable to attacks from unexpected eavesdroppers [8]–[14]. Secure communications in MISO SWIPT systems were studied in [15]–[17] where perfect channel state information (CSI) was considered. In practice, it is difficult to obtain perfect CSI because of channel estimation and quantization errors. Without SWIPT, the robust secure transmission in conventional MISO broadcast systems was widely studied in the literature [9], [11] where channel uncertainties are modeled by worst-case model. The robust secrecy transmission schemes with artificial noise (AN) and generalized AN were considered in [9], [10]. Considering SWIPT, Ng et al. proposed a robust secure beamforming scheme in multiuser MISO SWIPT systems [18]. Besides AN and generalized AN [9], [10], another efficient way to increase secrecy rate in wireless systems is cooperative jamming (CJ), which employs a friendly jammer to introduce jamming interference to degrade eavesdropper channel [11]– [14]. In [11], by assuming that the source and the jammer know perfect CSI from themselves to the legitimate destination and imperfect CSI from themselves to the eavesdropper, Huang et al. proposed a zero-forcing (ZF) based CJ aided robust secure transmission scheme in MISO channels where channel uncertainties are modeled by worst-case model. To the best of our knowledge, the research on CJ aided robust secure transmission scheme for SWIPT in MISO Channels is missing. In this paper, considering SWIPT, we investigate the robust secure transmission design problem in MISO channels, where a multi-antenna cooperative jammer introduces jamming interferences to degrade eavesdropper channels and assists a multiantenna source to supply wireless power for a multi-antenna energy receiver and a legitimate destination. The destination employs power splitting (PS) scheme proposed in [3] to split the received signals into two streams of different powers for ID and EH separately. We assume that the source and the jammer
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ZHANG et al.: COOPERATIVE JAMMING AIDED ROBUST SECURE TRANSMISSION
know imperfect CSI from themselves to legitimate destination, eavesdropper and energy receiver. The channel uncertainties are characterized by worst-case model as in [9], [11]. Compared with the conventional CJ aided robust secure transmission without SWIPT in [11], the transmission with SWIPT of source and jammer should satisfy additional worst-case EH constraints at energy receiver and legitimate destination. The aforementioned transmission problem with SWIPT is more challenging because the ZF scheme employed in conventional CJ aided robust secure transmission [11] is not available when SWIPT is considered. Furthermore, the employed PS scheme at legitimate destination introduces an additional multiplicative optimization variable, i.e., the PS factor. Our objective is to design the CJ aided robust secure transmission scheme which maximizes worst-case secrecy rate under transmit power constraints and worst-case EH constraints. We propose to decouple the problem into three optimization problems and employ alternating optimization algorithm to obtain the locally optimal solution. For the optimization problem of PS factor and transmit covariance matrices at source and jammer, we propose to employ S-procedure and its extension to reformulate it as a convex semidefinite programming (SDP). Furthermore, since the rank relaxation is used to solve the aforementioned problem, we prove that the rank of obtained transmit covariance matrix at the source is less than or equal to 2. We employ Gaussian randomization (GR) method to obtain the rank-one transmit covariance matrix at the source. The rest of this paper is organized as follows. Section II describes the system model. In Section III, we propose the CJ aided robust secure transmission scheme for SWIPT in MISO Channels. Simulation results are provided in Section IV. Finally, we conclude our paper in Section V. Notations: Boldface lowercase and uppercase letters denote vectors and matrices, respectively. The transpose, conjugate transpose, and trace of matrix A are denoted as AT , A† , and tr(A), respectively. vec(A) denotes to stack the columns of matrix A into a single vector. By A 0 or A 0, we mean that A is positive semidefinite or positive definite, respectively. λmin {A} denotes the minimum eigenvalue of A. a denotes Euclidean norm of vector a. The ⊗ denotes Kronecker product. Re{a} denotes the real part of a complex variable, a. CN (0, I) denotes the distribution of a circularly symmetric complex Gaussian vector with mean 0 and covariance I.
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Fig. 1. The system model of CJ aided robust secure transmission with SWIPT in MISO channels.
Fig. 2. The structure of legitimate destination.
and Hr ∈ CNs ×Nr , respectively. Denote the channel responses from cooperative jammer to destination, eavesdropper and energy receiver as gd ∈ CNj ×1 , ge ∈ CNj ×1 and Gr ∈ CNj ×Nr , respectively. In the network, the source transmits confidential signals to the legitimate destination while the cooperative jammer broadcasts the jamming interferences to degrade the eavesdropper channels. Different from the conventional CJ scheme considered in [11]–[14], the objective of the source and the jammer is also to supply wireless power to the energy receiver and the destination. When the source transmits confidential signal, x ∈ CNs ×1 , and the jammer broadcasts jamming interference, v ∈ CNj ×1 , the destination employs PS scheme to split the received signals into two streams of different powers for ID and EH separately, as shown in Fig. 2. Thus, the received signal at the legitimate destination for ID is √ √ (1) yd = θh†d x + θgd† v + nd
II. S YSTEM M ODEL Consider an MISO wireless communication network which consists of a source, a cooperative jammer, a legitimate destination, an energy receiver and an eavesdropper, as shown in Fig. 1. The source, the energy receiver and the jammer are equipped with Ns , Nr and Nj antennas, respectively. The legitimate destination and the eavesdropper are equipped with single antenna. A. Signal Transmission and Cooperative Jamming Denote the channel responses from source to destination, eavesdropper and energy receiver as hd ∈ CNs ×1 , he ∈ CNs ×1
where θ denotes the PS factor, i.e., percentage of signal power split for ID and nd ∼ CN (0, σd2 ) denotes additive Gaussian noise at the destination. The received signal at the eavesdropper, is ye = h†e x + ge† v + ne
(2)
where ne ∼ CN (0, σe2 ) denotes additive Gaussian noises at the eavesdropper. Without loss of generality, we assume that the noise variances at destination and eavesdropper are σd2 = σe2 = σ 2 = 1 in this paper. In (1) and (2), x ∼ CN (0, Qx ) and v ∼ CN (0, Qv ) where Qx 0 and Qv 0 are the transmit covariance matrices of x and v, respectively.
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IEEE TRANSACTIONS ON COMMUNICATIONS, VOL. 63, NO. 3, MARCH 2015
For secure MISO communication with the existence of eavesdropper, the achievable secrecy rate is expressed as [9]
Wi 0, Ti 0, i ∈ {1, 2, 3}, assumed to be known, determine the qualities of CSI. Considering worst-case channel uncertainties, our objective is to maximize worst-case secrecy rate subject to transmit power constraints and worst-case EH constraints by properly designing Qx and Qv , i.e.,
Rs = Cd (Qx , Qv ) − Ce (Qx , Qv )
(3)
where Cd (Qx , Qv ) and Ce (Qx , Qv ) denote mutual information at the legitimate destination and the eavesdropper, respectively, θh†d Qx hd (4) Cd (Qx , Qv ) = log2 1 + 1 + θgd† Qv gd h†e Qx he Ce (Qx , Qv ) = log2 1 + . (5) 1 + ge† Qv ge
max
Qx ,Qv ,θ
The harvested energy at energy receiver is ρtr H†r Qx Hr + G†r Qv Gr
where ρ is EH efficiency that accounts for the loss in energy transducer. The harvested energy at legitimate destination is
ρtr (1 − θ) · h†d Qx hd + gd† Qv gd . (8) Without loss of generality, the EH efficiency is assumed to be ρ = 1 in this paper [3].
(15a) (15b)
∀ Hr ∈ Hr , Gr ∈ Gr (15c)
(1 − θ) · h†d Qx hd + gd† Qv gd ≥ Ed ,
(6)
(7)
Rs (Qx , Qv )
s.t. tr(Qx ) ≤ P1 , tr(Qv ) ≤ P2 tr H†r Qx Hr + G†r Qv Gr ≥ Er ,
The transmit power constraints at source and cooperative jammer, denoted as P1 and P2 , respectively, are tr(Qx ) ≤ P1 and tr(Qv ) ≤ P2 .
min
hd ∈Hd ,gd ∈Gd , he ∈He ,ge ∈Ge
∀ hd ∈ Hd , gd ∈ Gd
(15d)
Qx 0, Qv 0, 0 < θ ≤ 1
(15e)
rank(Qx ) = 1
(15f)
where Er denotes the worst-case EH constraint at energy receiver and Ed denotes the worst-case EH constraint at legitimate destination. The optimization problem (15) is non-convex which is difficult to solve. Remark: In (15), it is noted that the rank of Qv is not required to be one because the jammer broadcasts jamming interferences. III. CJ A IDED ROBUST S ECURE T RANSMISSION W ITH B OUNDED C HANNEL U NCERTAINTIES Let Φ = θ−1 . We rewrite Rs (Qx , Qv ) as follows
B. Channel Uncertainties We assume that the source and the cooperative jammer know imperfect CSI on hd , he , Hr , gd , ge , and Gr . In practice, the CSI is imperfect because of channel estimation and quantization errors. In this paper, we model the channel uncertainties by worst-case model as in [9], [11]. The channel uncertainties of channel responses hd , he , Hr , gd , ge and Gr are bounded by elliptical regions, denoted as Hd , He , Hr , Gd , Ge , and Gr , respectively,
¯ d + Δhd , Δh† W1 Δhd ≤ 1 , Hd = hd |hd = h (9) d ¯ e + Δhe , Δh† W2 Δhe ≤ 1 , He = he |he = h (10) e ¯ r + ΔHr , tr ΔH† W3 ΔHr ≤ 1 , Hr = Hr |Hr = H r (11)
¯d + Δgd , Δgd† T1 Δgd ≤ 1 , Gd = gd |gd = g (12) ¯e + Δge , Δge† T2 Δge ≤ 1 , Ge = ge |ge = g (13) ¯ r + ΔGr , tr ΔG† T3 ΔGr ≤ 1 , Gr = Gr |Gr = G r
(14) ¯ d, h ¯ e, H ¯ r, g ¯ r denote the estimates of ¯d , g ¯e and G where h channels hd , he , Hr , gd , ge and Gr , respectively; Δhd , Δhe , ΔHr , Δgd , Δge and ΔGr denote the channel uncertainties;
Rs (Qx , Qv ) = ξ1 + ξ2 + ξ3 + ξ4 where
ξ1 = ln Φ + gd† Qv gd + h†d Qx hd ,
ξ2 = −ln Φ + gd† Qv gd , ξ3 = −ln 1 + ge† Qv ge + h†e Qx he , ξ4 = ln 1 + ge† Qv ge .
(16)
(17) (18) (19) (20)
In (16), since ξ1 and ξ4 are concave and ξ2 and ξ3 are convex, Rs (Qx , Qv ) is non-convex. We have the following proposition. Proposition 1: Let a ∈ 1×1 be a positive scalar and f (a) = −ab + ln a + 1. We have −ln b =
max
a∈ 1×1 ,a>0
f (a)
(21)
and the optimal solution to the right-hand side of (21) is a = 1b . Proof: Since f (a) is concave, the optimal solution to the (a) = 0. right hand side of (21) is obtained by letting ∂f∂a We transform ξ3 and ξ4 into convex optimization problems ξ2 = ξ3 =
max
ζ1 (a1 )
(21)
max
ζ2 (a2 )
(22)
a1 ∈ 1×1 ,a1 >0 a2 ∈ 1×1 ,a2 >0
ZHANG et al.: COOPERATIVE JAMMING AIDED ROBUST SECURE TRANSMISSION
where
ζ1 (a1 ) = −a1 Φ + gd† Qv gd + ln a1 + 1, (24) ζ2 (a2 ) = −a2 1 + ge† Qv ge + h†e Qx he + ln a2 + 1. (25) We propose to decouple (15) into three optimization problems and alternatively optimize (Qx , Qv , Φ), a1 , and a2 . In the (k) (k) (k + 1)th iteration, when the optimal a1 and a2 in the kth iteration is obtained, we propose to solve the following rankrelaxed problem
(k) (k) + ζ2 a 2 max min ξ1 + ξ4 + ζ1 a 1 Qx ,Qv ,Φ
hd ∈Hd ,gd ∈Gd , he ∈He ,ge ∈Ge
(26a) s.t. (15b), (15c), h†d Qx hd + gd† Qv gd ≥ φEd , ∀ hd ∈ Hd , gd ∈ Gd
(26b)
Qx 0, Qv 0, Φ ≥ 1
(26c)
where −1
φ = 1 + (Φ − 1) .
(27)
By introducing slack variables βi , i ∈ {1, 2, 3, 4}, the problem (26) is equivalent rewritten as max
Ω
(28a)
Qx 0,Qv 0,Φ≥1
s.t.
h†d Qx hd
≥ β1 , ∀ h d ∈ H d ,
(28b)
gd† Qv gd
≤ β2 , ∀ gd ∈ Gd ,
(28c)
h†e Qx he ≤ β3 , ∀ he ∈ He ,
(28d)
ge† Qv ge
(28e)
≥ β4 , ∀ ge ∈ Ge ,
(15b), (15c), (26b), βi ≥ 0, i ∈ {1, 2, 3, 4} where (k)
(k)
Ω = ln(Φ + β1 + β2 ) − a1 (Φ + β2 ) + ln a1 (k)
(k)
−a2 (1 + β3 + β4 ) + ln a2 + ln(1 + β4 ) + 2.
(29)
The problem (28) has semi-infinite constraints (28b)–(28e), (15c), and (26b), which are intractable. To make the problem tractable, we employ S-Procedure [19] to convert the constraints (28b)–(28e), (15c), and (26b) into linear matrix inequalities (LMIs). Lemma 1 (S-Procedure [19]): Define the functions
fj (x) = x† Aj x + 2Re b†j x + cj , j = 1, 2 where Aj = A†j ∈ Cn×n , bj ∈ Cn×1 , cj ∈ R. The implication f1 (x) ≤ 0 ⇒ f2 (x) ≤ 0 holds if and only if there exists λ ≥ 0 such that A1 b1 A2 b 2 λ − 0 b†1 c1 b†2 c2 provided that there exists a point x0 such that f1 (x0 ) < 0.
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To apply S-Procedure on the constrain (28b), we substitute (9) into (28b) and rewrite it as follows ∀ Δhd : Δh†d W1 Δhd − 1 ≤ 0; ¯ † Qx h ¯ d )† Δhd − h ¯ d +β1 ≤ 0. −Δh†d Qx Δhd −2Re (Qx h d (30) Applying S-Procedure, we convert (30) into an LMI as follows Υ1 (Qx , λ1 ) Δ λ1 W 1 + Qx = ¯ † Qx h d
¯d Qx h † ¯ ¯ d − β1 −λ1 + hd Qx h
0
(31)
for some λ1 ≥ 0. Similarly, the constraints (28c)–(28e) are also equivalently expressed as follows Υ2 (Qv , λ2 ) Δ λ 2 T1 − Q v = −¯ gd† Qv
¯d −Qv g ¯ d + β2 ¯d† Qv g −λ2 − g
Υ3 (Qx , λ3 ) Δ λ3 W 2 − Qx = ¯ † Qx −h e Υ4 (Qv , λ4 ) Δ λ 4 T2 + Q v = ¯e† Qv g
0,
¯e −Qx h ¯ † Qx h ¯ e + β3 −λ3 − h e ¯e Qv g ¯e† Qv g ¯ e − β4 −λ4 + g
(32)
0, (33)
0
(34)
for some λ2 ≥ 0, λ3 ≥ 0, λ4 ≥ 0. To covert the constraints (15c) into an LMI, we rewrite it as follows tr H†r Qx Hr ≥ Er − tr G†r Qv Gr , ∀ Hr ∈ Hr , Gr ∈ Gr .
(35)
Using the identity tr(ABCD) = vecT (DT )(CT ⊗A)vec(B), the constraint (35) is equivalently expressed as ∀ Δhr : Δh†r (I ⊗ W3 )Δhr − 1 ≤ 0; (36) h†r (I ⊗ Qx )hr ≥ Er − tr G†r Qv Gr , ∀ Gr ∈ Gr where hr = vec(Hr ). Applying S-Procedure with respect to Δhr , we have ¯r λ5 I ⊗ W 3 + I ⊗ Qx I ⊗ Qx h ˜ 0 Υ5 (Qx , λ5 ) = ¯ † I ⊗ Qx ηˆ1 h r (37) ¯ ¯ for some λ5 ≥ 0 where hr = vec(Hr ) and ¯ † (I ⊗ Qx )h ¯ r − Er + tr G† Qv Gr . ηˆ1 = −λ5 + h r r
(38)
We need the following extensions of S-Procedure [19] to covert (37) into an LMI. Lemma 2 ([19, Theorem 3.5]): The data matrices Ai , i ∈ {1, 2, · · · , 8}, satisfy A8 A6 + A 7 X 0, (A6 + A7 X)† A3 + X† A2 + A†2 X + X† A1 X ∀ I − X† A4 X 0
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if and only if there exists λ ≥ 0 such that ⎤ ⎡ ⎤ ⎡ A 8 A6 A7 0 0 0 ⎣ A†6 A3 A†2 ⎦ − λ ⎣ 0 I 0 ⎦ 0. 0 0 −A4 A†7 A2 A1
obtained, we should optimize a1 and a2 which maximize worstcase secrecy rate. For the optimization of a1 , we should solve g max −a1 Φ(k+1) + max gd† Q(k+1) d + ln a1 + 1. (45) v
To employ Lemma 2, we equivalently expressed the constraint (35) as follows ∀ Δg r : Δg †r (I ⊗ T3 )Δg r − 1 ≤ 0; (39) (37)
It is noted that in the derivation, we exchange the sequence of optimization of a1 and gd because the objective function of problem (45) is convex with respect to a1 and gd . Similarly, for the optimization of a2 , we should solve † (k+1) g + max h Q h max − a2 1 + min ge† Q(k+1) e e v e x
gd ∈Gd
a1 >0
ge ∈Ge
a2 >0
where g r = vec(Gr ). Using Lemma 2, (39) is equivalently transformed into the following LMI Υ5 (Qx , Qv , λ5 , λ6 ) ⎤ ⎡ ¯r λ5 I ⊗ W3 +I ⊗ Qx I ⊗ Qx h 0 Δ † ⎦0 ¯ I ⊗ Qx =⎣ ¯ †r I ⊗ Qv h η1 g r ¯ r λ6 I ⊗ T3 +I ⊗ Qv 0 I ⊗ Qv g (40)
+ ln a2 + 1. γ1 = max gd† Q(k+1) gd . v gd ∈Gd
Similarly, the constraint (26b) is equivalently expressed as follows ⎤ 0 ¯d† Qv ⎦ 0 g λ 8 T1 + Q v
(42)
for some λ7 ≥ 0, λ8 ≥ 0 where ¯ † Qx h ¯d + g ¯d† Qv g ¯d − φEd . η2 = −λ7 − λ8 + h d
(43)
Δgd
The Lagrangian function of problem (47) is
¯d† + Δgd† Q(k+1) L= g (¯ gd + Δgd ) v
+ κ Δgd† T1 Δgd − 1
Ω
where ω1 =
¯d ¯ † Qv g g
. d (k+1) −1 tr Qv T1
The closed-form solution to problem (48) is
−1 (k+1) = Φ(k+1) + γ1 . a1
Υ1 (Qx , λ1 ) 0, Υ2 (Qv , λ2 ) 0, Υ3 (Qx , λ3 ) 0, Υ4 (Qv , λ4 ) 0,
(51)
(52)
Similarly, we obtain the closed-form solution to problem (46) as follows
Υ5 (Qx , Qv , λ5 , λ6 ) 0,
(k+1)
Υ6 (Qx , Qv , λ7 , λ8 ) 0,
a2
tr(Qx ) ≤ P1 , tr(Qv ) ≤ P2 ,
where
βi ≥ 0, i ∈ {1, 2, 3, 4}, λl ≥ 0, l ∈ {1, 2, · · · , 8}
(49)
(k+1)
Qx 0,Qv 0,Φ≥1
s.t.
(48)
where κ denotes Lagrange multiplier. Since L is convex in Δgd , the Karush-Kuhn-Tucker (KKT) conditions are sufficient for maximizing (47). Thus, we have
√ −1 ¯d g ¯d† + T−1 (50) γ1 = tr Q(k+1) g v 1 + 2 ω1 T1
Combining (31)–(34), (40) and (42), the optimization problem (28) is recast as max
(47)
Substituting (12) into (47), we recast (47) as
¯d† + Δgd† Q(k+1) γ1 = max g (¯ gd + Δgd ) v s.t. Δgd† T1 Δgd ≤ 1.
¯ † (I ⊗ Qx )h ¯r + g ¯ †r (I ⊗ Qv )¯ η1 = −λ5 − λ6 + h g r − Er . r (41)
¯d Qx h η2 ¯d Qv g
(46)
To solve (45), we first solve the following optimization problem
¯ r ) and ¯ r = vec(G for some λ5 ≥ 0 where g
Υ6 (Qx , Qv , λ7 , λ8 ) ⎡ λ7 W 1 + Qx Δ ¯ † Qx =⎣ h d 0
he ∈He
(44)
which is a convex SDP. It can be solved efficiently using the interior-point method [20]. We have the following proposition. Proposition 2: The rank of the obtained solution Qx to (44) is less than or equal to 2. Proof: See Appendix A. In the (k + 1)th iteration, when the optimal (Qx , Qv , Φ) in (k+1) (k+1) the (k + 1)th iteration, denoted as (Qx , Qv , Φ(k+1) ), is
= (1 + γ2 + γ3 )−1
√ −1 ¯e† + T−1 ¯e g γ2 = tr Q(k+1) g , v 2 − 2 ω2 T2
(53)
(54)
¯† Q ¯e g g
, e v (55) (k+1) −1 tr Qv T2 ¯ eh ¯ † + W−1 + 2√ω3 W−1 , (56) h γ3 = tr Q(k+1) x e 2 2 (k+1)
ω2 =
ω3 =
¯e ¯ † Q(k+1) h h e x
. (k+1) tr Qx W2−1
(57)
ZHANG et al.: COOPERATIVE JAMMING AIDED ROBUST SECURE TRANSMISSION
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Thus, the proposed solution to the rank-relaxed problem of (15) is summarized as in Algorithm 1. Algorithm 1 The proposed alternating optimization algorithm for the rank-relaxed problem of (15) 1: 2:
3:
(0)
(0)
Initialize: k = 0, a1 = 1, a2 = 1; (k+1) , Repeat: Solve the problem (44) to obtain Qx (k+1) (k+1) (k+1) (k+1) , and Φ ; Obtain a1 and a2 by (52) Qv and (53), respectively; k := k + 1; Until: convergence.
We have the following proposition to theoretically prove the convergence of Algorithm 1. (k) (k) (k) (k) Proposition 3: The sequence {(Qx , Qv , Φ(k), a1 , a2 )} generated by the Algorithm 1 has limit point Γ = (Qx , Qv , Φ , a1 , a2 ) which is a KKT point of the rank-relaxed problem of (15). Proof: See Appendix B. It is noted that from Proposition 2, the obtained solution to the rank-relaxed problem of (15) by Algorithm 1, denoted as Qx , has the rank less than or equal to 2. This is because of the additional worst-case EH constraint. If rank(Qx ) = 1, we obtain the beamforming vector, denoted as qx , by decomposing Qx = qx (qx )† . If rank(Qx ) = 2, we employ the Gaussian randomization (GR) method to generate the suboptimal rankone solution. When the obtained solution to the rank-relaxed problem of (15) by Algorithm 1, denoted as Γ = (Qx , Qv , Φ , a1 , a2 ), is known, we generate L possible GR solutions of Qx as follows v = P1 Qx u−1 Qx u (58) where u is randomly generated Gaussian vector. In all the L possible Gaussian randomized solutions, the best one should satisfy worst-case EH constraints and maximize worst-case secrecy rate simultaneously. IV. S IMULATION R ESULTS In this section, we investigate the performance of proposed CJ aided robust secure transmission scheme through computer simulations. In the MISO network, we assume that all the entries in channel responses are independent and identically distributed complex Gaussian random variables with zero-mean and unit variance. The numbers of antennas equipped at the source and the jammer, if not specified, are Ns = Nj = 4. The number of antennas equipped at the energy receiver is Nr = 2. The channel uncertainty regions are assumed to be norm-bounded, i.e., Wi = Ti = (1/ωi ) I, i ∈ {1, 2, 3}
(59)
where (ω1 , ω2 , ω3 ) determines the qualities of the CSI. The parameters of channel uncertainties in (59) are ω1 = ω3 = 0.01 and ω2 = 0.1. The transmit power constraints at source and cooperative jammer, if not specified, are P1 = P2 = P .
Fig. 3. Average worst-case secrecy rate versus the worst-case EH constraint at energy receiver, i.e., α1 ; performance comparison of our proposed CJ aided robust secure transmission scheme before and after GR where P/σ 2 = 20 dB, Ns = Nj = 4, Nr = 2, ω1 = ω3 = 0.01 and ω2 = 0.1.
The worst-case EH constraints at the energy receiver and the legitimate destination are given by Er = α1 Nr P and Ed = α2 P,
(60)
respectively, where 0 ≤ α1 ≤ 1 is the ratio of Er to Nr P and 0 ≤ α2 ≤ 1 is the ratio of Ed to P . In the process of GR, we employ L = 10 in the simulations. For our proposed CJ aided robust secure transmission scheme, the optimal solution to the rank-relaxed problem of (15) without GR serves as a performance upper bound. In Fig. 3, we compare the average worst-case secrecy rates of proposed CJ aided robust secure transmission scheme after GR (denoted as “Robust CJ, GR” in the legend) and the performance upper bound (denoted as “Robust CJ, UB”) when the transmit power to noise power ratio, P/σ 2 , is 20 dB. From Fig. 3, it is observed that our proposed CJ aided robust secure transmission scheme after GR approaches the performance upper bound. This is because the probability that solution Qx to the rank-relaxed problem of (15) has rank of one is high. In Fig. 4, we compare the average worst-case secrecy rates of our proposed CJ aided robust secure transmission scheme, the robust directtransmission scheme without aid of CJ (denoted as “Robust DT”) and the CJ aided non-robust secure transmission scheme (denoted as “Non-RobustCJ”). The worst-case EH constraints at energy receiver and legitimate destination are 2Nr P and P , respectively, i.e., α1 = 2 and α2 = 1. The robust direct transmission scheme is obtained by solving (15) with transmit power constraints tr(Qx ) ≤ 2P and tr(Qv ) ≤ 0. The CJ aided non-robust secure transmission scheme is obtained by solving (15) where the parameters of channel uncertainties are mistaken as ω1 = ω3 = 0 and ω2 = 0.1. From Fig. 4, it is observedthat our proposed “Robust CJ” scheme achieves lower average worst-case secrecy rate than the “Robust DT” scheme when P/σ 2 is relatively low. This is because when P/σ 2 is low, the transmit power of source for our proposed “Robust CJ” scheme is only half of that of the “Robust DT” scheme. Furthermore, since the signal-to-noise ratio at eavesdropper is low, the jamming interferences from jammer is less useful to
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Fig. 4. Average worst-case secrecy rate versus the transmit power to noise power ratio, P/σ 2 ; performance comparison of our proposed CJ aided robust secure transmission scheme, the robust direct transmission scheme without aid of CJ and the CJ aided non-robust secure transmission scheme where Ns = Nj = 4, Nr = 2, ω1 = ω3 = 0.01 and ω2 = 0.1.
Fig. 6. Average worst-case secrecy rate versus the number of transmit antennas at source and at jammer Ns = Nj = N ; performance comparison of our proposed CJ aided robust secure transmission scheme, the robust direct transmission scheme without aid of CJ and the CJ aided non-robust secure transmission scheme where P/σ 2 = 20 dB, α1 = 2, α2 = 1, Nr = 2, ω1 = ω3 = 0.01 and ω2 = 0.1.
In Fig. 6, we present the average worst-case secrecy rate versus the number of transmit antennas at source and at jammer Ns = Nj = N , where P/σ 2 = 20 dB, α1 = 2, and α2 = 1. From Fig. 6, it is shown that the worst-case secrecy rate improves with increase of the number of transmit antennas. That is because more transmit antennas allow the source to steer its antenna beam towards legitimate destination and energy receiver. More transmit antennas also allow the jammer to steer its antenna beam towards eavesdropper and energy receiver. Furthermore, the gaps between our proposed “Robust CJ” scheme and other two schemes become larger with increase of the number of transmit antennas. V. C ONCLUSION Fig. 5. Average worst-case secrecy rate versus α1 ; performance comparison of our proposed CJ aided robust secure transmission scheme, the robust direct transmission scheme without aid of CJ and the CJ aided non-robust secure transmission scheme where P/σ 2 = 20 dB, α2 = 1, Ns = Nj = 4, Nr = 2, ω1 = ω3 = 0.01 and ω2 = 0.1.
increase the secrecy rate. When P/σ 2 is high, our proposed “Robust CJ” scheme achieves much higher average worst-case secrecy rate than the “Robust DT” scheme. It is also found from Fig. 4, when α1 = 2 and α2 = 1, average worst-case secrecy rate of the “Non-Robust CJ” scheme is zero whereas when α1 = 0 and α2 = 0, average worst-case secrecy rate of the “Non-Robust CJ” scheme approaches that of the “Robust CJ” scheme. This is because when α1 = 2 and α2 = 1, the worst-case EH constraints at energy receiver and legitimate destination are not satisfied for the “Non-Robust CJ” scheme. In Fig. 5, we show the effect of EH constraint at the energy receiver on average worst-case secrecy rate, where P/σ 2 = 20 dB and α2 = 1. From Fig. 5, it is observed that with increase of α1 , the worst-case secrecy rate decreases. It is also found that our proposed “Robust CJ” scheme has significant performance gain over the “Robust DT” scheme and the “Non-Robust CJ” scheme.
In this paper, we have proposed the CJ aided robust secure transmission scheme for SWIPT in MISO channels where the cooperative jammer introduces jamming interferences to degrade eavesdropper channels and assists the source to supply wireless power for the energy receiver and the legitimate destination. Simulation results demonstrate that although the obtained locally optimal transmit covariance matrix has rank of one or two, our proposed CJ aided robust secure transmission scheme after GR approaches the performance upper bound. It is also found our proposed CJ aided robust secure transmission scheme outperforms the robust direct transmission scheme without CJ and the CJ aided non-robust scheme. A PPENDIX A P ROOF OF P ROPOSITION 2 The Lagrangian dual function of (44) with respect to Qx is given by ¯ =− tr(Qx E0 ) − tr (Υ1 (Qx , λ1 )E1 ) − tr (Υ3 (Qx , λ3 )E2 ) L −tr(Υ5 (Qx , Qv , λ5 , λ6 )E3 )−tr(Υ6 (Qx , Qv , λ7 , λ8 )E4 ) + q (tr(Qx ) − P1 )
(61)
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where the dual variables E0 ∈ H+ , E1 ∈ H+ , E2 ∈ H+ , E3 ∈ H+ , E4 ∈ H+ , and q ≥ 0 are corresponding to the constraints Qx 0, Υ1 (Qx , λ1 ) 0, Υ3 (Qx , λ3 ) 0, Υ5 (Qx , Qv , λ5 , λ6 )) 0, Υ6 (Qx , Qv , λ7 , λ8 ) 0, and tr(Qx ) ≤ P1 in (44), respectively. It is noted the optimal solution to the problem (44) should satisfy that the constraint (28c) is active. From (28c), the constraint (26b) is equivalent to h†d Qx hd ≥ φEd − β2 , ∀ hd ∈ Hd .
(62)
Comparing the constraints (28b) and (62), we know that the probability that the constraints (28b) and (62) are equal is zero. Thus, either the constraint (62) is not satisfied or the constraint (62) is not active. If the constraint (62) is not satisfied, the problem (28) is infeasible. If the constraint (62) is not active, we have E4 = 0. We rewrite Υ5 (Qx , Qv , λ5 , λ6 ) as Υ5 (Qx , Qv , λ5 , λ6 ) = Ψ + P†1 (I ⊗ Qx )P1 + P†2 (I ⊗ Qv )P2
(63)
Ψ = diag(λ5 I ⊗ W3 , ηˆ1 , λ6 I ⊗ T3 ),
(64)
where
P1 = [ I
¯d h
0 ],
(65)
P2 = [ 0
¯d g
I ],
(66)
ηˆ1 = −λ5 − λ6 − Er .
(67)
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N + 1. From S-procedure [19], we have λ1 ≥ 0. It can be verified that λ1 > 0 such that rank(Υ1 (Qx , λ1 )) ≥ Ns and rank(E1 ) ≤ 1. Furthermore, rank(E1 ) = 0. Thus, rank(E1 ) = 1. Similarly, we have Υ3 (Qx , λ3 )E2 = −He Qx H†e E2 + diag(λ3 W2 , −λ3 + β3 )E2
(70)
¯ e ]† . Furthermore, rank(E2 ) = 1. where He = [I, h ¯ with respect to Qx and applyTaking partial derivative of L ing KKT conditions, we have Nr
E0 + H†d E1 Hd − H†e E2 He +
Ukk − qI = 0
(71)
⎤ U1Nr ⎥ .. ⎦. . UNr Nr
(72)
k=1
where
⎡
U11 ⎢ .. † P1 E3 P1 = ⎣ . UN r 1
··· .. . ···
Multiplying both sides of (71) with Qx , we have Nr † Ukk Qx = H†e E2 He + qI Qx . (73) Hd E1 Hd + k=1
Since H†e E2 He + qI 0 has full rank, we have Nr † Ukk Qx = rank(Qx ). rank Hd E1 Hd +
(74)
k=1
From KKT conditions, we have Υ5 (Qx , Qv , λ7 , λ8 )E3 = 0.
It is noted that
Since the size of Υ5 (Qx , Qv , λ7 , λ8 ) and E3 is (Ns Nr + 1 + Nj Nr ) × (Ns Nr + 1 + Nj Nr ), we have rank(Υ5 (Qx , Qv , λ7 , λ8 )) + rank(E3 ) ≤ Ns Nr + 1 + Nj Nr . From S-procedure [19], we have λ5 ≥ 0 and λ6 ≥ 0. We will prove that λ5 > 0 by reductio ad absurdum. If λ5 = 0, the constraint tr(ΔH†r W3 ΔHr ) ≤ 1 is not active because from (37), λ5 is its dual variable. If ΔH∗r where ∗ tr(ΔH∗† r W3 ΔHr ) < 1 is the worst channel uncertainty which † minimizes tr(Hr Qx Hr ), we can always find a scaler ν > 1 ∗ ∗ which satisfies tr(ν 2 ΔH∗† r W3 ΔHr ) ≤ 1. Substituting νΔHr † into tr(Hr Qx Hr ), we obtain the lower value than that obtained by ΔH∗r . It is contradictory to the assumption that ΔH∗r is the worst channel uncertainty which minimizes tr(H†r Qx Hr ). Thus, λ5 > 0. Similarly, we have λ6 > 0. Therefore, rank(Υ5 (Qx , Qv , λ7 , λ8 )) ≥ Ns Nr + Nj Nr and rank(E3 ) ≤ 1. For the constraint Υ1 (Qx , λ1 ) 0, we have Υ1 (Qx , λ1 )E1 = Hd Qx H†d E1 + diag(λ1 W1 , −λ1 − β1 )E1
(68)
(69)
¯ d ]† . From KKT conditions, we have Υ1 (Qx , where Hd = [I, h λ1 )E1 = 0. Since the size of E1 and Υ1 (Qx , λ1 ) is (Ns + 1) × (Ns + 1), we have rank(E1 ) + rank(Υ1 (Qx , λ1 )) ≤
rank
H†d E1 Hd
+
Nr
Ukk
Qx ≤ 2,
(75)
k=1
we have rank(Qx ) ≤ 2. A PPENDIX B P ROOF OF P ROPOSITION 3 We have the following lemma. Lemma 3 [Corollary 2]: Consider the problem min f (X, a) X,a
s.t. (X, a) ∈ X × A
(76)
where f (X, a) is a continuously differentiable function; X ⊆ CN ×N and A ⊆ R are closed, nonempty, and convex subsets. Suppose that the sequence {(X(k) , a(k) )} generated by optimizing X and a alternatively has limit points. Every limit point of {(X(k) , a(k) )} is a stationary point of (76). It is noted that by Proposition 1, the rank-relaxed problem of max Γ∈Θ
min
hd ∈Hd ,gd ∈Gd , he ∈He ,ge ∈Ge
ξ1 + ξ4 + ζ1 (a1 ) + ζ2 (a2 )
(77)
where Γ = (Qx , Qv , Φ, a1 , a2 ) and Θ = {Γ|(15b), (15c), (26b), (15e), a1 > 0, a2 > 0} .
(78)
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The objective function of (77) is continuously differentiable. The feasible set is closed, nonempty, and convex. Further(k) (k) (k) (k) more, the sequence {Γ(k) } = {(Qx , Qv , Φ(k) , a1 , a2 )} generated by optimizing (Qx , Qv , Φ), a1 , and a2 alternatively has limit points because of the individual transmit power constraints in (15b). By Bolzano-Weierstrass theorem, we know that {Γ(k) } have limit points. Therefore, invoking Lemma 3, we conclude that every limit point Γ generated by Algorithm 1 is a stationary point of (77). In the following, we will prove that every stationary point of (77) is also a stationary point of the rank-relaxed problem of (15). Denote the objectives of problem (77) and the rank-relaxed problem of (15) as ϕ1 (Γ) and ϕ2 (Qx , Qv , Φ), respectively. Since Γ is a stationary point of (77), we have tr ∇Qx ϕ1 (Γ )† (Qx − Qx ) ≤ 0, ∀ Qx ∈ Θ, (79) tr ∇Qv ϕ1 (Γ )† (Qv − Qv ) ≤ 0, ∀ Qv ∈ Θ, (80)
[4] C. Xing, N. Wang, J. Ni, Z. Fei, and J. Kuang, “MIMO beamforming designs with partial CSI under energy harvesting constraints,” IEEE Signal Process. Lett., vol. 20, no. 4, pp. 363–366, Apr. 2013. [5] Z. Xiang and M. Tao, “Robust beamforming for wireless information and power transmission,” IEEE Wireless Commun. Lett., vol. 1, no. 4, pp. 372– 375, Aug. 2012. [6] B. K. Chalise, W.-K. Ma, Y. D. Zhang, H. A. Suraweera, and M. G. Amin, “Optimum performance boundaries of OSTBC based AF-MIMO relay system with energy harvesting receiver,” IEEE Trans. Signal Process., vol. 61, no. 17, pp. 4199–4213, Sep. 2013. [7] J. Huang, Q. Li, Q. Zhang, G. Zhang, and J. Qin, “Relay beamforming for amplify-and-forward multi-antenna relay networks with energy harvesting constraint,” IEEE Signal Process. Lett., vol. 21, no. 4, pp. 454–458, Apr. 2014. [8] Y. Pei, Y.-C. Liang, K. C. Teh, and K. H. Li, “Secure communication in multiantenna cognitive radio networks with imperfect channel state information,” IEEE Trans. Signal Process., vol. 59, no. 4, pp. 1683–1693, Apr. 2011. [9] Q. Li and W.-K. Ma, “Spatially selective artificial-noise aided transmit optimization for MISO multi-eves secrecy rate maximization,” IEEE Trans. Signal Process., vol. 61, no. 10, pp. 2704–2717, May 2013. [10] P.-H. Lin, S.-H. Lai, S.-C. Lin, and H.-J. Su, “On secrecy rate of the generalized artificial-noise assisted secure beamforming for wiretap channels,” IEEE J. Sel. Areas Commun., vol. 31, no. 9, pp. 1728–1740, Sep. 2013. [11] J. Huang and A. L. Swindlehurst, “Robust secure transmission in MISO channels based on worst-case optimization,” IEEE Trans. Signal Process., vol. 60, no. 4, pp. 1696–1707, Apr. 2012. [12] J. Huang and A. L. Swindlehursr, “Cooperative jamming for secure communications in MIMO relay networks,” IEEE Trans. Signal Process., vol. 59, no. 10, pp. 4871–4884, Oct. 2011. [13] J. Yang, I.-M. Kim, and D. I. Kim, “Optimal cooperative jamming for multiuser broadcast channel with multiple eavesdroppers,” IEEE Trans. Wireless Commun., vol. 12, no. 6, pp. 2840–2852, Jun. 2013. [14] K.-H. Park, T. Wang, and M.-S. Alouini, “On the jamming power allocation for secure amplify-and-forward relaying via cooperative jamming,” IEEE J. Sel. Areas Commun., vol. 31, no. 9, pp. 1741–1750, Sep. 2013. [15] L. Liu, R. Zhang, and K. C. Chua, “Secrecy wireless information and power transfer with MISO beamforming,” IEEE Trans. Signal Process., vol. 62, no. 7, pp. 1850–1863, Apr. 2014. [16] D. W. K. Ng and R. Schober, “Resource allocation for secure communication in systems with wireless information and power transfer,” in Proc. IEEE Globecom Workshops, 2013, pp. 1251–1257. [17] D. W. K. Ng, L. Xiang, and R. Schober, “Multi-objective beamforming for secure communication in systems with wireless information and power transfer,” in Proc. IEEE PIMRC, 2013, pp. 7–12. [18] D. W. K. Ng, E. S. Lo, and R. Schober, “Robust beamforming for secure communication in systems with wireless information and power transfer,” IEEE Trans. Wireless Commun., vol. 13, no. 8, pp. 4599–4615, Aug. 2014. [19] Z.-Q. Luo, J. F. Sturm, and S. Zhang, “Multivariate nonnegative quadratic mappings,” SIAM J. Optim., vol. 14, no. 4, pp. 1140–1162, 2004. [20] S. Boyd and L. Vandenberghe, Convex Optimization. Cambridge, U.K.: Cambridge Univ. Press, 2004. [21] L. Grippo and M. Sciandrone, “On the convergence of the block nonlinear Gauss-Seidel method under convex constraints,” Oper. Res. Lett., vol. 26, no. 3, pp. 127–136, Apr. 2000.
∇ai ϕ1 (Γ )† (ai − ai ) ≤ 0, ∀ ai > 0, i ∈ {1, 2}. From Proposition 1, (45), (46), and (81), we have −1 a1 = Φ + max gd† Qv gd ,
(82)
gd ∈Gd
a2 =
1 + max ge† Qv ge + max h†e Qx he ge ∈Ge
(81)
−1
he ∈He
.
(83)
Substituting (82), (83) into (79), (80), it can be verified that ∇Qx ϕ2 (Qx , Qv , Φ ) = ∇Qx ϕ1 (Γ ),
(84)
∇Qv ϕ2 (Qx , Qv , Φ )
(85)
= ∇Qv ϕ1 (Γ ).
Therefore, we conclude from (84), (85) and (79), (80) that tr ∇Qx ϕ2 (Qx , Qv , Φ )† (Qx − Qx ) ≤ 0, ∀ Qx ∈ Θ,
(86)
tr ∇Qv ϕ2 (Qx , Qv , Φ )† (Qv − Qv ) ≤ 0, ∀ Qv ∈ Θ, (87) i.e., (Qx , Qv ) is an optimal solution of the following problem max tr ∇Qx ϕ2 (Γ )† (Qx − Qx ) Qx ∈Θ,Qv ∈Θ
+ tr ∇Qv ϕ2 (Γ )† (Qv − Qv ) .
(88)
Hence, (Qx , Qv , Φ ) must satisfy the KKT conditions of (88). The KKT conditions of (88) are exactly the KKT conditions of the rank-relaxed problem of (15). R EFERENCES [1] L. R. Varshney, “Transporting information and energy simultaneously,” in Proc. IEEE ISIT, 2008, pp. 1612–1616. [2] P. Grover and A. Sahai, “Shannon meets Tesla: Wireless information and power transfer,” in Proc. IEEE ISIT, 2010, pp. 2363–2367. [3] R. Zhang and C. K. Ho, “MIMO broadcasting for simultaneous wireless information and power transfer,” IEEE Trans. Wireless Commun., vol. 12, no. 5, pp. 1989–2001, May 2013.
Qi Zhang (S’04-M’11) received the B.Eng. (Hons.) and M.S. degrees from the University of Electronic Science and Technology of China (UESTC), Chengdu, Sichuan, China, in 1999 and 2002, respectively. He received the Ph.D. degree in electrical and computer engineering from the National University of Singapore (NUS), Singapore, in 2007. He is currently an Associate Professor with the School of Information Science and Technology, Sun Yat-Sen University, China. From 2007 to 2008, he was a Research Fellow in the Communications Lab, Department of Electrical and Computer Engineering, NUS. From 2008 to 2011, he was at the Center for Integrated Electronics, Shenzhen Institutes of Advanced Technology, Chinese Academy of Sciences and The Chinese University of Hong Kong. His research interests are in simultaneous wireless information and power transfer (SWIPT), cooperative communications, and ultra-wideband (UWB) communications.
ZHANG et al.: COOPERATIVE JAMMING AIDED ROBUST SECURE TRANSMISSION
Xiaobin Huang received the B.S. degree from Sun Yat-Sen University (SYSU), Guangzhou, China, in 2012. He is currently working toward the M.S. degree at the School of Information Science and Technology, SYSU. His research interests are in simultaneous wireless information and power transfer (SWIPT), full-duplex wireless communications, and cooperative communications.
Quanzhong Li received the B.S. and Ph.D. degrees from Sun Yat-Sen University (SYSU), Guangzhou, China, in 2009 and 2014, respectively. He is currently a Lecturer with the School of Advanced Computing, SYSU. His research interests are in simultaneous wireless information and power transfer (SWIPT), cognitive radio, cooperative communications, and multiple-input-multiple-output (MIMO) communications.
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Jiayin Qin received the M.S. degree in radio physics from Huazhong Normal University, China, in 1992, and the Ph.D. degree in electronics from Sun Yat-Sen University (SYSU), Guangzhou, China, in 1997. Since 1999, he has been a Professor with the School of Information Science and Technology, SYSU. From 2002 to 2004, he was the Head of the Department of Electronics and Communication Engineering, SYSU. From 2003 to 2008, he was the Vice Dean of the School of Information Science and Technology, SYSU. His research areas include wireless communication and submillimeter wave technology. Dr. Qin is the recipient of the IEEE Communications Society Heinrich Hertz Award for Best Communications Letter in 2014, the Second Young Teacher Award of Higher Education Institutions, Ministry of Education (MOE), China in 2001, the Seventh Science and Technology Award for Chinese Youth in 2001, the New Century Excellent Talent, MOE, China in 1999.
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Cooperative Jamming Aided Robust Secure Transmission for Wireless Information and Power Transfer in MISO Channels Qi Zhang, Member, IEEE, Xiaobin Huang, Quanzhong Li, and Jiayin Qin
Abstract—Considering simultaneous wireless information and power transfer (SWIPT), we investigate cooperative-jamming (CJ) aided robust secure transmission design in multiple-inputsingle-output channels, where a cooperative jammer introduces jamming interferences and assists a source to supply wireless power for both an energy receiver and a legitimate destination. The destination employs a power splitting (PS) scheme to split the received signals for both information decoding and energy harvesting (EH). Compared with conventional transmission without SWIPT, the transmission with SWIPT should satisfy additional worst-case EH constraints. Furthermore, the PS scheme introduces an additional multiplicative optimization variable, i.e., the PS factor. Our objective is to maximize worst-case secrecy rate under transmit power constraints and worst-case EH constraints. We propose to decouple the problem into three optimization problems and employ alternating optimization algorithm to obtain the locally optimal solution. For the optimization of transmit covariance matrices and PS factor, we propose to employ the S-procedure and its extension to reformulate it as a convex semidefinite programming. It is shown through the simulation results that our proposed CJ aided robust secure transmission scheme outperforms the robust direct transmission scheme without CJ and the CJ aided non-robust scheme. Index Terms—Cooperative jamming (CJ), energy harvesting (EH), multiple-input-single-output (MISO), power splitting (PS), security, simultaneous wireless information and power transfer (SWIPT).
I. I NTRODUCTION
S
IMULTANEOUS wireless information and power transfer (SWIPT), which belongs to energy harvesting (EH) techniques, is promising to solve energy scarcity problem in energyconstrained wireless networks [1], [2]. The SWIPT scheme for single-input-single-output (SISO) channel was investigated in [1], [2]. Motivated by benefits of multi-antenna techniques, the SWIPT schemes for multiple-input-single-output (MISO) and multiple-input-multiple-output (MIMO) channels were studied Manuscript received December 20, 2014; accepted February 9, 2015. Date of publication February 20, 2015; date of current version March 13, 2015. This work was supported in part by the National Natural Science Foundation of China under Grant 61472458, Grant 61202498, and Grant 61173148 and in part by the Fundamental Research Funds for the Central Universities under Grant 15lgzd10 and Grant 15lgpy15. The associate editor coordinating the review of this paper and approving it for publication was M. Tao. Q. Zhang, X. Huang, and J. Qin are with the School of Information Science and Technology, Sun Yat-Sen University, Guangzhou 510006, China (e-mail: [email protected]; [email protected]; issqjy@ mail.sysu.edu.cn). Q. Li is with the School of Advanced Computing, Sun Yat-Sen University, Guangzhou 510006, China (e-mail: [email protected]). Digital Object Identifier 10.1109/TCOMM.2015.2405063
in [3]–[5]. The SWIPT scheme for MIMO relay networks was investigated in [6], [7]. For co-located information decoding (ID) and EH receivers, two practical receiver designs were proposed for SWIPT, namely, time switching (TS) and power splitting (PS) [3]. With TS, the receiver switches over time between ID and EH, while with PS, the receiver splits the received signal into two streams of different powers for ID and EH separately. It is worth noting that TS can be regarded as a special form of PS with only binary PS ratios and thus in general PS achieves better rate-energy transmission tradeoff than TS [3]. Because of broadcast nature of radio propagation and inherent randomness of wireless channel, radio transmission is vulnerable to attacks from unexpected eavesdroppers [8]–[14]. Secure communications in MISO SWIPT systems were studied in [15]–[17] where perfect channel state information (CSI) was considered. In practice, it is difficult to obtain perfect CSI because of channel estimation and quantization errors. Without SWIPT, the robust secure transmission in conventional MISO broadcast systems was widely studied in the literature [9], [11] where channel uncertainties are modeled by worst-case model. The robust secrecy transmission schemes with artificial noise (AN) and generalized AN were considered in [9], [10]. Considering SWIPT, Ng et al. proposed a robust secure beamforming scheme in multiuser MISO SWIPT systems [18]. Besides AN and generalized AN [9], [10], another efficient way to increase secrecy rate in wireless systems is cooperative jamming (CJ), which employs a friendly jammer to introduce jamming interference to degrade eavesdropper channel [11]– [14]. In [11], by assuming that the source and the jammer know perfect CSI from themselves to the legitimate destination and imperfect CSI from themselves to the eavesdropper, Huang et al. proposed a zero-forcing (ZF) based CJ aided robust secure transmission scheme in MISO channels where channel uncertainties are modeled by worst-case model. To the best of our knowledge, the research on CJ aided robust secure transmission scheme for SWIPT in MISO Channels is missing. In this paper, considering SWIPT, we investigate the robust secure transmission design problem in MISO channels, where a multi-antenna cooperative jammer introduces jamming interferences to degrade eavesdropper channels and assists a multiantenna source to supply wireless power for a multi-antenna energy receiver and a legitimate destination. The destination employs power splitting (PS) scheme proposed in [3] to split the received signals into two streams of different powers for ID and EH separately. We assume that the source and the jammer
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ZHANG et al.: COOPERATIVE JAMMING AIDED ROBUST SECURE TRANSMISSION
know imperfect CSI from themselves to legitimate destination, eavesdropper and energy receiver. The channel uncertainties are characterized by worst-case model as in [9], [11]. Compared with the conventional CJ aided robust secure transmission without SWIPT in [11], the transmission with SWIPT of source and jammer should satisfy additional worst-case EH constraints at energy receiver and legitimate destination. The aforementioned transmission problem with SWIPT is more challenging because the ZF scheme employed in conventional CJ aided robust secure transmission [11] is not available when SWIPT is considered. Furthermore, the employed PS scheme at legitimate destination introduces an additional multiplicative optimization variable, i.e., the PS factor. Our objective is to design the CJ aided robust secure transmission scheme which maximizes worst-case secrecy rate under transmit power constraints and worst-case EH constraints. We propose to decouple the problem into three optimization problems and employ alternating optimization algorithm to obtain the locally optimal solution. For the optimization problem of PS factor and transmit covariance matrices at source and jammer, we propose to employ S-procedure and its extension to reformulate it as a convex semidefinite programming (SDP). Furthermore, since the rank relaxation is used to solve the aforementioned problem, we prove that the rank of obtained transmit covariance matrix at the source is less than or equal to 2. We employ Gaussian randomization (GR) method to obtain the rank-one transmit covariance matrix at the source. The rest of this paper is organized as follows. Section II describes the system model. In Section III, we propose the CJ aided robust secure transmission scheme for SWIPT in MISO Channels. Simulation results are provided in Section IV. Finally, we conclude our paper in Section V. Notations: Boldface lowercase and uppercase letters denote vectors and matrices, respectively. The transpose, conjugate transpose, and trace of matrix A are denoted as AT , A† , and tr(A), respectively. vec(A) denotes to stack the columns of matrix A into a single vector. By A 0 or A 0, we mean that A is positive semidefinite or positive definite, respectively. λmin {A} denotes the minimum eigenvalue of A. a denotes Euclidean norm of vector a. The ⊗ denotes Kronecker product. Re{a} denotes the real part of a complex variable, a. CN (0, I) denotes the distribution of a circularly symmetric complex Gaussian vector with mean 0 and covariance I.
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Fig. 1. The system model of CJ aided robust secure transmission with SWIPT in MISO channels.
Fig. 2. The structure of legitimate destination.
and Hr ∈ CNs ×Nr , respectively. Denote the channel responses from cooperative jammer to destination, eavesdropper and energy receiver as gd ∈ CNj ×1 , ge ∈ CNj ×1 and Gr ∈ CNj ×Nr , respectively. In the network, the source transmits confidential signals to the legitimate destination while the cooperative jammer broadcasts the jamming interferences to degrade the eavesdropper channels. Different from the conventional CJ scheme considered in [11]–[14], the objective of the source and the jammer is also to supply wireless power to the energy receiver and the destination. When the source transmits confidential signal, x ∈ CNs ×1 , and the jammer broadcasts jamming interference, v ∈ CNj ×1 , the destination employs PS scheme to split the received signals into two streams of different powers for ID and EH separately, as shown in Fig. 2. Thus, the received signal at the legitimate destination for ID is √ √ (1) yd = θh†d x + θgd† v + nd
II. S YSTEM M ODEL Consider an MISO wireless communication network which consists of a source, a cooperative jammer, a legitimate destination, an energy receiver and an eavesdropper, as shown in Fig. 1. The source, the energy receiver and the jammer are equipped with Ns , Nr and Nj antennas, respectively. The legitimate destination and the eavesdropper are equipped with single antenna. A. Signal Transmission and Cooperative Jamming Denote the channel responses from source to destination, eavesdropper and energy receiver as hd ∈ CNs ×1 , he ∈ CNs ×1
where θ denotes the PS factor, i.e., percentage of signal power split for ID and nd ∼ CN (0, σd2 ) denotes additive Gaussian noise at the destination. The received signal at the eavesdropper, is ye = h†e x + ge† v + ne
(2)
where ne ∼ CN (0, σe2 ) denotes additive Gaussian noises at the eavesdropper. Without loss of generality, we assume that the noise variances at destination and eavesdropper are σd2 = σe2 = σ 2 = 1 in this paper. In (1) and (2), x ∼ CN (0, Qx ) and v ∼ CN (0, Qv ) where Qx 0 and Qv 0 are the transmit covariance matrices of x and v, respectively.
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For secure MISO communication with the existence of eavesdropper, the achievable secrecy rate is expressed as [9]
Wi 0, Ti 0, i ∈ {1, 2, 3}, assumed to be known, determine the qualities of CSI. Considering worst-case channel uncertainties, our objective is to maximize worst-case secrecy rate subject to transmit power constraints and worst-case EH constraints by properly designing Qx and Qv , i.e.,
Rs = Cd (Qx , Qv ) − Ce (Qx , Qv )
(3)
where Cd (Qx , Qv ) and Ce (Qx , Qv ) denote mutual information at the legitimate destination and the eavesdropper, respectively, θh†d Qx hd (4) Cd (Qx , Qv ) = log2 1 + 1 + θgd† Qv gd h†e Qx he Ce (Qx , Qv ) = log2 1 + . (5) 1 + ge† Qv ge
max
Qx ,Qv ,θ
The harvested energy at energy receiver is ρtr H†r Qx Hr + G†r Qv Gr
where ρ is EH efficiency that accounts for the loss in energy transducer. The harvested energy at legitimate destination is
ρtr (1 − θ) · h†d Qx hd + gd† Qv gd . (8) Without loss of generality, the EH efficiency is assumed to be ρ = 1 in this paper [3].
(15a) (15b)
∀ Hr ∈ Hr , Gr ∈ Gr (15c)
(1 − θ) · h†d Qx hd + gd† Qv gd ≥ Ed ,
(6)
(7)
Rs (Qx , Qv )
s.t. tr(Qx ) ≤ P1 , tr(Qv ) ≤ P2 tr H†r Qx Hr + G†r Qv Gr ≥ Er ,
The transmit power constraints at source and cooperative jammer, denoted as P1 and P2 , respectively, are tr(Qx ) ≤ P1 and tr(Qv ) ≤ P2 .
min
hd ∈Hd ,gd ∈Gd , he ∈He ,ge ∈Ge
∀ hd ∈ Hd , gd ∈ Gd
(15d)
Qx 0, Qv 0, 0 < θ ≤ 1
(15e)
rank(Qx ) = 1
(15f)
where Er denotes the worst-case EH constraint at energy receiver and Ed denotes the worst-case EH constraint at legitimate destination. The optimization problem (15) is non-convex which is difficult to solve. Remark: In (15), it is noted that the rank of Qv is not required to be one because the jammer broadcasts jamming interferences. III. CJ A IDED ROBUST S ECURE T RANSMISSION W ITH B OUNDED C HANNEL U NCERTAINTIES Let Φ = θ−1 . We rewrite Rs (Qx , Qv ) as follows
B. Channel Uncertainties We assume that the source and the cooperative jammer know imperfect CSI on hd , he , Hr , gd , ge , and Gr . In practice, the CSI is imperfect because of channel estimation and quantization errors. In this paper, we model the channel uncertainties by worst-case model as in [9], [11]. The channel uncertainties of channel responses hd , he , Hr , gd , ge and Gr are bounded by elliptical regions, denoted as Hd , He , Hr , Gd , Ge , and Gr , respectively,
¯ d + Δhd , Δh† W1 Δhd ≤ 1 , Hd = hd |hd = h (9) d ¯ e + Δhe , Δh† W2 Δhe ≤ 1 , He = he |he = h (10) e ¯ r + ΔHr , tr ΔH† W3 ΔHr ≤ 1 , Hr = Hr |Hr = H r (11)
¯d + Δgd , Δgd† T1 Δgd ≤ 1 , Gd = gd |gd = g (12) ¯e + Δge , Δge† T2 Δge ≤ 1 , Ge = ge |ge = g (13) ¯ r + ΔGr , tr ΔG† T3 ΔGr ≤ 1 , Gr = Gr |Gr = G r
(14) ¯ d, h ¯ e, H ¯ r, g ¯ r denote the estimates of ¯d , g ¯e and G where h channels hd , he , Hr , gd , ge and Gr , respectively; Δhd , Δhe , ΔHr , Δgd , Δge and ΔGr denote the channel uncertainties;
Rs (Qx , Qv ) = ξ1 + ξ2 + ξ3 + ξ4 where
ξ1 = ln Φ + gd† Qv gd + h†d Qx hd ,
ξ2 = −ln Φ + gd† Qv gd , ξ3 = −ln 1 + ge† Qv ge + h†e Qx he , ξ4 = ln 1 + ge† Qv ge .
(16)
(17) (18) (19) (20)
In (16), since ξ1 and ξ4 are concave and ξ2 and ξ3 are convex, Rs (Qx , Qv ) is non-convex. We have the following proposition. Proposition 1: Let a ∈ 1×1 be a positive scalar and f (a) = −ab + ln a + 1. We have −ln b =
max
a∈ 1×1 ,a>0
f (a)
(21)
and the optimal solution to the right-hand side of (21) is a = 1b . Proof: Since f (a) is concave, the optimal solution to the (a) = 0. right hand side of (21) is obtained by letting ∂f∂a We transform ξ3 and ξ4 into convex optimization problems ξ2 = ξ3 =
max
ζ1 (a1 )
(21)
max
ζ2 (a2 )
(22)
a1 ∈ 1×1 ,a1 >0 a2 ∈ 1×1 ,a2 >0
ZHANG et al.: COOPERATIVE JAMMING AIDED ROBUST SECURE TRANSMISSION
where
ζ1 (a1 ) = −a1 Φ + gd† Qv gd + ln a1 + 1, (24) ζ2 (a2 ) = −a2 1 + ge† Qv ge + h†e Qx he + ln a2 + 1. (25) We propose to decouple (15) into three optimization problems and alternatively optimize (Qx , Qv , Φ), a1 , and a2 . In the (k) (k) (k + 1)th iteration, when the optimal a1 and a2 in the kth iteration is obtained, we propose to solve the following rankrelaxed problem
(k) (k) + ζ2 a 2 max min ξ1 + ξ4 + ζ1 a 1 Qx ,Qv ,Φ
hd ∈Hd ,gd ∈Gd , he ∈He ,ge ∈Ge
(26a) s.t. (15b), (15c), h†d Qx hd + gd† Qv gd ≥ φEd , ∀ hd ∈ Hd , gd ∈ Gd
(26b)
Qx 0, Qv 0, Φ ≥ 1
(26c)
where −1
φ = 1 + (Φ − 1) .
(27)
By introducing slack variables βi , i ∈ {1, 2, 3, 4}, the problem (26) is equivalent rewritten as max
Ω
(28a)
Qx 0,Qv 0,Φ≥1
s.t.
h†d Qx hd
≥ β1 , ∀ h d ∈ H d ,
(28b)
gd† Qv gd
≤ β2 , ∀ gd ∈ Gd ,
(28c)
h†e Qx he ≤ β3 , ∀ he ∈ He ,
(28d)
ge† Qv ge
(28e)
≥ β4 , ∀ ge ∈ Ge ,
(15b), (15c), (26b), βi ≥ 0, i ∈ {1, 2, 3, 4} where (k)
(k)
Ω = ln(Φ + β1 + β2 ) − a1 (Φ + β2 ) + ln a1 (k)
(k)
−a2 (1 + β3 + β4 ) + ln a2 + ln(1 + β4 ) + 2.
(29)
The problem (28) has semi-infinite constraints (28b)–(28e), (15c), and (26b), which are intractable. To make the problem tractable, we employ S-Procedure [19] to convert the constraints (28b)–(28e), (15c), and (26b) into linear matrix inequalities (LMIs). Lemma 1 (S-Procedure [19]): Define the functions
fj (x) = x† Aj x + 2Re b†j x + cj , j = 1, 2 where Aj = A†j ∈ Cn×n , bj ∈ Cn×1 , cj ∈ R. The implication f1 (x) ≤ 0 ⇒ f2 (x) ≤ 0 holds if and only if there exists λ ≥ 0 such that A1 b1 A2 b 2 λ − 0 b†1 c1 b†2 c2 provided that there exists a point x0 such that f1 (x0 ) < 0.
909
To apply S-Procedure on the constrain (28b), we substitute (9) into (28b) and rewrite it as follows ∀ Δhd : Δh†d W1 Δhd − 1 ≤ 0; ¯ † Qx h ¯ d )† Δhd − h ¯ d +β1 ≤ 0. −Δh†d Qx Δhd −2Re (Qx h d (30) Applying S-Procedure, we convert (30) into an LMI as follows Υ1 (Qx , λ1 ) Δ λ1 W 1 + Qx = ¯ † Qx h d
¯d Qx h † ¯ ¯ d − β1 −λ1 + hd Qx h
0
(31)
for some λ1 ≥ 0. Similarly, the constraints (28c)–(28e) are also equivalently expressed as follows Υ2 (Qv , λ2 ) Δ λ 2 T1 − Q v = −¯ gd† Qv
¯d −Qv g ¯ d + β2 ¯d† Qv g −λ2 − g
Υ3 (Qx , λ3 ) Δ λ3 W 2 − Qx = ¯ † Qx −h e Υ4 (Qv , λ4 ) Δ λ 4 T2 + Q v = ¯e† Qv g
0,
¯e −Qx h ¯ † Qx h ¯ e + β3 −λ3 − h e ¯e Qv g ¯e† Qv g ¯ e − β4 −λ4 + g
(32)
0, (33)
0
(34)
for some λ2 ≥ 0, λ3 ≥ 0, λ4 ≥ 0. To covert the constraints (15c) into an LMI, we rewrite it as follows tr H†r Qx Hr ≥ Er − tr G†r Qv Gr , ∀ Hr ∈ Hr , Gr ∈ Gr .
(35)
Using the identity tr(ABCD) = vecT (DT )(CT ⊗A)vec(B), the constraint (35) is equivalently expressed as ∀ Δhr : Δh†r (I ⊗ W3 )Δhr − 1 ≤ 0; (36) h†r (I ⊗ Qx )hr ≥ Er − tr G†r Qv Gr , ∀ Gr ∈ Gr where hr = vec(Hr ). Applying S-Procedure with respect to Δhr , we have ¯r λ5 I ⊗ W 3 + I ⊗ Qx I ⊗ Qx h ˜ 0 Υ5 (Qx , λ5 ) = ¯ † I ⊗ Qx ηˆ1 h r (37) ¯ ¯ for some λ5 ≥ 0 where hr = vec(Hr ) and ¯ † (I ⊗ Qx )h ¯ r − Er + tr G† Qv Gr . ηˆ1 = −λ5 + h r r
(38)
We need the following extensions of S-Procedure [19] to covert (37) into an LMI. Lemma 2 ([19, Theorem 3.5]): The data matrices Ai , i ∈ {1, 2, · · · , 8}, satisfy A8 A6 + A 7 X 0, (A6 + A7 X)† A3 + X† A2 + A†2 X + X† A1 X ∀ I − X† A4 X 0
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if and only if there exists λ ≥ 0 such that ⎤ ⎡ ⎤ ⎡ A 8 A6 A7 0 0 0 ⎣ A†6 A3 A†2 ⎦ − λ ⎣ 0 I 0 ⎦ 0. 0 0 −A4 A†7 A2 A1
obtained, we should optimize a1 and a2 which maximize worstcase secrecy rate. For the optimization of a1 , we should solve g max −a1 Φ(k+1) + max gd† Q(k+1) d + ln a1 + 1. (45) v
To employ Lemma 2, we equivalently expressed the constraint (35) as follows ∀ Δg r : Δg †r (I ⊗ T3 )Δg r − 1 ≤ 0; (39) (37)
It is noted that in the derivation, we exchange the sequence of optimization of a1 and gd because the objective function of problem (45) is convex with respect to a1 and gd . Similarly, for the optimization of a2 , we should solve † (k+1) g + max h Q h max − a2 1 + min ge† Q(k+1) e e v e x
gd ∈Gd
a1 >0
ge ∈Ge
a2 >0
where g r = vec(Gr ). Using Lemma 2, (39) is equivalently transformed into the following LMI Υ5 (Qx , Qv , λ5 , λ6 ) ⎤ ⎡ ¯r λ5 I ⊗ W3 +I ⊗ Qx I ⊗ Qx h 0 Δ † ⎦0 ¯ I ⊗ Qx =⎣ ¯ †r I ⊗ Qv h η1 g r ¯ r λ6 I ⊗ T3 +I ⊗ Qv 0 I ⊗ Qv g (40)
+ ln a2 + 1. γ1 = max gd† Q(k+1) gd . v gd ∈Gd
Similarly, the constraint (26b) is equivalently expressed as follows ⎤ 0 ¯d† Qv ⎦ 0 g λ 8 T1 + Q v
(42)
for some λ7 ≥ 0, λ8 ≥ 0 where ¯ † Qx h ¯d + g ¯d† Qv g ¯d − φEd . η2 = −λ7 − λ8 + h d
(43)
Δgd
The Lagrangian function of problem (47) is
¯d† + Δgd† Q(k+1) L= g (¯ gd + Δgd ) v
+ κ Δgd† T1 Δgd − 1
Ω
where ω1 =
¯d ¯ † Qv g g
. d (k+1) −1 tr Qv T1
The closed-form solution to problem (48) is
−1 (k+1) = Φ(k+1) + γ1 . a1
Υ1 (Qx , λ1 ) 0, Υ2 (Qv , λ2 ) 0, Υ3 (Qx , λ3 ) 0, Υ4 (Qv , λ4 ) 0,
(51)
(52)
Similarly, we obtain the closed-form solution to problem (46) as follows
Υ5 (Qx , Qv , λ5 , λ6 ) 0,
(k+1)
Υ6 (Qx , Qv , λ7 , λ8 ) 0,
a2
tr(Qx ) ≤ P1 , tr(Qv ) ≤ P2 ,
where
βi ≥ 0, i ∈ {1, 2, 3, 4}, λl ≥ 0, l ∈ {1, 2, · · · , 8}
(49)
(k+1)
Qx 0,Qv 0,Φ≥1
s.t.
(48)
where κ denotes Lagrange multiplier. Since L is convex in Δgd , the Karush-Kuhn-Tucker (KKT) conditions are sufficient for maximizing (47). Thus, we have
√ −1 ¯d g ¯d† + T−1 (50) γ1 = tr Q(k+1) g v 1 + 2 ω1 T1
Combining (31)–(34), (40) and (42), the optimization problem (28) is recast as max
(47)
Substituting (12) into (47), we recast (47) as
¯d† + Δgd† Q(k+1) γ1 = max g (¯ gd + Δgd ) v s.t. Δgd† T1 Δgd ≤ 1.
¯ † (I ⊗ Qx )h ¯r + g ¯ †r (I ⊗ Qv )¯ η1 = −λ5 − λ6 + h g r − Er . r (41)
¯d Qx h η2 ¯d Qv g
(46)
To solve (45), we first solve the following optimization problem
¯ r ) and ¯ r = vec(G for some λ5 ≥ 0 where g
Υ6 (Qx , Qv , λ7 , λ8 ) ⎡ λ7 W 1 + Qx Δ ¯ † Qx =⎣ h d 0
he ∈He
(44)
which is a convex SDP. It can be solved efficiently using the interior-point method [20]. We have the following proposition. Proposition 2: The rank of the obtained solution Qx to (44) is less than or equal to 2. Proof: See Appendix A. In the (k + 1)th iteration, when the optimal (Qx , Qv , Φ) in (k+1) (k+1) the (k + 1)th iteration, denoted as (Qx , Qv , Φ(k+1) ), is
= (1 + γ2 + γ3 )−1
√ −1 ¯e† + T−1 ¯e g γ2 = tr Q(k+1) g , v 2 − 2 ω2 T2
(53)
(54)
¯† Q ¯e g g
, e v (55) (k+1) −1 tr Qv T2 ¯ eh ¯ † + W−1 + 2√ω3 W−1 , (56) h γ3 = tr Q(k+1) x e 2 2 (k+1)
ω2 =
ω3 =
¯e ¯ † Q(k+1) h h e x
. (k+1) tr Qx W2−1
(57)
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Thus, the proposed solution to the rank-relaxed problem of (15) is summarized as in Algorithm 1. Algorithm 1 The proposed alternating optimization algorithm for the rank-relaxed problem of (15) 1: 2:
3:
(0)
(0)
Initialize: k = 0, a1 = 1, a2 = 1; (k+1) , Repeat: Solve the problem (44) to obtain Qx (k+1) (k+1) (k+1) (k+1) , and Φ ; Obtain a1 and a2 by (52) Qv and (53), respectively; k := k + 1; Until: convergence.
We have the following proposition to theoretically prove the convergence of Algorithm 1. (k) (k) (k) (k) Proposition 3: The sequence {(Qx , Qv , Φ(k), a1 , a2 )} generated by the Algorithm 1 has limit point Γ = (Qx , Qv , Φ , a1 , a2 ) which is a KKT point of the rank-relaxed problem of (15). Proof: See Appendix B. It is noted that from Proposition 2, the obtained solution to the rank-relaxed problem of (15) by Algorithm 1, denoted as Qx , has the rank less than or equal to 2. This is because of the additional worst-case EH constraint. If rank(Qx ) = 1, we obtain the beamforming vector, denoted as qx , by decomposing Qx = qx (qx )† . If rank(Qx ) = 2, we employ the Gaussian randomization (GR) method to generate the suboptimal rankone solution. When the obtained solution to the rank-relaxed problem of (15) by Algorithm 1, denoted as Γ = (Qx , Qv , Φ , a1 , a2 ), is known, we generate L possible GR solutions of Qx as follows v = P1 Qx u−1 Qx u (58) where u is randomly generated Gaussian vector. In all the L possible Gaussian randomized solutions, the best one should satisfy worst-case EH constraints and maximize worst-case secrecy rate simultaneously. IV. S IMULATION R ESULTS In this section, we investigate the performance of proposed CJ aided robust secure transmission scheme through computer simulations. In the MISO network, we assume that all the entries in channel responses are independent and identically distributed complex Gaussian random variables with zero-mean and unit variance. The numbers of antennas equipped at the source and the jammer, if not specified, are Ns = Nj = 4. The number of antennas equipped at the energy receiver is Nr = 2. The channel uncertainty regions are assumed to be norm-bounded, i.e., Wi = Ti = (1/ωi ) I, i ∈ {1, 2, 3}
(59)
where (ω1 , ω2 , ω3 ) determines the qualities of the CSI. The parameters of channel uncertainties in (59) are ω1 = ω3 = 0.01 and ω2 = 0.1. The transmit power constraints at source and cooperative jammer, if not specified, are P1 = P2 = P .
Fig. 3. Average worst-case secrecy rate versus the worst-case EH constraint at energy receiver, i.e., α1 ; performance comparison of our proposed CJ aided robust secure transmission scheme before and after GR where P/σ 2 = 20 dB, Ns = Nj = 4, Nr = 2, ω1 = ω3 = 0.01 and ω2 = 0.1.
The worst-case EH constraints at the energy receiver and the legitimate destination are given by Er = α1 Nr P and Ed = α2 P,
(60)
respectively, where 0 ≤ α1 ≤ 1 is the ratio of Er to Nr P and 0 ≤ α2 ≤ 1 is the ratio of Ed to P . In the process of GR, we employ L = 10 in the simulations. For our proposed CJ aided robust secure transmission scheme, the optimal solution to the rank-relaxed problem of (15) without GR serves as a performance upper bound. In Fig. 3, we compare the average worst-case secrecy rates of proposed CJ aided robust secure transmission scheme after GR (denoted as “Robust CJ, GR” in the legend) and the performance upper bound (denoted as “Robust CJ, UB”) when the transmit power to noise power ratio, P/σ 2 , is 20 dB. From Fig. 3, it is observed that our proposed CJ aided robust secure transmission scheme after GR approaches the performance upper bound. This is because the probability that solution Qx to the rank-relaxed problem of (15) has rank of one is high. In Fig. 4, we compare the average worst-case secrecy rates of our proposed CJ aided robust secure transmission scheme, the robust directtransmission scheme without aid of CJ (denoted as “Robust DT”) and the CJ aided non-robust secure transmission scheme (denoted as “Non-RobustCJ”). The worst-case EH constraints at energy receiver and legitimate destination are 2Nr P and P , respectively, i.e., α1 = 2 and α2 = 1. The robust direct transmission scheme is obtained by solving (15) with transmit power constraints tr(Qx ) ≤ 2P and tr(Qv ) ≤ 0. The CJ aided non-robust secure transmission scheme is obtained by solving (15) where the parameters of channel uncertainties are mistaken as ω1 = ω3 = 0 and ω2 = 0.1. From Fig. 4, it is observedthat our proposed “Robust CJ” scheme achieves lower average worst-case secrecy rate than the “Robust DT” scheme when P/σ 2 is relatively low. This is because when P/σ 2 is low, the transmit power of source for our proposed “Robust CJ” scheme is only half of that of the “Robust DT” scheme. Furthermore, since the signal-to-noise ratio at eavesdropper is low, the jamming interferences from jammer is less useful to
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Fig. 4. Average worst-case secrecy rate versus the transmit power to noise power ratio, P/σ 2 ; performance comparison of our proposed CJ aided robust secure transmission scheme, the robust direct transmission scheme without aid of CJ and the CJ aided non-robust secure transmission scheme where Ns = Nj = 4, Nr = 2, ω1 = ω3 = 0.01 and ω2 = 0.1.
Fig. 6. Average worst-case secrecy rate versus the number of transmit antennas at source and at jammer Ns = Nj = N ; performance comparison of our proposed CJ aided robust secure transmission scheme, the robust direct transmission scheme without aid of CJ and the CJ aided non-robust secure transmission scheme where P/σ 2 = 20 dB, α1 = 2, α2 = 1, Nr = 2, ω1 = ω3 = 0.01 and ω2 = 0.1.
In Fig. 6, we present the average worst-case secrecy rate versus the number of transmit antennas at source and at jammer Ns = Nj = N , where P/σ 2 = 20 dB, α1 = 2, and α2 = 1. From Fig. 6, it is shown that the worst-case secrecy rate improves with increase of the number of transmit antennas. That is because more transmit antennas allow the source to steer its antenna beam towards legitimate destination and energy receiver. More transmit antennas also allow the jammer to steer its antenna beam towards eavesdropper and energy receiver. Furthermore, the gaps between our proposed “Robust CJ” scheme and other two schemes become larger with increase of the number of transmit antennas. V. C ONCLUSION Fig. 5. Average worst-case secrecy rate versus α1 ; performance comparison of our proposed CJ aided robust secure transmission scheme, the robust direct transmission scheme without aid of CJ and the CJ aided non-robust secure transmission scheme where P/σ 2 = 20 dB, α2 = 1, Ns = Nj = 4, Nr = 2, ω1 = ω3 = 0.01 and ω2 = 0.1.
increase the secrecy rate. When P/σ 2 is high, our proposed “Robust CJ” scheme achieves much higher average worst-case secrecy rate than the “Robust DT” scheme. It is also found from Fig. 4, when α1 = 2 and α2 = 1, average worst-case secrecy rate of the “Non-Robust CJ” scheme is zero whereas when α1 = 0 and α2 = 0, average worst-case secrecy rate of the “Non-Robust CJ” scheme approaches that of the “Robust CJ” scheme. This is because when α1 = 2 and α2 = 1, the worst-case EH constraints at energy receiver and legitimate destination are not satisfied for the “Non-Robust CJ” scheme. In Fig. 5, we show the effect of EH constraint at the energy receiver on average worst-case secrecy rate, where P/σ 2 = 20 dB and α2 = 1. From Fig. 5, it is observed that with increase of α1 , the worst-case secrecy rate decreases. It is also found that our proposed “Robust CJ” scheme has significant performance gain over the “Robust DT” scheme and the “Non-Robust CJ” scheme.
In this paper, we have proposed the CJ aided robust secure transmission scheme for SWIPT in MISO channels where the cooperative jammer introduces jamming interferences to degrade eavesdropper channels and assists the source to supply wireless power for the energy receiver and the legitimate destination. Simulation results demonstrate that although the obtained locally optimal transmit covariance matrix has rank of one or two, our proposed CJ aided robust secure transmission scheme after GR approaches the performance upper bound. It is also found our proposed CJ aided robust secure transmission scheme outperforms the robust direct transmission scheme without CJ and the CJ aided non-robust scheme. A PPENDIX A P ROOF OF P ROPOSITION 2 The Lagrangian dual function of (44) with respect to Qx is given by ¯ =− tr(Qx E0 ) − tr (Υ1 (Qx , λ1 )E1 ) − tr (Υ3 (Qx , λ3 )E2 ) L −tr(Υ5 (Qx , Qv , λ5 , λ6 )E3 )−tr(Υ6 (Qx , Qv , λ7 , λ8 )E4 ) + q (tr(Qx ) − P1 )
(61)
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where the dual variables E0 ∈ H+ , E1 ∈ H+ , E2 ∈ H+ , E3 ∈ H+ , E4 ∈ H+ , and q ≥ 0 are corresponding to the constraints Qx 0, Υ1 (Qx , λ1 ) 0, Υ3 (Qx , λ3 ) 0, Υ5 (Qx , Qv , λ5 , λ6 )) 0, Υ6 (Qx , Qv , λ7 , λ8 ) 0, and tr(Qx ) ≤ P1 in (44), respectively. It is noted the optimal solution to the problem (44) should satisfy that the constraint (28c) is active. From (28c), the constraint (26b) is equivalent to h†d Qx hd ≥ φEd − β2 , ∀ hd ∈ Hd .
(62)
Comparing the constraints (28b) and (62), we know that the probability that the constraints (28b) and (62) are equal is zero. Thus, either the constraint (62) is not satisfied or the constraint (62) is not active. If the constraint (62) is not satisfied, the problem (28) is infeasible. If the constraint (62) is not active, we have E4 = 0. We rewrite Υ5 (Qx , Qv , λ5 , λ6 ) as Υ5 (Qx , Qv , λ5 , λ6 ) = Ψ + P†1 (I ⊗ Qx )P1 + P†2 (I ⊗ Qv )P2
(63)
Ψ = diag(λ5 I ⊗ W3 , ηˆ1 , λ6 I ⊗ T3 ),
(64)
where
P1 = [ I
¯d h
0 ],
(65)
P2 = [ 0
¯d g
I ],
(66)
ηˆ1 = −λ5 − λ6 − Er .
(67)
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N + 1. From S-procedure [19], we have λ1 ≥ 0. It can be verified that λ1 > 0 such that rank(Υ1 (Qx , λ1 )) ≥ Ns and rank(E1 ) ≤ 1. Furthermore, rank(E1 ) = 0. Thus, rank(E1 ) = 1. Similarly, we have Υ3 (Qx , λ3 )E2 = −He Qx H†e E2 + diag(λ3 W2 , −λ3 + β3 )E2
(70)
¯ e ]† . Furthermore, rank(E2 ) = 1. where He = [I, h ¯ with respect to Qx and applyTaking partial derivative of L ing KKT conditions, we have Nr
E0 + H†d E1 Hd − H†e E2 He +
Ukk − qI = 0
(71)
⎤ U1Nr ⎥ .. ⎦. . UNr Nr
(72)
k=1
where
⎡
U11 ⎢ .. † P1 E3 P1 = ⎣ . UN r 1
··· .. . ···
Multiplying both sides of (71) with Qx , we have Nr † Ukk Qx = H†e E2 He + qI Qx . (73) Hd E1 Hd + k=1
Since H†e E2 He + qI 0 has full rank, we have Nr † Ukk Qx = rank(Qx ). rank Hd E1 Hd +
(74)
k=1
From KKT conditions, we have Υ5 (Qx , Qv , λ7 , λ8 )E3 = 0.
It is noted that
Since the size of Υ5 (Qx , Qv , λ7 , λ8 ) and E3 is (Ns Nr + 1 + Nj Nr ) × (Ns Nr + 1 + Nj Nr ), we have rank(Υ5 (Qx , Qv , λ7 , λ8 )) + rank(E3 ) ≤ Ns Nr + 1 + Nj Nr . From S-procedure [19], we have λ5 ≥ 0 and λ6 ≥ 0. We will prove that λ5 > 0 by reductio ad absurdum. If λ5 = 0, the constraint tr(ΔH†r W3 ΔHr ) ≤ 1 is not active because from (37), λ5 is its dual variable. If ΔH∗r where ∗ tr(ΔH∗† r W3 ΔHr ) < 1 is the worst channel uncertainty which † minimizes tr(Hr Qx Hr ), we can always find a scaler ν > 1 ∗ ∗ which satisfies tr(ν 2 ΔH∗† r W3 ΔHr ) ≤ 1. Substituting νΔHr † into tr(Hr Qx Hr ), we obtain the lower value than that obtained by ΔH∗r . It is contradictory to the assumption that ΔH∗r is the worst channel uncertainty which minimizes tr(H†r Qx Hr ). Thus, λ5 > 0. Similarly, we have λ6 > 0. Therefore, rank(Υ5 (Qx , Qv , λ7 , λ8 )) ≥ Ns Nr + Nj Nr and rank(E3 ) ≤ 1. For the constraint Υ1 (Qx , λ1 ) 0, we have Υ1 (Qx , λ1 )E1 = Hd Qx H†d E1 + diag(λ1 W1 , −λ1 − β1 )E1
(68)
(69)
¯ d ]† . From KKT conditions, we have Υ1 (Qx , where Hd = [I, h λ1 )E1 = 0. Since the size of E1 and Υ1 (Qx , λ1 ) is (Ns + 1) × (Ns + 1), we have rank(E1 ) + rank(Υ1 (Qx , λ1 )) ≤
rank
H†d E1 Hd
+
Nr
Ukk
Qx ≤ 2,
(75)
k=1
we have rank(Qx ) ≤ 2. A PPENDIX B P ROOF OF P ROPOSITION 3 We have the following lemma. Lemma 3 [Corollary 2]: Consider the problem min f (X, a) X,a
s.t. (X, a) ∈ X × A
(76)
where f (X, a) is a continuously differentiable function; X ⊆ CN ×N and A ⊆ R are closed, nonempty, and convex subsets. Suppose that the sequence {(X(k) , a(k) )} generated by optimizing X and a alternatively has limit points. Every limit point of {(X(k) , a(k) )} is a stationary point of (76). It is noted that by Proposition 1, the rank-relaxed problem of max Γ∈Θ
min
hd ∈Hd ,gd ∈Gd , he ∈He ,ge ∈Ge
ξ1 + ξ4 + ζ1 (a1 ) + ζ2 (a2 )
(77)
where Γ = (Qx , Qv , Φ, a1 , a2 ) and Θ = {Γ|(15b), (15c), (26b), (15e), a1 > 0, a2 > 0} .
(78)
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IEEE TRANSACTIONS ON COMMUNICATIONS, VOL. 63, NO. 3, MARCH 2015
The objective function of (77) is continuously differentiable. The feasible set is closed, nonempty, and convex. Further(k) (k) (k) (k) more, the sequence {Γ(k) } = {(Qx , Qv , Φ(k) , a1 , a2 )} generated by optimizing (Qx , Qv , Φ), a1 , and a2 alternatively has limit points because of the individual transmit power constraints in (15b). By Bolzano-Weierstrass theorem, we know that {Γ(k) } have limit points. Therefore, invoking Lemma 3, we conclude that every limit point Γ generated by Algorithm 1 is a stationary point of (77). In the following, we will prove that every stationary point of (77) is also a stationary point of the rank-relaxed problem of (15). Denote the objectives of problem (77) and the rank-relaxed problem of (15) as ϕ1 (Γ) and ϕ2 (Qx , Qv , Φ), respectively. Since Γ is a stationary point of (77), we have tr ∇Qx ϕ1 (Γ )† (Qx − Qx ) ≤ 0, ∀ Qx ∈ Θ, (79) tr ∇Qv ϕ1 (Γ )† (Qv − Qv ) ≤ 0, ∀ Qv ∈ Θ, (80)
[4] C. Xing, N. Wang, J. Ni, Z. Fei, and J. Kuang, “MIMO beamforming designs with partial CSI under energy harvesting constraints,” IEEE Signal Process. Lett., vol. 20, no. 4, pp. 363–366, Apr. 2013. [5] Z. Xiang and M. Tao, “Robust beamforming for wireless information and power transmission,” IEEE Wireless Commun. Lett., vol. 1, no. 4, pp. 372– 375, Aug. 2012. [6] B. K. Chalise, W.-K. Ma, Y. D. Zhang, H. A. Suraweera, and M. G. Amin, “Optimum performance boundaries of OSTBC based AF-MIMO relay system with energy harvesting receiver,” IEEE Trans. Signal Process., vol. 61, no. 17, pp. 4199–4213, Sep. 2013. [7] J. Huang, Q. Li, Q. Zhang, G. Zhang, and J. Qin, “Relay beamforming for amplify-and-forward multi-antenna relay networks with energy harvesting constraint,” IEEE Signal Process. Lett., vol. 21, no. 4, pp. 454–458, Apr. 2014. [8] Y. Pei, Y.-C. Liang, K. C. Teh, and K. H. Li, “Secure communication in multiantenna cognitive radio networks with imperfect channel state information,” IEEE Trans. Signal Process., vol. 59, no. 4, pp. 1683–1693, Apr. 2011. [9] Q. Li and W.-K. Ma, “Spatially selective artificial-noise aided transmit optimization for MISO multi-eves secrecy rate maximization,” IEEE Trans. Signal Process., vol. 61, no. 10, pp. 2704–2717, May 2013. [10] P.-H. Lin, S.-H. Lai, S.-C. Lin, and H.-J. Su, “On secrecy rate of the generalized artificial-noise assisted secure beamforming for wiretap channels,” IEEE J. Sel. Areas Commun., vol. 31, no. 9, pp. 1728–1740, Sep. 2013. [11] J. Huang and A. L. Swindlehurst, “Robust secure transmission in MISO channels based on worst-case optimization,” IEEE Trans. Signal Process., vol. 60, no. 4, pp. 1696–1707, Apr. 2012. [12] J. Huang and A. L. Swindlehursr, “Cooperative jamming for secure communications in MIMO relay networks,” IEEE Trans. Signal Process., vol. 59, no. 10, pp. 4871–4884, Oct. 2011. [13] J. Yang, I.-M. Kim, and D. I. Kim, “Optimal cooperative jamming for multiuser broadcast channel with multiple eavesdroppers,” IEEE Trans. Wireless Commun., vol. 12, no. 6, pp. 2840–2852, Jun. 2013. [14] K.-H. Park, T. Wang, and M.-S. Alouini, “On the jamming power allocation for secure amplify-and-forward relaying via cooperative jamming,” IEEE J. Sel. Areas Commun., vol. 31, no. 9, pp. 1741–1750, Sep. 2013. [15] L. Liu, R. Zhang, and K. C. Chua, “Secrecy wireless information and power transfer with MISO beamforming,” IEEE Trans. Signal Process., vol. 62, no. 7, pp. 1850–1863, Apr. 2014. [16] D. W. K. Ng and R. Schober, “Resource allocation for secure communication in systems with wireless information and power transfer,” in Proc. IEEE Globecom Workshops, 2013, pp. 1251–1257. [17] D. W. K. Ng, L. Xiang, and R. Schober, “Multi-objective beamforming for secure communication in systems with wireless information and power transfer,” in Proc. IEEE PIMRC, 2013, pp. 7–12. [18] D. W. K. Ng, E. S. Lo, and R. Schober, “Robust beamforming for secure communication in systems with wireless information and power transfer,” IEEE Trans. Wireless Commun., vol. 13, no. 8, pp. 4599–4615, Aug. 2014. [19] Z.-Q. Luo, J. F. Sturm, and S. Zhang, “Multivariate nonnegative quadratic mappings,” SIAM J. Optim., vol. 14, no. 4, pp. 1140–1162, 2004. [20] S. Boyd and L. Vandenberghe, Convex Optimization. Cambridge, U.K.: Cambridge Univ. Press, 2004. [21] L. Grippo and M. Sciandrone, “On the convergence of the block nonlinear Gauss-Seidel method under convex constraints,” Oper. Res. Lett., vol. 26, no. 3, pp. 127–136, Apr. 2000.
∇ai ϕ1 (Γ )† (ai − ai ) ≤ 0, ∀ ai > 0, i ∈ {1, 2}. From Proposition 1, (45), (46), and (81), we have −1 a1 = Φ + max gd† Qv gd ,
(82)
gd ∈Gd
a2 =
1 + max ge† Qv ge + max h†e Qx he ge ∈Ge
(81)
−1
he ∈He
.
(83)
Substituting (82), (83) into (79), (80), it can be verified that ∇Qx ϕ2 (Qx , Qv , Φ ) = ∇Qx ϕ1 (Γ ),
(84)
∇Qv ϕ2 (Qx , Qv , Φ )
(85)
= ∇Qv ϕ1 (Γ ).
Therefore, we conclude from (84), (85) and (79), (80) that tr ∇Qx ϕ2 (Qx , Qv , Φ )† (Qx − Qx ) ≤ 0, ∀ Qx ∈ Θ,
(86)
tr ∇Qv ϕ2 (Qx , Qv , Φ )† (Qv − Qv ) ≤ 0, ∀ Qv ∈ Θ, (87) i.e., (Qx , Qv ) is an optimal solution of the following problem max tr ∇Qx ϕ2 (Γ )† (Qx − Qx ) Qx ∈Θ,Qv ∈Θ
+ tr ∇Qv ϕ2 (Γ )† (Qv − Qv ) .
(88)
Hence, (Qx , Qv , Φ ) must satisfy the KKT conditions of (88). The KKT conditions of (88) are exactly the KKT conditions of the rank-relaxed problem of (15). R EFERENCES [1] L. R. Varshney, “Transporting information and energy simultaneously,” in Proc. IEEE ISIT, 2008, pp. 1612–1616. [2] P. Grover and A. Sahai, “Shannon meets Tesla: Wireless information and power transfer,” in Proc. IEEE ISIT, 2010, pp. 2363–2367. [3] R. Zhang and C. K. Ho, “MIMO broadcasting for simultaneous wireless information and power transfer,” IEEE Trans. Wireless Commun., vol. 12, no. 5, pp. 1989–2001, May 2013.
Qi Zhang (S’04-M’11) received the B.Eng. (Hons.) and M.S. degrees from the University of Electronic Science and Technology of China (UESTC), Chengdu, Sichuan, China, in 1999 and 2002, respectively. He received the Ph.D. degree in electrical and computer engineering from the National University of Singapore (NUS), Singapore, in 2007. He is currently an Associate Professor with the School of Information Science and Technology, Sun Yat-Sen University, China. From 2007 to 2008, he was a Research Fellow in the Communications Lab, Department of Electrical and Computer Engineering, NUS. From 2008 to 2011, he was at the Center for Integrated Electronics, Shenzhen Institutes of Advanced Technology, Chinese Academy of Sciences and The Chinese University of Hong Kong. His research interests are in simultaneous wireless information and power transfer (SWIPT), cooperative communications, and ultra-wideband (UWB) communications.
ZHANG et al.: COOPERATIVE JAMMING AIDED ROBUST SECURE TRANSMISSION
Xiaobin Huang received the B.S. degree from Sun Yat-Sen University (SYSU), Guangzhou, China, in 2012. He is currently working toward the M.S. degree at the School of Information Science and Technology, SYSU. His research interests are in simultaneous wireless information and power transfer (SWIPT), full-duplex wireless communications, and cooperative communications.
Quanzhong Li received the B.S. and Ph.D. degrees from Sun Yat-Sen University (SYSU), Guangzhou, China, in 2009 and 2014, respectively. He is currently a Lecturer with the School of Advanced Computing, SYSU. His research interests are in simultaneous wireless information and power transfer (SWIPT), cognitive radio, cooperative communications, and multiple-input-multiple-output (MIMO) communications.
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Jiayin Qin received the M.S. degree in radio physics from Huazhong Normal University, China, in 1992, and the Ph.D. degree in electronics from Sun Yat-Sen University (SYSU), Guangzhou, China, in 1997. Since 1999, he has been a Professor with the School of Information Science and Technology, SYSU. From 2002 to 2004, he was the Head of the Department of Electronics and Communication Engineering, SYSU. From 2003 to 2008, he was the Vice Dean of the School of Information Science and Technology, SYSU. His research areas include wireless communication and submillimeter wave technology. Dr. Qin is the recipient of the IEEE Communications Society Heinrich Hertz Award for Best Communications Letter in 2014, the Second Young Teacher Award of Higher Education Institutions, Ministry of Education (MOE), China in 2001, the Seventh Science and Technology Award for Chinese Youth in 2001, the New Century Excellent Talent, MOE, China in 1999.
