Secure Relay Beamforming for Simultaneous Wireless Information ...

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IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. 63, NO. 5, JUNE 2014

Secure Relay Beamforming for Simultaneous Wireless Information and Power Transfer in Nonregenerative Relay Networks Quanzhong Li, Qi Zhang, and Jiayin Qin Abstract—For simultaneous wireless information and power transfer (SWIPT), secure communication is an important issue. In this correspondence, we study the secure relay beamforming (SRB) scheme for SWIPT in a nonregenerative multiantenna relay network. We propose a constrained concave convex procedure (CCCP)-based iterative algorithm that is able to achieve a local optimum, where the secrecy rate is maximized, and the relay transmit power and energy harvesting constraints are satisfied. Simulation results have shown that our proposed CCCP-based iterative algorithm achieves a larger secrecy rate and lower computational complexity than the convectional SRB schemes. Since the CCCP-based iterative algorithm is still complex, we propose a semidefinite programming (SDP)-based noniterative suboptimal algorithm and a closed-form suboptimal algorithm. It is shown that when the maximum transmit power of the relay to noise power ratio is high, the SDP-based noniterative suboptimal algorithm performs close to the CCCP-based iterative algorithm. Index Terms—Beamforming, energy harvesting (EH), relay networks, security, simultaneous wireless information and power transfer (SWIPT).

I. I NTRODUCTION Simultaneous wireless information and power transfer (SWIPT), which belongs to energy harvesting (EH) techniques, is a promising approach to solving the energy scarcity problem in energy-constrained wireless networks [1], [2]. For example, sensor networks, which are typically powered by small batteries and have a limited lifetime, will prolong their network operation time by using the SWIPT scheme. The SWIPT scheme for a single-input–single-output (SISO) channel was studied in [1] and [2]. Motivated by the benefits of multiantenna techniques, SWIPT for multiple-input–multiple-output (MIMO) and multiple-input–single-output (MISO) broadcast channels was investigated in [3]–[5]. The SWIPT schemes for MIMO relay networks were studied in [6] and [7]. Because of the openness of the wireless transmission medium, wireless information is susceptible to eavesdropping. Thus, secure communication is a critical issue for SWIPT. The secure beamforming schemes for SWIPT in a MISO broadcast channel were studied in [8]–[10]. However, to the best of our knowledge, there has been no research on the secure relay beamforming (SRB) scheme for SWIPT in nonregenerative relay networks. In this correspondence, we focus on the SRB scheme for SWIPT in nonregenerative multiantenna relay networks. Our objective is to maximize the secrecy rate under the relay transmit power constraint and the EH constraint. It is noted that the conventional SRB schemes in relay networks were considered in [11]–[13]. However, the conventional SRB schemes cannot be directly applied for SWIPT in the relay networks. This is due to the nonconvexity of the EH constraint. In this correspondence, we transform the SRB problem to a difference

Manuscript received July 6, 2013; revised September 15, 2013; accepted October 25, 2013. Date of publication January 2, 2014; date of current version June 12, 2014. This work was supported in part by the National Natural Science Foundation of China under Grant 61173148 and Grant 61202498 and in part by the Scientific and Technological Project of Guangzhou City under Grant 12C42051578. The review of this paper was coordinated by Dr. I. Krikidis. The authors are with the School of Information Science and Technology, Sun Yat-Sen University, Guangzhou 510006, China (e-mail: liquanzhong2009@ gmail.com; [email protected]; [email protected]). Digital Object Identifier 10.1109/TVT.2013.2288318

Fig. 1. System model for SWIPT in the nonregenerative multiantenna relay network.

of convex (DC) programming [14]. We propose an iterative algorithm to solve this DC programming to find a local optimum of the SRB problem, which is based on the constrained concave convex procedure (CCCP) [15]. During each iteration of the CCCP-based iterative algorithm, only one second-order cone programming (SOCP) [16] is solved. Furthermore, to reduce the computational complexity, two noniterative suboptimal algorithms based on the zero-forcing (ZF) scheme are proposed. Notations: Boldface lowercase and uppercase letters denote vectors and matrices, respectively. AT , A∗ , A† , A, and tr(A) denote the transpose, conjugate, conjugate transpose, Frobenius norm, and trace of matrix A, respectively. ⊗ denotes the Kronecker product. vec(A) denotes to stack the columns of matrix A into a single vector. Re{a} denotes the real part of a complex variable, i.e., a. λmax {A} denotes the maximum eigenvalue of A. By A 0, we mean that A is positive semidefinite. II. S YSTEM M ODEL Consider a nonregenerative multiantenna relay network, shown in Fig. 1, which consists of one source, one relay, one legitimate destination, one eavesdropper, and one energy receiver. The relay is equipped with N antennas. Each of the other nodes is equipped with a single antenna. The scenario is typical for device-to-device communications [17], where two mobile phones directly communicate with the help of a femtocell or a laptop. We assume that there is no direct link between the source and other nodes except the relay as in [13]. We also assume that the channel state information (CSI) of the whole network is available at the relay such that the SRB can be performed at the relay as in [11] and [12]. This assumption is valid when the eavesdropper is active. When the eavesdropper is passive, it is shown in [18] that at a high signal-to-noise ratio (SNR), the additional knowledge of the eavesdropper CSI yields no gains in terms of the secrecy rate for slowfading channels. Denote the channels from the source to the relay, from the relay to the destination, from the relay to the eavesdropper, and from the relay to the energy receiver as hr , h†d , h†e , and h†g , respectively. The network operates in the time-division duplex (TDD) mode. In the first time slot, the source transmits signal to the relay. In the second time slot, the relay multiplies the received signal with an SRB matrix and forwards it to the destination and the energy receiver while the eavesdropper eavesdrops. The received signals at the destination and the eavesdropper, which are denoted by yd and ye , respectively, are expressed as yd = h†d Fhr x + h†d Fnr + nd

(1)

ye = h†e Fhr x

(2)

+

h†e Fnr

+ ne

0018-9545 © 2014 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications_standards/publications/rights/index.html for more information.


where x denotes the transmit signal from the source; F denotes the linear SRB matrix at the relay; and nr , nd , and ne denote the additive Gaussian noise at the relay, destination, and eavesdropper, respectively, which have zero mean and variance of σ 2 = 1. From (1) and (2), the received SNR at the destination and the eavesdropper, which are denoted by γd and γe , respectively, are γd = γe =

f † Af +1

(3)

f † Cf f † Df + 1

(4)

f † Bf

where f = vec(F), A = Ps (h∗r hTr ) ⊗ (hd h†d ), B = I ⊗ (hd h†d ), C = Ps (h∗r hTr ) ⊗ (he h†e ), and D = I ⊗ (he h†e ), in which Ps is the power of the transmit signal from source x. As a result, the achievable secrecy rate, which is denoted by Rs , is given by [11]–[13] Rs =

1 + γd 1 log2 . 2 1 + γe

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it is proved that the CCCP is able to achieve a local optimum of DC programming. To derive the CCCP-based iterative algorithm for the SRB problem, we have Theorem 1. Theorem 1: For SRB problem (11), the optimal SRB vector f should satisfy that transmit power constraint (6) is active, i.e., f † Gf = Pr .

Proof: See the Appendix. It is noted that at the optimum of problem (11), EH constraint (7) is not always active. This is explained as follows. If we remove EH constraint (7) in problem (11) and find its optimal solution, which is denoted by fo , it is observed that fo† Hf o > Q occurs with certain probability. Substituting (12) into SRB problem (11), we obtain

(5)

(6)

ρf † Hf ≥ Q

(7)

where Pr is the maximum transmit power of the relay, Q is the threshold of the harvested energy at the energy receiver, ρ is the EH efficiency that accounts for the loss in energy transducer, and

G = Ps h∗r hTr ⊗ I + I

H = Ps h∗r hTr ⊗ hg h†g + I ⊗ hg h†g .

(8) (9)

In (7), without loss of generality, we assume that the EH efficiency ρ = 1 [3]. According to [3] and [4], threshold Q should be chosen such that 0 ≤ Q ≤ Qmax , where Qmax = λmax {G−1 H}Pr .

(10)

max

¯ ¯ f † Af f † Df · †¯ † ¯ f Cf f Bf

s.t.

f † Gf ≤ Pr ,

f

The constraints on the transmit power of the relay and the harvested energy at the energy receiver are f † Gf ≤ Pr

s.t.

f † Gf ≤ Pr ,

f

f † Hf ≥ Q.

(13)

f ,t

¯ − s.t. f † Cf

¯ f † Af ≤ 0, t1

¯ − f † Bf

¯ f † Df ≤0 t2

¯ ≤ 0, f † Gf ≤ Pr , t1 > 0, t2 > 0. f † Gf − f † Hf

(14)

√ It is noted that the functions of the types such as − xy, f † Af , and † f Af /x, where x > 0, y > 0, A 0, are convex [16]. Hence, problem (11) is transformed to DC programming [14]. In the following, we will employ the CCCP proposed in [15] to find a local optimum of DC programming (14). Let f † Af x

(15)

¯ . ζ(f ) = f † Hf

(16)

ξA (f , x) =

Using (3)–(10), the SRB problem for SWIPT in the nonregenerative relay network is formulated as f † (A + B)f + 1 f † Df + 1 · f † (C + D)f + 1 f † Bf + 1

¯ ≤0 f † Gf − f † Hf

¯ = B + (1/Pr )G, C ¯ =C+D+ ¯ = A + B + (1/Pr )G, B where A ¯ = D + (1/Pr )G, and H ¯ = (Pr /Q)H. (1/Pr )G, D By introducing slack variables t1 and t2 , which form vector t = [t1 , t2 ]T , we rewrite (13) as √ max t1 t2

III. S ECURE R ELAY B EAMFORMING

max

(12)

The first-order Taylor expansions of (15) and (16) around the point (˜f , x ˜) are computed as [20] (11)

SRB problem (11) is a nonconvex problem because of the nonconvexity of the objective and the EH constraint. To the best of our knowledge, problem (11) has no current globally optimal solution. Therefore, we develop an algorithm to achieve the local optimum of problem (11). A. CCCP-Based Iterative Algorithm Here, we transform SRB problem (11) into an equivalent DC programming. An optimization problem is called DC programming if its objective and/or constraints can be written as DC functions [14]. To solve this DC programming, we propose a CCCP-based iterative algorithm. The concave convex procedure (CCP) was introduced by Yuille and Rangarajan [19] to deal with unconstrained DC programming. It was extended to the constrained case by Smola et al. in [15], where

¯ } ˜f † A ¯ ˜f 2Re{˜f † Af − f, x ˜) = x ξA ¯ (f , x, ˜ x ˜ x ˜2 ¯ } − ˜f † H ¯ ˜f . ζ(f , ˜f ) = 2Re{˜f † Hf

(17) (18)

In the (n + 1)th iteration of the proposed CCCP-based iterative algorithm, we solve the following convex optimization problem: √ t1 t2 (19a) max f ,t

s.t.

(n) ¯ − ξA f , t1 , ˜f (n) , t˜1 ≤0 f † Cf ¯

(n) ¯ − ξD f , t2 , ˜f (n) , t˜2 ≤0 f † Bf ¯

(n)

f † Gf − ζ f , ˜f f † Gf ≤ Pr ,

(19b)

(19c)

≤0

t1 > 0,

t2 > 0

(19d)

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where the point (˜f (n) , ˜t(n) ) denotes the solution to problem (19) at the nth iteration. We will show that problem (19) can be further transformed into an SOCP. The objective of problem (19) can be converted into a conic quadratic-representable function by introducing slack variable z. That is, (19a) is equivalent to √ (20) max z s.t. t1 t2 ≥ z

Algorithm 1 The Proposed CCCP-Based Iterative Algorithm 1: Initialization: n = 0, (˜f (n) , ˜t(n) ) = (f0 , t0 ); 2: Repeat: Solve SOCP (26) with (˜f (n) , ˜t(n) ) and denote the optimal solution in the (n + 1)th iteration as f ∗ and t∗ ; Update (˜f (n+1) , ˜t(n+1) ) = (f ∗ , t∗ ), n := n + 1; 3: Until: convergence or n > Nmax .

which can be converted into a conic quadratic-representable function, i.e., max z

s.t. [2z, (t1 − t2 )] ≤ t1 + t2 .

(21)

B. Semidefinite Programming (SDP)-Based Noniterative Suboptimal Algorithm

(22)

To reduce the computational complexity, we propose a noniterative suboptimal SRB algorithm, which is based on the ZF scheme. In the proposed algorithm, we force the information leakage to the eavesdropper to be zero, i.e.,

By letting a=

1 (n) t˜1

b= −

2

˜f (n)

†

¯ ˜f (n) A

2 ¯ ˜(n) Af (n) ˜ t1

Cf = 0.

(23)

(31)

The SRB vector, i.e., f , in (31) is expressed as

(19b) is rewritten as ¯ + Re{b† f } + at1 ≤ 0 f † Cf

f = Vw 2

(25) max

Similarly, we can also convert (19c) and (19d) into second-order cone constraints. Thus, problem (19) is converted into the following SOCP: max f ,t,z

s.t.

[2z, (t1 − t2 )] ≤ t1 + t2

¯ 12 f 2C † −Re{b† f } − at1 − 1 ≤ −Re{b f } − at1 + 1

Pr , t1 > 0, t2 > 0

−2

(n) c = t˜2

˜f

(n) d = −2 t˜2

e = ˜f (n)

(n) †

†

−1

¯ ˜f (n) D

¯ ˜f (n) H

¯ ˜f (n) . g = −2H

(33)

(34) (35)

Problem (33) is transformed into the following SDP: max S,ν

tr(R1 S) + ν

s.t. tr(R2 S) + ν = 1, tr(R3 S) ≤ νPr , (26)

¯ ˜f (n) D

s.t. w† V† GVw ≤ Pr , w† V† HVw ≥ Q

tr(V BVW) + 1 = 1/ν.

where

ˆ w† V† AVw +1 w† V† BVw + 1

†

1 2G 2 f † −Re{g† f } − e − 1 ≤ −Re{g f } − e + 1 G f ≤

w

W = ww† = S/ν

¯ 12 f 2B † −Re{d† f } − ct2 − 1 ≤ −Re{d f } − ct2 + 1

2

ˆ = A + B. Problem (33) is a fractional quadratically conwhere A strained quadratic problem (QCQP) with two quadratic constraints. It is shown in [21] that this problem can be solved by employing the Charnes–Cooper transformation [22] and rank-one decomposition theorem [23]. Define

z

1 2

2

where w ∈ C(N −1)×1 is an arbitrary vector, and V ∈ CN ×(N −1) consists of N 2 − 1 singular vectors of matrix C associated with zero singular values. Substituting (32) into problem (11), we obtain

which can be converted into a second-order cone constraint, i.e.,

¯ 12 f 2C † −Re{b† f } − at1 − 1 ≤ −Re{b f } − at1 + 1.

(32)

(24)

(27) (28) (29) (30)

Denoting Nmax as the number of maximum iteration times, we summarize the proposed CCCP-based iterative algorithm for SRB problem (11) as in Algorithm 1.

tr(R4 S) ≥ νQ, S 0, ν ≥ 0

(36)

ˆ where R1 = V† AV, R2 = V† BV, R3 = V† GV, and R4 = V† HV. SDP (36) is convex and can be effectively solved using the interior-point method [16]. Assume that (So , νo ) is the optimal solution to SDP (36). If So is rank-one, which is denoted by So = so s†o , √ the optimal solution to the fractional QCQP (33) is wo = so / νo according to [21]. If rank(So ) ≥ 2, we have Theorem 2. Theorem 2 [23, Th. 2.3]: Let Ai ∈ Cn×n , i ∈ I = {1, 2, 3, 4}, be a Hermitian matrix, and Z ∈ Cn×n be a nonzero Hermitian positive semidefinite matrix. Suppose that n ≥ 3 and for any nonzero Hermitian positive semidefinite matrix Y ∈ Cn×n , [tr(A1 Y), tr(A2 Y), tr(A3 Y), tr(A4 Y)] = [0, 0, 0, 0]. If rank(Z) ≥ 2, we can find a rank-one matrix zz† such that tr(Ai zz† ) = tr(Ai Z), i ∈ I. Since R3 is Hermitian positive definite, we have [tr(R1 Y), tr(R2 Y), tr(R3 Y), tr(R4 Y)] = [0, 0, 0, 0] for any nonzero Y 0.


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When rank(So ) ≥ 2, from Theorem 2, we can find a rank-one matrix zo z†o such that tr(Ri zo z†o ) = tr(Ri So ), i ∈ I. The optimal solution √ to the fractional QCQP (33) is wo = zo / νo . C. Closed-Form Suboptimal Algorithm To further reduce the computational complexity, we propose a suboptimal closed-form solution to problem (33), which avoids solving the SDP. From Theorem 1, the transmit power constraint (6) is active at the optimum, i.e., w† V† GVw = Pr .

(37)

Substituting (37) into problem (33), we have max 1 + w

Pr w† V† AVw † w V† (Pr B + G)Vw

s.t. w† V† GVw = Pr , w† V† (QG − Pr H)Vw ≤ 0.

(38)

Define U as a matrix that consists of the eigenvectors of matrix V† (QG − Pr H)V, which are associated with the eigenvalues being no greater than zero. We have w = Ux

(39)

where x is an arbitrary vector such that †

†

w V (QG − Pr H)Vw ≤ 0.

(40)

Substituting (39) into problem (38), we have max x

1+

Pr x† U† V† AVUx † x U† V† (Pr B + G)VUx

s.t. x† U† V† GVUx = Pr .

(41)

The optimal solution to problem (41) is well known, which is expressed as follows:

xo = α U† V† (Pr B + G)VU

−1

U† V† (h∗r ⊗ hd )

(42)

where α is a scalar satisfying the transmit power constraint. Thus, the suboptimal closed-form solution to problem (33), which is denoted by wsub , is given as wsub = Uxo .

(43)

Fig. 2. Average secrecy rate versus Pr /σ 2 . The average secrecy rate comparison of our proposed CCCP-based iterative algorithm, our proposed SDP-based noniterative suboptimal algorithm, our proposed closed-form suboptimal algorithm, the SDP-based algorithm with one-dimensional search and Gaussian randomization proposed in [12], and the SDP-based algorithm with 2-D search and Gaussian randomization proposed in [11], where N = 3, Ps /σ 2 = 15 dB, Nmax = 20, and Q = 0.6 Qmax .

as “SDP+1D+Gaussian”) proposed in [12], and the SDP-based algorithm with two-dimensional search and Gaussian randomization (denoted as “SDP+2D+Gaussian”) proposed in [11]. In the simulations, the numbers of iteration times for “SDP+1D+Gaussian” and “SDP+2D+Gaussian” algorithms are 100 and 1000, respectively. The initial point (f0 , t0 ) for the CCCP-based iterative algorithm is obtained by the closed-form suboptimal algorithm. The threshold of the harvested energy at the energy receiver is Q = 0.6 Qmax , where Qmax is obtained from (10). We plot the average secrecy rate versus the maximum transmit power of the relay to noise power ratio, i.e., Pr /σ 2 . In Fig. 2, it is observed that our proposed CCCP-based iterative algorithm has a larger average secrecy rate than the “SDP+1D+Gauss” and “SDP+2D+Gauss” algorithms. It is also found that when the maximum transmit power of the relay to noise power ratio, i.e., Pr /σ 2 , is high, the SDP-based noniterative suboptimal algorithm performs close to the CCCP-based iterative algorithm. When Pr /σ 2 is higher than 35 dB, the average secrecy rate is saturated because the link from the source to the relay becomes the bottleneck of system performance. In Fig. 3, we illustrate the effect of the EH threshold on the average secrecy rate. By letting

IV. S IMULATION R ESULTS

Q = τ Qmax

Here, we present the computer simulation results of our proposed SRB schemes. We assume that in the nonregenerative relay network, all the channel responses are independent and identically distributed complex Gaussian random variables with zero mean and unit variance. In all simulations, the number of antennas equipped at the relay is N = 3. The transmit power at the source to noise power ratio is Ps /σ 2 = 15 dB. The number of maximum iteration times is Nmax = 20. In Fig. 2, we present the average secrecy rate comparison of our proposed CCCP-based iterative algorithm (denoted as “CCCPAlg” in the legend), our proposed SDP-based noniterative suboptimal algorithm (denoted as “SDP-Alg”), our proposed closed-form suboptimal algorithm (denoted as “CF-Alg”), the SDP-based algorithm with one-dimensional search and Gaussian randomization (denoted

where τ is the ratio of Q to Qmax , we plot the average secrecy rate versus τ , where Pr /σ 2 = 20 dB. In Fig. 3, it is observed that with the increase of τ , the average secrecy rate decreases. When τ is small, the average secrecy rate slowly decreases, whereas when τ is large, the average secrecy rate rapidly decreases. It is also found that when τ is small, our proposed SDP-based noniterative suboptimal algorithm performs close to the CCCP-based iterative algorithm. In Table I, we compare the computational complexity of all algorithms, where denotes the accuracy requirement, and T1D and T2D are the numbers of iterative times of “SDP+1D+Gaussian” and “SDP+2D+Gaussian” algorithms, respectively. The computational complexity for solving SDP and SOCP is obtained from [24]. From Table I, our proposed CCCP-based iterative algorithm has lower computational complexity than the “SDP+1D+Gaussian” and

(44)

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¯U ¯ † fo , where β > 0. We have ˆf † Gˆf > f † Gf o , values. Let Δf = β U o ˆf † Hˆf > f † Hf o , and o ˆf † (A + B)ˆf + 1 f † (A + B)fo + 1 > o † ˆf † Bˆf + 1 fo Bfo + 1

(45)

ˆf † Dˆf + 1 f † Dfo + 1 > † o ˆf † (C + D)ˆf + 1 fo (C + D)fo + 1

(46)

where ˆf = fo + Δf . Therefore, we can choose β appropriately such that ˆf † Gˆf = Pr . It is noted that ˆf , which is feasible, has a larger objective value than fo . R EFERENCES

Fig. 3. Average secrecy rate versus τ . The average secrecy rate comparison of our proposed CCCP-based iterative algorithm, our proposed SDP-based noniterative suboptimal algorithm, our proposed closed-form suboptimal algorithm, the SDP-based algorithm with 1-D search and Gaussian randomization proposed in [12], and the SDP-based algorithm with 2-D search and Gaussian randomization proposed in [11], where N = 3, Ps /σ 2 = 15 dB, Nmax = 20, and Pr /σ 2 = 20 dB. TABLE I C OMPUTATIONAL C OMPLEXITY C OMPARISON OF A LGORITHMS

“SDP+2D+Gaussian” algorithms. Among all the algorithms, our proposed closed-form suboptimal algorithm has the lowest computational complexity. V. C ONCLUSION In this correspondence, we have proposed three SRB algorithms for SWIPT in the nonregenerative relay network, i.e., the CCCP-based iterative algorithm, the SDP-based noniterative suboptimal algorithm, and the closed-form suboptimal algorithm. The CCCP-based iterative algorithm is able to achieve a local optimum where the secrecy rate is maximized, and the relay transmit power and EH constraints are satisfied. The SDP-based noniterative and closed-form suboptimal algorithms, which are based on the ZF scheme, have lower computational complexity. Simulation results have shown that our proposed CCCP-based iterative algorithm achieves a higher average secrecy rate and lower computational complexity than the convectional SRB schemes. It is also shown that when the maximum transmit power of the relay to noise power ratio, i.e., Pr /σ 2 , is high, the SDP-based noniterative suboptimal algorithm performs close to the CCCP-based iterative algorithm. A PPENDIX We prove Theorem 1 by reductio ad absurdum. Assume that fo ¯ ∈ is the optimal solution to (11) such that fo† Gf o < Pr . Define U 2 2 CN ×(N −N −1) as a matrix that consists of N 2 − N − 1 singular vectors of matrix [B† , C† ]† , which are associated with zero singular

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PRADA: Prioritized Random Access With Dynamic Access Barring for MTC in 3GPP LTE-A Networks Tzu-Ming Lin, Chia-Han Lee, Member, IEEE, Jen-Po Cheng, and Wen-Tsuen Chen, Fellow, IEEE

Abstract—Due to the huge amount of machine-type communications (MTC) devices, radio access network (RAN) overload is a critical issue in cellular-based MTC. The prioritized random access with dynamic access barring (PRADA) framework was proposed to efficiently tackle the RAN overload problem and provide quality of service (QoS) for different classes of MTC devices in Third-Generation Partnership Project (3GPP) Long-Term Evolution Advanced (LTE-A) networks. The RAN overload issue is solved by preallocating random access channel (RACH) resources for different MTC classes with class-dependent back-off procedures and preventing a large number of simultaneous random access requests using dynamic access barring. In this paper, the performances of LTE-A without access barring, extended access barring (EAB), and PRADA are mathematically derived and compared, showing the superior performance of the PRADA scheme. Index Terms—Access barring, long-term evolution-A (LTE-A), machine-to-machine (M2M), machine-type communication (MTC), random access network (RAN).

I. I NTRODUCTION Machine-type communications (MTC) or machine-to-machine communications emerge to achieve ubiquitous and automatic communication among devices without any human intervention. MTC devices are connected through networks and the Internet to form the so-called Internet of Things [1], enabling a wide range of applications in domains spanning domotics [2], e-health [3], smart grid [4], etc. Cellular systems are expected to play a major role in the successful deployment of MTC devices due to the benefits of widely deployed infrastructures and the support of long-range high-mobility communications [5]–[7]. In particular, the Third-Generation Partnership Project (3GPP) Long-Term Evolution Advanced (LTE-A) has been regarded Manuscript received March 21, 2013; revised June 12, 2013, August 16, 2013, and October 9, 2013; accepted October 17, 2013. Date of publication January 23, 2014; date of current version June 12, 2014. The review of this paper was coordinated by Dr. W. Song. T.-M. Lin is with the Information and Communications Research Laboratories, Industrial Technology Research Institute, Hsinchu 31040, Taiwan, and also with the Institute of Communication Engineering, National Tsing Hua University, Hsinchu 300, Taiwan. C.-H. Lee and J.-P. Cheng are with the Research Center for Information Technology Innovation, Academia Sinica, Taipei 115, Taiwan. W.-T. Chen is with the Institute of Information Science, Academia Sinica, Taipei 115, Taiwan, and also with the Institute of Communication Engineering, National Tsing Hua University, Hsinchu 300, Taiwan. Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TVT.2013.2290128

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as a promising system for facilitating MTC. However, one major challenge that the deployment of MTC over cellular networks faces is the radio access network (RAN) overload issue. Current cellular networks are designed for human-to-human (H2H) communications, and LTE-A, in particular, is designed for broadband high-data-rate applications, whereas most MTC devices transmit and receive a small amount of data. Moreover, the number of MTC devices is expected to be much larger than that of H2H communications in the near future, to reach a number ranging from billions to trillions [1], [8]. Thus, the deployment of massive MTC devices will generate a huge amount of signaling and data, yielding congestion of RAN and core network. Among the 3GPP proposals for solving this issue, extended access barring (EAB) is considered the most efficient scheme to control the potential surge of access requests [9]. Nevertheless, EAB lacks a mechanism to determine the timing of activation and the parameters to use, leading to unsatisfactory performance. Therefore, the prioritized random access with dynamic access barring (PRADA) framework [10] was proposed to efficiently tackle the overload problem for MTC operating under 3GPP LTE-A networks. In this paper, the PRADA scheme is analyzed. The access success probabilities of LTE-A without access barring, with EAB, and by applying PRADA are mathematically analyzed. Comparing with the simulation results confirms the accuracy of the theoretical analyses. The rest of this paper is organized as follows. The PRADA framework is reviewed in Section II. Performances of EAB and PRADA are analyzed in Section III and numerically compared in Section IV. Finally, Section V concludes this paper. II. P RIORITIZED R ANDOM ACCESS W ITH DYNAMIC ACCESS BARRING F RAMEWORK Prior to sending data, a user equipment (UE) gets attention of the eNB through the physical random access channel (PRACH), which carries the random access preamble. PRACH occupies several resource blocks in the frequency domain and appears every several subframes, depending on the configuration. The UE then requests for radio resources by a four-step random access (RA) procedure: random access preamble selection and transmission (called Msg1), random access response (RAR), connection request, and contention resolution [10], [11]. A collision is detected by UEs if RAR is not received within the RA response window. This happens if two or more UEs select the same preamble such that the eNB is unable to decode any of the preambles and does not send RAR. Since the number of preambles is limited, a large amount of UEs would have a high probability of selecting the same preambles. Without the unique preamble selection, a UE cannot be granted access and has to repeat the random access procedure. Thus, UEs may experience low access success rate and significant access delay if the number of UEs is huge. The PRADA framework solves the RAN overload problem by preallocating PRACH resources for different MTC classes while preventing a large number of simultaneous random access requests. The PRADA framework is composed of two core components: virtual resource allocation with class-dependent back-off procedures and dynamic access barring (DAB). To guarantee quality of service, traffic is classified into five categories: emergency, H2H, high priority, low priority, and scheduled [10]. According to the traffic classification, PRADA preassigns different amount of PRACH slots for different classes. The PRACH slots allocated to a specific class is called the virtual resource for that class. The physical resource is the PRACHs allocated by eNB, whereas the virtual resource represents the specific PRACHs that can be used for each class. Virtual resources are assigned to different kinds of traffic according to the rules specified in [10].

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