Secure Energy-Efﬁcient Resource Allocation Algorithm of Massive MIMO System with SWIPT

: In this paper, we consider the resource allocation problem to maximize the minimum (max–min) user’s secure energy efﬁciency (SEE) in downlink massive multiple-input multiple-output (MIMO) systems with simultaneous wireless information and power transfer (SWIPT). First, transmission power and power splitting ratio are designed to achieve the max–min user’s SEE subject to harvested energy threshold, the constraints of transmission power, and power splitting ratio. Secondly, the optimization problem is non-convex and very difﬁcult to tackle. In order to solve the optimization problem, we converted to a series of parameter optimization subproblems by fractional programming. Then, we employ the ﬁrst-order Taylor expansion and successive convex approximation (SCA) method to solve parameter optimization problems. Next, a secure energy-efﬁcient resource allocation (SERA) algorithm with the bisection method is proposed to ﬁnd the max–min SEE of the system. Finally, simulation results show the effectiveness and superiority of the SERA algorithm.


Introduction
With the rapid development of mobile internet technology, the broadcast characteristics of wireless information have led to severe information leakage problems. Physical layer security has increasingly attracted research interests in 5th-Generation (5G) mobile communication because it can ensure safe protection from information theory even when eavesdroppers have a powerful computing ability [1]. Massive multiple-input multiple-output (MIMO) is a promising technology in 5G which can be used to improve the spectrum efficiency and security of wireless communication. Moreover, massive MIMO can be used to enhance the security and power transfer efficiency of a simultaneous wireless information and power transfer (SWIPT) system because it can beamform the energy and information more accurately with large array gain [2,3].
Secure problems in massive MIMO systems have been investigated in References [4][5][6][7][8][9][10][11]. The authors in Reference [4] studied the impact of residual hardware impairment (HWI) on massive MIMO secure communication and showed the HWI has a negative impact on information security. In Reference [5], S. Timilsina et al. studied the effect of active eavesdropping on physical layer security and revealed that active eavesdroppers had a stronger ability to eavesdrop confidential information with higher pilot power. In Reference [6], Z. Chu et al. studied a MIMO secrecy channel with SWIPT. The minimum harvested energy is maximized under the secrecy rate requirements. In Reference [7], H. D. Tuan et al. considered the problem of power allocation to maximize the worst links' secrecy

System Model
As shown in Figure 1, a single-cell downlink massive MIMO system with SWIPT consists of one BS connected with K users and one eavesdropper [17][18][19]. The number of transmitting antennas at BS is N, which satisfies N >> K. Each user and the eavesdropper are equipped with a single antenna. The BS simultaneously serves K users in the same time-frequency resource block [20]. Especially, it is assumed that the active eavesdropper perfectly knows the pilot sequence transmitted by the mth user node [21], where m ∈ {1, ..., K}. Without loss of generally, we suppose that each time slot has a unit length. Each time slot has two parts. In the first time slot τ, users use the energy harvested by the previous time block to transmit pilot information to the BS. The active eavesdropper also transmits pilot information to the BS. In the 1 − τ time slot, BS transmits information or energy to users and the eavesdropper. The user's terminal receiver decodes the signal into two parts; one part is used for information decoding, and the other is used for energy harvesting. The eavesdropper mainly is used for information decoding [15]. The BS-to-user and BS-to-eavesdropper channels are denoted by G, h, which is given by are the small scale Rayleigh fading and where D m,m = β m , m = {1, ..., K} and ϑ are the path loss from BS-to-user and BS-to-eavesdropper channels, respectively. The path loss is modeled as β m = l −r m and ϑ = d −r , where r is the path loss exponent factor, l m is the distance between the BS and user m, and d is the distance between the BS and eavesdropper [5].
In TDD massive MIMO, the users-to-BS and eavesdropper-to-BS channels are estimated at the BS via uplink pilots transmitted. The BS stores the channel state information (CSI) through channel reciprocity. The superimposed pilot signal received at BS is where p u and p e express the average transmit powers from the users and the eavesdropper; s = {s 1 , ..., s m , ...s K } T , where s m s H m = 1 and s m s H m = 0 for m = m and m, m ∈ {1, ..., K}. n is the noise with independent and identically distributed (i.i.d.) ∼ CN (0, 1) distribution for each element. Assuming that BS uses the minimum mean squared error (MMSE) estimation, the BS-to-user channel is obtained as follows [5,19]: To prevent the eavesdropper from stealing confidential information, the BS introduces AN subsidiary communications [13]. The BS uses the power splitting ratio to information power and AN transmission power [5,19]; the transmission information at BS is given as follows: where P t represents the transmit power; ϕ = diag(ϕ 1 , ϕ 2 , ..., ϕ K ), where ϕ m is the power splitting ratio coefficient of the BS for user m(m = 1, · · · , K); channel matricesŴ ∈ C N×K and V ∈ C N×K denote the precoding matrix for the data and AN [13,22] is an AN sequence. The users utilize the power splitting ratio to decode information from BS simultaneously, where one part is used to harvest energy and the other part is decoded into useful information, and the eavesdropper mainly wiretaps useful information from BS [23]. Therefore, the mth user and the eavesdropper receiving useful information is given as follows [5,19,20]: where ρ = {ρ 1 , ..., ρ m , ..., ρ K } express the power splitting receiver from users. The first item denotes the desired signal, the second term is the beamforming gain uncertainty, the third term is the inter-user interference, and the remaining terms are AN leaked to legitimate users and the additive white Gaussian noise (AWGN) at the mth user node. The mth user harvest energy is given by where η m (0 < η m ≤ 1) is the energy conversion efficiency for user m, which transfers the harvested energy into electric energy stored by the users and eavesdropper. Provided that the worst-case uncorrelated additive noise distributed as independent Gaussian noise has the same variance [5], the achievable rate of the mth user can be lower bounded by the following expression where γ m is given by where γ m,o is the effective noise which is defined as follows: Provided that the eavesdropper eliminates the other users interference terms [5,19], the upper bounded achievable rate of the mth user signal leaked into eavesdropper can be written as where γ e,m is expressed as Hence, the mth user achievable secure rate is as follows [5,19]: Using wishart matrix to simplify Equations (8)- (14) as in References [5,19], the harvesting energy by user m can be written as follows: The achievable secure rate of user m is given by [5,19] The achievable rate of the mth user signal leaked into eavesdropper is simplified as follows [5,19]: where

Problem Formulation and Energy-Efficient Algorithm
With the above analysis for achievable rate and energy for user and eavesdropper, the max-min SEE optimization problem of the system can be expressed as In P 1 , the objective is to maximize and minimize SEE of the system. C 1 and C 3 are the transmit power constraints, and C 2 is the energy harvested constraint for user m. ε(P t ϕ m (1 − τ) + p u τ) and P c,m denote the power consumption of the mth user and circuit consumption, and ε denotes the power consumption coefficient.
The optimal solution to Equation (18) can be solved by fractional programming [24] to find zero roots of the following parameter optimization problem F(λ) [25]: According to the conclusions in References [24,25], the optimal solution to Equation (19) is λ * such that F(λ * ) = 0 is held. We define Γ m as Due to the non-smoothness of the objective function, we introduce a new variable t to transform the equivalent non-smooth optimization problem in Equation (20) into a smooth optimization problem. Equation (18) can be equivalently reformulated as , ∀m P 2 has four optimization variables. First, fix BS' power splitting ratio coefficient ϕ m and the transmit power P t are used to obtain a ρ m suboptimal solution. Then, use the suboptimal solution of ρ m iterative optimization power splitting ratio coefficient ϕ m and the BS transmit power P t . Finally, update variable t.
Firstly, optimize ρ m . Because ρ m is only associated with R l m (P t , ϕ m , ρ m ) from Equations (16) and (20), which is monotonic decreasing function about ρ m , ρ m depends on constraint C 2 .
Then, optimize ϕ m , and P t is a hard problem. In Equation (21), the difference of two convex functions is non-convex. Therefore, we need to replace the non-convex part in Equation (21) by linear approximation and we rewrite constraint C 5 ; let Finally, we use the difference of convex functions algorithm (DCA) from References [14,26]. P 3 is as follows: In Equation (25), C 5 is the difference between two concave functions, which can be effectively solved by sequential convex programming. At step n, we get an iterative power allocation. We use first-order Taylor expansion h m (P t , ϕ m ) We further transform P 3 into , ∀m P 4 now is a smooth and standard convex optimization problem, and thus, it can be efficiently solved by successive convex approximation (SCA) method [15].
Up till now, the convex programming P 4 is capable of successively approximating the solution of the original SEE optimization problem. We will employ the bisection method in one-dimension to update λ where ρ * m is the optimal values of ρ m in Equation (22) and where P * t and ϕ * m are the optimal values of P t and ϕ m from Algorithm 1.
Solve (27) to obtain P * t and ϕ * m Set n = n + 1, and P n t = P * t and ϕ n m = ϕ * m Calculate F n = min m [ f m (ϕ n m , P n t ) − h m (ϕ n m , P n t )] until F n − F n−1 < ζ Based on the above discussion, we propose a SERA algorithm for the max-min SEE in massive MIMO systems by Algorithm 2.
Then, we characterize the computational complexity of the proposed algorithm to get a better insight into the computational complexity of the SERA algorithm. The SCA method complexity is O(IK 3 2 log 1 ς ) [27]; ς is the convergence precision, and I denotes the value of iterations. Therefore, the total computational complexity of the SERA algorithm is about O(I 2 K 3 2 log L ς 2 ), and L is the length of the value.

Simulation Results
In this part, simulation results are presented to show the effectiveness of the proposed algorithm. The simulation parameters are given as follows. The number of users is K = 4. The coordinates of BS are (40,0)m; the users are randomly distributed in the rectangular area [−20, 20] × [−20, 20] m. The path loss model is adopted with path loss exponent r = 3.3. The background noise is σ 2 m = σ 2 e = σ 2 z = −90 dBm [14], and the user fixed circuit power loss is P c,m = 5 dBm. Figure 2 compares the minimum SEE of each algorithm for different P max . When the transmit power P max of the BS increases, the minimum SEE obtained by the min user' SEE maximization and users' system SEE maximization gradually increases to remain unchanged; this is because the increase of the BS transmit power resistant against eavesdroppers achieves a balance in the information rates leaked into the eavesdropper. Moreover, as can be seen from the secure rate maximization algorithm, with the increase of power, the ultimate SEE decreases. Therefore, it shows the stability of the SERA algorithm.   Figure 3 shows the minimum SEE of the three algorithms for the different number of BS antennas. The minimum SEE is monotone increasing with the antenna number of BS for three algorithms. This is because of the array gain due to the multi-antenna diversity. As the number of BS antennas increases, the secure rate of three algorithms increases faster than the power consumption. In addition, it can be observed that the minimum SEE performance of the SERA algorithm is better than the other two algorithms.  In Figure 4, we show the convergence performance of the different P max . It can be seen that the SERA algorithm can quickly converge. In the three cases under consideration, the number of iterations that the algorithm converges to the optimal value is within four times. When the number of BS antennas is N = 100, the numerical results reveal that the performance of the P max = 30 dBm has increased about 20.1% and 41.5% more than P max = 25 dBm and P max = 15 dBm.  In Figure 5, we show the minimum SEE versus the eavesdropper transmit power under different algorithms. When the number of BS antennas is N = 100 and BS transmit power P max = 30 dBm, as the eavesdropper transmit power increases, the minimum SEE gradually decreases. From Equation (4), increasing the eavesdropper transmit power impacts the channel estimation. This leads to a decrease in the SEE and an increase in the information rates leaked into the eavesdropper.  Figure 6 shows the minimum SEE of the three algorithms for a different number of users. The minimum SEE is monotone decreasing with the number of users. The minimum SEE obtained by SERA algorithms is about 3% and 62.2% compared with the users' system SEE maximization and secure rate maximization algorithm when the number of users K is 4 and BS maximum transmit power is P max = 30 dBm. In addition, it can be observed that the minimum SEE performance of the SERA algorithm is better than the other two algorithms.

Conclusions
In this paper, we consider downlink massive MIMO systems employing AN auxiliary communication for the physical layer. The users use the energy harvested by the previous time block for channel estimation. At the BS, the power splitting ratio is used to reasonably allocate the information transmission power and the AN transmission power; the eavesdropper's eavesdropping ability is reduced while ensuring the integrity of the secret information transmission. The non-convex SEE maximization problem is first converted into a series of parameter optimization subproblems, which is then solved by the SCA method. A SERA algorithm with joint power splitting ratio and BS transmitted power allocation is proposed to max-min SEE of the systems. Simulation results show that the proposed algorithm can provide higher SEE compared with other benchmark algorithms.
Author Contributions: Z.W. conceived and designed the system model; X.W. analyzed the data; Z.F. contributed the formal analysis; X.Y. performed the simulation and wrote the paper. All authors have read and agreed to the published version of the manuscript.