## I Introduction

For the sake of green communication, wireless devices are urged to transmit with a very low power. However, due to the broadcast nature of wireless signals, wireless information is still vulnerable to eavesdroppers. Consequently, energy-efficient secure communication has arisen to be an important problem in wireless networks [1, 2]

. In public places, since eavesdroppers can easily hide themselves and are hard to be distinguished, secure information is easy to be overheard by the eavesdroppers and secure communication is difficult to be guaranteed. Thus, this paper focuses on secure communication issues in public places, especially in city public transportation vehicles. For example, when a manager takes a city train or light rail for one-hour business trip, he would make the best use of the travel time to fulfill commercial tasks via wireless networks, including e-transaction, classified file transfer and email transmission. Meanwhile, a commercial spy/eavesdropper who is disguised as a passenger in the same carriage can easily capture those wireless signals carrying the sensitive information, which may cause huge loss to the company as well as the individual. Therefore, when potential eavesdroppers are detected, security techniques should be employed immediately to protect information transmission.

To address this issue, apart from the traditional encryption techniques at the application layer, physical-layer (PHY) security techniques dedicate to prevent eavesdroppers from intercepting wireless messages, thus enhancing security from the most bottom layer and from the first beginning. One important performance criterion of PHY security is achievable secrecy rate (SR) which is defined as the difference between the transmission rate of the legitimate channel and that of the wiretap channel [3]. Here the legitimate channel is the channel between the transmission node and the intended destination, while the wiretap channel is the channel between the transmitter and the eavesdropper. A positive SR can be achieved when the wiretap channel is worse than legitimate channel. But if the SR is downgraded below zero, secure transmission will not be guaranteed and the eavesdropper may successfully capture confidential information. In order to improve the secrecy performance of wireless communication systems, many effective schemes have been proposed such as artificial noise [2, 4], directional modulation (DM) [5, 6] and cooperative jamming (CJ) [7, 8, 9]. Artificial noise is often generated by the transmission node which is equipped multiple antennas so that the noise can be steered to only degrade the wiretap channel. The DM synthesis is achievable by transmitting confidential messages directly towards the desired receivers [5]. However, DM is not so feasible in the scenario of city public transportation because it is technically difficult for a remote Base Station (BS) to generate such narrow beams to directionally distinguish the mobile nodes in the same carriage of a public vehicle.

On the contrary, CJ is preferable in the concerned application scenario because mobile devices carried by passengers in the same vehicle are potentially helpful cooperative nodes. The main idea of CJ is that all cooperative nodes assist the transmitter in the secure transmission by generating artificial noise signals to interfere with the eavesdropper. Although CJ can enhance the SR by taking advantage of user cooperation, the good performance is achieved with the help of cooperative nodes which consume their energy to generate and transmit interference signals. One main obstacle that hinder the employment of CJ-based schemes is that cooperative nodes are usually themselves energy starving, e.g., mobile users in the scenario of this article. Therefore, it is critical to fully compensate the energy consumption of cooperative nodes through energy harvesting techniques.

Wireless energy harvesting is an emerging approach to power the energy-constrained networks and help prolonging the lifetime of wireless nodes [10, 11]. In recent works, radio frequency (RF) energy harvesting techniques are separated into two main families: simultaneous wireless information and power transfer (SWIPT) and wireless powered tranfer (WPT) [12]. In SWIPT, the transmitted signals carry both energy and information to contemporaneously achieve information delivery and wireless energy recharging [13]. In contrast, WPT divides wireless communication into two phases. The power transfer phase first broadcasts energy-containing signals to recharge the energy harvesting wireless nodes; then, these nodes transmit packets by utilizing the harvested energy in the previous phase. From the aspect of complexity, WPT is more suitable than SWIPT in the scenario of this article because the cooperative jammers only need the energy of radio signals from power station and they have no interest in the content of those signals.

Although either cooperative jamming or wireless power transfer has been well studied in literature, it is in recent years that their combination has become an attractive research topic [14, 15, 16, 17]. The authors in [14] proposed a hybrid base station (BS) which first transfers power to the source and then executes cooperative jamming while the source transmits the information using the harvested energy. However, in the scenario of public transportation, rather than the hybrid BS, it is more reasonable to deploy a power station inside a vehicle to wireless charge cooperative nodes, considering the long distance between the BS and each cooperative node. The wireless-powered network described in [15] assumed cooperative nodes to be untrusted. In that scenario, the cooperative nodes also acted as relays, i.e., they need to relay the information from the source. The secure network in [16] comprises of one source, one jammer and one destination. The SR at the destination is maximized by jointly optimizing the power allocation on each subcarrier at the source and the jammer as well as the time allocation between two time slots. In [17], the authors provided an overview on cooperative jamming strategies for wireless powered communication networks. Designed for different application scenarios, those CJ strategies cannot be directly employed in public transportation. To the best of our knowledge, this is the first paper investigating the PHY security issue for public transportation. The main contributions of this paper are summarized as follows:

(1) A cooperative jamming based secure communication model with energy harvesting capability is established for public transportation. In this model, cooperative jamming is fulfilled by both fixed jammers and mobile jammers. The fixed jamming nodes pre-installed in the vehicle can help to guarantee basic secrecy performance in the worst-case scenario with no mobile users in the vehicle. On the contrary, when there are other mobile users in the vehicle, they can act as mobile jammers to greatly interfere with the eavesdropper and to maximize the SR. Since mobile jammers consume their limited energy to transmit the interference signals, energy compensation is provided in the model through energy harvesting.

(2) To obtain the best secrecy and power performance, two CJ based optimal schemes are proposed, namely beamforming-CJ-SR-maximization (B-CJ-SRM) and beamforming-CJ-transmit-power-minimization (B-CJ-TPM). These two schemes are designed to maximize the SR and to minimize the transmit power of the BS, respectively. As to B-CJ-SRM, with the constraint on the maximum signal-to-interference-noise-ratio (SINR) of the eavesdropper, the original optimization problem is first converted into a tractable problem, then into a standard semidefinite programming (SDP) problem by the semidefinite relaxation (SDR) technique. Similarly, the original problem of B-CJ-TPM is also transformed into a SDP which can be easily solved by CVX tools. Simulation results show that our schemes have better secrecy and power performance than some existing schemes such as zero-forcing [8] and QoSD [18].

(3) Due to the relatively high complexity of the proposed two optimal schemes, we then design two corresponding low-complexity schemes, namely LC-B-CJ-SRM and LC-B-CJ-TPM. These two schemes both employ concave convex procedure (CCCP) iterative method to obtain sub-optimal solutions of their original optimization. The main ideas of two proposed low-complexity schemes are described as follows. First, the optimization problem is transformed into an equivalent difference of convex (DC) programming. Then the CCCP-based iterative method is employed to solve the DC programming. During each iteration, only a second-order cone programming (SOCP) needs to be solved. Finally the complexity of the two proposed schemes are derived, proved to be much lower than that of their original schemes. Simulation results show that our low-complexity schemes have similar performance to our optimal schemes.

The rest of this paper is organized as follows. In Section II, a CJ based secure communication model with energy harvesting capability is introduced. Section III describes our proposed two CJ based schemes namely B-CJ-SRM and B-CJ-TPM. In Section IV, to reduce the complexity of the proposed schemes, we further design their low-complexity versions namely LC-B-CJ-SRM and LC-B-CJ-TPM. Section V presents simulation results to validate the effectiveness and advantage of the proposed schemes. Finally, Section VI concludes the paper.

Notations: In this paper, the lower-case, boldface lower-case and boldface upper-case letters are used to denote scalars, vectors and matrices, respectively. The transpose, conjugate, conjugate transpose, rank and trace of the matrix are denoted as , , , and Tr(), respectively. denotes that is Hermitian positive semidefinite matrix. denotes expectation.

denotes the circularly symmetric, complex Gaussian distribution with mean

and variance

. denotes the base-2 logarithm.## Ii System model

As shown in Fig. 1, we consider a downlink secure communication system with one Base Station (BS), one destination user, one eavesdropper, one power station and, totally cooperative nodes. Except the BS, all other nodes are deployed in a public transportation vehicle. The destination user can be actually a mobile user, who is a passenger in the vehicle. The BS is equipped with antennas and each of all other users is equipped with a single antenna. The power station is pre-installed in the vehicle for wirelessly transferring power to the cooperative nodes. The cooperative nodes marked as are used to transmit jamming signals to deliberately confuse the eavesdropper. We assume that, among the total cooperative nodes, the first two nodes are fixed and pre-installed in the vehicle, while the remaining nodes are mobile jamming nodes, which are actually mobile users (e.g., passengers). This assumption is to guarantee a certain level of secrecy in the worst-case scenario, where there is no mobile jamming node in the vehicle, which may happen during the non-peak hours. In this worst-case scenario, the fixed jamming nodes can still transmit jamming signals to create interference at the eavesdropper. Instead of only one node, at least two single-antenna jamming nodes are required in order to enable the jamming nodes to deliberately create different amounts of interference at the eavesdropper and destination user.

Besides those two fixed cooperative nodes, the mobile users who are also passengers in the vehicle can participate as mobile cooperative jamming nodes. These mobile users are potentially excellent jamming helpers because they may locate close to the eavesdropper. For example, in peak hours, a number of mobile users in the same vehicle can be used to greatly interfere with the eavesdropper such that to improve the secrecy performance. We note that, when these mobile users perform cooperative jamming, they consume the limited energy of their batteries. Compensation or incentive mechanism should be introduced for these helpers. As such, in this work we consider that a power station is available to transfer power to the cooperative jamming nodes. In addition, we assume that when each cooperative node transmits jamming signal, its transmit power should not exceed the power received from the power station.

The information signal vector transmitted from the BS and the jamming signal vector transmitted from the cooperative nodes are denoted by and respectively, where is beamforming vector adopted by the BS, represents the confidential information signal for the destination user with . Then the received signals at the destination user and the eavesdropper can be expressed as

(1) |

and

(2) |

respectively, where the vectors and denote the transmission channel and wiretap channel respectively, while the vectors and denote the jamming channels from the

cooperative nodes to the destination user and the eavesdropper, respectively. In this work, we assume that all the channel state information is available for designing the secure system. The assumption that the eavesdropper’s channel state information is available can be justified by the fact that the eavesdropper can be a potential legitimate user and thus it has already cooperated with the BS to conduct channel estimation in order to potentially receive information from the BS. In (

1) and (2), and represent the Additive white Gaussian noise (AWGN) with variance , at the destination and eavesdropper, respectively, while is the zero-mean Gaussian artificial noise (AN) vector with covariance matrix , i.e., and .We denote the maximum transmit power of the BS as and then we have

(3) |

As assumed, the transmit power of each cooperative node is no more than its harvested power from the power station, i.e.,

(4) |

where is the harvested power of -th cooperative node, while is a column vector in which the -th element is 1 and all other elements are all 0’s. Following (1), the achievable rate from the BS to the destination is given by

(5) |

Likewise, following (2) the achievable rate from the BS to the eavesdropper is given by

(6) |

Then, the achievable SR is given by . In this work, a positive SR can be guaranteed due to the known CSI in the considered system model. For example, the BS can transmit the confidential information in the null space of the eavesdropper’s channel to guarantee and such that . As such, in this work the achievable SR can be directly written as . As such, following (5) and (6) the achievable SR as a function of and is given by

(7) |

With the aid of the cooperative nodes, the ultimate goal of the BS is to maximize subject to the power constraints at the BS and the cooperative nodes or to minimize some power consumption while guaranteeing a certain level of SR. In the following section, we will tackle the optimization of and in order to achieve these ultimate goals.

## Iii Proposed Joint Design of Secure Beamforming and Cooperative Jamming

In this section, we joint design the beamforming vector at the BS (i.e., ) and the covariance matrix of the transmitted AN at the cooperative nodes (i.e., ) in order to achieve different goals of the BS. Specifically, we first propose the B-CJ-SRM scheme to maximize the achievable SR subject to the power constraints at the BS and the cooperative nodes. In addition, we propose the B-CJ-TPM scheme to minimize the power consumption at the BS while guaranteeing , where is the minimum required value of .

### Iii-a Proposed B-CJ-SRM

Originally, our objective is to maximize the SR given in (II) subject to the power constraints at the BS and the cooperative nodes. However, as per (II

) we can see that maximizing the achievable SR is to maximize a product of two correlated and generalized eigenvectors, which is a challenging problem to solve. Although a linear search method is employed to solve this kind of problem in

[19], the entire computation is quite complex, resulting in considerable energy consumption. Nevertheless, a less complex solution is feasible if the secure system has a requirement on the maximum SINR of the eavesdropper. To achieve a certain level of secrecy, it is rational to demand the SINR of the eavesdropper stay below a certain value denoted as . Then a tractable solution can be achieved by reforming the maximization of into the maximization of the destination’s SINR. So the optimization problem is given by(8) | ||||

s.t. | ||||

Expanding the square terms in (8) and using to denote (i.e., ), the optimization problem given in (8) can be rewritten as

(9) | ||||

s.t. | ||||

We note that in (9) is a non-convex constraint. For now, we remove this constraint and the optimization problem given in (9) is given by

(10) | ||||

s.t. | ||||

We note that the objective function in (10) is quasi-convex, while all other constraints are convex. Fortunately, we can convert the objective function to a convex one by Charnes-Cooper transformation [20]. Thus the optimization problem given in (10) can be again rewritten as

(11) | ||||

s.t. | ||||

where is a slack variable, , , , , , and .

Since (11) is a standard semidefinite programming (SDP) problem, the optimal solution to it can be found by using SDP solvers such as CVX tools. If the optimal solution of (11) is , then the optimal solution of (10) is [21, 22]. If the rank of is 1, can be written as

based on the eigenvalue decomposition. Therefore, the original optimization problem given in (

8) is solved and its optimal solution is . We recall that when we transfer the optimization problem (9) into (10), the constraint is removed. As such, in order to prove that the solution to (10) can offer the solution to (9), we only have to prove . This proof is detailed in Appendix A. Then, the procedure of B-CJ-SRM scheme can be summarized in Algorithm 1.### Iii-B Proposed B-CJ-TPM

In previous subsection, the SR is maximized with transmit power constraint, i.e., the transmit power of the BS cannot exceed a threshold . In that case, to obtain the optimal SR, the actual transmit power of the BS always reaches . However, green communication systems are sensitive to energy consumption. Reducing the transmit power of the BS has considerable importance to green communication, because the BS usually consume much more energy than other nodes in the network. To fulfill the coverage, the transmit power of the BS can reach as high as dozens of watts, while the cooperative nodes transmit with much lower power. So how to minimize the transmit power of the BS becomes an important issue. In this subsection, the system is designed with the objective of transmit power minimization with SR constraint, i.e., the SR cannot go below a threshold . So the problem of transmit power minimization can be formulated as

(12) | ||||

s.t. | ||||

Similar to the objective function in (8), the SR constraint in (12) is also intractable to deal with. To simplify the SR constraint, we replace it with two thresholds which separately limit the destination’s and the eavesdropper’s SINRs. Then (12) can be reformulated as

(13) | ||||

s.t. | ||||

The relationship between and is .Thus in (13) can be expressed as a function of and . Expanding the square terms in (13) and defining as , we can turn the problem (13) to

(14) | ||||

s.t. | ||||

The constraint is non-convex, but in fact it can be removed (proof can be found in Appendix B). Without this rank constraint, (14) can be rewritten as

(15) | ||||

s.t. | ||||

Defining as , as , as and as , we can transform (15) into

(16) | ||||

s.t. | ||||

Because the problem (16) is a standard SDP problem, its optimal solution denoted as can be found by using SDP solvers such as CVX tools. The rank of is proved to be 1 in Appendix B, thus the rank one constraint in (14) can be removed. Moreover, can be written as through eigenvalue decomposition. Therefore the problem (13) is solved and its optimal solution is .

Finally the procedure of our proposed B-CJ-TPM scheme can be summarized as follows.

### Iii-C Complexity Analysis

Since solving optimization problems is the major component in all our proposed schemes, the complexity of our schemes depends on the type of the optimization problems and the methods to solve them. In the following, the complexity will be analyzed according to the steps in the literature [23].

Our proposed B-CJ-SRM and B-CJ-TPM schemes are finally converted to SDP problems as (11) and (16), respectively. As a result, they can both be solved by CVX software. The solvers used by the CVX software, such as SDPT3, employ a symmetric primal-dual interior-point method. The complexity of this method is derived in [23] as

(17) |

where represents a tolerable error or computational accuracy. , and denote the dimension of the -th constraint, the number of constraints (one equality constraint is equivalent to two inequality constraints), and the total dimensions of all optimization variables, respectively, in an optimization problem.

As for B-CJ-SRM scheme, its SDP optimization problem is (11). Since equals to the number of constraints in (11), we have . Similarly, according to the aforementioned definition, we can also derive , , , . In order to differentiate the same for other schemes, we name the parameter as for B-CJ-SRM, i.e., . Then, the complexity of B-CJ-SRM is expressed as

(18) | ||||

Similarly, for B-CJ-TPM, since the corresponding SDP optimization problem is (16), we have , , , , . The complexity of B-CJ-TPM is calculated as

(19) | ||||

## Iv Proposed Low-complexity Schemes

In the scenario of this article, due to the time-varying characteristic of wireless channel, the BS should be able to solve the aforementioned optimization problems as fast as possible, so that the optimal beamforming vector and interference covariance matrix can be renewed in time. Therefore, the proposed schemes should not only keep good secrecy/power performance, but also have low computation complexity. B-CJ-SRM and B-CJ-TPM proposed in last section both have relatively high computation complexity because in order to obtain the optimal performance, rather than directly optimize the beamforming vector , the two schemes both optimize the matrix which has quadratic dimensions compared with . Therefore, the low complex schemes proposed in this section will directly optimize . These two schemes namely LC-B-CJ-SRM and LC-B-CJ-TPM both employ concave convex procedure (CCCP) iterative algorithm [24] to obtain the sub-optimal solutions of the optimization problems in B-CJ-SRM and B-CJ-TPM. The main ideas of two proposed low-complexity schemes are illustrated as follows. Firstly, if necessary, the optimization problem is transformed into an equivalent difference of convex (DC) programming [25]. Then the CCCP-based iterative algorithm is used to solve the DC programming. During each iteration of the CCCP-based iterative algorithm, only one second-order cone programming (SOCP) [26] is solved.

### Iv-a Proposed LC-B-CJ-SRM

The optimization problem (8) is a nonconvex problem because of the nonconvexity of the objective function. Next we first transform problem (8) into an equivalent DC programming and then solve this DC programming by CCCP-based iterative algorithm. At the first beginning, we rewrite the interference signals transmitted by all cooperative nodes as , where is a random artificial noise with unit power, i.e., and is a weight vector, in which denotes the weight for the th cooperative node. Then we reformulate problem (8) as

(20) | ||||

s.t. | ||||

where , , and .

By introducing a slack variable , we rewrite (20) as

(21) | ||||

s.t. | ||||

It is noted that the functions such as , , and (, ) are convex [26]. Hence, problem (21) is a DC programming. In the following, we will employ the CCCP-based iteration algorithm to find a local optimum of DC programming (21). Let

(22) |

(23) |

According to the literature [27], the first-order Tayor expansions of (22) and (23) around the point are computed as

(24) |

(25) |

In the th iteration of the CCCP-based iterative algorithm, we solve the following convex optimization problem:

(26a) | ||||

s.t. | (26b) | |||

(26c) | ||||

(26d) | ||||

(26e) | ||||

(26f) |

where the point denotes the solution to problem (26) at the th iteration.

(26b) is rewritten as

(29) |

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

(30) |

Similarly, we can also convert (26c), (26d) and (26e) into second-order cone constraints. Thus, problem (26) is converted into the following SOCP:

(31) | ||||

s.t. | ||||

where

(32) |

(33) |

Denoting as the iteration convergence threshold, we summarize the proposed LC-B-CJ-SRM scheme as Algorithm 3.

### Iv-B Proposed LC-B-CJ-TPM

For the optimization problem (13), we first transform it into an equivalent DC programming

(34a) | ||||

s.t. | (34b) | |||

(34c) | ||||

(34d) |

In the following, the CCCP-based iteration algorithm will be used to solve the DC programming (34). According to (23) and (25), we derive the th iteration of the CCCP-based iterative algorithm to solving the following optimization problem:

(35a) | ||||

s.t. | (35b) | |||

(35c) | ||||

(35d) |

Similarly, problem (35) can also be further converted to a SOCP. Since both (35b) and (35c) can be written as second-order cone constraint, therefore, problem (35) is equivalent to

(36) | ||||

s.t. | ||||

where

(37) |

(38) |

(39) |

Denoting as the iteration convergence threshold, we summarize the proposed LC-B-CJ-TPM scheme as Algorithm 4.

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