The secure communication that multiple OFDMA-based cell-edge mobile stations (MS) can only transmit confidential messages to base station (BS) through an untrusted intermediate relay (UR) is discussed. Specifically, with the destination-based jamming (DBJ) scheme and fixed MS transmission power assumption, our focus is on the joint BS and US power allocation to maximize system sum secrecy rate. We first analyze the challenges in solving this problem. The result indicates that our nonconvex joint power allocation is equivalent to a joint MS access control and power allocation. Then, by problem relaxation and the alternating optimization approach, two suboptimal joint MS access control and power allocation algorithms are proposed. These algorithms alternatively solve the subproblem of joint BS and UR power allocation and the subproblem of MS selection until system sum secrecy rate is nonincreasing. In addition, the convergence and computational complexity of the proposed algorithms are analyzed. Finally, simulations results are presented to demonstrate the performance of our proposed algorithms.

Broadcast is a fundamental property of the wireless medium. This property makes wireless communication susceptible to eavesdropping. Traditionally, this problem is typically addressed via upper layer approaches, such as the cryptographic protocols in the application layer which relies on computational complexity. Nowadays, information-theoretic security which exploits the properties of wireless channel to secure communications has received considerable attention.

In fact, the secret communication in the presence of an eavesdropper was first introduced and studied by Wyner who considered a wiretap channel model [

Although the property of broadcasting makes wireless communication susceptible to eavesdropping, it also provides us with the opportunity to improve the security of wireless transmission by cooperation and relay [

The untrusted relay model was first studied in [

All the above-mentioned literatures [

As depicted in Figure

System model.

In our considered scenario, the MS-BS secure communication process is performed by two phases. During the first phase (Phase I, shown with solid lines in Figure

During the secondary phase (Phase II, shown with dashed line in Figure

In this section, the problem of system sum secrecy rate maximization is first introduced and we analyze the challenges in solving this problem. Second, the alternating optimization (AO) approach is provided to handle our problem and then an AO algorithm is given. The convergence and computational complexity of the AO algorithm are also analyzed. Finally, another suboptimal algorithm with lower complexity is presented.

As mentioned earlier, in our considered system, BS plays the role of jammer and relay is untrusted. The system aims to maximize sum secrecy rate by joint BS and UR power allocation. From [

With the problem definition in (

For MS-

Please see Appendix

By Lemma

For OP2, constraint (

By observing OP3, one can find that it has three important properties: (i) OP3 can be decomposed into two subproblems: the inner joint power allocation and the outer MS access selection; (ii) the inner subproblem has convex constraint set; (iii) the optimal solution of OP3 and OP2 has the following relationship.

Let

Please see Appendix

Due to the properties of OP3, solving OP3 instead of OP2 would be more sensible. However, there are four challenges should be overcome: (i) OP3 is still a MINLP which is known to be nondeterministic polynomial-time hard (NP-hard); (ii) although OP3 could be handled by alternatively solving the outer and inner subproblem, the attained solution may be outside the feasible region of OP2 (because we have removed constraint (

In this subsection, we first assume that the MS access set has been predetermined and alternatively discuss the relay and jammer power allocation. Then, a suboptimal MS access control scheme is proposed.

We first discuss relay power allocation under fixed jamming power

For OP4, its optimal solution is as follows:

Please see Appendix

At the moment, one may note that, in the above relay power allocation, we have not used the conditions presented in Lemma

Now, our attention turns to the jamming power allocation at BS for given

For OP5 with given

If

If

Please see Appendix

By the results in Theorem

Based on the alternative optimization result, a suboptimal access control scheme which can find a feasible suboptimal solution for OP3 (or OP2) is provided herein. The main idea of this scheme is as follows: when the alternative relay and jamming power optimization is convergent, we remove the MS in

In Algorithm

Algorithm

Please see Appendix

For two reasons, we propose another suboptimal algorithm for our problem: (i) pursuing lower complexity algorithm and (ii) as the benchmark scheme of Algorithm

One can note that the complexity of Algorithm

In this section, we present simulation results to demonstrate the performance of all proposed algorithms. Our simulation scenario is shown in Figure

The simulated network configuration.

In this section, we plot the MS (e.g., MS-

General secrecy rate as a function of relay power and jamming power.

In this section, we evaluate the performance of the proposed algorithms under different UR positions, number of MS, and the available BS and UR power.

We first evaluate the system performance under different UR positions and the results are presented in Figures

System sum secrecy rate versus UR-BS distance.

Number of successively accessed MS versus UR-BS distance.

Total power consumption at BS versus UR-BS distance.

From Figure

Figure

We then analyze the system performance under different MS numbers, and the results are depicted in Figures

System sum secrecy rate versus number of MS.

Number of successively accessed MS number versus number of MS.

At last, how system sum secrecy rate is affected by available UR and BS power is analyzed, and the result is shown in Figure

System sum secrecy rate versus UR and BS total power.

In this work, based on the DBJ secure communication protocol [

First, condition (

Let

In order to prove this proposition, we should first prove

If

If

If

If

Therefore, for

In fact, under the conclusion that

For given

For the first part of

Now we prove the second part of

(S1) If

(S2) If

(S2-1) For the case

(S2-2) For the case

(S2-3) For the case

From the KKT conditions, we know that, at the optimal solution

For conclusion

(S1) If

(S2) If

Then, we know that the solution of (

The legend of

For OP3 with given

The authors declare that there is no conflict of interests regarding the publication of this paper.

This work was supported by Fundamental Research Funds for the Central Universities (CDJXS11162236).