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We investigate a secure multiuser time division multiple access (TDMA) system with statistical delay quality of service (QoS) guarantee in terms of secure effective capacity. An optimal resource allocation policy is proposed to minimize the

Due to the broadcast nature of wireless communications, much more attention has been paid to the issues of privacy and security in wireless communication networks. Traditionally, security is achieved by cryptographic encryption protocols of the upper layers. However, the security of encryption will be invalid if the wiretappers have huge computational power. From the information-theoretic perspective, physical-layer security can guarantee the reliable secure transmission via utilizing the physical characteristics of wireless channels. The concept of information-theoretic secrecy was originally introduced by Shannon [

In recent years, a large amount of work has been devoted to the resource allocation based on physical-layer security. In [

It is worth mentioning that the framework employed above is not suitable for the delay-sensitive multimedia applications since Shannon theory places no restriction on the delay of the transmission scheme. However, delay-tolerant guarantee as one of the essential QoS merits plays a pivotal important role in the secure communications. Furthermore, deterministic delay bound QoS is commonly not available in wireless networks due to the unpredictable nature of the wireless fading channels. Based on the effective capacity theory proposed by Wu and Negi in [

As the extended application of the secure effective capacity for secure wireless networks, we propose a cross-layer model based power and time slot allocation policy for wiretap time division multiple access (TDMA) systems, where the delay-tolerant requirement is considered. Regarding the existence of multiple users in the system, a class of so-called

To summarize, the main contributions of this work are as follows.

(1) The secure effective capacity based on the cross-layer framework is employed for the wiretap TDMA system.

(2) Based on the cross-layer framework, two resource allocation schemes are addressed, the optimal resource allocation policy, and the non-delayed resource allocation policy. The optimal policy adaptively allocates the power and time slot to minimize the utility functions of the average user power subjected to the delay QoS requirement. The non-delayed policy minimizes the objective function without considering the delay QoS guarantee.

(3) The optimization problem is solved and analyzed based on the Lagrangian duality theory and the stochastic optimization theory. The optimal policy can get better energy efficiency and also achieve the balance of the energy efficiency and the fairness.

The rest of the paper is organized as follows. Section

In this section, we first present the system model of the wiretap TDMA system. Then, the issues of the statistical delay QoS guarantee are addressed based on the secure effective capacity.

In this paper, we investigate a network consisting of multiple users, one legitimate receiver, and one eavesdropper.

System model of the multiuser TDMA secrecy networks.

In this subsection, we utilize the secure effective capacity to measure the throughput of the secrecy system under QoS constraint. The effective capacity characterizes the maximum constant arrival rate that the channel can support and guarantees a given delay QoS requirement.

The information source stream from the upper layers and the service process driven by the resource control scheme at the physical layer are matched via the queue at the data link layer. It is assumed that the source message stream has a specified delay bound

Note that, for the secrecy system mentioned in this paper, if the channel gains during one frame satisfy

Obviously, the secure effective capacity bounded by the minimal service rate is a monotonically decreasing function of

In this section, we investigate the joint power and time slot allocation policy to minimize the total cost of average power subjected to the given delay QoS constraint specified by the secure effective capacity of each user. The cost function is a

To guarantee the QoS requirement of the secrecy system, the secure effective capacity with the corresponding delay QoS exponent should be no less than the effective bandwidth denoted as

By evaluating the Hessian matrix

In this subsection, an optimal time slot and power allocation algorithm for the optimization problem (

The master dual function is further expressed as

For each user

For the subfunction (

In this subsection, we aim to investigate the convex optimization function (

Define

Assume that, for each channel realization, i.e.,

The users in the system whose channel gains may not satisfy the secrecy communication condition

Here, we substitute

Since the constraint must be satisfied, only the user whose

Given a time slot, there will be a set

According to Lagrangian duality theory [

For ergodic fading channel with continuous CDF, if the primary system (

Trajectory locking is the key of the asymptotic optimality of the stochastic iterations.

The optimal resource allocation which satisfies the delay QoS constraint has been investigated above. In this section, we also present a non-delayed resource allocation scheme without considering the delay QoS requirement for comparison. When the delay QoS constraint of the optimization problem (

In fact, for a given time slot, the power allocation algorithm (

In this section, the numerical results of the proposed optimal resource allocation policy and non-delayed policy are provided to verify the foregoing theoretical analysis. We assume that the TDMA secrecy networks include three transmit users, one legitimate receiver, and one eavesdropper. The fading channels of different users are independent to each other. Besides, the channel power gains of the main user channels

The convergence performance of the Lagrange multipliers of the proposed optimal resource allocation policy is shown in Figure

Convergence of Lagrange multipliers.

Figure

Total average power and individual average power.

For comparison, Figure

In Figures

Total average power versus delay QoS exponent with wiretap channel conditions

Total average power versus delay QoS exponent with wiretap channel conditions

We provide the performance of the total average power versus the violation probability with delay bound

Total average power versus violation probability with delay boundary

In this paper, we propose a fair energy-efficient resource allocation policy for the multiuser TDMA secrecy system. The system model is established for the secure transmission in the presence of an eavesdropper. By employing the secure effective capacity and

The data used to support the findings of this study are available from the corresponding author upon request.

The authors declare that there are no conflicts of interest regarding the publication of this paper.

This work was supported in part by International Science & Technology Cooperation Program of China (2015DFG12580), National Science Foundation of China (61771291 and 61571272), Key R&D Program of Shandong Province (2018GGX101009), the Fundamental Research Funds of Shandong University (2016JC010), and the Ministry of Science, ICT (MSIT), South Korea, supervised by the IITP through the ITRC support program (IITP-2018-2014-1-00729).