EnergyEfficient Subcarrier Pairing and Power Allocation for DF Relay Networks with an Eavesdropper
Abstract
:1. Introduction
 In contrast to [13,14,15,16,17], where the secure sum rate/EE maximization for a single subcarrier is served as the main design goal, in this paper, a joint optimization problem is formulated to maximize the secure EE of the network, subject to a total transmit power budget. The original optimization problem is NPhard. We first transform the secure EE problem into an equivalent convex problem for finding the optimal power allocation under given subcarrier pairing. The optimization problem then becomes a mixedinteger binary nonlinear programming problem. Instead of searching over all possible subcarrier pairing combinations, a nearoptimal EE maximization (EEM) algorithm is found by using the Hungarian method to reduce the computational burden. To get more insights, we derive a closedform expression for the source and the relay power allocation.
 Furthermore, a suboptimal algorithm with even less complexity but acceptable performance degradation is investigated. Next, we analyze the complexity of the proposed algorithms, and evaluate the performance and compare with an EEM algorithm without an eavesdropper (EEM w/o E) by computer simulation for understanding the tradeoff between them.
2. System Model and Problem Formulation
2.1. System Model
2.2. Optimization Problem Formulation
3. EnergyEfficient Subcarrier Pairing and Power Allocation Algorithm
3.1. Solution of the Subproblem
3.2. Solution of the Master Problem
Algorithm 1: Iterative EEM Algorithm. 

4. EnergyEfficient Suboptimal Resource Allocation Algorithm
 Intuitively, a higher power value is allocated to a subcarrier pair with better channel quality from the source to the destination nodes. Hence, the subcarriers of the SR and RD links with a higher endtoend channel gain are paired together with a higher priority. Firstly, the SR subcarriers are organized in a descending order according to their channel gains, and the RD subcarriers are also ordered in similar way. Then, the corresponding subcarriers are paired with each other in sequence. We set ${\rho}_{i,j}=1$, if the ith subcarrier of the SR link is paired with the jth subcarrier of the RD link; otherwise, ${\rho}_{i,j}=0$.
 The next step is to get the optimal power allocation $\left({\mathbf{P}}_{S},{\mathbf{P}}_{R}\right)$ for maximizing EE by solving $(\mathrm{P}.3)$ for the obtained subcarrier pairing ${\rho}_{i,j}$ in the step 1.
5. Complexity Analysis
6. Simulation Results and Discussion
7. Conclusions
Acknowledgments
Author Contributions
Conflicts of Interest
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Algorithm  Complexity 

Optimal ES  $\mathcal{O}\left({2}^{2\varrho}WLK!\left({V}^{3}+1\right)\right)$ 
EEM  $\mathcal{O}\left({2}^{2\varrho}{K}^{2}WL\left({V}^{3}+K+1\right)\right)$ 
Suboptimal  $\mathcal{O}\left({2}^{2\varrho}KWL\left({V}^{3}+3\right)\right)$ 
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Singh, K.; Ku, M.L.; Biswas, S.; Ratnarajah, T. EnergyEfficient Subcarrier Pairing and Power Allocation for DF Relay Networks with an Eavesdropper. Energies 2017, 10, 1953. https://doi.org/10.3390/en10121953
Singh K, Ku ML, Biswas S, Ratnarajah T. EnergyEfficient Subcarrier Pairing and Power Allocation for DF Relay Networks with an Eavesdropper. Energies. 2017; 10(12):1953. https://doi.org/10.3390/en10121953
Chicago/Turabian StyleSingh, Keshav, MengLin Ku, Sudip Biswas, and Tharmalingam Ratnarajah. 2017. "EnergyEfficient Subcarrier Pairing and Power Allocation for DF Relay Networks with an Eavesdropper" Energies 10, no. 12: 1953. https://doi.org/10.3390/en10121953