Study of Power Optimization Algorithms for Secure Communication with Untrusted AF Relays

This paper compares various power optimization algorithms for secure transmission in an amplify-and-forward (AF) network with multiple untrusted relay nodes and an external eavesdropper. In order to prevent the untrusted nodes from intercepting the source message and to achieve a positive secrecy rate, source-based-jamming (SBJ) is used. The optimization algorithms employed for secrecy rate maximization include the Nelder–Mead, Broyden–Fletcher–Goldfarb–Shanno, and Conjugate-Gradient methods. The performance of the untrusted relay is compared to the worst-case situation, in which it is assumed that all nodes cooperate with each other. The two-dimensional exhaustive search, derivative test, and equal power allocation (EPA) approaches are used as performance comparison benchmark systems. The analysis is done for symmetric and asymmetric relay positions and with different numbers of untrusted nodes. The complexity of the optimization algorithms has also been derived. Numerical results reveal that the optimal technique for secrecy rate maximization depends on the position of the selected relay. Also, there exists a trade-off between the complexity and convergence of the algorithms.