On Power Control and Secrecy Capacity: M−Matrix Theory Based Analysis

We consider power control in multi-terminal networks and study its impact on secrecy capacities of transmitreceive pairs. Note that most approaches in the current literature on secrecy capacity consider only single terminals. Impact of power control on secrecy capacity has seldom been studied. This paper investigates a new approach using the theory of M−matrices to utility based power control with pricing in multiterminal networks. The power control problem with pricing is formulated as a non-cooperative game and necessary and sufficient conditions for the existence of a unique Nash equilibrium are obtained. Our formulation results in maximum utility for each transmit-receive pair and in maximum system utility. Some of the results reported in the literature on power control are shown to be special cases of the analysis presented here. We then address the impact of power control on the secrecy capacity in the presence of an eavesdropper, whose existence is not known to the transmit-receive pairs. Numerical results indicate that power control could improve the secrecy capacity. Also, the proposed linear pricing improves the secrecy capacity in systems with large bandwidth and non-linear pricing improves that in the low bandwidth case. Index Terms – Power control, secrecy capacity, pricing, M-matrices, multi-terminal.