Minimizing Source-Sum-Power Consumption in Multi-Sensor Single-Relay Networks

This letter provides an exact and optimal power allocation for a sensor network that consists of multiple sensor-destination pairs and a single relay. The objective of the power allocation is to minimize the sum of transmitting powers by the sensors that have a signal-to-noise-ratio (SNR) constraint. After checking the feasibility of power allocation, an optimal solution is provided using Karush-Kuhn-Tucker (KKT) condition. With numerical investigation, the optimality of the proposed solution is illustratively verified and it is also shown that the extent of reduction in the sum-power consumption achieved by introducing the relay depends on the available relaying power and the number of sources.