Optimal power allocation for variable-hop cooperative relay in cognitive networks

In this work, we present an optimal power allocation scheme dedicated for variable-hop cooperative relays in cognitive networks, which consists of Secondary users (SUs) operating in Amplify-and-Forward (AF) mode, with a Primary user (PU) receiver nearby. In order to assure the quality of service (QoS) for PU, transmit power of cognitive radio (CR) nodes must be tightly controlled which leads to narrow communication range. The issue of minimal feasible hop count Nmin and energy-saving with relays which can only cause limited interference to PU are considered to enable the communication between remote nodes under the constraint of minimal signal to noise ratio (SNR) γth. Closed-form solution for the optimal power allocation scheme is obtained by Lagrangian algorithm along with an O(N) complexity dichotomy method to achieve Nmin. We prove that the energy consumption in the system is reduced with the growth of N by both theoretical derivation and extensive simulation, and the general relation between Nmin and γth.