Power Adaptation for Enhancing Spectral Efficiency and Energy Efficiency in Multi-Hop Full Duplex Cognitive Wireless Relay Networks

This work investigates the energy efficiency (EE) and the spectral efficiency (SE) performance of multi-hop full duplex cognitive relay networks (MH-FDCRNs) operating in the spectrum sharing mode, under the influence of interference from the primary source. We formulate three distinct optimization problems for finding the optimal power allocation (OPA) for the secondary nodes in MH-FDCRN: (i) EE optimization with minimum SE requirement; (ii) SE optimization with minimum EE requirement; and (iii) EE-SE trade-off optimization. The impact of residual self-interference (RSI) arising due to full duplex operation at the relay nodes and the inter relay interference (IRI) arising due to frequency re-use are considered. For the EE/SE optimization problems, we transform the original non-convex optimization problems to their convex forms by expressing the numerator of the objective function as the difference of concave functions, and by using parametric transformation. For the EE-SE trade-off optimization problem, we first transform the original multi objective optimization problem into a single objective form; and then into its convex form by introducing an auxiliary variable. Computationally efficient algorithms are proposed to solve the considered problems. The convergence properties of the proposed algorithms are established through mathematical analysis as well as through computer simulation studies. We prove that the points of convergence of the proposed iterative algorithms are the Karush-Kuhn-Tucker (KKT) points of the initial non-convex problems. With the help of detailed numerical results, the best trade-off among EE and SE can be achieved by proper selection of priority factor, compared to the individual optimization approaches.