Vol.:(0123456789) Wireless Personal Communications (2020) 114:1963–1981 https://doi.org/10.1007/s11277-020-07457-1 1 3 An Energy‑Eﬃcient Model of Random Cognitive Radio Network: Rayleigh‑Lognormal Environment Saifur Rahman Sabuj 1 · Tabassum E Nur 2 · Masanori Hamamura 3 Published online: 26 May 2020 © Springer Science+Business Media, LLC, part of Springer Nature 2020 Abstract Motivated by the current demand for improvements in transmission rate and energy eﬃ- ciency of random wireless cellular networks, we investigate the theoretical model of ran- dom cognitive radio network in Rayleigh-lognormal fading environment. In such a net- work, we derive an analytical expression for the connection probability, transmission rate, and energy eﬃciency of a secondary network in a single-tier downlink scenario, consider- ing the probabilities of unoccupied channel selection and of successful transmission, where source-destination pairs are randomly located according to Poisson point processes. More- over, we approach the problem of optimization of transmission rate and energy eﬃciency using a required connection probability constraint to improve the system performance. Our numerical results indicate that there exists an optimal combination of transmission power and secondary transmitter density where transmission rate and energy eﬃciency are maximized. Keywords Cognitive radio network · Energy eﬃciency · Stochastic geometry · Rayleigh- lognormal fading Some parts of this paper were presented at the IEEE CCNC conference, 2017 [22]. * Saifur Rahman Sabuj s.r.sabuj@ieee.org Tabassum E Nur tabassum.vnsc@gmail.com Masanori Hamamura hamamura.masanori@kochi-tech.ac.jp 1 Department of Electronics and Control Engineering, Hanbat National University, Daejeon, South Korea 2 Department of Electrical and Electronic Engineering, Bangladesh University, Dhaka, Bangladesh 3 Graduate School of Engineering, Kochi University of Technology, Kami, Japan Content courtesy of Springer Nature, terms of use apply. Rights reserved.