Ergodic Capacity Performance for Cognitive Radio under Lognormal Shadowing from Secondary User Perspective Mohammed Abdel-Hafez 1 , Nedaa Al Hussien 1 , Khaled Shuaib 2 , and Farag Sallabi 2 1 Department of Electrical Engineering, College of Engineering, United Arab Emirates University, P.O. Box 15551, Al- Ain, UAE 2 College of Information Technology, United Arab Emirates University, P.O. Box 15551, Al-Ain, UAE Email: {mhafez, nedaa_yousef, k.shuaib, f.sallabi}@uaeu.ac.ae Abstract —In a cognitive radio network, spectrum sensing is the first and most vital function. It identifies spectrum opportunities that can be utilized by secondary users to enhance spectrum utilization and ergodic capacity. However, sensing performance is very tormented by channel fading and shadowing. This paper addresses the performance of ergodic capacity in cognitive radio networks under a Lognormal shadowing environment. We derived a new mathematical model for the secondary user network ergodic capacity when both accessing and sensing channels undergo Lognormal shadowing. Moreover, we developed exact analytical expressions for the capacity followed by numerical evaluation under different channel sensing and accessing conditions. Finally, the paper explored the effects of detection and accessing channels’ parameters on the capacity. Index Terms—Spectrum sensing; opportunistic access; cognitive radio; lognormal shadowing; ergodic capacity I. INTRODUCTION The evolution of wireless communications has introduced new services and applications that require high data rates and various Qualities of Services (QoS). This resulted in dramatically increasing demand on frequency spectrum to accommodate these new services or to enhance existing ones. However, the frequency spectrum is characterized by static frequency allocation schemes that assign the existing frequency bands only to licensed users. This is the case despite that measurements indicate underutilization of the spectrum by licensed users for significant periods of time [1]. This aggravates spectrum scarcity and makes it more difficult to accommodate the need for a higher range of the spectrum. Therefore, Cognitive Radio (CR) concept is a promising technology that has been planned to alleviate frequency spectrum scarceness and under-utilization by permitting unlicensed or Secondary Users (SU) to access the spectrum once licensed or Primary Users (PU) are inactive. The two main characteristics of cognitive radio are cognitive capability and configurability [2]. The cognitive capability enables CR devices to interact with the surrounding radio environment in a real-time manner and Manuscript received April 20, 2018; revised September 20, 2018. Corresponding author email: mhafez@uaeu.ac.ae. doi:10.12720/jcm.13.10.546-552 be aware of signal parameters such as waveform, RF spectrum, communication network type/protocols, geographical information, user needs and security policies, etc. CR devices then adjust their radio operating parameters according to the information sensed to achieve optimal performance. The authors in [3] investigated the effect of user collaboration in a Rayleigh fading channel. Their results showed that using more collaborative users would improve the spectrum utilization. In [4], the authors investigated and analyzed linear soft combination-based cooperative spectrum sensing schemes in Cognitive Radio networks. They focused on the allocation of optimal weights to individual cooperative SUs in AWGN channel. In [5], the authors used a different methodology where they studied sensing in Nakagami fading channel with integer fading parameter in non-collaborative situations. While in [6] the authors solved the spectrum- sensing problem in Nakagami fading with non-integer fading parameters in collaborative scenarios. Recently, the authors of [7] have produced a closed form and accurate solution to the spectrum-sensing problem in Lognormal shadowing channel. The Complementary Receiver Operating Characteristics (CROC) curves are one way to evaluate the detection system performance. However, CROC does not show the percentage increase in spectrum utilization or ergodic capacity when using opportunistic spectrum access technique. Some researchers used capacity calculations to quantify the resulting increment in utilization. The authors in [8] studied the problem of designing sensing duration to maximize the achievable throughput (capacity) for the secondary network in AWGN channels. The authors formulated the sensing throughput trade-off problem mathematically and used an energy detection sensing scheme to prove that the formulated problem is indeed an optimal sensing time which yields the highest throughput for the secondary network. The authors of [9] investigated the capacity of fading channels subject to constraints on the power received at a third-party (primary) receiver when perfect channel information is available to both transmitter and receiver. The contribution of [10] extended the work done in previous studies for the case of imperfect knowledge of 546 ©2018 Journal of Communications Journal of Communications Vol. 13, No. 10, October 2018