1186 IEEE COMMUNICATIONS LETTERS, VOL. 23, NO. 7, JULY 2019 On the Energy Detection Performance of Arbitrarily Correlated Dual Antenna Receiver for Vehicular Communication Sagar Kavaiya , Dhaval K. Patel , Member, IEEE, Yong Liang Guan , Senior Member, IEEE , Sumei Sun , Fellow, IEEE , Yoong Choon Chang, and Joanne Mun-Yee Lim, Member, IEEE Abstract—In this letter, we investigate the energy detection performance over arbitrarily correlated Nakagami-m channels under vehicle mobility. We consider that vehicle is under the protection range of the primary user. We derive the probability density function of the received signal-to-noise ratio by means of the ratio of two distributions. Next, closed-form expression for the average probability of detection is derived considering maximal ratio combining diversity for dual-antenna branches under vehicle mobility. The numerical results demonstrate that that the impact of the arbitrary correlation under vehicle mobility in terms of receiver operating characteristic. Detection performance may vary under various antenna correlation types, such as exponential or uniform. Based on the numerical results obtained, we posit that the joint effect of high-antenna correlation and mobility of vehicle can degrade detection performance with a single antenna; furthermore, dual-antenna branches can provide a remedy to the deterioration. Index Terms— Cognitive vehicular networks, arbitrary corre- lation, inter branch correlation, Nakagami-m fading, detection probability. I. I NTRODUCTION I NCREASING number of connected vehicles on road requires huge bandwidth. Cognitive Radio (CR) technology emerges as a key solution to solve spectrum scarcity for Vehicle to Vehicle (V2V) communications and can provide an opportunistic way for the SU to access the Primary User’s (PU) band when PU is inactive [1]. Energy Detection (ED) is proposed to detect unknown deter- ministic signal in presence of white Gaussian noise [2]. The ED, detection probability for various fading channels has been investigated in [3], [4] for static CR users with and without diversity reception. Further, spectrum sensing for multiple antenna receiver over Nakagami-m fading is carried out for uniformly and exponentially correlated branches [5]. CR for Vehicular Ad-Hoc Network (VANET) is presented briefly in [6]. Furthermore, by considering the SU velocity, Improved Manuscript received April 11, 2019; accepted May 1, 2019. Date of publication May 13, 2019; date of current version July 10, 2019. Authors would like to thank for financial support received from DST-ASEAN (Grant ref. IMRC/AISTDF/R&D/P-09/2017). The associate editor coordinating the review of this letter and approving it for publication was H. Zhang. (Corresponding author: Sagar Kavaiya.) S. Kavaiya and D. K. Patel are with the School of Engineering and Applied Science, Ahmedabad University, Ahmedabad 380009, India (e-mail: sagar.k@ahduni.edu.in; dhaval.patel@ahduni.edu.in). Y. L. Guan is with the Department of Electrical and Electronic Engineering, Nanayang Technological University, Singapore 639798 (e-mail: eylguan@ ntu.edu.sg). S. Sun is with the Institute of Infocomm Research, Singapore 138632 (e-mail: sunsm@i2r.a-star.edu.sg). Y. C. Chang is with the Lee Kong Chian Faculty of Engineering and Science, UTAR, Kajang 43000, Malaysia (e-mail: ycchang@utar.edu.my). J. M.-Y. Lim is with the Department of Electrical and Computer Systems Engineering, Monash University, Malaysia Campus, Subang Jaya 47500, Malaysia (e-mail: Joanne.Lim@monash.edu). Digital Object Identifier 10.1109/LCOMM.2019.2916317 Energy Detector has been proposed in [7]. A common limita- tion of above works is that they considered static and mobile SU without antenna correlation to investigate ED performance. However in practice due to space limitations multiple antennas can cause the correlation. The antennas which are linearly spaced may results in an arbitrary correlation [8] Motivated from the common limitation existing in literature, the detection performance of ED should be evaluated for a mobile SU in which antenna elements are linearly placed which causes the arbitrary correlation among them. Under SU mobility, it is advantageous to have statistical knowledge of received SNR which contains the combined effect of SU mobility and antenna correlation. Further, to the best of our knowledge, there is no preexisting work in the literature that considers the arbitrarily correlated Nakagami-m fading under vehicle mobility to provide the detection performance for Cognitive Vehicular Network (CVN). Our main contributions based on the motivations are as below: • Firstly, we obtain the PDF of received SNR under vehicle mobility from the ratio of two distributions. Our work differs in two ways, firstly we have considered the chan- nel gain following the arbitrary correlated Nakagami-m fading. Secondly, we have considered the distribution of distance (d) of vehicle for two cases in which vehicle is near to, or far away from PU, which is an integral of log-normal random variable from 0 to time t given in [9]. • Secondly, by using the received SNR expression, we derive the closed form expression of detection prob- ability under arbitrarily correlated Nakagami-m fading by considering vehicle mobility over the MRC scheme. Benefits of our expression will lead to the detection performance by means of energy detection for CVN. The rest of the letter is organized as follows. In section II, system model is explained specifically illustrating the network model for CVN under dense traffic and signal model. Section III focuses on the derivation of the SNR distribution under correlated Nakagami-m fading with SU mobility and the analysis of detection probability. The simulation results are presented in section IV and Section V elucidates the conclusions of the work followed by References. II. SYSTEM MODEL In this section, we describe the dense traffic network model and signal model. A. Network Model The road traffic scenario with dense traffic as a CVN model is shown in Fig. (1). The road length is 2a and width is b. The Cartesian coordinates of the primary user is p(x,y). The protec- tion range of primary user is R. The network model illustrates the location of secondary user under two cases. d 0 denotes the initial distance between primary user and secondary user. The 1558-2558 © 2019 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications_standards/publications/rights/index.html for more information.