The Second Order Performance of Macrodiversity Reception in the Presence of Weibull Fading, Gamma Fading and α-κ-µ Co-channel Interference DRAGANA KRSTIĆ, SINIŠA MINIĆ*, SUAD SULJOVIĆ, MIHAJLO STEFANOVIĆ Faculty of Electronic Engineering, University of Niš Aleksandra Medvedeva 14, 18000 Niš *University of Pristina, Kosovska Mitrovica Teachers' training faculty in Prizren-Leposavić Nemanjina bb, 38218 Leposavic SERBIA dragana.krstic@elfak.ni.ac.rs Abstract: - In this paper, the wireless system consisting of macrodiversity selection combining (SC) receiver and two microdiversity SC receivers under the influence of small scale fading and large scale fading, as well as co-channel interference is observed. Small scale fading has Weibull distribution. Correlated large scale fading is described by Gamma distribution. Co-channel interference is disturbed by α-κ-µ fading and Gamma large scale fading. Probability density function (PDF) and cumulative distribution function (CDF) of the ratio of Weibull random variable and α-κ-µ random variable are given. The formula for CDF of macrodiversity SC receiver output signal to interference ratio (SIR) is also presented. Level crossing rates at the outputs of microdiversity SC receivers are determined. Then, the level crossing rate (LCR) of wireless system output signal to interference ratio is derived and shown in some figures. Based on them, the influence of Weibull fading nonlinearity parameter, α-κ-µ fading severity parameter, α-κ-µ fading nonlinearity parameter, Rician factor, Gamma long term fading severity parameter and Gamma long term fading correlation coefficient is studied. Key-Words: - macrodiversity receiver; microdiversity receiver; selection combining (SC); Gamma fading; Weibull fading; α-κ-µ fading; level crossing rate 1 Introduction The characteristics of the first and the second orders of the wireless system are impaired owing to the influence of small scale fading, large scale fading fading and co-channel interference. The second order performances are level crossing rate (LCR) and average fade duration (AFD) of wireless mobile communication system [1]. To mitigate the small scale fading, large scale fading fading and co- channel interference effects on the level crossing rate it is necessary to use a macrodiversity system. The macrodiversity system consists of one macrodiversity receiver and two or more microdiversity receivers [2]. The macrodiversity receiver is the most often of selection combining (SC) type. Its SC receiver selects microdiversity receiver with higher signal envelope (or signal to interference ratio) average power at inputs, resulting in Gamma large scale fading reduction. The microdiversity receivers could be maximal ratio combining (MRC), equal gain combining (EGC), or selection combining receivers [3]. The simplest is SC receiver which chooses the branch with the highest signal, or signal to interference ratio, which implies the small scale fading effects reduction and co-channel interference effects reduction [1]. Many different distributions describe signal envelope in fading environments such as Rayleigh, Rician, Nakagami, Weibull distribution, or general distributions like α-κ-µ distribution [4]. Weibull distribution describes small scale signal envelope variation in nonlinear, non line of sight (NLoS) fading surroundings [5]. It has parameter α, called nonlinearity parameter. Weibull distribution is general distribution because for α=2, Weibull distribution reduces to Rayleigh distribution. For α tends to infinity Weibull channel becomes no fading channel. On the other side, the α-κ-µ distribution is characterized by three parameters, where parameter α is nonlinearity parameter, κ is Rician factor and µ is small scale fading severity parameter [6]-[9]. Rician factor is the ratio of dominant component power and scattering components powers. Dragana Krstić et al. International Journal of Communications http://www.iaras.org/iaras/journals/ijoc ISSN: 2367-8887 41 Volume 2, 2017