Outage probability of macrodiversity reception in the presence of Gamma long-term fading, Rayleigh short-term fading and Rician co-channel interference Dragana Krstić 1 & Suad Suljović 1 & Dejan Milić 1 & Stefan Panić 2 & Mihajlo Stefanović 1 Received: 21 February 2017 /Accepted: 2 July 2017 # Institut Mines-Télécom and Springer-Verlag France SAS 2017 Abstract Macrodiversity (MACD) system with MACD selec- tion combining (SC) receiver and two microdiversity (MICD) selection receivers in the presence of Gamma long-term fading, Rayleigh short-term fading, and co-channel interference affect- ed to Rician short-term fading is studied in this article. The closed-form expressions for probability density function (PDF) and cumulative distribution function (CDF) of the ratio of Rayleigh random variable and Rician random variable are presented, and probability density function and cumulative dis- tribution function of MICD SC receiver output signal to inter- ference ratio are derived. These results are used for evaluation of the outage probability (P out ) of considered MACD system, and the influence of Rician factor and Gamma long-term fading severity parameter on the outage probability is analyzed. Keywords Gamma long-term fading . Rayleigh short-term fading . Rician co-channel interference . Cumulative distribution function (CDF) . Probability density function (PDF) . Outage probability (P out ) 1 Introduction Radio waves are subjected to refractions, reflections, and dif- fractions that cause multipath propagation resulting in varia- tions of signal envelope, and in turn—degradation of telecom- munication system outage probability (P out ) and bit error rate (BER). Also, large obstacles between transmitter and receiver cause signal shadowing resulting in comparatively slow vari- ations of average power, and consequently, degradation of system performance. For interference limited channels in cel- lular system, the effect of Gaussian noise on the system per- formance can largely be ignored [1], thus making the propa- gation effects dominant performance degradation mechanism. MACD reception can be used to simultaneously reduce long-term fading effects, short-term fading effects, and co- channel interference effects on the outage probability of wireless communication systems. MACD selection combining (SC) re- ceiver selects the MICD SC branch with higher average power of signal envelope at its output and routes it to the user, resulting in large scale fading effects reduction. MICD SC receiver se- lects the branch with higher signal to interference ratio resulting in reduction of small scale fading. Combination of MACD SC and MICD SC reception is therefore able to mitigate also the co-channel interference effects on the system performance. There is a number of papers in open technical literature addressing the performance of MACD wireless communica- tion systems in the presence of long-term fading and short- term fading [2–11], and also wireless communication systems operating over shadowed multipath fading channels in the presence of co-channel interference [12, 13]. Also, perfor- mance of wireless communication systems in the simulta- neous presence of large scale fading, small scale fading, and co-channel interference, with using micro and macrodiversity systems for reduction of these impacts is observed in [14]. However, the process of considering the effect of fading and shadowing on the useful signal, as well as on the interference, and reduction of their influence by using MICD and MACD systems has started recently [15–17]. In [2, 3], macrodiversity SC receiver with two or three microdiversity SC branches is considered. Received signal * Dragana Krstić dragana.krstic@elfak.ni.ac.rs 1 Faculty of Electronic Engineering, University of Niš, Aleksandra Medvedeva 14, Niš, Serbia 2 Faculty of Natural Sciences, University of Pristina, Lole Ribara 29, Kosovska Mitrovica, Serbia Ann. Telecommun. DOI 10.1007/s12243-017-0593-4