PRZEGLĄD ELEKTROTECHNICZNY (Electrical Review), ISSN 0033-2097, R. 88 NR 3a/2012 237 Mihajlo STEFANOVIĆ 1 , Petar NIKOLIĆ 2 , Dragana KRSTIĆ 1 , Vesad DOLJAK 3 Faculty of Electronic Engineering, Niš, Serbia (1), Tigar Tyres, Pirot, Serbia (2), Teachnical School in Novi Pazar, Serbia (3) Outage probability of the SSC/SC combiner at two time instants in the presence of lognormal fading Abstract. The outage probability of the Switch and Stay Combining/Selection Combining (SSC/SC) combiner output signal at two time instants, in the presence of log-normal fading, is determined in this paper. The probability density function (PDF) of the combiner output signal is derived. Then, the outage probability is numerically calculated using this PDF. The results are shown graphically to compare performances of the SSC/SC combiner with regard to classical SSC and SC combiners at one time instant. Streszczenie. W artykule analizuje się prawdopodobieństwo przerw połączenia SSC/SC w obecności zaników o rozkładzie logarytmiczno- normalnym. Prawdopodobieństwo to jest liczone na podstawie krzywej gęstości prawdopodobieństwa PDF. Porównano połączenia SSC/SC z klasycznymi SSC i SC. (Prawdopodobieństwo przerw połączenia SSC/SC w obecności zaników o rozkładzie logarytmiczno-normalnym) Keywords: lognormal fading, SSC Combining, SC combining, two time Instants, outage probability Słowa kluczowe: zaniki połączenia, prawdopodobieństwo. Introduction In wireless communications, a variation of an instantaneous value of the received signal, i.e. fading of signal envelope is very common effect, due to the multipath propagation. Fading is one of the main causes of performance degradation of the receiver. Diversity technique is certainly one of the most frequently used methods for combating the deleterious effect of channel fading. Particular diversity methods and combining techniques are presented in [1]. Since the selection combining (SC) and switch and stay combining (SSC) do not require signal cophasing and fading envelope estimation, they are very often implemented in practice. The SC is combining technique where the strongest signal is chosen among L branches of diversity system [1]. In the case of dual branch SSC, the first branch stay selected as long as its instantaneous signal-to-noise ratio (SNR) is greater than predetermined switching threshold, even if the instantaneous SNR in the second branch maybe has a larger value at that time [1, 2]. The consideration of SSC systems in the literature has been restricted to low-complexity mobile units where the number of diversity antennas is typically limited to two ([3], [4], [5]). In the paper [5] Alouini and Simon develop, analyze and optimize a simple form of dual-branch switch and stay combining (SSC). The probability density function (PDF) of the SSC combiner output signal at one time instant and the joint probability density function of the SSC combiner output signal at two time instants in the presence of Rayleigh, Nakagami-m, Weibull and lognormal fading are determined in [7-10], respectively. The probability density function and the outage probability of the SSC/SC combiner output signal at two time instants in the presence of Rayleigh fading is determined in [11]. In this paper the probability density function and the outage probability of the SSC/SC combiner output signal at two time instants in the presence of lognormal fading will be determined. The remainder of this paper is organized as follows. The next section presents the system model and determines the probability density function, the joint PDF and the outage probability for the SSC/SC combiner output signal at two time instants. Sections III presents the numerical results obtained for performances introduced in section II. Finally, the main results of the paper are given as conclusions. System model The model of the SSC/SC combiner with two inputs at two time instants, considering in this paper, is shown in Figure 1. The SSC combiner input signals are r 11 and r 21 at first time moment and they are r 12 and r 22 at the second time moment. The output signals from SSC part are r 1 and r 2 . The indexes for the input signals are: first index is the ordinal branch number and the other signs time instant observed. For the output signals, the index represents the time instant observed. So found SSC combiner output signals r 1 and r 2 become the inputs in SC combiner. The overall output signal from the entire system is r. Fig.1. Model of the SSC/SC combiner with two inputs at two time instants The probability densities of the combiner input signals, r 1i and r 2i in the presence of log-normal fading, are [1]: (1)   0 , 2 1 ) ( 1 2 ln 1 1 1 2 1 2 1 1 1     i r i i r r e r r p i     (2)   0 , 2 1 ) ( 2 2 ln 2 2 2 2 2 2 2 2 2     i r i i r r e r r p i     where i=1,2, μ i is mean value and  i is standard deviation of log-normal fading. The probability of the event that combiner first examines the signal at the first input is P 1 , and for the second input is P 2 . The first case is: r 1 < r T and r 2 < r T . In this case all signals at the input are below r T , i.e.: r 11 < r T , r 12 < r T , r 21 < r T and r 22 < r T . Let the SSC combiner first examines the signal r 11 . Because r 11 < r T , it follows that r 1 = r 21 , and since r 22 < r T it is r 2 = r 12 . The probability of this event is P 1 . When SSC combiner first examines the signal r 21 , then r 1 = r 11 because r 21 < r T . Since r 12 < r T , then it is r 2 = r 22 . The probability of this event is P 2 . After the previous, the joint probability density of the SSC combiner output signals at two time instants, r 1 and r 2 , is [10]: