Outage Performance and Symbol Error Rate Analysis of L-Branch Maximal-Ratio Combiner for κ-μ and η-μ Fading

This chapter treats performances of Maximal-Ratio Combiner (MRC) in presence of two general fading distributions, the κ-μ distribution and the η-μ distribution (Yacoub, 2007.). Namely, performances of Maximal-Ratio Combiner in fading channels have been of interest for a long time, which can be seen by a numerous publications concerning this topic. Most of these papers are concerned by Rayleigh, Nakagami-m, Hoyt (Nakagami-q), Rice (Nakagamin) and Weibull fading (Kim et al., 2003), (Annamalai et al., 2002), (da Costa et al., 2005), (Fraidenraich et al., a, 2005), and (Fraidenraich et al., b, 2005). Beside MRC, performances of selection combining, equal-gain combining, hybrid combining and switched combining in fading channels have also been studied. Most of the papers treating diversity combining have examined only dual-branch combining because of the inability to obtain closed-form expressions for evaluated parameters of diversity system. Scenarios of correlated fading in combiner’s branches have also been examined in numerous papers. Nevertheless, depending on system used and combiner’s implementation, one must take care of resources available at the receiver, such as: space, frequency, complexity, etc. Moreover, fading statistic doesn't necessary have to be the same in each branch, e.g. probability density function (PDF) can be the same, but with different parameters (Nakagami-m fading in i-th and j-th branches, with mi≠mj), or probability density functions (PDF) in different branches are different (Nakagami-m fading in i-th branch, and Rice fading in j-th branch). This chapter treats MRC outage performances in presence of κ-μ and η-μ distributed fading (Milišić et al., a, 2008), (Milišić et al., b, 2008), (Milišić et al., a, 2009) and (Milišić et al., b, 2009). This types of fading have been chosen because they include, as special cases, Nakagami-m and Nakagami-n (Rice) fading, and their entire special cases as well (e.g. Rayleigh and one-sided Gaussian fading). It will be shown that the sum of κ-μ squares is a κ-μ square as well (but with different parameters), which is an ideal choice for MRC analysis. This also applies to η-μ distribution. Throughout this chapter probability of outage and average symbol error rate, at the L-branch Maximal-Ratio Combiner’s output, will be analyzed. Chapter will be organized as follows. In the first part of the chapter we will present κ-μ and η-μ distributions, their importance, physical models, derivation of the probability density function, and relationships to other commonly used distributions. Namely, these distributions are fully characterized in terms of