A review of selection combining receivers over correlated Rician fading

Selection combiner output (SCO) cumulative distribution functions (cdfs) of multivariate equally-correlated and exponentially-correlated (e.c.) Rician, and other correlated fading environments for positive channel correlation coefficients are rigorously surveyed and mathematically reviewed. Specifically, (i) new findings for the cdf of bivariate correlated and non-identically distributed Rician fading, and (ii) a simplified cdf of trivariate e.c. Rician fading, are reported. Applications of correlated fading into physical layer security are highlighted. Distributions of multivariate equally-correlated fading are discussed for even-degree-of-freedom (DoF), and even-and-odd-DoF non-central chi-square distributed envelopes. Schematic diagrams are employed to offer top-down view on progress for SCO distributions of multivariate correlated Rician fading, and their mathematical inter-relations. From that, knowledge gaps can systematically be identified. Detailed verification revealing mathematical links among published results is shown in detail, from which unidentified special cases can be unified to their corresponding generalised cases. Simulation results are obtained under two scenarios: (i) equal-channel gains, and (ii) unequal-channel gains. Apart from reviewing cdfs of multivariate correlated Rician fading, this paper serves as a tutorial, in which detailed insight into key mathematical developments are given in Appendices A-I, which (i) attract new researchers to the field, and (ii) progress this topic to fruitful ground.