On Selection Combining Diversity in Dual-Hop Relaying Systems Over Double Rice Channels: Fade Statistics and Performance Analysis

This paper investigates the performance of selection combining (SC) diversity in dual-hop cooperative networks under double Rice fading channels. Expressions for the probability density function (PDF), cumulative distribution function (CDF), level-crossing rate (LCR), and average duration of fades (ADF) of the SC output fading processes are first investigated. The obtained quantities are in the form of finite and semi-infinite range integrals, which can be easily computed using numerical tools. For the PDF, CDF, and LCR statistics corresponding approximate solutions are determined using the Laplace method's of integration. The PDF and CDF are then applied to derive exact and approximate solutions for the average symbol error probability (SEP) of non-coherent M-ary differential phase-shift keying (M-DPSK) modulation. Moreover, results corresponding to the special cases of mixed Rayleigh × Rice and double Rayleigh fading channels are extracted. The validity of the derived expressions and the accuracy of the approximations have been checked by using computer simulations. The results can be useful in the performance assessment of mobile-to-mobile (M2M) communications with dual-hop cooperative SC diversity and millimeter wave (mmWave) bands where, in general, the line-of-sight (LOS) propagation arises.