Opportunistic Outdated Relays Under Even-Degree-of-Freedom Generalized-Rician Fading

Using a distribution of a non-central chi-square random variable and selection combining, statistics of wireless systems employing decode-and-forward (DF) opportunistic relays (ORs) under outdated channel state information (CSI), and independent and identically distributed (i.i.d.) generalized-Rician fading environments are derived. By mathematically rewriting the Marcum $Q$-function in its infinite-summation form, the distribution of non-central chi-square is mathematically simplified to its desirable form under different scenarios, which are then employed to compute average bit error rates for popular modulation schemes. Distributions of end-to-end system signal-to-noise ratio, useful for fifth-generation backhaul wireless communications, are also derived under integer and non-integer fading parameters. The new findings generalize existing findings employing DF ORs under i.i.d. Rayleigh fading environments. Mathematical predictions are shown to match simulation results.