Fundamentals of acute relay CSI severity

A probability density function (pdf) of bivariate exponential-correlated (exp.c.) Rayleigh fading"”the simplest under correlated fading"”has chronically been employed to model decode-and-forward relay networks under outdated channel state information (CSI) conditions. In addition to CSI outdatedness, CSI imperfection exists, however, their compound co-modelling"”defined as acute imperfect CSI-outdated CSI"”has not yet been performed in the existing literature. Using a joint pdf of trivariate exp.c. Nakagami-m fading"”which is more advanced than the pdf of bivariate exp.c. Rayleigh fading"”this paper models acute imperfect CSI-outdated CSI, and examines its impact on relay networks. Selection combining (SC) is also employed to improve the practicality of this work. Using a pdf of bivariate exp.c. Nakagami-m fading, conditional pdfs of relay SNRs under acute-CSI severity are derived. Using the newly-derived conditional functions, pdfs of Rayleigh fading for SC deployment under acute imperfect CSI-outdated CSI severity are then obtained. Ergodic channel capacity, diversity gains, average-SNR gains, and outage probability are then computed to (a) obtain insight into the proposed findings, and (b) examine the impact of acute-CSI conditions on network performance. Existing results are employed for clarification purposes, and to show the advantage of the proposed work. Monte Carlo simulation is given, which matches theoretical predictions.