New, exact expressions for the probability density and distribution functions of a bivariate Hoyt (Nakagami-q) process with arbitrary correlation pattern in a nonstationary environment are derived, a solution to a longstanding unsolved problem. More specifically, the following are obtained: joint probability density function, joint cumulative distribution function, power and envelope correlation coefficients, and some statistics related to the signal-to-noise ratio at the output of the selection combiner, namely, outage probability and probability density function. The exact expressions are given in infinite series form, but are mathematically tractable, easy to evaluate, and flexible enough to accommodate a myriad of correlation scenarios, useful in the analysis of a more general fading environment. The power correlation coefficient is found in an exact, simple, closed-form formula, whereas the envelope one, also exact, is more mathematically elaborate. Approximate, simple closed-form expressions for the joint distribution are also obtained that yield (i) excellent results for small to medium correlation coefficients and (ii) reasonable ones for high correlation coefficient.

A number of realistic wireless applications can be found for which the propagated signal may experience extreme fading conditions. In particular, a recent work has reported on an experiment conducted within an enclosed environment where it has been shown that the fading conditions are indeed harsh, drastically departing from those predicted by traditional fading models. This paper investigates the κ-μ Extreme fading distribution, a member of the κ-μ fading model and obtained from it when its parameters reach their extreme values (κ → ∞ and μ → 0) for a fixed amount of fading. Field data reported elsewhere and collected in enclosed environment, along with other fading data collected by the authors' team, are used to compare the curve fit performance of the κ-μ Extreme model and the recently proposed Two-Ray distribution. The results show that the κ-μ Extreme distribution is flexible and suitable to model these scenarios. The performance of this new model is then explored in the three basic combining techniques, namely selection, maximum ratio, and equal gain, and a number of exact, closed-form formulas are obtained. Interestingly, it is shown that in extreme fading conditions, the selection combiner may outperform the equal gain combiner.

This paper derives an exact, easily computable series-type formulation for the multivariate α-µ joint cumulative distribution function. Then, based on useful and practical assumptions, alternative, new, simpler formulations for the α-µ multivariate joint density function and its corresponding distribution function are provided. The formulations are still general and yet very simple, assuming arbitrary parameters and arbitrary correlation among the marginal α-µ variates. As an application example, the outage probability of the selection combining scheme is obtained, again in an exact manner. The results show that only a few number of terms of the series is sufficient to provide an excellent agreement between approximate and exact results.