In this paper, the fundamental statistics of fluctuating Beckmann shadowed (FBS) fading model which is composite of fluctuating Beckmann (FB) and inverse Nakagami-$m$ distributions, are provided. Accordingly, a wide range of composite generalized fading distributions are obtained as special cases of the proposed distribution, such as, double shadowed $\kappa-\mu$ fading Type I. To this effect, mathematically tractable expressions of both the exact and asymptotic at high signal-to-noise (SNR) regime of the probability density function (PDF), cumulative distribution function (CDF), and generalised-moment generating function (G-MGF) are derived. In addition, the fundamental statistics for integer $m$ and even value of $\mu$ that represent the shadowing of the dominant components and real extension of the number of the multipath clusters, respectively, are given in simple closed-from formats. These statistical characterizations are then used to evaluate the performance of the wireless communications in terms of the outage probability (OP), average bit error probability (ABEP), amount-of-fading (AF), channel quality estimation index (CQEI), error vector magnitude (EVM), average channel capacity (ACC), and effective throughput (ET). Furthermore, the area under the receiver operating characteristics (AUC) curve of the energy detection based spectrum sensing and the secure outage probability (SOP) as well as lower bound of SOP (SOP$^L$) of the physical layer are also analysed. The validation of the derived expressions is verified via comparing the numerical results with the Monte-Carlo simulations for different values of the fading parameters.

In this paper, the extended α-η-F composite fading distribution is proposed. In this model, the propagation environment of the extended η-F composite fading is assumed to be non-linear via usingα-root instead of square-root for the signal envelope. Hence, the fundamental statistics, namely, the probability density function (PDF), cumulative distribution function (CDF), and moment generating function (MGF) are derived. The performance of wireless communications systems undergoing extended α-η-F composite fading is then analysed in terms of the outage probability (OP), outage capacity (OC), and average bit error rate (ABER). To obtain more insights into the impact of α on the systems performance, the asymptotic expressions at high average signal-to-noise (SNR) regime of the OP,OC, and ABER are also given. The numerical results of the proposed model are affirmed via comparing them with the Monte-Carlo simulations as well as some special cases.

In this paper, the impact of the non-linearity of the propagation medium on the extended $\eta$-$\mu$ fading distribution is studied. In particular, the extended $\alpha$-$\eta$-$\mu$ fading model in which the parameter $\alpha$ represents the non-linearity of the propagation environment is presented via providing the exact and asymptotic of the statistical properties, namely, the probability density function (PDF), cumulative distribution function (CDF), and generalized-moment generating function (G-MGF).