Summary
In this work, we have comprehensively investigated the impact of non‐linearity (α − μ) and shadowing (inverse gamma) collectively over the wireless channel. To this effect, an approximate closed‐form probability density function (PDF) expression is derived over α − μ/inverse gamma fading channel by employing Gauss–Laguerre quadrature polynomial. The accuracy of the proposed approximate solution is validated through the Kullback–Leibler divergence test. Subsequently, the proposed solution is utilized in the development of various fundamental statistics like commutative distribution function (CDF), moment generating function (MGF) and nth moment. This contribution also includes the derivation of coding gain and diversity gain to study average symbol error probability (SEP) with MRC and EGC diversity. It is observed that diversity gain is independent of shadowing and as the channel condition improves, the coding gain decreases. Finally, the closed‐form solutions of spectral efficiency under different adaptive transmission policies are also developed specifically, optimal power and rate adaptation (OPRA) and effective capacity along with simpler low‐ and high‐power expressions. Monte‐Carlo simulations are utilized to validate the proposed analytical and numerical results.
In this work, the mathematical characterization of the cascaded ηprefix−μ$$ \eta -\mu $$ fading channel based on multiplicative modeling is discussed. The proposed cascaded ηprefix−μ$$ \eta -\mu $$ probability density function is derived by taking the product of N$$ N $$ statistically independent, but not necessarily identically distributed ηprefix−μ$$ \eta -\mu $$ fading random variables, which encompasses various well‐known distributions as cascaded Nakagami‐m, Hoyt, and Rayleigh distributions. In particular, other statistical measures such as cumulative distribution function, moment generating function, and moment of the cascaded channels, are developed. This set of derived results is further utilized in studying the reliability performance of the wireless cascaded fading channels. The system reliability is comprehensively investigated through various statistical metrics like average symbol error probability, ergodic capacity, outage probability, and effective capacity. All the developed results are of intractable univariate Foxs H‐function form. The accuracy of the numerical results is extensively validated through Monte‐Carlo simulation.
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