Novel unified expressions for error rates and ergodic channel capacity analysis over generalized fading subject to AWGGN

Many generalized fading distributions are given in terms of special functions, complicating the analysis of wireless performance metrics. This paper presents novel approximations to the extended incomplete gamma function, the modified Bessel function of the second type, and the generalized Q-function. New simpler and unified form for the probability density function of the extended generalized-K (EGK) and M-N distributions is developed, avoiding complicated and computationally-expensive functions, e.g. Fox and Meijer-G. Based on the new unified PDF and the proposed approximations, we derive novel generic and unified expressions for the average bit error rate and average channel capacity for the recently introduced six most generalized fading channels, namely the EGK, the M-N, the α-η-μ, α-λ-μ, α-κ-μ, and α-λ-η-μ, including the generalized-K, generalized Nakagami-m, the α-μ, the η-μ, the λ-μ, the κ-μ, the Nakagami-Lognormal, the Weibull, the Rice, the Hoyt, the Maxwell and other fading scenarios as special cases. The Additive White Generalized Gaussian Noise (AWGGN) is considered as the noise model, that includes the AWGN, the Laplacian, the Gamma and the impulsive noise as special cases, being an application to the generalized Q-function approximation. Moreover, novel analysis for Space-Time Block Codes in generalized-K fading is also developed as an application to the developed approximation of the modified Bessel function. The derived expressions are very simple and analytically traceable. Monte Carlo simulation and published work corroborate our obtained results.