Error exponents analysis of dual-hop η-μ and κ-μ fading channel with amplify-and-forward relaying

In this study, the authors investigate the Gallager's error exponents of dual-hop amplify-and-forward systems over generalised eta-mu and kappa-mu fading channels, two versatile channel models which encompass a number of popular fading channels such as Rayleigh, Rician, Nakagami-m, Hoyt and one-sided Gaussian fading channels. The authors present new analytical expressions for the probability density function of the end-to-end signal-to-noise-ratio (SNR) of the system. These analytical expressions are then applied to analyse the system performance through the study of Gallager's exponents, which are classical tight bounds of error exponents and present the tradeoff between practical information rate and the reliability of communication. Two types of Gallager's exponents, namely, random coding error exponent and expurgated error exponent, are studied. Based on the newly derived analytical expressions, the authors provide an efficient method to compute the required codeword length to achieve a predefined upper bound of error probability. In addition, the analytical expressions are derived for the cutoff rate and ergodic capacity of the system. Moreover, simplified expressions are presented at the high SNR regime. All the analytical results are verified via Monte-Carlo simulations.