Error Exponent for Cooperative Communications Under α-μ Multipath Fading

In this paper, we derive a novel analytical expression for random coding error exponent of a dual-hop amplify and-forward wireless communication system over independent and identically distributed α-μ fading channels. Random coding error exponent is an information theoretic performance measure which gives an insight into the fundamental trade-off between the achievable rate of information and the reliability of communication. It can be used to find the length of the code-word required to achieve a pre-determined probability of error at a rate below the capacity of the channel. Furthermore, the derived random coding error exponent expression is utilized to derive closed form expressions for the cutoff rate and the capacity of the system. Moreover, the derived expressions can be reduced to study the performance of the system over Nakagami-m, Weibull, One-sided Gaussian, Rayleigh, and Negative Exponential fading models which are included in the α-μ fading model as special cases. Numerical results are further presented to corroborate the analysis.