The $\eta-\mu$/Inverse Gamma Channel: Statistical Characterization and Performance Evaluation

In this paper, new closed-form expressions for probability density function, cumulative distribution function, and moment generating function of signal-to-noise ratio (SNR) for
$\eta-\mu$
/Inverse Gamma composite channel and the sum of
$L$
independent and identically
$\eta-\mu$
/Inverse Gamma distributed SNRs are derived in the form of multivariate Fox-
$H$
function. The derived expressions of cumulative distribution function and moment generating function have an advantage over the existing expressions that these do not contain infinite series summations which lead to truncation error. The derived expression of moment generating function also overcomes the integer constrain present in the expression reported in literature. Finally, to analyze the performance of wireless communication systems, the obtained expressions are used to determine average symbol error rate (ASER) and outage probabilities of various digital modulation techniques. Moreover, ASERs for multi-branch maximum ratio combining receiver is also determined.