Approximating Ergodic Mutual Information for Mixture Gamma Fading Channels With Discrete Inputs

To evaluate the performance of wireless multi-path channels with discrete inputs, this letter investigates the ergodic mutual information (EMI) of a generalized fading type named mixture gamma distribution (MGD) under $M$ -ary quadrature amplitude modulation ( $M$ -QAM) signaling. An accurate closed-form expression for the EMI is developed to approximate the exact value. The MGD fading can be specialized into several regularly used fading cases including Rayleigh fading, Nakagami- $m$ fading, $\eta -\mu $ fading, $\kappa -\mu $ fading, and ${\mathcal {K}}_{G}$ fading, and then the corresponding closed-form EMI formulas are separately derived to measure these fadings. Compared with the Gaussian source signals based research on MGD fading, this work sheds light on the performance with discrete inputs instead of Gaussian inputs, thereby being more practical. This study can be regarded as a unified tool to evaluate the EMI with discrete inputs over arbitrary wireless channels.