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.

中文翻译：

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使用离散输入逼近混合伽马衰落通道的遍历互信息

为了评估具有离散输入的无线多径信道的性能，这封信研究了广义衰落类型的遍历互信息 (EMI)，称为混合伽马分布 (MGD) 下 百万美元 -ary 正交调幅 ( 百万美元 -QAM) 信令。开发了 EMI 的精确闭式表达式来近似精确值。MGD 衰落可以专门用于几种经常使用的衰落情况，包括瑞利衰落、Nakagami- 百万美元 衰退， $\eta -\mu $ 衰退， $\kappa -\mu $ 褪色，和 ${\mathcal {K}}_{G}$ 衰落，然后分别推导出相应的闭式 EMI 公式来测量这些衰落。与基于高斯源信号的MGD衰落研究相比，这项工作揭示了离散输入而不是高斯输入的性能，从而更实用。这项研究可以看作是评估任意无线信道上离散输入的 EMI 的统一工具。