# Ergodic Mutual Information for Generalized Fadings

## TL;DR

This paper derives simplified expressions for ergodic mutual information in SISO systems over generalized fading channels, enabling easier numerical evaluation without complex special functions.

## Contribution

It introduces novel, simplified formulas for EMI in generalized fading channels, including discrete inputs, avoiding complex special functions used in prior work.

## Key findings

- Derived EMI expressions for $ ext{eta}$-$ ext{mu}$ and $ ext{kappa}$-$ ext{mu}$ fading channels.
- Validated formulas for specific fading types like Rayleigh, Nakagami-$m$, and Rician.
- Provided a unified approach that simplifies numerical computation of EMI.

## Abstract

In this paper, novel expressions are derived to evaluate the ergodic mutual information (EMI) under BPSK modulation of single-input single-output (SISO) systems operating in generalized fading channels, including $\eta$-$\mu$ fading and $\kappa$-$\mu$ fading. To verify our derivation, we first investigate the specific fading types, namely Rayleigh, Nakagami-$m$ and Rician, and then turn to generalized fading scenarios. It is shown that all the expressions concluded from the generalized cases can be specialized into those derived from the specific ones. Different from the conventional results of the EMI, our developed expressions contain only the simplest numerical calculations, without any Meijer's G-functions which must be implemented in the particular computing software. Additionally, it should be noted that our work provides a complete analysis of the EMI in wireless channel under discrete inputs.