# Ergodic H-S/MRC Mutual Information

## TL;DR

This paper derives recursive formulas for the ergodic mutual information of a SIMO system employing hybrid selection and MRC under Rayleigh fading, validated by simulations.

## Contribution

It introduces a recursive analytical method to estimate ergodic mutual information in H-S/MRC systems with Rayleigh fading channels.

## Key findings

- Recursive expression for ergodic mutual information derived
- Analytical results validated by simulations
- Applicable to SIMO systems with BPSK/QPSK modulations

## Abstract

This paper studies the ergodic mutual information of hybrid selection/maximal-ratio combining (H-S/MRC) diversity system under BPSK/QPSK modulations. We consider a simple single-input multiple-output (SIMO) channel, where a subset of branches are selected and combined using maximal-ratio combining (MRC) to maximize the instantaneous Signal to Noise Ratio (SNR) at the receiver. For independent and identically distributed (i.i.d.) Rayleigh flat fading, a general recursive expression is developed to estimate the ergodic input-output mutual information of the whole system. Besides analytical derivations, simulations are provided to demonstrate the feasibility and validity of the derived results.