# A double EP-based proposal for turbo equalization

## TL;DR

This paper introduces a double expectation propagation (EP) based turbo equalizer that reduces iteration count and computational complexity, offering three implementation variants and demonstrating improved performance over existing EP-based methods.

## Contribution

It proposes a novel double EP-based equalizer combining multiple approaches to enhance turbo equalization efficiency and reduce complexity compared to prior EP-based solutions.

## Key findings

- Reduces the number of iterations needed for turbo equalization.
- Achieves computational complexity twice that of linear MMSE.
- Shows improved performance over existing EP-based proposals.

## Abstract

This letter deals with the application of the expectation propagation (EP) algorithm to turbo equalization. The EP has been successfully applied to obtain either a better approximation at the output of the equalizer or at the output of the channel decoder to better initialize the Gaussian prior used by the equalizer. In this letter we combine both trends to propose a novel double EP-based equalizer that is able to decrease the number of iterations needed, reducing the computational complexity to twice that of the linear MMSE. This novel equalizer is developed in three different implementations: a block design that exploits the whole vector of observations, a Wiener filter-type approach that just uses the observations within a predefined window and a Kalman smoothing filter-type approach that emulates the BCJR behavior. Finally, we include some experimental results to compare the three different implementations and to detail their improvements with respect to other EP-based proposals in the literature.