Modified LMMSE turbo equalization

This letter presents a modified linear minimum mean square error (LMMSE) turbo equalization scheme that uses an augmented real matrix representation for quadrature modulation systems. In the proposed scheme, the estimates of the two quadrature components of the transmitted symbol have both their individual variances and their covariance considered. Hence, the new scheme is able to achieve a significant performance improvement while retaining a complexity similar to that of the existing LMMSE turbo equalization scheme.

I. Introduction

Inspired by turbo codes [1], turbo equalization was introduced to improve the performance of digital communication systems with intersymbol interference (ISI) [2]. A turbo equalization system consists of two soft-in-soft-out elements: a channel equalizer and a channel decoder. These two elements are operated in an iterative manner. However, the computational complexity of the conventional maximum a posteriori probability (MAP) equalizer is very high [2]–[4]. A low-cost approach based on a linear minimum mean square error (LMMSE) equalizer was proposed in [5], [6]. It is assumed implicitly in [5], [6] that the estimates of the two quadrature components of the transmitted symbol have the same conditional variance and zero covariance. This assumption simplifies the derivation but it potentially introduces a performance degradation.