16QAM Blind Equalization via Maximum Entropy Density Approximation Technique and Nonlinear Lagrange Multipliers

R Mauda,M Pinchas

doi:10.1155/2014/548714

Abstract

Recently a new blind equalization method was proposed for the 16QAM constellation input inspired by the maximum entropy density approximation technique with improved equalization performance compared to the maximum entropy approach, Godard's algorithm, and others. In addition, an approximated expression for the minimum mean square error (MSE) was obtained. The idea was to find those Lagrange multipliers that bring the approximated MSE to minimum. Since the derivation of the obtained MSE with respect to the Lagrange multipliers leads to a nonlinear equation for the Lagrange multipliers, the part in the MSE expression that caused the nonlinearity in the equation for the Lagrange multipliers was ignored. Thus, the obtained Lagrange multipliers were not those Lagrange multipliers that bring the approximated MSE to minimum. In this paper, we derive a new set of Lagrange multipliers based on the nonlinear expression for the Lagrange multipliers obtained from minimizing the approximated MSE with respect to the Lagrange multipliers. Simulation results indicate that for the high signal to noise ratio (SNR) case, a faster convergence rate is obtained for a channel causing a high initial intersymbol interference (ISI) while the same equalization performance is obtained for an easy channel (initial ISI low).

Highlights

It is well known that intersymbol interference (ISI) is a limiting factor in many communication environments where it causes an irreducible degradation of the bit error rate, imposing an upper limit on the data symbol rate
Simulation results indicate that when we deal with an easy channel, no difference is seen in the equalization performance if we use the Lagrange
When we deal with a difficult channel and high signal to noise ratio (SNR) case, a much faster convergence rate is obtained when using the Lagrange multipliers from the nonlinear equation for the Lagrange multipliers instead of those calculated from the linear part

Summary

Introduction

It is well known that ISI is a limiting factor in many communication environments where it causes an irreducible degradation of the bit error rate, imposing an upper limit on the data symbol rate. A linear closed-form approximated expression was obtained for the Lagrange multipliers from which the proposed Lagrange multipliers [1] were calculated for the 16QAM case. Up to now, it is not clear whether it is worth finding those Lagrange multipliers that bring the approximated MSE to minimum. We derive the Lagrange multipliers for the 16QAM input case that bring the approximated expression for the MSE to minimum. When we deal with a difficult channel (where the initial ISI is considered as very high) and high SNR case, a much faster convergence rate is obtained when using the Lagrange multipliers from the nonlinear equation for the Lagrange multipliers instead of those calculated from the linear part.

System Description

New Lagrange Multipliers

Simulation

Conclusion