A Closed-Form Solution for the Finite Length Constant Modulus Receiver

TL;DR

This paper derives a closed-form solution for the finite-length constant modulus receiver, showing its equivalence to the MMSE equalizer under Gaussian interference assumptions, with supporting simulations.

Contribution

It provides a novel closed-form solution for the finite-length CM receiver and establishes its theoretical link to the MMSE equalizer under practical conditions.

Findings

CM receiver is equivalent to MMSE equalizer under Gaussian approximation

Simulation results support the Gaussian approximation assumption

Closed-form solution simplifies implementation of CM receivers

Abstract

In this paper, a closed-form solution minimizing the Godard or Constant Modulus (CM) cost function under the practical conditions of finite SNR and finite equalizer length is derived. While previous work has been reported by Zeng et al., IEEE Trans. Information Theory. 1998, to establish the link between the constant modulus and Wiener receivers, we show that under the Gaussian approximation of intersymbol interference at the output of the equalizer, the CM finite-length receiver is equivalent to the nonblind MMSE equalizer up to a complex gain factor. Some simulation results are provided to support the Gaussian approximation assumption.