A closed-form solution for the finite length constant modulus receiver

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.

Blind equalization and Automatic Modulation Classification based on pdf fitting

“…The key idea here is that we assume that after equalization, we roughly obtain a Gaussian mixture with modes centered on constellation points. The Gaussian nature of equalizer output conditional to transmitted symbol has been discussed in [10]. The rest of the paper is organized as follows.…”

A Study on Radial Velocity Transformation and Uncertainty Propagation

“…At low SNR, each cluster of symbols overlaps with one another, which makes it difficult to recognize the number of clusters and overall distribution of the constellation. With severe fading, proper equalization should be preceded, making the constellation 2D Gaussian Mixture (GM) [3]. Without any pilot signal, however, blind channel equalization is the only option.…”