Vector-CM stable equilibrium analysis

A. Touzni

doi:10.1109/97.817379

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Vector-CM stable equilibrium analysis

2000-02-01

PRE

DOI：10.1109/97.817379

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Abstract

En 中文

The vector-constant modulus (VCM) criterion is an extension of the constant modulus (CM) criterion [2] introduced recently for equalization of channels involving Gaussian sources [1], [5]. In this letter, we analyze the behavior of VCM for arbitrary source distributions and combined channel-receiver impulse responses of finite dimension. We begin by pointing out the difference between the VCM and CM cost functions and showing that the VCM criterion can be expressed as a composite criterion combining the CM cost function and a penalty term involving cross-correlations of the equalizer output. We continue by providing conditions for noise-free channels, under which VCM admits stable minima corresponding to zero-forcing (ZF) channel receivers. We find that for sub-Gaussian sources, the VCM and CM criteria share the same global minima. For Gaussian and super-Gaussian sources, however, it appears that only ZF receivers corresponding to input/output transmission delays at the extremes of the range of possible delays are truly stable equilibria of VCM.

Keywords:

blind equalization

source shaping

vector-CM criterion

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