A Novel HOS Approach for Blind Channel Equalization

Abstract

We present in this paper a new equalization method with over 8 dB advantage in the residual ISI compared to the classical results presented by Godard and Shalvi/Weinstein (kurtosis criteria). A systematic derivation is presented for obtaining the conditional expectation for f (x/z) that does not rely on the knowledge of the convolutional noise power nor imposes any restrictions on the probability distribution of the (unobserved) input sequence. We use Edgeworth series which is directly related to quasi moments thus to cumulants, and the Laplace integral method. Although the Edgeworth expansion and the Laplace integral method are well known in non-linear optimal filtering theory, they have not yet been used in the field of blind equalization.

New Lagrange Multipliers for the Blind Adaptive Deconvolution Problem Applicable for the Noisy Case

“…Thus, [38,[49][50][51] cannot cope with a source having a general pdf shape. In [20,52,53], the conditional expectation was given as approximated closed-form expressions suitable for the real or two independent quadrature carrier input case. Those expressions [20,52,53] are suitable for a wider range of source probability density function compared to [38,[49][50][51].…”

“…In [20,52,53], the conditional expectation was given as approximated closed-form expressions suitable for the real or two independent quadrature carrier input case. Those expressions [20,52,53] are suitable for a wider range of source probability density function compared to [38,[49][50][51]. The input pdf was approximated in [20,52] with the maximum entropy density approximation technique, while in [53], the input pdf was approximated with the Edgeworth expansion series.…”

“…Those expressions [20,52,53] are suitable for a wider range of source probability density function compared to [38,[49][50][51]. The input pdf was approximated in [20,52] with the maximum entropy density approximation technique, while in [53], the input pdf was approximated with the Edgeworth expansion series. The equalized output pdf was calculated in [20] and [53] via the approximated input pdf, while in [52], the equalized output pdf was approximated with the maximum entropy density approximation technique.…”

“…The input pdf was approximated in [20,52] with the maximum entropy density approximation technique, while in [53], the input pdf was approximated with the Edgeworth expansion series. The equalized output pdf was calculated in [20] and [53] via the approximated input pdf, while in [52], the equalized output pdf was approximated with the maximum entropy density approximation technique. According to simulation results carried out in [52] for the 16QAM constellation input case, the equalization method based on the conditional expectation from [52] has better equalization performance compared to the maximum entropy equalization technique [20], which was shown to have significant equalization improvement compared to Godard's [39], the reduced constellation algorithm (RCA) [54], the sign reduced constellation algorithm (SRCA) [55] and others.…”

A Maximum Entropy inspired model for the convolutional noise PDF

“…This distortion is referred to as intersymbol interference (ISI) [2]. Thus, a blind adaptive filter is used to remove the convolutive efadaptive equalizers while in [1,3,[6][7][8][9][10][11] the Gaussian pdf model was applied to obtain the conditional expectation of the source signal given the equalized output via Bayes rules. There is no doubt that applying the Gaussian pdf model for the convolution noise pdf simplifies the calculations but at the same time leads to suboptimum solutions from the residual ISI point of view [1,3].…”