Blind restoration of binary signals using a line spectrum fitting approach

In this paper we present a new blind equalization algorithm that exploits the parallelism between the probability density function (PDF) of a random variable and a power spectral density (PSD). By using the PDF/PSD analogy, instead of minimizing the distance between the PDF of the input signal and the PDF at the output of the equalizer (an information-theoretic criterion), we solve a line spectrum fitting problem (a second-order statistics criterion) in a transformed domain. For a binary input, we use the fact that the ideal autocorrelation matrix in the transformed domain has rank 2 to develop batch and online projection-based algorithms. Numerical simulations demonstrate the performance of the proposed technique in comparison to batch cumulant-based methods as well as to conventional online blind algorithms such as the constant modulus algorithm (CMA).

[1]  S. Kay.  Model-based probability density function estimation , 1998, IEEE Signal Processing Letters.

[2]  Philip Schniter,et al.  Blind equalization using the constant modulus criterion: a review , 1998, Proc. IEEE.

[3]  Zhi Ding,et al.  Blind Equalization and Identification , 2001 .

[4]  A. Benveniste,et al.  Robust identification of a nonminimum phase system: Blind adjustment of a linear equalizer in data communications , 1980 .

[5]  Josep Sala-Alvarez,et al.  Statistical reference criteria for adaptive signal processing in digital communications , 1997, IEEE Trans. Signal Process..

[6]  Miguel Angel Lagunas,et al.  Joint probability density function estimation by spectral estimate methods , 1996, 1996 IEEE International Conference on Acoustics, Speech, and Signal Processing Conference Proceedings.

[7]  Deniz Erdogmus,et al.  Matched pdf-based blind equalization , 2003, 2003 IEEE International Conference on Acoustics, Speech, and Signal Processing, 2003. Proceedings. (ICASSP '03)..

[8]  Miguel Angel Lagunas,et al.  Fourier models for non-linear signal processing , 1999, Signal Process..

[9]  Steven Kay,et al.  A Fast and Accurate Single Frequency Estimator , 2022 .

[10]  D. Youla,et al.  Image Restoration by the Method of Convex Projections: Part 1ߞTheory , 1982, IEEE Transactions on Medical Imaging.