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).