A Maximum Entropy approach for blind deconvolution

In this paper we propose a new closed approximated formed expression for the conditional expectation based on the Maximum Entropy principle and Laplace integral method. Our proposed expression does not impose any restrictions (except of even symmetric) on the probability distribution of the (unobserved) input sequence, thus it is suitable for a wider range of source probability density function compared with Bellini's, Fiori's or Haykin's expression. In addition, we propose a new, efficient and noniterative approximation for the Lagrange multipliers related to the blind deconvolution problem. Our proposed Lagrange multipliers are based on our new proposed expression for the conditional expectation and on the mean square error (MSE) criteria. Based on our new derivations, a new blind deconvolution algorithm is proposed with improved equalization performance compared with Godard's, reduced constellation algorithm (RCA), Fiori's and the sign reduced constellation algorithm (SRCA). In addition, a theoretical analysis shows that our algorithm achieves perfect equalization in the real valued and two independent quadrature carrier case. These results imply a significant improvement over Godard's algorithm in the 16 quadrature amplitude modulation (QAM) case.