Super-exponential methods for blind deconvolution

A class of iterative methods for solving the blind deconvolution problem, i.e., for recovering the input of an unknown possibly nonminimum phase linear system by observation of its output is presented. These methods are universal in the sense that they do not impose any restrictions on the probability distribution of the input process provided that it is non-Gaussian. Furthermore, they do not require prior knowledge of the input distribution. These methods are computationally efficient, statistically stable (i.e., small error variance), and they converge to the desired solution regardless of initialization (no spurious local stationary points) at a very fast nearly super-exponential (exponential to the power) rate. The effects of finite length of the data, finite length of the equalizer and additive noise in the system on the attainable performance (intersymbol-interference) are analyzed. It is shown that in many cases of practical interest the performance of the proposed methods is far superior to linear prediction methods even for minimum phase systems. Recursive and sequential algorithms are also developed, which allow real-time implementation and adaptive equalization of time-varying systems.