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 do not require prior knowledge of the input distribution, are computationally efficient and statistically stable, and converge to the desired solution regardless of initialization at a very fast 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