Blind Deconvolution of SISO Systems with Binary Source Based on Recursive Channel Shortening

We treat the problem of Blind Deconvolution of Single Input – Single Output (SISO) systems with real or complex binary sources. We explicate the basic mathematical idea by focusing on the noiseless case. Our approach leads to a recursive channel shortening algorithm based on simple data gouping. The channel shortening process eventually results in an instantaneous binary system with trivial solution. The method is both deterministic and very fast. It does not involve any iterative optimization or stochastic approximation procedure. It does however, require sufficiently large datasets in order to meet the source richness condition.