Bussgang blind deconvolution for impulsive signals

Many blind deconvolution algorithms have been designed to extract digital communications signals corrupted by intersymbol interference (ISI). Such algorithms generally fail when applied to signals with impulsive characteristics, such as acoustic signals. While it is possible to stabilize such procedures in many cases by imposing unit-norm constraints on the adaptive equalizer coefficient vector, these modifications require costly divide and square-root operations. In this paper, we provide a theoretical analysis and explanation as to why unconstrained Bussgang-type algorithms are generally unsuitable for deconvolving impulsive signals. We then propose a novel modification of one such algorithm (the Sato algorithm) to enable it to deconvolve such signals. Our approach maintains the algorithmic simplicity of the Sato algorithm, requiring only additional multiplies and adds to implement. Sufficient conditions on the source signal distribution to guarantee local stability of the modified Sato algorithm about a deconvolving solution are derived. Computer simulations show the efficiency of the proposed approach as compared with various constrained and unconstrained blind deconvolution algorithms when deconvolving impulsive signals.