ASYMPTOTICALLY EFFICIENT BLIND DECONVOLUTION

A solution is proposed for the discrete blind deconvolution problem, i.e., the estimation of the impulse response of a sampled system given its output and some statistical information on its input. The input sequence is supposed to be independent and identically distributed. The estimate uses the crosscorrelation between the output samples and a nonlinear function of the output samples. The technique is efficient when the residual unknown channel distortion is small, i.e., asymptotically. Therefore, it is recommended as a final step to clean up the noise left by any preferred blind deconvolution method. The variance of the estimation error and the optimal nonlinear function, which depends on the input probability density, are given. The variance is checked against the Cramer-Rao bound. The rms error of the suboptimal solution that adopts the nonlinear function 'sign' depends on simple moments of the input data sequence and on the probability density at the origin. Moderate losses ensue in the case of generalized Gaussians. When the distortion is not small, simulations show that this technique is still useful, but iterations are needed to remove the estimation bias. Polyspectral techniques, that could give unbiased solutions for any channel distortion, cannot be any better asymptotically. The paper discusses whey they could be much noisier. The extension of the technique described in this paper to complex data and impulse response and to parameter dependent distortions is straightforward and is briefly sketched. © 1990.