Asymptotic performance analysis for direct and indirect HOS-based deconvolution

In blind deconvolution problems, the main objective is to reconstruct the input sequence to a linear time invariant system from output measurements only. In order for the blind deconvolution problem to have a solution, the unobserved input sequence must be non-Gaussian. Methods based on autocorrelation statistics, can accurately reconstruct the input sequence only if the model is known beforehand to be minimum phase. In practice, this is not always the case and the system can be non-minimum phase. The ability of HOS (higher order statistics) to preserve phase information, makes HOC-based (higher order cumulant based) algorithms particularly suitable for the blind deconvolution problem. The authors discuss the deconvolution of MA processes using HOC-based methods. Two kinds of methods for the estimation of the inverse filter coefficients are examined