Natural gradient multichannel blind deconvolution and speech separation using causal FIR filters

Natural gradient adaptation is an especially convenient method for adapting the coefficients of a linear system in inverse filtering tasks such as convolutive blind source separation and multichannel blind deconvolution. When developing practical implementations of such methods, however, it is not clear how best to window the signals and truncate the filter impulse responses within the filtered gradient updates. In this paper, we show how inadequate use of truncation of the filter impulse responses and signal windowing within a well-known natural gradient algorithm for multichannel blind deconvolution and source separation can introduce a bias into its steady-state solution. We then provide modifications of this algorithm that effectively mitigate these effects for estimating causal FIR solutions to single- and multichannel equalization and source separation tasks. The new multichannel blind deconvolution algorithm requires approximately 6.5 multiply/adds per adaptive filter coefficient, making its computational complexity about 63% greater than the originally-proposed version. Numerical experiments verify the robust convergence performance of the new method both in multichannel blind deconvolution tasks for i.i.d. sources and in convolutive BSS tasks for real-world acoustic sources, even for extremely-short separation filters.