WAVE-FORM-PRESERVING BLIND ESTIMATION OF MULTIPLE INDEPENDENT SOURCES

The problem of blind estimation of source signals is to estimate the source signals without knowing the transmission channel. The so-called waveform-preserving blind estimation minimizes the difference between the signal waveforms and their estimates. In this paper, it is shown that the minimum-variance unbiased estimates can be obtained if and only if the transmission channel can be identified (blindly). We then show that the channel can be blindly identified if and only if there is no more than one Gaussian source. This condition suggests that waveform-preserving blind estimation can be achieved over a wide range of signal processing applications, including those cases when the source signals have identical non-Gaussian distributions. The constructive proof of the necessary and sufficient condition serves as a foundation for the development of waveform-preserving blind signal estimation algorithms. Examples are also presented to demonstrate the applications of the theoretical results.