Unified formulation of closed-form estimators for blind source separation in real instantaneous linear mixtures

This contribution provides a unified framework for the analytic or closed-form estimators for blind separation of independent source signals in real-valued instantaneous linear mixtures, in the noiseless two-source two-sensor scenario. First, the connections among three existing 4th-order analytic formulae (CF, AML and EML) are clarified. Next, a general expression for the estimation of the relevant separation parameter from the data nth-order statistics is unveiled, of which the extended maximum likelihood (EML) estimator is a particular case at n=4, and from which a novel third-order estimator is derived at n=3. Asymptotic performance analysis results are also presented. Associated contrast-function optimization criteria are shown to extend the applicability of a known 4th-order contrast function in the two-signal case. Simulations illustrate and validate the theoretical exposition.