Blind identification and signal separation of two-input two-output FIR systems (Q1389905)

Signal enhancement or separation based on a two-sensor scenario is considered. The outputs \(x_1(t)\) and \(x_2(t)\) of a \(2\times 2\) linear time invariant system with independent sources \(s_1(t)\) and \(s_2(t)\), and with frequency response \(A(\omega)\) is observed. The \(2\times 2\) linear time invariant system has the following components: the transfer functions of \(A_{11} (\omega)\) and \(A_{22} (\omega)\) are unitary transformations, and \(A_{12} (\omega)\) and \(A_{21} (\omega)\) represent the cross-coupling effects between the channels. The objective of the so-called ``blind identification and signal separation'' is to identify the unknown system \(A\) and sources \(s_1(t)\) and \(s_2(t)\) simultaneously, only utilizing the observations \(x_1(t)\) and \(x_2(t)\). The paper presents a new kind of higher order statistics (HOS) based approach for blind identification and signal separation of two-input two-output FIR systems. The approach consists of eigenanalysis of higher order spectrum matrices of measurements at different frequency slices and then exploiting the structural information of the coupling system to eliminate the identification indeterminacy. The authors prove that under some weak restrictions, the proposed approach can guarantee the uniqueness of a solution and leads to the desired solution; the procedure is quite different from other existing methods.