Blind adaptive equalization and simultaneous separation of convolutive mixtures

Blind equalization and simultaneous separation of convolutive mixtures is a challenging problem that has received increased attention. Developments in multichannel equalization/identification show that this problem is perfectly solvable assuming some conditions called multichannel identifiability. We choose to use the constant modulus (CM) criterion since it can, under the previous conditions, retrieve and equalize one source perfectly. Moreover, the CM is quite robust to these conditions and to channel additive noise. However, applying the CM criterion may sometimes result in selecting the same source several times, but with different delays. A decorrelation criterion is then required to select the different sources. We propose two approaches to combine the CM with a decorrelation procedure in order to obtain an adaptive algorithm. In a noise free context, we prove that its minima achieve restoration of the separated sources