Channel Shortening of Multi-Input Multi-Output Convolutive Systems with Binary Sources

In this paper we treat the problem of channel shortening of convolutive multi-input multi-output (MIMO) systems with binary source signals. Our approach exploits the constellation properties of the distant successor values. In the noiseless case the Magged successor of each output prototype form a characteristic finite set of clusters (lagged successor constellation). The shape of this constellation is invariant of the predecessor value and it only depends on the I last filter taps. Consequently, the localization of the Magged successors constellation can lead to the annihilation of I filter taps - a process we call channel shortening. Next we show that if the observation dataset is rich enough, the proposed method can transform the convolutive MIMO system into an instantaneous one, which is a much simpler system for blind separation. Furthermore, the treatment of the system in the presence of noise is described using data clustering techniques.