Blind Deconvolution of Multi-Input Single-Output Systems With Binary Sources

The problem of blind source separation for multi-input single-output (MISO) systems with binary inputs is treated in this paper. Our approach exploits the constellation properties of the successor values for each output sample. In the absence of noise, the successors of each output value form a characteristic finite set of clusters (successor constellation). The shape of this constellation is invariant of the predecessor value and it only depends on the last filter tap. Consequently, the localization of the successors constellation can lead to the removal of the last filter tap, thus reducing the length of the filter-a process we call channel deflation. Based on the successor observation clustering (SOC), we develop two algorithms for blind source separation-SOC-1 and SOC-2-differing mainly on the required size of the data set. Furthermore, the treatment of the system in the presence of noise is described using data clustering and data correction. The problem of noise is attacked using a statistical-mode-based method. Moreover, we correct the problem of misclassified observations using an iterative scheme based on the Viterbi algorithm for the decoding of a hidden Markov model (HMM)