Blind Channel Identification and Extraction of more Sources than Sensors

Abstract : It is often admitted that a static system with more inputs (sources) than outputs (sensors, or channels) cannot be blindly identified, that is, identified only from the observation of its outputs, and without any a priori knowledge on the source statistics but their independence. By resorting to High-Order Statistics, it turns out that static MIMO systems with fewer outputs than inputs can be identified, as demonstrated in the present paper. The principle, already described in a recent rather theoretical paper, had not yet been applied to a concrete blind identification problem. Here, in order to demonstrate its feasibility, the procedure is detailed in the case of a 2-sensor 3-source mixture; a numerical algorithm is devised, that blindly identifies a 3-input 2-output mixture. Computer results show its behavior as a function of the data length when sources are QPSK-modulated signals, widely used in digital communications. Then another algorithm is proposed to extract the 3 sources from the 2 observations, once the mixture has been identified. Contrary to the first algorithm, this one assumes that the sources have a known discrete distribution. Computer experiments are run in the case of three BPSK sources in presence of Gaussian noise.
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Franklin T. Luk. Advanced Signal Processing Algorithms, Architectures, and Implementations VIII, Jul 1998, San Diego, United States. SPIE, 3461, pp.2-13, 1998, <10.1117/12.325670>
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Pierre Comon. Blind Channel Identification and Extraction of more Sources than Sensors. Franklin T. Luk. Advanced Signal Processing Algorithms, Architectures, and Implementations VIII, Jul 1998, San Diego, United States. SPIE, 3461, pp.2-13, 1998, <10.1117/12.325670>. <hal-00499421>

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