Blind channel identification and extraction of more sources than sensors

It is often admitted that a static with more inputs than outputs 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 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.