1. A method for the non-linear estimation of wireless signals from several sources, the time/frequency representation of which shows an unknown non-zero proportion of zero components, comprising:using a listening system comprising an antenna array having P>2 antennas to receive a signal at each of the antennas that results from no more than two mixed signals from separate sources for which the directional vectors U and V of the sources emitting the no more than two mixed signals are known or estimated;
transmitting the signal received at each of the antennas to a computing unit that is communicatively coupled to the antennas;
calculating, by the computing unit, successive discrete Fourier transforms of the signals received by the antennas and sampled to obtain a time-frequency P-vector grid of the signals received by the antennas, each element of the time-frequency P-vector grid providing a time-frequency representation of the signals received by the antennas for a respective time interval and a respective frequency interval and being referred to as a box and containing a complex vector X forming a measurement; and
for each box, calculating, from said box, by the computing unit, an estimation of a dual-source signal S=(s, c)T, s being a time-frequency representation of the signals received by the antennas and associated with a first source and c being a time-frequency representation of the signals received by the antennas and associated with a second source and (.)T being the transpose of (.) , ?=(?,?)T based upon an approximation of a conditional expectation estimator of the signals s and c such that the estimation utilizes, as an a priori information, knowledge that the signals s and c have a non-zero proportion of components equal to zero estimate values of non-zero components of s and c, a probability density of S being modeled as a mixture of centered Gaussians weighted by coefficients q1, q2, q3, q4 representing probabilities of four respective situations in each box which are: (1) presence of the first and second sources, (2) presence of the first source and absence of the second source, (3) absence of the first source and presence of the second source, and (4) absence of the first and second sources, this approximation being:
wherein (.)* is the conjugated transpose of the matrix (.),
wherein detQ1 det?1, detQ2 det?2, detQ3 det?3, and detQ4 det?4 are respectively equal to: (1?|U*V|2)?1 ?4/?12?22, ?2/?12, ?2/?22, and 1;
wherein 2?12, 2?22 are respectively power of the signal s associated with the first source and power of the signal c associated with the second source;
wherein 2?2 is power of noise presumed Gaussian, spatially, frequentially, and temporally white; andwherein M=(U V).