Extension of the Pisarenko method to sparse linear arrays

When applied to array processing, the Pisarenko harmonic retrieval method is limited to linear equispaced arrays. The author presents an approach that allows to extend it to general arrays. For the ease of exposition, the author considers only sparse linear arrays. Though limited in generality, these arrays already permit to localize up to N(N-1)/2 narrow-band sources with N-sensors. The author actually shows that the Pisarenko approach can be seen as a deconvolution or model-fitting approach that minimizes an l₁ norm and can be implemented as a standard linear program. Further extensions allowing to model and take into account the statistical nature of the data (the estimation errors) are also proposed