Field Agnostic Sub-Nyquist Spectrum Reconstruction and Source Localization

In dealing with multiple sources emitting narrow band and spectrally non-overlapping signals, usually referred to as Multiband Signals (MBS), one encounters the situation where a receiver has to be designed not only to reconstruct MBS blindly, but also capable of localizing the individual sources irrespective of whether they are in the far field or in near field. The problem becomes more challenging when the sensor receiver array is operated at sub-Nyquist sampling rates. This triple combination of sub-Nyquist field agnostic MBS reconstruction is hitherto not considered in the existing literature. This paper proposes a novel methodlogy to achieve the said outcome and in the process also relax the requirements on the geometry of the sensor array by dealing with generic Uniform Centro-Symmetric structure. An effort has been made to systematically present the algorithmic pipeline which involves (1) an ESPRIT based technique to estimate the frequency and the direction of arrival pair of each of the sources (2) a strategy to determine whether a source is in near or far field by suitably using the MUSIC algorithm and also simultaneously obtaining the range information for the near-field sources (3) the MBS signal spectrum estimation using the estimated parameters. Typical results of extensive simulation study are provided to demonstrate the performance and usefulness of the approach, particularly in the mixed-field scenarios. Apart from appropriate comparisons, the rigor of the work is also reinforced by providing appropriate theoretical results on the identifiability conditions.