Spectrum blind reconstruction and direction of arrival estimation at sub-Nyquist sampling rates with uniform linear array

This paper considers the problem of sparse spectrum blind reconstruction and its constituent narrow band (bandwidth not exceeding B Hz) source direction of arrival (DOA) estimation, at sub-Nyquist sampling rates and with an M element uniform linear array. We propose a modification to the receiver architecture by adding an M channel delay network to only the first sensor element. This delay network in practice can simply be realized by cascading M identical delays. Further, a novel ESPRIT based algorithm, by making use of new transformation matrices, which automatically pairs the carrier frequencies along with their corresponding DOAs is presented. We show that with the proposed approach, an ADC sampling frequency of ƒs ≥ B Hz is sufficient and upto M − 2 source DOAs and their corresponding spectrum can be reconstructed even if all the frequencies exactly alias to the same frequency.