Unambiguous DOA Estimation Using Multi-Frequency Rational Sparse Arrays

In this paper, we consider the conditions for unique identifiability of the direction-of-arrival (DOA) estimation problem under a multi-frequency sparse rational array framework. Previous studies on the multi-frequency scenario involved integer locations of the virtual sensor locations at each frequency. The rational array framework removes such requirements and thus provides higher flexibility in multi-frequency sparse array design. We provide a generalized necessary condition for the unambiguous detection of signal DOAs in terms of the maximum spatial correlation coefficient between distinct signal directions, and the applicability of direct MUSIC for the unambiguous detection of signals exploiting rational sparse arrays is considered. The effectiveness of multi-frequency rational sparse arrays and the proposed analyses is verified using simulation results.