Multi-frequency based underdetermined direction-of-arrival estimation for irregularly positioned sparse array

With the increasing complexity of modern electromagnetic environments, it is more and more common that the number of sources is more than the number of physical sensors, hence underdetermined direction-of-arrival (DOA) estimation has been a key problem. Sparse array is able to increase degrees-of-freedom (DOFs) in the context of difference coarray equivalence. However, most of the related methods have strict restrictions on sparse array configurations and are difficult to apply in engineering. Therefore, in this paper, we study the underdetermined DOA estimation method based on irregularly positioned sparse arrays. Firstly, we extend the virtual array elements by multi-frequency, and then, to address the DOA ambiguity caused by the existence of holes in the virtual array, we take advantage of the difference in the positions of the virtual array elements generated by different frequency and realize the unambiguous DOA estimation by the spatial spectral multiplication of the different virtual array. In addition, we discuss the theoretical constraints on the random layout of sparse array elements and gives a design solution which can exploit all of the DOFs. The simulation results demonstrate the effectiveness of the method.