Non-coherent DOA estimation via proximal gradient based on a dual-array structure

Although the non-coherent direction of arrival (DOA) estimation problem can be solved by sparse phase retrieval algorithms, known reference signals are required to deal with the inherent ambiguity issue of this approach. To avoid the use of reference signals, an effective array structure employing two uniform linear arrays is proposed (although other array structures are possible, such as the circular array), based on which a phase retrieval problem employing group sparsity is formulated. It is then replaced by its convex surrogate alternative by applying the majorization-minimization technique and the proximal gradient method is employed to solve the surrogate problem. The proposed algorithm is referred to as fasT grOup sparsitY Based phAse Retreival (ToyBar). Unlike the existing phase-retrieval based DOA estimation algorithm GESPAR, it does not need to know the number of incident signals in advance. Simulation results indicate that the proposed algorithm has a fast convergence speed and a better estimation performance is achieved.