Abstract
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.
Highlights
Direction of arrival (DOA) estimation has various applications such as radar, sonar and wireless communications [1]
Liu: Non-Coherent DOA Estimation via Proximal Gradient Based on a Dual-Array Structure mirroring and spatial shift ambiguities, a new ambiguity issue called spatial order ambiguity is identified for the first time and discussed in detail and a solution to avoid this ambiguity is to limit the inter-sensor spacing of the employed uniform linear arrays (ULAs) to be less than a quarter of the signal wavelength for the normal DOA range of [−90◦, 90◦]
By exploiting the spatial information of both sub-arrays of the dual-array simultaneously, a joint group sparsity based non-coherent DOA estimation problem with multiple snapshots was formulated. This problem can be solved by the proximal gradient method after transforming the original non-convex problem to its convex surrogate via the majorization-minimization
Summary
Direction of arrival (DOA) estimation has various applications such as radar, sonar and wireless communications [1]. Liu: Non-Coherent DOA Estimation via Proximal Gradient Based on a Dual-Array Structure mirroring and spatial shift ambiguities, a new ambiguity issue called spatial order ambiguity is identified for the first time and discussed in detail and a solution to avoid this ambiguity is to limit the inter-sensor spacing of the employed uniform linear arrays (ULAs) to be less than a quarter of the signal wavelength for the normal DOA range of [−90◦, 90◦]. To avoid the mirroring and spatial shift ambiguities, a dual-array structure without the need of any reference signals for multiple impinging sources is proposed with a detailed derivation to show its working In essence, it utilizes the non-linear property of the sinusoidal function, and a unique DOA result is guaranteed with two sets of sinusoidal difference values. Where n1 and n2 are random Gaussian noise vectors, while | · | is the element-wise absolute value operation
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