Abstract
In this paper, a novel parallel factor (PARAFAC) model for processing the nested vector-sensor array is proposed. It is first shown that a nested vector-sensor array can be divided into multiple nested scalar-sensor subarrays. By means of the autocorrelation matrices of the measurements of these subarrays and the cross-correlation matrices among them, it is then demonstrated that these subarrays can be transformed into virtual scalar-sensor uniform linear arrays (ULAs). When the measurement matrices of these scalar-sensor ULAs are combined to form a third-order tensor, a novel PARAFAC model is obtained, which corresponds to a longer vector-sensor ULA and includes all of the measurements of the difference co-array constructed from the original nested vector-sensor array. Analyses show that the proposed PARAFAC model can fully use all of the measurements of the difference co-array, instead of its partial measurements as the reported models do in literature. It implies that all of the measurements of the difference co-array can be fully exploited to do the 2-D direction of arrival (DOA) and polarization parameter estimation effectively by a PARAFAC decomposition method so that both the better estimation performance and slightly improved identifiability are achieved. Simulation results confirm the efficiency of the proposed model.
Highlights
The vector sensors, e.g., the acoustic [1] and electromagnetic (EM) [2] ones, can record two to six signal components on a collocated sensor
In [4,5], the vector sensors were applied to the target localization
A multiple-input multiple-output (MIMO) array system with the EM vector antennas was presented in [6]. All these contributions utilized the so-called “long-vector” approach which could destroy the multidimensional structure of the received signals of vector sensors [7]
Summary
The vector sensors, e.g., the acoustic [1] and electromagnetic (EM) [2] ones, can record two to six signal components on a collocated sensor. From the autocorrelation matrices of the received signals of the M subarrays and cross-correlation matrices among them, M measurement matrices corresponding to M virtual ULAs with N 2 /2 + N − 1 scalar sensors are obtained Since these virtual scalar-sensor ULAs enjoy the same spatial and equivalent temporal diversity spaces, we can combine them to form a new virtual ULA with N 2 /2 + N − 1 vector sensors and M snapshots, and model it as a tensor with a PARAFAC decomposition form. In this way, all of the measurements from the difference co-array of the original nested vector-sensor array are described as a PARAFAC model, instead of a matrix one reported in [19]. Notations: (·)∗ , (·) T , ◦, ⊗, and denote conjugation, transpose, outer product, Kronecker product, and Khatri-Rao product, respectively
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