We propose a new class of nested vector-sensor arrays which is capable of significantly increasing the degrees of freedom (DOF). This is not a simple extension of the nested scalar-sensor array, but a novel signal model. The structure is obtained by systematically nesting two or more uniform linear arrays with vector sensors. By using one component's information of the interspectral tensor, which is equivalent to the higher-dimensional second-order statistics of the received data, the proposed nested vector-sensor array can provide O(N~2) DOF with only N physical sensors. To utilize the increased DOF, a novel spatial smoothing approach is proposed, which needs multilinear algebra in order to preserve the data structure and avoid reorganization. Thus, the data is stored in a higher-order tensor. Both the signal model of the nested vector-sensor array and the signal processing strategies, which include spatial smoothing, source number detection, and direction of arrival (DOA) estimation, are developed in the multidimensional sense. Based on the analytical results, we consider two main applications: electromagnetic (EM) vector sensors and acoustic vector sensors. The effectiveness of the proposed methods is verified through numerical examples.
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