In this paper, vertical motions of sparse linear arrays (SLAs) are utilized to generate equivalent synthetic planar arrays for two-dimensional (2D) direction-of-arrival (DOA) estimation. The proposed array geometry named vertical synthetic planar array (VSPA) consists of an arbitrary SLA on the x-axis and a series of its time-shifted arrays in the vertical orientation. With the original linear array and the moving trail known, the difference coarray of VSPA can be easily obtained. By utilizing both the synthetic aperture processing and the coarray technique, VSPA has the ability to construct a synthetic planar array with only an SLA used. Compared with the traditional sparse planar arrays (SPAs), such as 2D nested array and 2D coprime array, VSPA can achieve higher degree-of-freedom and improved 2D DOA estimation performance with the same number of sensors. Moreover, as different original linear arrays and moving trails can be chosen for different applications, the construction of VSPA is of high flexibility. Numerical simulations are presented to verify the superiority of the proposed VSPA geometry over other typical SPAs.

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In this paper, we propose a new strategy with increased element spacings placed on two-side subarrays and increase the physical sparse sensors array aperture. In order to ensure the continuity of difference co-array, four conditions are proposed. Based on these conditions, a new array structure named TS2-ENA is derived. Compared with other nested-like arrays with a fixed number of elements, our proposed structure possesses a higher degree of freedom, closed-form expression and outstanding performance. Simulation results show the superiority of the new configuration with the spacial smoothing MUSIC algorithm conducted.