Multi‐level prime array for sparse sampling

Abstract

Sensor array configurations such as coprime and nested arrays have attracted many researchers because they increase the degree of freedom (DOF). For example, in the direction of arrival estimation, the number of sources that can be estimated is greater than the total number of sensors. This study proposes a multi-level prime array (MLPA) configuration for sparse sampling that can further increase the DOF. The proposed array uses multiple uniform linear subarrays where the number of sensors in the subarrays is pairwise coprime integers. The inter-element spacing between the sensors is formulated as a scaled multiple of half-wavelength where the subarrays share only their first element. For a fixed number of sensors, multiple MLPA configurations can be constructed by controlling the number of sensors in the subarrays or by adjusting the interelement spacing. For a given number of sensors, the proposed array has a smaller aperture and achieves more number of unique and consecutive lags compared with coprime arrays. The proposed configuration has limited holes in the difference coarray. The analytical expressions of both the difference coarray and the aperture size are derived. Simulation results confirm the advantage of the proposed configurations compared with the two level coprime arrays.

Novel method for digital beamforming in co‐prime sensor arrays using product and min processors

“…The obtained array is a sparse NULA, in which the total number of sensors and array aperture are c ( N 1 + N 2 −1) and cN 1 ( N 2 −1) λ/ 2, respectively. Hence, the CSA resolution is comparable to a fully populated uniform linear array (full ULA) with cN 1 N 2 sensors spaced every λ/ 2 [6, 7]. Fig.…”

“…Therefore, the main goal in beam-forming with a NULA is to achieve the performance of the equivalent-aperture ULA [3]. So far the various NULA configurations, such as non-redundant array [3], minimum redundant array [4], nested sensor array [5], co-prime sensor array (CSA) [6], and multi-level prime array [7] are introduced in literature. The NULAs use difference co-array (DCA) processing concept to achieve more degree of freedom (DOF) in DOA estimation [5][6][7].…”

“…Also, in the presence of multiple signals the output of the CSA prod processor include cross-terms, which can be mitigated by temporal averaging when the arriving signals are uncorrelated. In [7,8], it is shown that the SLL of the product processor can be reduced by decreasing the width of the grating lobes, which is achieved by adding more sensors to the subarrays. This approach is not feasible when the size of the array is limited by the costs or the environmental constraints.…”

“…So far the various NULA configurations, such as non‐redundant array [3], minimum redundant array [4], nested sensor array [5], co‐prime sensor array (CSA) [6], and multi‐level prime array [7] are introduced in literature. The NULAs use difference co‐array (DCA) processing concept to achieve more degree of freedom (DOF) in DOA estimation [5–7]. The CSA has high performance and less mutual coupling compared to other sparse arrays.…”

The Multi-Level Dilated Nested Array for Direction of Arrival Estimation

“…In order to solve the contradiction between the improved DoFs and the reduced number of array elements, the issue of underdetermined DOA estimation in sparse array, has been attracting the related researchers and practitioners in recent years. Kinds of sparse array structures, such as minimum redundancy array (MRA) [18], coprime array (CA) [19]- [23], nested array (NA) [24]- [29] and so on, have been put forward. MRA is a linear sparse array designed to obtain the largest possible virtual uniform linear array aperture.…”