Multi-level prime array for sparse sampling

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 inter-element 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.