Three-level prime arrays for sparse sampling in direction of arrival estimation

2018

IET signal process.

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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.

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“…In the following subsections, we present the coprime arrays [9] and the three-level prime arrays in [29] as special cases of the proposed MLPA configuration.…”

Section: Special Cases Of Mlpa Configurationsmentioning

confidence: 99%

“…When N p = 3, the array utilises three subarrays. The resultant array is referred to as a 3LPA [29] and (1) for sensor locations results in…”

Section: Three-level Prime Array (3lpa) and Pythagorean Array (Pa)mentioning

confidence: 99%

“…When

N_{normalp} = 3

, the array utilises three subarrays. The resultant array is referred to as a 3LPA [29] and (1) for sensor locations results in

double-struckP = (}{, k_{1} M_{j} d falsefalse|, j \neq 1) \cup (}{, k_{2} M_{j} d |, j \neq 2) \cup (}{, k_{3} M_{j} d falsefalse|, j \neq 3) .

In 3LPA, the sensors within the first subarray can be spaced by either

M_{3} d

M_{2} d

. Based on this choice, the inter‐element spacing of the remaining two subarrays is adjusted.…”

Section: System Modelmentioning

confidence: 99%

“…1 (iv). In this case, the 3LPA configurations have a total of

N = \sum_{i} M_{i} - 2 = 10

sensors [29]. The aperture size of the first and second configurations is

D = M_{2} ()(, M_{3} - 1) d = 18 d

and

D = M_{3} ()(, M_{2} - 1) d = 14 d

, respectively.…”

Section: System Modelmentioning

confidence: 99%

“…Henceforth, the number of configurations is

N_{normalc} = N_{normals}

. As an example for N = 10 or 12 sensors, the 3LPA has

N_{normalc} = 2 \times 2 = 4

configurations as in [29].…”

Section: Mlpa Design Alternativesmentioning

confidence: 99%

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