Sparse linear nested array for active sensing

Abstract

Abstract-Sparse sensor arrays can match the performance of fully populated arrays using substantially fewer elements. However, finding the array configuration with the smallest number of elements is generally a computationally difficult problem. Consequently, simple to generate array configurations that may be suboptimal are of high practical interest. This paper presents a novel closed-form sparse linear array configuration designed for active sensing, called the Concatenated Nested Array (CNA). The key parameters of the CNA are derived. The CNA is also compared to the optimal Minimum-Redundancy Array (MRA) in numerical simulations. The CNA is shown to require only about 10% more elements than the MRA in the limit of large apertures.

Symmetric Sparse Linear Array for Active Imaging

“…A lower bound on number of elements is obtained by setting β = 4 and solving for N , yielding N ≥ ( √ 32L + 25−3)/2 = O( √ 8L). For comparison, the CNA also achieves N = O( √ 8L) [13]. Similarly, substituting (13) into (9) yields the number of unit spacings: υ ∆ (1) = N/2 + 1, when N ≤ 8, and N/4 + ζ otherwise.…”

“…Again, ζ depends on N as α and β, and assumes values ζ = {1, 1/2, 0, 3/2}. Note that this is only half of the number of unit spacings in the CNA with υ ∆ (1) ≈ N/2 [13].…”

“…Unfortunately, the number of elements N in the RRA scales linearly with aperture L, whereas N ∝ √ L would be preferable. A modification of the Nested Array [9], called the Concatenated Nested Array (CNA), was recently proposed to address this problem [13]. However, the CNA still has many closely spaced elements, which may degrade performance when mutual coupling is considered.…”

Sparse Low-redundancy Linear Array with Uniform Sum Co-array

“…Another option is to find parametric designs based on the properties of the desired co-array. Examples include nested [3,14] and Wichmann arrays [15,16]. Parametric configurations often scale well for large apertures, since they can be easily optimized, e.g., for redundancy.…”

Sparse Active Rectangular Array With Few Closely Spaced Elements

“…Hence, several authors have investigated closed-form, but possibly sub-optimal configurations, such as the Wichmann [13]- [15], Nested [3], or Co-prime array [16]. These arrays have primarily been developed for passive sensing of incoherent sources, although some of them are easily adapted to active array processing tasks, such as coherent imaging with co-located transceivers [17], [18]. Note that optimal active sparse linear arrays with distinct transmitting and The authors are with the Department of Signal Processing and Acoustics, Aalto University School of Electrical Engineering, Espoo 02150, Finland (email: robin.rajamaki@aalto.fi, visa.koivunen@aalto.fi).…”