Maximally sparsen arrays via continuous compressive sensing

Abstract

An innovative technique for the synthesis of a nonuniform sonar array with as few elements as possible is proposed. This paper introduces a new method for linear array pattern synthesis based on continuous compressive sensing (CCS). Given a reference pattern subject to aperture constraints, the proposed approach allows the exact solution of the positions of sonar sensors, whose number is maximally reduced. The excitations and positions of sensors are exactly estimated without constraints of sampling grids used in convetional CS methods. Numerical experiments show that the proposed synthesis method is able to maximally save array elements for the design of sparse linear arrays, also compared to state-of-the-art sparse array synthesis methods.Index Terms-Array design; pattern synthesis; sparse nonuniform linear array; continuous compressive sensing.978-1-4673-9724-7/16/$31.00 ©2016 IEEE

Synthesis of sparse linear arrays using reweighted gridless compressed sensing

“…Following from Ref. [38], Equation (2) can be reformulated as the gridless convex optimisation through the following steps:…”

“…Different from Ref. [38], this modified relationship is derived from the beam samples within the entire pattern range, thus providing an extension of the gridless model to synthesise asymmetric patterns.…”

“…Moreover, note that the constraint of Equation ( 7) is different from that in Ref. [38], and η denotes the small tolerance error of the synthesised pattern. To be specific, ANM is equivalent to the following semi-definite programing (SDP) [31,39,40]:…”

“…More specifically, the Dolph-Chebyshev and Taylor patterns [46] characterised by (L, SLL) ∈ {(4.5 λ, −20 dB), (7 λ, −20 dB), (9.5 λ, −20 dB), (9.5 λ, −30 dB)} have been chosen as the reference patterns. In addition, we also introduce CS [2], BCS [23,24], and GCS [38] with the modified relationship Equation ( 6) for performance comparison.…”

“…More recently, the gridless CS (GCS) algorithm (the algorithm is sometimes called continuous CS) has been developed for frequency estimation [31][32][33][34][35] as well as direction of arrival (DOA) [36,37]. The GCS can effectively solve the grid mismatch problem through the atomic norm minimisation (ANM), and has been utilised for synthesising the focussed-beam patterns [38]. However, the GCS algorithm cannot synthesise the asymmetricshaped-beam patterns since only half of the beam pattern is considered in the synthesis model.…”