Abstract
In this paper, an off-grid direction-of-arrival (DoA) estimation algorithm which can work on a non-uniform linear array (NULA) is proposed. The original semidefinite programming (SDP) representation of the atomic norm exploits a summation of one-rank matrices constructed by atoms, where the summation of one-rank matrices equals a Hermitian Toeplitz matrix when using the uniform linear array (ULA). On the other hand, when the antennas in the array are placed arbitrarily, the summation of one-rank matrices is a Hermitian matrix whose diagonal elements are equivalent. Motivated by this property, the proposed algorithm replaces the Hermitian Toeplitz matrix in the original SDP with the constrained Hermitian matrix. Additionally, when the antennas are placed symmetrically, the performance can be enforced by adding extra constraints to the Hermitian matrix. The simulation results show that the proposed algorithm achieves higher estimation accuracy and resolution than other algorithms on both array structures; i.e., the arbitrary array and the symmetric array.
Highlights
Direction-of-arrival (DoA) estimation is one of the longest-studied research topics in array signal processing
We enable the usage of the non-uniform linear array (NULA) by replacing the Hermitian Toeplitz matrix with the constrained Hermitian matrix
We propose a novel off-grid DoA estimation algorithm which can work on two types of NULA; i.e., an arbitrary array and a symmetric array
Summary
Direction-of-arrival (DoA) estimation is one of the longest-studied research topics in array signal processing. Existing studies regarding off-grid DoA estimation are limited to a uniform linear array (ULA). We propose a novel approach for off-grid DoA estimation which can work on an NULA. Most of the existing works regarding off-grid DoA estimation are limited to ULA To overcome this disadvantage, we propose a novel approach for an off-grid DoA estimation algorithm which can work on the NULA. When antennas of the NULA are symmetrically placed, the summation of the one-rank matrices corresponds to a unique Hermitian matrix whose particular elements are equal in a certain manner. We model this unique Hermitian matrix by adding extra constraints to the SDP. If A B, a matrix A − B is positive semidefinite. a(i ) denotes the i-th element in a vector a, and A(i, j) denotes the (i, j)-th element in a matrix A. 0 N denotes a N × 1 zero vector, and I N denotes a N × N identity matrix. b(·)c denotes rounding down
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