Paper Info
Title
Coprime Sensing via Chinese Remaindering Over Quadratic Fields—Part II: Generalizations and Applications
Abstract
The practical application of a new class of coprime arrays based on the Chinese remainder theorem (CRT) over quadratic fields is presented in this paper. The proposed CRT arrays are constructed by ideal lattices embedded from coprime quadratic integers with <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\mathbf {B}_1$</tex-math></inline-formula> and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\mathbf {B}_2$</tex-math></inline-formula> being their matrix representations, respectively, whereby the degrees of freedom (DOF) surges to <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$O(|\det {(\mathbf {B}_1\mathbf {B}_2)}|)$</tex-math></inline-formula> with <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$|\det (\mathbf {B}_1)| + |\det (\mathbf {B}_2)|$</tex-math></inline-formula> sensors. The geometrical constructions and theoretical foundations were discussed in the accompanying paper in great detail, while this paper focuses on aspects of the application of the proposed arrays in two-dimensional (2-D) remote sensing. A generalization of CRT arrays based on two or more pairwise coprime ideal lattices is proposed with closed-form expressions on sensor locations, the total number of sensors, and the achievable DOF. The issues pertaining to the coprimality of any two quadratic integers are also addressed to explore all possible ideal lattices. Exploiting the symmetry of lattices, sensor reduction methods are discussed with the coarray remaining intact for economic maximization. In order to extend conventional angle estimation techniques based on uniformly distributed arrays to the method that can exploit any coarray configurations based on lattices, this paper introduces a hexagon-to-rectangular transformation to 2-D spatial smoothing, providing the possibility of finding more compact sensor arrays. Examples are provided to verify the feasibility of the proposed methods.
Year
DOI
Venue
2019
10.1109/TSP.2019.2910480
IEEE Transactions on Signal Processing
Keywords
Field
DocType
Remote sensing,DOA estimation,sparse arrays,coprime matrices,spatial smoothing,hexagon-to-rectangular transformation,Voronoi cell
Discrete mathematics,Mathematical optimization,Quadratic integer,Lattice (order),Generalization,Matrix (mathematics),Chinese remainder theorem,Quadratic equation,Smoothing,Coprime integers,Mathematics
Journal
Volume
Issue
ISSN
67
11
1053-587X
Citations 
PageRank 
References 
0
0.34
0
Authors
3
Name
Order
Citations
PageRank
Conghui Li101.01
Lu Gan232425.46
Cong Ling368868.90