Sparse coprime sensing: new array geometries and applications

This thesis introduces a new class of array geometries based on Chinese remaindering theorem (CRT). These arrays include two-dimensional (2D) CRT arrays, hole-free symmetric CRT-based arrays, sliced CRT arrays, and cross CRT arrays. Generated from rings of algebraic integers, the proposed arrays enjoy simple and closed-form expressions, surged degrees of freedom (DOF), and sparse geometries: Because of the bijective mapping between algebraic lattices and ideals, the array geometry can be described by ideals associated with algebraic integers offering simple and closed-form expressions. Another desirable property of ideal lattice is that it is applicable to the generalized CRT which asserts the increased DOF in a mathematical manner. The prime factorization and generalized Bezout's identity over algebraic integers provide approaches to attain sparse coprime CRT arrays. Considering noise interference between sensors, because the interference decreases inversely proportional to the distance between two adjacent sensors, it is appropriate to use the sparse geometry for sensor placement. By employing algebraic integers of dimension three, the three-dimensional (3D) CRT arrays is also introduced as an extension of 2D CRT arrays. Another main contribution of this thesis is to propose the generalized spatial smoothing methods incorporating the statistic model for angle estimation in both active and passive sensing scenarios. By deploying the prior knowledge of array configuration in conjunction with extracted data, a generalized spatial smoothing framework is developed to perform estimation algorithms such as subspace-based techniques and maximum likelihood approaches on an arbitrary lattice-based sparse array. This framework is centered on the electromagnetic wave propagation underlying a statistical model and can be leveraged for a wide range of applications such as radar and sonar systems, communications, imaging, and so forth. The proposed new array geometries and the generalized spatial smoothing framework together moveforward the investigation of sparse sensing and open up exciting future research in signal processingexploiting concepts in algebraic number theory.Open Acces