Extension of Co-Prime Arrays Based on the Fourth-Order Difference Co-Array Concept

An effective sparse array extension method for maximizing the number of consecutive lags in the fourth-order difference co-array is proposed, leading to a novel enhanced sparse array structure based on co-prime arrays (CPAs) with significantly increased number of degrees of freedom (DOFs). One method to exploit the increased DOFs based on nonstationary signals is also proposed, with simulation results provided to demonstrate the effectiveness of the proposed structure

Simplified and enhanced multiple level nested arrays exploiting high order difference co-arrays

Based on the high order difference co-array concept, an enhanced four level nested array (E-FL-NA) is first proposed, which optimizes the consecutive lags at the fourth order difference co-array stage. To simplify the formulations for sensor locations for comprehensive illustration and also convenient structure construction, a simplified and enhanced four level nested array (SE-FL-NA) is then proposed, whose performance is compromised but still better than the four level nested array (FL-NA). This simplified structure is further extended to the higher order case with multiple sub-arrays, referred to as simplified and enhanced multiple level nested arrays (SE-ML-NAs), where significantly increased degrees of freedom (DOFs) can be provided and exploited for underdetermined DOA estimation. Simulation results are provided to verify the superior performance of the proposed E-FL-NA, while a higher number of detectable sources is achieved by the SE-ML-NA with a limited number of physical sensors

An Expanding and Shift Scheme for Constructing Fourth-Order Difference Co-Arrays

An expanding and shift (EAS) scheme for efficient fourth-order difference co-array construction is proposed. It consists of two sparse sub-arrays, where one of them is modified and shifted according to the analysis provided. The number of consecutive lags of the proposed structure at the fourth order is consistently larger than two previously proposed methods. Two effective construction examples are provided with the second sparse sub-array chosen to be a two-level nested array, as such a choice can increase the number of consecutive lags further. Simulations are performed to show the improved performance by the proposed method in comparison with existing structures

Extension of Nested Arrays with the Fourth-Order Difference Co-Array Enhancement

To reach a higher number of degrees of freedom by exploiting the fourth-order difference co-array concept, an effective structure extension based on two-level nested arrays is proposed. It increases the number of consecutive lags in the fourth-order difference coarray, and a virtual uniform linear array (ULA) with more sensors and a larger aperture is then generated from the proposed structure, leading to a much higher number of distinguishable sources with a higher accuracy. Compressive sensing based approach is applied for direction-of-arrival (DOA) estimation by vectorizing the fourthorder cumulant matrix of the array, assuming non-Gaussian impinging signals

Wideband DOA Estimation with Frequency Decomposition via a Unified GS-WSpSF Framework

A unified group sparsity based framework for wideband sparse spectrum fitting (GS-WSpSF) is proposed for wideband direction-of-arrival (DOA) estimation, which is capable of handling both uncorrelated and correlated sources. Then, by making four different assumptions on a priori knowledge about the sources, four variants under the proposed framework are formulated as solutions to the underdetermined DOA estimation problem without the need of employing sparse arrays. As verified by simulations, improved estimation performance can be achieved by the wideband methods compared with narrowband ones, and adopting more a priori information leads to better performance in terms of resolution capacity and estimation accuracy

Underdetermined DOA Estimation Under the Compressive Sensing Framework: A Review

Direction of arrival (DOA) estimation from the perspective of sparse signal representation has attracted tremendous attention in past years, where the underlying spatial sparsity reconstruction problem is linked to the compressive sensing (CS) framework. Although this is an area with ongoing intensive research and new methods and results are reported regularly, it is time to have a review about the basic approaches and methods for CS-based DOA estimation, in particular for the underdetermined case. We start from the basic time-domain CSbased formulation for narrowband arrays and then move to the case for recently developed methods for sparse arrays based on the co-array concept. After introducing two specifically designed structures (the two-level nested array and the co-prime array) for optimizing the virtual sensors corresponding to the difference coarray, this CS-based DOA estimation approach is extended to the wideband case by employing the group sparsity concept, where a much larger physical aperture can be achieved by allowing a larger unit inter-element spacing and therefore leading to further improved performance. Finally, a specifically designed ULA structure with associated CS-based underdetermined DOA estimation is presented to exploit the difference co-array concept in the spatio-spectral domain, leading to a significant increase in DOFs. Representative simulation results for typical narrowband and wideband scenarios are provided to demonstrate their performance

Non-uniform Array and Frequency Spacing for Regularization-free Gridless DOA

Gridless direction-of-arrival (DOA) estimation with multiple frequencies can be applied in acoustics source localization problems. We formulate this as an atomic norm minimization (ANM) problem and derive an equivalent regularization-free semi-definite program (SDP) thereby avoiding regularization bias. The DOA is retrieved using a Vandermonde decomposition on the Toeplitz matrix obtained from the solution of the SDP. We also propose a fast SDP program to deal with non-uniform array and frequency spacing. For non-uniform spacings, the Toeplitz structure will not exist, but the DOA is retrieved via irregular Vandermonde decomposition (IVD), and we theoretically guarantee the existence of the IVD. We extend ANM to the multiple measurement vector (MMV) cases and derive its equivalent regularization-free SDP. Using multiple frequencies and the MMV model, we can resolve more sources than the number of physical sensors for a uniform linear array. Numerical results demonstrate that the regularization-free framework is robust to noise and aliasing, and it overcomes the regularization bias

Multi-source parameter estimation and tracking using antenna arrays

This thesis is concerned with multi-source parameter estimation and tracking using antenna arrays in wireless communications. Various multi-source parameter estimation and tracking algorithms are presented and evaluated. Firstly, a novel multiple-input multiple-output (MIMO) communication system is proposed for multi-parameter channel estimation. A manifold extender is presented for increasing the degrees of freedom (DoF). The proposed approach utilises the extended manifold vectors together with superresolution subspace type algorithms, to achieve the estimation of delay, direction of departure (DOD) and direction of arrival (DOA) of all the paths of the desired user in the presence of multiple access interference (MAI). Secondly, the MIMO system is extended to a virtual-spatiotemporal system by incorporating the temporal domain of the system towards the objective of further increasing the degrees of freedom. In this system, a multi-parameter es- timation of delay, Doppler frequency, DOD and DOA of the desired user, and a beamformer that suppresses the MAI are presented, by utilising the proposed virtual-spatiotemporal manifold extender and the superresolution subspace type algorithms. Finally, for multi-source tracking, two tracking approaches are proposed based on an arrayed Extended Kalman Filter (arrayed-EKF) and an arrayed Unscented Kalman Filter (arrayed-UKF) using two type of antenna arrays: rigid array and flexible array. If the array is rigid, the proposed approaches employ a spatiotemporal state-space model and a manifold extender to track the source parameters, while if it is flexible the array locations are also tracked simultaneously. Throughout the thesis, computer simulation studies are presented to investigate and evaluate the performance of all the proposed algorithms.Open Acces

Statistical Nested Sensor Array Signal Processing

Source number detection and direction-of-arrival (DOA) estimation are two major applications of sensor arrays. Both applications are often confined to the use of uniform linear arrays (ULAs), which is expensive and difficult to yield wide aperture. Besides, a ULA with N scalar sensors can resolve at most N − 1 sources. On the other hand, a systematic approach was recently proposed to achieve O(N 2 ) degrees of freedom (DOFs) using O(N) sensors based on a nested array, which is obtained by combining two or more ULAs with successively increased spacing. This dissertation will focus on a fundamental study of statistical signal processing of nested arrays. Five important topics are discussed, extending the existing nested-array strategies to more practical scenarios. Novel signal models and algorithms are proposed. First, based on the linear nested array, we consider the problem for wideband Gaussian sources. To employ the nested array to the wideband case, we propose effective strategies to apply nested-array processing to each frequency component, and combine all the spectral information of various frequencies to conduct the detection and estimation. We then consider the practical scenario with distributed sources, which considers the spreading phenomenon of sources. Next, we investigate the self-calibration problem for perturbed nested arrays, for which existing works require certain modeling assumptions, for example, an exactly known array geometry, including the sensor gain and phase. We propose corresponding robust algorithms to estimate both the model errors and the DOAs. The partial Toeplitz structure of the covariance matrix is employed to estimate the gain errors, and the sparse total least squares is used to deal with the phase error issue. We further propose a new class of nested vector-sensor arrays which is capable of significantly increasing the DOFs. This is not a simple extension of the nested scalar-sensor array. Both the signal model and the signal processing strategies are developed in the multidimensional sense. Based on the analytical results, we consider two main applications: electromagnetic (EM) vector sensors and acoustic vector sensors. Last but not least, in order to make full use of the available limited valuable data, we propose a novel strategy, which is inspired by the jackknifing resampling method. Exploiting numerous iterations of subsets of the whole data set, this strategy greatly improves the results of the existing source number detection and DOA estimation methods