Direction of Arrival Estimation using EM-ESPRIT with nonuniform arrays

International audienceAbstract This paper deals with the problem of the Direction Of Arrival (DOA) estimation with nonuniform linear arrays. The proposed method is based on the Expectation Maximization method where ESPRIT is used in the maximization step. The key idea is to iteratively interpolate the data to a virtual uniform linear array in order to apply ESPRIT to estimate the DOA. The iterative approach allows to improve the interpolation using the previously estimated DOA. One of this method novelties lies in its capacity of dealing with any nonuniform array geometry. This technique manifests significant performance and computational advantages over previous algorithms such as Spectral MUSIC, EM-IQML and the method based on manifold separation technique. EM-ESPRIT is shown to be more robust to additive noise. Furthermore, EM-ESPRIT fully exploits the advantages of using a nonuniform array over a uniform array: simulations show that for the same aperture and with less number of sensors, the nonuniform array presents almost identical performance as the equivalent uniform array

EM-ESPRIT ALGORITHM FOR DIRECTION FINDING WITH NONUNIFORM ARRAYS

International audienceThis paper deals with the problem of the Direction Of Arrival (DOA) estimation with nonuniform linear arrays. The proposed method is a combination of the Expectation Maximization (EM) and the ESPRIT methods. The EM algorithm interpolates the nonuniform array to an equivalent uniform array, and then, the application of ESPRIT is possible, in order to estimate the DOA. One of this method novelties lies in its capacity of dealing with any nonuniform array geometry. This technique manifests significant performance and computational advantages over previous algorithms such as MUSIC, specially in the preasymptotic domain, and the comparison with the theoretical Cramer-Rao Bounds (CRB) shows its efficiency

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

EM-Type Algorithms for DOA Estimation in Unknown Nonuniform Noise

The expectation--maximization (EM) algorithm updates all of the parameter estimates simultaneously, which is not applicable to direction of arrival (DOA) estimation in unknown nonuniform noise. In this work, we present several efficient EM-type algorithms, which update the parameter estimates sequentially, for solving both the deterministic and stochastic maximum--likelihood (ML) direction finding problems in unknown nonuniform noise. Specifically, we design a generalized EM (GEM) algorithm and a space-alternating generalized EM (SAGE) algorithm for computing the deterministic ML estimator. Simulation results show that the SAGE algorithm outperforms the GEM algorithm. Moreover, we design two SAGE algorithms for computing the stochastic ML estimator, in which the first updates the DOA estimates simultaneously while the second updates the DOA estimates sequentially. Simulation results show that the second SAGE algorithm outperforms the first one.Comment: arXiv admin note: text overlap with arXiv:2208.0751

MIMO Radar Target Localization and Performance Evaluation under SIRP Clutter

Multiple-input multiple-output (MIMO) radar has become a thriving subject of research during the past decades. In the MIMO radar context, it is sometimes more accurate to model the radar clutter as a non-Gaussian process, more specifically, by using the spherically invariant random process (SIRP) model. In this paper, we focus on the estimation and performance analysis of the angular spacing between two targets for the MIMO radar under the SIRP clutter. First, we propose an iterative maximum likelihood as well as an iterative maximum a posteriori estimator, for the target's spacing parameter estimation in the SIRP clutter context. Then we derive and compare various Cram\'er-Rao-like bounds (CRLBs) for performance assessment. Finally, we address the problem of target resolvability by using the concept of angular resolution limit (ARL), and derive an analytical, closed-form expression of the ARL based on Smith's criterion, between two closely spaced targets in a MIMO radar context under SIRP clutter. For this aim we also obtain the non-matrix, closed-form expressions for each of the CRLBs. Finally, we provide numerical simulations to assess the performance of the proposed algorithms, the validity of the derived ARL expression, and to reveal the ARL's insightful properties.Comment: 34 pages, 12 figure

Agregados 2D de antenas microstrip não uniformes para aplicações sem fios

Doutoramento em Engenharia ElectrotécnicaWireless communications have undergone over the last decades a tremendous progress as a consequence of the exponential growth in demand for mobile devices, and nowadays are more and more involved in people's lives. This presence is re ected through the use of a large number of applications of which they become increasingly dependent on. The antenna, in its most di erent forms, are crucial elements in the establishment this type of communication. Each application involves a number of speci c characteristics, whereby, the improvement of wireless communications is related to the appropriateness of the used antenna. Many applications require antennas with radiation pattern with its particular shapes (in terms of beamwidth, side lobes levels, direction, etc ..), static or dynamic (adaptive antennas), involving in most cases the use antenna arrays to meet to such constraints. In this thesis, a number of techniques to synthesize antennas consisting of planar arrays with nonuniform excitation of their elements, are addressed. A group of the direction of arrival and beamforming estimation algorithms are also presented and analyzed, in order to enable their application in adaptive antenna array with dynamic beamforming. A vast and diversi ed set of arrays with di erent radiation requirements, and for di erent applications were developed. These arrays have great applicability in current research topics in antennas, such as vehicle communications, Wi-Fi in sports venues and smart antennas.As comunicações sem os têm sofrido, ao longo das ultimas décadas, um enorme progresso em consequência do aumento exponencial da procura de dispositivos móveis, estando hoje em dia cada vez mais presentes na vida das pessoas. Esta presença re ete-se através do uso de um elevado número de aplicações das quais se tornam cada vez mais dependentes. As antenas, nas suas mais diversi cadas formas, são elementos cruciais no estabelecimento deste tipo de comunicações. Cada aplicação envolve um conjunto de características especí cas, pelo que a melhoria das comunica ções sem os está relacionada com a adequação da antena usada. Muitas aplicações necessitam de antenas com diagramas de radiação com formatos próprios (em termos de larguras de feixe, níveis de lobos secund ários, direção, etc..), sejam eles estáticos ou dinâmicos (antenas adaptativas), implicando na maioria dos casos o uso de agregados de antenas para fazer face a tais condições. Nesta tese são abordadas várias técnicas de desenho de antenas constituídas por agregados planares, com alimentação não uniforme dos seus elementos. Um conjunto de algoritmos de estimação dos ângulos de chegada e de formação de feixe são também apresentados e analisados com vista à sua aplicação em agregados de antenas adaptativas, com formação de feixe dinâmico. Um vasto e diversi cado conjunto de agregados com diferentes requisitos de radiação, destinados a diferentes aplicações foram desenvolvidos. Estes agregados têm grande aplicabilidade nos atuais tópicos de investiga ção em antenas, tais como as comunicações veiculares, Wi-Fi em espaços desportivos e smart antenas

Scaling transform based information geometry method for DOA estimation

By exploiting the relationship between probability density and the differential geometry structure of received data and geodesic distance, the recently proposed information geometry (IG) method can provide higher accuracy and resolution ability for direction of arrival (DOA) estimation than many existing methods. However, its performance is not robust even for high signal to noise ratio (SNR). To have a deep understanding of its unstable performance, a theoretical analysis of the IG method is presented by deriving the relationship between the cost function and the number of array elements, powers and DOAs of source signals, and noise power. Then, to make better use of the nonlinear and super resolution property of the cost function, a Scaling TRansform based INformation Geometry (STRING) method is proposed, which simply scales the array received data or its covariance matrix by a real number. However, the expression for the optimum value of the scalar is complicated and related to the unknown signal DOAs and powers. Hence, a decision criterion and a simple search based procedure are developed, guaranteeing a robust performance. As demonstrated by computer simulations, the proposed STRING method has the best and robust angle resolution performance compared with many existing high resolution methods and even outperforms the classic Cramer-Rao bound (CRB), although at the cost of a bias in the estimation results