Covariance fitting (CF) is a comprehensive approach for direction of arrival (DoA) estimation, consolidating many common solutions. Standard practice is to use Euclidean criteria for CF, disregarding the intrinsic Hermitian positive-definite (HPD) geometry of the spatial covariance matrices. We assert that this oversight leads to inherent limitations. In this paper, as a remedy, we present a comprehensive study of the use of various Riemannian metrics of HPD matrices in CF. We focus on the advantages of the Affine-Invariant (AI) and the Log-Euclidean (LE) Riemannian metrics. Consequently, we propose a new practical beamformer based on the LE metric and derive analytically its spatial characteristics, such as the beamwidth and sidelobe attenuation, under noisy conditions. Comparing these features to classical beamformers shows significant advantage. In addition, we demonstrate, both theoretically and experimentally, the LE beamformer's robustness in scenarios with small sample sizes and in the presence of noise, interference, and multipath channels.
Learning the covariance matrices of spatially-correlated wireless channels, in millimeter-wave (mmWave) vehicular communication, can be utilized in designing environmen-taware beamforming codebooks. Such channel covariance matrices can be represented on non-Euclidean Riemannian manifolds, thanks to their symmetric positive definite (SPD) characteristics. Consequently in this paper, we propose a Riemannian-Geometric machine learning (G-ML) approach for estimating the channel covariance matrices based on unsupervised K-Means model. The proposed K-means algorithm utilizes Log-Euclidean metric (LE…
We present a gridless sparse iterative covariance-based estimation method based on alternating projections for direction-of-arrival (DOA) estimation. The gridless DOA estimation is formulated in the reconstruction of Toeplitz-structured low rank matrix, and is solved efficiently with alternating projections. The method improves resolution by achieving sparsity, deals with single-snapshot data and coherent arrivals, and, with co-prime arrays, estimates more DOAs than the number of sensors. We evaluate the proposed method using simulation results focusing on co-prime arrays.
Hybrid Architecture Gets Fluid: A New Paradigm for Direction-of-arrival Estimation in 6G Networks
Ningbo University（宁波大学）；City University of Hong Kong（香港城市大学）；Hong Kong Polytechnic University（香港理工大学）；Queen Mary University of London（伦敦大学玛丽女王学院）；West Virginia University（西弗吉尼亚大学）；The University of Texas at Dallas（德克萨斯大学达拉斯分校）
A blind Direction-of-Arrivals (DOAs) estimate of narrowband signals for Acoustic Vector-Sensor (AVS) arrays is proposed. Building upon the special structure of the signal measured by an AVS, we show that the covariance matrix of all the received signals from the array admits a natural low-rank 4-way tensor representation. Thus, rather than estimating the DOAs directly from the raw data, our estimate arises from the unique parametric Canonical Polyadic Decomposition (CPD) of the observations' Second-Order Statistics (SOSs) tensor. By exploiting results from fundamental statistics and the recent…
This paper proposes a strategy to handle missing data for the classification of electroencephalograms using covariance matrices. It relies on the observed-data likelihood within an expectation-maximization algorithm. This approach is compared to two existing state-of-the-art methods: (i) covariance matrices computed with imputed data; (ii) Riemannian averages of partially observed covariance matrix. All approaches are combined with the minimum distance to Riemannian mean classifier and applied to a classification task of two widely known paradigms of brain-computer interfaces. In addition to b…
Unified Constrained Geometric Configuration Optimization for Source Localization Systems: A Riemannian Manifold-Based Approach
College of Information Science and Engineering, Hohai University（河海大学信息科学与工程学院）；School of Information and Communication Engineering, Hainan University（海南大学信息与通信工程学院）
The estimation of the covariance function of a stochastic process, or signal, is of integral importance for a multitude of signal processing applications. In this work, we derive closed-form expressions for the variance of covariance estimates for mixed-spectrum signals, i.e., spectra containing both absolutely continuous and singular parts. The results cover both finite-sample and asymptotic regimes, allowing for assessing the exact speed of convergence of estimates to their expectations, as well as their limiting behavior. As is shown, such covariance estimates may converge even for non-ergo…
Optimal Maximum Likelihood (ML), narrow-band direction finding cannot be easily initialized in coherent and low signal to noise ratio environments. Sparse under-determined solvers are considered as viable solutions to this problem, since they drastically reduce the dimensionality of the search space by exploiting the array model sparseness. However, because of quantized locations, conventional sparse solvers present some ambiguity problems. In this work, we propose a novel boosting scheme for ML-type estimators, referred to as Parallel BOOSTer (P-BOOST), where a set of generalized MUSIC soluti…
Covariance matrix reconstruction is a topic of great significance in the field of one-bit signal processing and has numerous practical applications. Despite its importance, the conventional arcsine law with zero threshold is incapable of recovering the diagonal elements of the covariance matrix. To address this limitation, recent studies have proposed the use of non-zero clipping thresholds. However, the relationship between the estimation error and the sampling threshold is not yet known. In this paper, we undertake an analysis of the mean squared error by computing the Fisher information mat…
Inserm（法国国家健康与医学研究院）；Paris Diderot University（巴黎第七大学）；Lariboisière Hospital（拉里博瓦西耶医院）；Assistance Publique Hôpitaux de Paris（巴黎公共援助医院）；Université Paris-Saclay（巴黎萨克雷大学）；Inria（法国国家信息与自动化研究所）；CEA（法国原子能和替代能源委员会）
Magnetoencephalography and electroencephalography (M/EEG) can reveal neuronal dynamics non-invasively in real-time and are therefore appreciated methods in medicine and neuroscience. Recent advances in modeling brain-behavior relationships have highlighted the effectiveness of Riemannian geometry for summarizing the spatially correlated time-series from M/EEG in terms of their covariance. However, after artefact-suppression, M/EEG data is often rank deficient which limits the application of Riemannian concepts. In this article, we focus on the task of regression with rank-reduced covariance ma…
A vector sensor, a type of sensor array with six collocated antennas to measure all electromagnetic field components of incident waves, has been shown to be advantageous in estimating the angle of arrival and polarization of the incident sources. While angle estimation with machine learning for linear arrays has been well studied, there has not been a similar solution for the vector sensor. In this paper, we propose neural networks to determine the number of the sources and estimate the angle of arrival of each source, based on the covariance matrix extracted from received data. Also, we provi…
In this paper, an accurate direction-of-arrival (DOA) estimator is developed based on the real-valued singular value decomposition (SVD) of covariance matrix. Unitary transform on the complex-valued covariance matrix is first applied, and then SVD performs on the resulting real-valued data matrix. The singular vector is then utilized with a weighted least squares (WLS) method to achieve DOA estimation. The performance of the proposed algorithm is compared with several state-of-the-art methods as well as the CRB. The results indicate the accuracy and effectiveness of the proposed method.
Spatial channel covariance information can replace full instantaneous channel state information for the analog precoder design in hybrid analog/digital architectures. Obtaining spatial channel covariance estimation, however, is challenging in the hybrid structure due to the use of fewer radio frequency (RF) chains than the number of antennas. In this paper, we propose a spatial channel covariance estimation method based on higher-order tensor decomposition for spatially sparse time-varying frequency-selective channels. The proposed method leverages the fact that the channel can be represented …
Multiple signal classification (MUSIC) has been widely applied in multiple-input multiple-output (MIMO) receivers for direction-of-arrival (DOA) estimation. To reduce the cost of radio frequency (RF) chains operating at millimeter-wave bands, hybrid analog-digital structure has been adopted in massive MIMO transceivers. In this situation, the received signals at the antennas are unavailable to the digital receiver, and as a consequence, the spatial covariance matrix (SCM), which is essential in MUSIC algorithm, cannot be obtained using traditional sample average approach. Based on our previous…
In this work, we consider direction-of-arrival (DoA) estimation in the presence of extreme noise using Deep Learning (DL). In particular, we introduce a Convolutional Neural Network (CNN) that is trained from mutli-channel data of the true array manifold matrix and is able to predict angular directions using the sample covariance estimate. We model the problem as a multi-label classification task and train a CNN in the low-SNR regime to predict DoAs across all SNRs. The proposed architecture demonstrates enhanced robustness in the presence of noise, and resilience to a small number of snapshot…
In this work, we propose a subspace-based algorithm for direction-of-arrival (DOA) estimation applied to the signals impinging on a two-level nested array, referred to as multi-step knowledge-aided iterative nested MUSIC method (MS-KAI-Nested-MUSIC), which significantly improves the accuracy of the original Nested-MUSIC. Differently from existing knowledge-aided methods applied to uniform linear arrays (ULAs), which make use of available known DOAs to improve the estimation of the covariance matrix of the input data, the proposed Multi-Step KAI-Nested-MU employs knowledge of the structure of t…
Pontifical Catholic University of Rio de Janeiro（里约热内卢天主教大学）；University of York（约克大学）
In this work, we present direction-of-arrival (DoA) estimation algorithms based on the Krylov subspace that effectively exploit prior knowledge of the signals that impinge on a sensor array. The proposed multi-step knowledge-aided iterative conjugate gradient (CG) (MS-KAI-CG) algorithms perform subtraction of the unwanted terms found in the estimated covariance matrix of the sensor data. Furthermore, we develop a version of MS-KAI-CG equipped with forward-backward averaging, called MS-KAI-CG-FB, which is appropriate for scenarios with correlated signals. Unlike current knowledge-aided methods,…
