2-D DOA Estimation for L-Shaped Array With Array Aperture and Snapshots Extension Techniques

A two-dimensional (2-D) direction of arrival estimation method for L-shaped array with automatic pairing is proposed. It exploits the conjugate symmetry property of the array manifold matrix to increase the effective array aperture and the number of virtual snapshots simultaneously, and then applies the principle of MUSIC to construct an angle cost function and transforms the conventional 2-D search into 1-D via a Rayleigh quotient, which can greatly reduce the computation complexity. Finally, the azimuth and elevation angles are estimated without pair matching. Simulation results show that the proposed method has a better performance and can resolve more sources than some existing computationally efficient methods

Gridless Two-dimensional DOA Estimation With L-shaped Array Based on the Cross-covariance Matrix

The atomic norm minimization (ANM) has been successfully incorporated into the two-dimensional (2-D) direction-of-arrival (DOA) estimation problem for super-resolution. However, its computational workload might be unaffordable when the number of snapshots is large. In this paper, we propose two gridless methods for 2-D DOA estimation with L-shaped array based on the atomic norm to improve the computational efficiency. Firstly, by exploiting the cross-covariance matrix an ANM-based model has been proposed. We then prove that this model can be efficiently solved as a semi-definite programming (SDP). Secondly, a modified model has been presented to improve the estimation accuracy. It is shown that our proposed methods can be applied to both uniform and sparse L-shaped arrays and do not require any knowledge of the number of sources. Furthermore, since our methods greatly reduce the model size as compared to the conventional ANM method, and thus are much more efficient. Simulations results are provided to demonstrate the advantage of our methods

Parallel Complementary Virtual Arrays Algorithm for Direction of Arrival (DOA) Estimation

This Paper discusses the challenges faced by previous method 2D Direction of Arrival (DOA) systems, such as low degrees of freedom, poor resolution, and significant estimation errors in scenarios with small snapshots. In response to these issues, the present method proposes a low-complexity 2D Direction of Arrival (DOA) estimation algorithm based on a parallel complementary virtual array. The algorithm utilizes two mutually parallel complementary linear arrays to generate a virtual array, addressing the limitations of traditional parallel arrays. It constructs an extended matrix with enhanced 2D angular degrees of freedom using covariance and cross-covariance matrices. The final step involves obtaining automatic matching 2D angle estimates through Singular Value Decomposition (SVD) and Estimation of Signal Parameters via Rotational Invariance Techniques (ESPRIT). In comparison to traditional 2D DOA estimation methods, the proposed algorithm better exploits the information from the array's received data. It can identify more incoming signals, offering high resolution without the need for 2D linear search or angle parameter matching. Importantly, it demonstrates effective estimation even in scenarios with low Signal-to-Noise Ratio (SNR) and small snapshots. Experimental simulation results validate the effectiveness and reliability of the proposed algorithm

A Cramér-Rao bounds based analysis of 3D antenna array geometries made from ULA branches

International audienceIn the context of passive sources localization using antenna array, the estimation accuracy of elevation, and azimuth are related not only to the kind of estimator which is used, but also to the geometry of the considered antenna array. Although there are several available results on the linear array, and also for planar arrays, other geometries existing in the literature, such as 3D arrays, have been less studied. In this paper, we study the impact of the geometry of a family of 3D models of antenna array on the estimation performance of elevation, and azimuth. The Cramer-Rao Bound (CRB), which is widely spread in signal processing to characterize the estimation performance will be used here as a useful tool to find the optimal configuration. In particular, we give closed-form expressions of CRB for a 3D antenna array under both conditional, and unconditional observation models. Thanks to these explicit expressions, the impact of the third dimension to the estimation performance is analyzed. Particularly, we give criterions to design an isotropic 3D array depending on the considered observation model. Several 3D particular geometry antennas made from uniform linear array (ULA) are analyzed, and compared with 2D antenna arrays. The isotropy condition of such arrays is analyzed. The presented framework can be used for further studies of other types of arrays

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

Space Time MUSIC: Consistent Signal Subspace Estimation for Wide-band Sensor Arrays

Wide-band Direction of Arrival (DOA) estimation with sensor arrays is an essential task in sonar, radar, acoustics, biomedical and multimedia applications. Many state of the art wide-band DOA estimators coherently process frequency binned array outputs by approximate Maximum Likelihood, Weighted Subspace Fitting or focusing techniques. This paper shows that bin signals obtained by filter-bank approaches do not obey the finite rank narrow-band array model, because spectral leakage and the change of the array response with frequency within the bin create \emph{ghost sources} dependent on the particular realization of the source process. Therefore, existing DOA estimators based on binning cannot claim consistency even with the perfect knowledge of the array response. In this work, a more realistic array model with a finite length of the sensor impulse responses is assumed, which still has finite rank under a space-time formulation. It is shown that signal subspaces at arbitrary frequencies can be consistently recovered under mild conditions by applying MUSIC-type (ST-MUSIC) estimators to the dominant eigenvectors of the wide-band space-time sensor cross-correlation matrix. A novel Maximum Likelihood based ST-MUSIC subspace estimate is developed in order to recover consistency. The number of sources active at each frequency are estimated by Information Theoretic Criteria. The sample ST-MUSIC subspaces can be fed to any subspace fitting DOA estimator at single or multiple frequencies. Simulations confirm that the new technique clearly outperforms binning approaches at sufficiently high signal to noise ratio, when model mismatches exceed the noise floor.Comment: 15 pages, 10 figures. Accepted in a revised form by the IEEE Trans. on Signal Processing on 12 February 1918. @IEEE201

Direction of Arrival Estimation and Tracking with Sparse Arrays

Direction of Arrival (DOA) estimation and tracking of a plane wave or multiple plane waves impinging on an array of sensors from noisy data are two of the most important tasks in array signal processing, which have attracted tremendous research interest over the past several decades. It is well-known that the estimation accuracy, angular resolution, tracking capacity, computational complexity, and hardware implementation cost of a DOA estimation and/or tracking technique depend largely on the array geometry. Large arrays with many sensors provide accurate DOA estimation and perfect target tracking, but they usually suffer from a high cost for hardware implementation. Sparse arrays can yield similar DOA estimates and tracking performance with fewer elements for the same-size array aperture as compared to the traditional uniform arrays. In addition, the signals of interest may have rich temporal information that can be exploited to effectively eliminate background noise and significantly improve the performance and capacity of DOA estimation and tracking, and/or even dramatically reduce the computational burden of estimation and tracking algorithms. Therefore, this thesis aims to provide some solutions to improving the DOA estimation and tracking performance by designing sparse arrays and exploiting prior knowledge of the incident signals such as AR modeled sources and known waveforms. First, we design two sparse linear arrays to efficiently extend the array aperture and improve the DOA estimation performance. One scheme is called minimum redundancy sparse subarrays (MRSSA), where the subarrays are used to obtain an extended correlation matrix according to the principle of minimum redundancy linear array (MRLA). The other linear array is constructed using two sparse ULAs, where the inter-sensor spacing within the same ULA is much larger than half wavelength. Moreover, we propose a 2-D DOA estimation method based on sparse L-shaped arrays, where the signal subspace is selected from the noise-free correlation matrix without requiring the eigen-decomposition to estimate the elevation angle, while the azimuth angles are estimated based on the modified total least squares (TLS) technique. Second, we develop two DOA estimation and tracking methods for autoregressive (AR) modeled signal source using sparse linear arrays together with Kalman filter and LS-based techniques. The proposed methods consist of two common stages: in the first stage, the sources modeled by AR processes are estimated by the celebrated Kalman filter and in the second stage, the efficient LS or TLS techniques are employed to estimate the DOAs and AR coefficients simultaneously. The AR-modeled sources can provide useful temporal information to handle cases such as the ones, where the number of sources is larger than the number of antennas. In the first method, we exploit the symmetric array to transfer a complex-valued nonlinear problem to a real-valued linear one, which can reduce the computational complexity, while in the second method, we use the ordinary sparse arrays to provide a more accurate DOA estimation. Finally, we study the problem of estimating and tracking the direction of arrivals (DOAs) of multiple moving targets with known signal source waveforms and unknown gains in the presence of Gaussian noise using a sparse sensor array. The core idea is to consider the output of each sensor as a linear regression model, each of whose coefficients contains a pair of DOAs and gain information corresponding to one target. These coefficients are determined by solving a linear least squares problem and then updating recursively, based on a block QR decomposition recursive least squares (QRD-RLS) technique or a block regularized LS technique. It is shown that the coefficients from different sensors have the same amplitude, but variable phase information for the same signal. Then, simple algebraic manipulations and the well-known generalized least squares (GLS) are used to obtain an asymptotically-optimal DOA estimate without requiring a search over a large region of the parameter space