Multiple and single snapshot compressive beamforming

For a sound field observed on a sensor array, compressive sensing (CS) reconstructs the direction-of-arrival (DOA) of multiple sources using a sparsity constraint. The DOA estimation is posed as an underdetermined problem by expressing the acoustic pressure at each sensor as a phase-lagged superposition of source amplitudes at all hypothetical DOAs. Regularizing with an $\ell_1$-norm constraint renders the problem solvable with convex optimization, and promoting sparsity gives high-resolution DOA maps. Here, the sparse source distribution is derived using maximum a posteriori (MAP) estimates for both single and multiple snapshots. CS does not require inversion of the data covariance matrix and thus works well even for a single snapshot where it gives higher resolution than conventional beamforming. For multiple snapshots, CS outperforms conventional high-resolution methods, even with coherent arrivals and at low signal-to-noise ratio. The superior resolution of CS is demonstrated with vertical array data from the SWellEx96 experiment for coherent multi-paths.Comment: In press Journal of Acoustical Society of Americ

Coherent, super resolved radar beamforming using self-supervised learning

High resolution automotive radar sensors are required in order to meet the high bar of autonomous vehicles needs and regulations. However, current radar systems are limited in their angular resolution causing a technological gap. An industry and academic trend to improve angular resolution by increasing the number of physical channels, also increases system complexity, requires sensitive calibration processes, lowers robustness to hardware malfunctions and drives higher costs. We offer an alternative approach, named Radar signal Reconstruction using Self Supervision (R2-S2), which significantly improves the angular resolution of a given radar array without increasing the number of physical channels. R2-S2 is a family of algorithms which use a Deep Neural Network (DNN) with complex range-Doppler radar data as input and trained in a self-supervised method using a loss function which operates in multiple data representation spaces. Improvement of 4x in angular resolution was demonstrated using a real-world dataset collected in urban and highway environments during clear and rainy weather conditions.Comment: 28 pages 10 figure

3-D Beamspace ML Based Bearing Estimator Incorporating Frequency Diversity and Interference Cancellation

The problem of low-angle radar tracking utilizing an array of antennas is considered. In the low-angle environment, echoes return from a low flying target via a specular path as well as a direct path. The problem is compounded by the fact that the two signals arrive within a beamwidth of each other and are usually fully correlated, or coherent. In addition, the SNR at each antenna element is typically low and only a small number of data samples, or snapshots, is available for processing due to the rapid movement of the target. Theoretical studies indicates that the Maximum Likelihood (ML) method is the only reliable estimation procedure in this type of scenario. However, the classical ML estimator involves a multi-dimensional search over a multi-modal surface and is consequently computationally burdensome. In order to facilitate real time processing, we here propose the idea of beamspace domain processing in which the element space snapshot vectors are first operated on by a reduced Butler matrix composed of three orthogonal beamforming weight vectors facilitating a simple, closed-form Beamspace Domain ML (BDML) estimator for the direct and specular path angles. The computational simplicity of the method arises from the fact that the respective beams associated with the three columns of the reduced Butler matrix have all but three nulls in common. The performance of the BDML estimator is enhanced by incorporating the estimation of the complex reflection coefficient and the bisector angle, respectively, for the symmetric and nonsymmetric multipath cases. To minimize the probability of track breaking, the use of frequency diversity is incorporated. The concept of coherent signal subspace processing is invoked as a means for retaining the computational simplicity of single frequency operation. With proper selection of the auxiliary frequencies, it is shown that perfect focusing may be achieved without iterating. In order to combat the effects of strong interfering sources, a novel scheme is presented for adaptively forming the three beams which retains the feature of common nulls

Arrayed synthetic aperture radar

In this thesis, the use of array processing techniques applied to Single Input Multiple Output (SIMO) SAR systems with enhanced capabilities is investigated. In Single Input Single Output (SISO) SAR systems there is a high resolution, wide swath contradiction, whereby it is not possible to increase both cross-range resolution and the imaged swath width simultaneously. To overcome this, a novel beamformer for SAR systems in the cross-range direction is proposed. In particular, this beamformer is a superresolution beamformer capable of forming wide nulls using subspace based approaches. SIMO SAR systems also give rise to additional sets of received data, which includes geometrical information about the SAR and target environment, and can be used for enhanced target parameter estimation. In particular, this thesis looks at round trip delay, joint azimuth and elevation angle, and relative target power estimation. For round trip delay estimation, the use of the traditional matched filter with subspace partitioning is proposed. Then by using a joint 2D Multiple Signal Classification (MUSIC) algorithm, joint Direction of Arrival (DOA) estimation can be achieved. Both the use of range lines of raw SAR data and the use of a Region of Interest (ROI) of a SAR image are investigated. However in terms of imaging, MUSIC is not well-suited for SAR, due to its target response not corresponding to the target's true power return. Therefore a joint DOA and target power estimation algorithm is proposed to overcome this limitation. These algorithms provide the framework for the development of three processing techniques. These allow sidelobe suppression in the slant range direction, along with the reconstruction of undersampled data and region enhancement using MUSIC with power preservation.Open Acces

Efficient Beamspace Eigen-Based Direction of Arrival Estimation schemes

The Multiple SIgnal Classification (MUSIC) algorithm developed in the late 70\u27s was the first vector subspace approach used to accurately determine the arrival angles of signal wavefronts impinging upon an array of sensors. As facilitated by the geometry associated with the common uniform linear array of sensors, a root-based formulation was developed to replace the computationally intensive spectral search process and was found to offer an enhanced resolution capability in the presence of two closely-spaced signals. Operation in beamspace, where sectors of space are individually probed via a pre-processor operating on the sensor data, was found to offer both a performance benefit and a reduced computationa1 complexi ty resulting from the reduced data dimension associated with beamspace processing. Little progress, however, has been made in the development of a computationally efficient Root-MUSIC algorithm in a beamspace setting. Two approaches of efficiently arriving at a Root-MUSIC formulation in beamspace are developed and analyzed in this Thesis. In the first approach, a structura1 constraint is placed on the beamforming vectors that can be exploited to yield a reduced order polynomial whose roots provide information on the signal arrival angles. The second approach is considerably more general, and hence, applicable to any vector subspace angle estimation algorithm. In this approach, classical multirate digital signal processing is applied to effectively reduce the dimension of the vectors that span the signal subspace, leading to an efficient beamspace Root-MUSIC (or ESPRIT) algorithm. An auxiliaay, yet important, observation is shown to allow a real-valued eigenanalysis of the beamspace sample covariance matrix to provide a computational savings as well as a performance benefit, particularly in the case of correlated signal scenes. A rigorous theoretical analysis, based upon derived large-sample statistics of the signal subspace eigenvectors, is included to provide insight into the operation of the two algorithmic methodologies employing the real-valued processing enhancement. Numerous simulations are presented to validate the theoretical angle bias and variance expressions as well as to assess the merit of the two beamspace approaches

Twenty-five years of sensor array and multichannel signal processing: a review of progress to date and potential research directions

In this article, a general introduction to the area of sensor array and multichannel signal processing is provided, including associated activities of the IEEE Signal Processing Society (SPS) Sensor Array and Multichannel (SAM) Technical Committee (TC). The main technological advances in five SAM subareas made in the past 25 years are then presented in detail, including beamforming, direction-of-arrival (DOA) estimation, sensor location optimization, target/source localization based on sensor arrays, and multiple-input multiple-output (MIMO) arrays. Six recent developments are also provided at the end to indicate possible promising directions for future SAM research, which are graph signal processing (GSP) for sensor networks; tensor-based array signal processing, quaternion-valued array signal processing, 1-bit and noncoherent sensor array signal processing, machine learning and artificial intelligence (AI) for sensor arrays; and array signal processing for next-generation communication systems