Wavefield modeling and signal processing for sensor arrays of arbitrary geometry

Sensor arrays and related signal processing methods are key technologies in many areas of engineering including wireless communication systems, radar and sonar as well as in biomedical applications. Sensor arrays are a collection of sensors that are placed at distinct locations in order to sense physical phenomena or synthesize wavefields. Spatial processing from the multichannel output of the sensor array is a typical task. Such processing is useful in areas including wireless communications, radar, surveillance and indoor positioning. In this dissertation, fundamental theory and practical methods of wavefield modeling for radio-frequency array processing applications are developed. Also, computationally-efficient high-resolution and optimal signal processing methods for sensor arrays of arbitrary geometry are proposed. Methods for taking into account array nonidealities are introduced as well. Numerical results illustrating the performance of the proposed methods are given using real-world antenna arrays. Wavefield modeling and manifold separation for vector-fields such as completely polarized electromagnetic wavefields and polarization sensitive arrays are proposed. Wavefield modeling is used for writing the array output in terms of two independent parts, namely the sampling matrix depending on the employed array including nonidealities and the coefficient vector depending on the wavefield. The superexponentially decaying property of the sampling matrix for polarization sensitive arrays is established. Two estimators of the sampling matrix from calibration measurements are proposed and their statistical properties are established. The array processing methods developed in this dissertation concentrate on polarimetric beamforming as well as on high-resolution and optimal azimuth, elevation and polarization parameter estimation. The proposed methods take into account array nonidealities such as mutual coupling, cross-polarization effects and mounting platform reflections. Computationally-efficient solutions based on polynomial rooting techniques and fast Fourier transform are achieved without restricting the proposed methods to regular array geometries. A novel expression for the Cramér-Rao bound in array processing that is tight for real-world arrays with nonidealities in the asymptotic regime is also proposed. A relationship between spherical harmonics and 2-D Fourier basis, called equivalence matrix, is established. A novel fast spherical harmonic transform is proposed, and a one-to-one mapping between spherical harmonic and 2-D Fourier spectra is found. Improvements to the minimum number of samples on the sphere that are needed in order to avoid aliasing are also proposed

Sensor array signal processing : two decades later

Caption title.Includes bibliographical references (p. 55-65).Supported by Army Research Office. DAAL03-92-G-115 Supported by the Air Force Office of Scientific Research. F49620-92-J-2002 Supported by the National Science Foundation. MIP-9015281 Supported by the ONR. N00014-91-J-1967 Supported by the AFOSR. F49620-93-1-0102Hamid Krim, Mats Viberg

A structure-aware DOA estimation method for sources with short known waveforms

For direction of arrival (DOA) estimation with known waveform information, with a larger number of snapshots and a longer duration of the known waveforms, the required storage space for hardware implementation will increase. To save storage resources and also reduce the response time of the array system, the DOA estimation problem with short known waveforms in snapshot size is studied in this paper. We first establish the connection between DOA estimation for known waveform sources and the structured least squares (SLS) technique utilizing a potential rotation invariant property. Next, a constraint is formulated and then transformed into its real and imaginary parts to satisfy the requirements of SLS, and the resultant SLS optimization problem is solved iteratively. Simulation results show that the proposed method has a better performance than the existing DEML method for small numbers of snapshots

Rational invariant subspace approximations with applications

Includes bibliographical references.Subspace methods such as MUSIC, Minimum Norm, and ESPRIT have gained considerable attention due to their superior performance in sinusoidal and direction-of-arrival (DOA) estimation, but they are also known to be of high computational cost. In this paper, new fast algorithms for approximating signal and noise subspaces and that do not require exact eigendecomposition are presented. These algorithms approximate the required subspace using rational and power-like methods applied to the direct data or the sample covariance matrix. Several ESPRIT- as well as MUSIC-type methods are developed based on these approximations. A substantial computational saving can be gained comparing with those associated with the eigendecomposition-based methods. These methods are demonstrated to have performance comparable to that of MUSIC yet will require fewer computation to obtain the signal subspace matrix

High-resolution Direction-of-Arrival estimation

Direction of Arrival (DOA) estimation is considered one of the most crucial problems in array signal processing, with considerable research efforts for developing efficient and effective direction-finding algorithms, especially in the transportation industry, where the demand for an effective, real-time, and accurate DOA algorithm is increasing. However, challenges must be addressed before real-world deployment can be realised. Firstly, there is the requirement for fast computational time for real-time detection. Secondly, there is a demand for high-resolution and accurate DOA estimation. In this thesis, two state-of-the-art DOA estimation algorithms are proposed and evaluated to address the challenges. Firstly, a novel covariance matrix reconstruction approach for single snapshot DOA estimation (CbSS) was proposed. CbSS was developed by exploiting the relationship between the theoretical and sample covariance matrices to reduce estimation error for a single snapshot scenario. CbSS can resolve accurate DOAs without requiring lengthy peak searching computational time by computationally changing the received sample covariance matrix. Simulation results have verified that the CbSS technique yields the highest DOA estimation accuracy by up to 25.5% compared to existing methods such as root-MUSIC and the Partial Relaxation approach. Furthermore, CbSS presents negligible bias when compared to the existing techniques in a wide range of scenarios, such as in multiple uncorrelated and coherent signal source environments. Secondly, an adaptive diagonal-loading technique was proposed to improve DOA estimation accuracy without requiring a high computational load by integrating a modified novel and adaptive diagonal-loading method (DLT-DOA) to further improve estimation accuracy. An in-depth simulation performance analysis was conducted to address the challenges, with a comparison against existing state-of-the-art DOA estimation techniques such as EPUMA and MODEX. Simulation results verify that the DLT-DOA technique performs up to 8.5% higher DOA estimation performance in terms of estimation accuracy compared to existing methods with significantly lower computational time. On this basis, the two novel DOA estimation techniques are recommended for usage in real-world scenarios where fast computational time and high estimation accuracy are expected. Further research is needed to identify other factors that could further optimize the algorithms to meet different demands

Compact Formulations for Sparse Reconstruction in Fully and Partly Calibrated Sensor Arrays

Sensor array processing is a classical field of signal processing which offers various applications in practice, such as direction of arrival estimation or signal reconstruction, as well as a rich theory, including numerous estimation methods and statistical bounds on the achievable estimation performance. A comparably new field in signal processing is given by sparse signal reconstruction (SSR), which has attracted remarkable interest in the research community during the last years and similarly offers plentiful fields of application. This thesis considers the application of SSR in fully calibrated sensor arrays as well as in partly calibrated sensor arrays. The main contributions are a novel SSR method for application in partly calibrated arrays as well as compact formulations for the SSR problem, where special emphasis is given on exploiting specific structure in the signals as well as in the array topologies