Sensor Array Signal Processing via Eigenanalysis of Matrix Pencils Composed of Data Derived from Translationally Invariant Subarrays

An algorithm is developed for estimating characteristic parameters associated with a scene of radiating sources given the data derived from a pair of translationally invariant arrays, the X and Y arrays, which are displaced relative to one another. The algorithm is referred to as PR O—E SPRIT and is predicated on invoking two recent mathematical developments: (1) the SVD based solution to the Procrustes problem of optimally approximating an invariant subspace rotation and (2) the Total Least Squares method for perturbing each of the two estimates of a common subspace in a minimal fashion until the two perturbed spaces are the same. For uniform linear array scenarios, the use of forward-backward averaging (FBAVG) in conjunction with PR O—E S PR IT is shown to effect a substantial reduction in the computational burden, a significant improvement in performance, a simple scheme for estimating the number of sources and source decorrelation. These gains may be attributed to FBAVG’s judicious exploitation of the diagonal invariance operator relating the Direction of Arrival matrix of the Y array to that associated with the X array. Similar gains may be achieved in the case where the X and Y arrays are either not linear or not uniformly spaced through the use of pseudo-forward-backward averaging (PFBAVG). However, the use of PFBAVG does not effect source decorrelation and reduces the maximum number of resolvable sources by a factor of two. Simulation studies and the results of applying PR O—E S PR IT to real data demonstrate the excellent performance of the method

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

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

Multi-Resolution Codebook and Adaptive Beamforming Sequence Design for Millimeter Wave Beam Alignment

Millimeter wave (mmWave) communication is expected to be widely deployed in fifth generation (5G) wireless networks due to the substantial bandwidth available at mmWave frequencies. To overcome the higher path loss observed at mmWave bands, most prior work focused on the design of directional beamforming using analog and/or hybrid beamforming techniques in largescale multiple-input multiple-output (MIMO) systems. Obtaining potential gains from highly directional beamforming in practical systems hinges on sufficient levels of channel estimation accuracy, where the problem of channel estimation becomes more challenging due to the substantial training overhead needed to sound all directions using a high-resolution narrow beam. In this work, we consider the design of multi-resolution beamforming sequences to enable the system to quickly search out the dominant channel direction for single-path channels. The resulting design generates a multilevel beamforming sequence that strikes a balance between minimizing the training overhead and maximizing beamforming gain, where a subset of multilevel beamforming vectors is chosen adaptively to provide an improved average data rate within a constrained time. We propose an efficient method to design a hierarchical multiresolution codebook utilizing a Butler matrix, a generalized discrete Fourier transform (DFT) matrix implemented using analog RF circuitry. Numerical results show the effectiveness of the proposed algorithm

Applying Phenomenography to Develop a Comprehensive Understanding of Ethics in Engineering Practice

This Work-in-Progress Research paper describes (1) the contemporary research space on ethics education in engineering; (2) our long-term research plan; (3) the theoretical underpinnings of Phase 1 of our research plan (phenomenography); and (4) the design and developmental process of a phenomenographic interview protocol to explore engineers' experiences with ethics. Ethical behavior is a complex phenomenon that is complicated by the institutional and cultural contexts in which it occurs. Engineers also have varied roles and often work in a myriad of capacities that influence their experiences with and understanding of ethics in practice. We are using phenomenography, a qualitative research approach, to explore and categorize the ways engineers experience and understand ethical engineering practice. Specifically, phenomenography will allow us to systematically investigate the range and complexity of ways that engineers experience ethics in professional practice in the health products industry. Phenomenographic data will be obtained through a specialized type of semi-structured interview. Here we introduce the design of our interview protocol and its four sections: Background, Experience, Conceptual, and Summative. We also describe our iterative process for framing questions throughout each section

Video and image systems engineering education for the 21st century

Includes bibliographical references.We are developing a new graduate program at Purdue in Video and Image Systems Engineering (VISE). The project is comprised of three parts: a new curriculum centered around a degree option in VISE to be earned as part of the Masters or Ph.D. degrees; a state-of-the-art lecture/laboratory facility for instruction, laboratory experiments, and project and homework activities in VISE courses; and enhancement of existing courses and development of new courses in the VISE area.Supported by an Image Systems Engineering Grant from Hewlett-Packard Company

Circadian oscillator proteins across the kingdoms of life : Structural aspects 06 Biological Sciences 0601 Biochemistry and Cell Biology

Circadian oscillators are networks of biochemical feedback loops that generate 24-hour rhythms and control numerous biological processes in a range of organisms. These periodic rhythms are the result of a complex interplay of interactions among clock components. These components are specific to the organism but share molecular mechanisms that are similar across kingdoms. The elucidation of clock mechanisms in different kingdoms has recently started to attain the level of structural interpretation. A full understanding of these molecular processes requires detailed knowledge, not only of the biochemical and biophysical properties of clock proteins and their interactions, but also the three-dimensional structure of clockwork components. Posttranslational modifications (such as phosphorylation) and protein-protein interactions, have become a central focus of recent research, in particular the complex interactions mediated by the phosphorylation of clock proteins and the formation of multimeric protein complexes that regulate clock genes at transcriptional and translational levels. The three-dimensional structures for the cyanobacterial clock components are well understood, and progress is underway to comprehend the mechanistic details. However, structural recognition of the eukaryotic clock has just begun. This review serves as a primer as the clock communities move towards the exciting realm of structural biology

Signal Subspace Techniques for Source Localization with Circular Sensor Arrays

Estimating the directions-of-arrival (DOAs) of propagating plane waves is a problem of interest in a variety of applications including radar, mobile communications, sonar, and seismology. The widely studied uniform linear array (ULA) can only provide estimates of source bearings relative to the array axis. A planar. array is required if estimates of source azimuth and elevation are required (2D angle estimation). Uniform circular arrays (UCAs) have several properties that make them attractive for 2D angle estimation; e.g., directional patterns synthesized with UCAs can be electronically rotated in the plane of the array without significant change of beam shape. Two signal subspace algorithms for 2D angle estimation with UC.4s have been developed. Both algorithms operate in beamspace and employ phase mode excitation based beamformers. The first algorithm, UCA-RB-MUSIC, offers numerous advantages over element space MUSIC. These advantages include reduced computation due to the ability to compute subspace estimates via a real-valued eigenvalue decomposition and the applicability of ULA techniques such as Root-MUSIC. The second algorithm, UCA-ESPRIT, represents a significant advance in the area of 2D angle estimation. It is a novel closed-form algorithm that provides automatically paired source azimuth and elevation angle estimates via the eigenvalues of a matrix. The eigenvalues have the form p = sin 8 ejd, where 8 and q5 are the elevation and azimuth angles, respectively. UCA-ESPRIT avoids expensive search procedures and is thus superior to existing 2D angle estimation algorithms with respect to computational complexity. The statistical performance of element space MUSIC, UCA-RB-MUSIC, and UCA-ESPRIT has been analyzed. Computer simulations that demonstrate the efficacy of the algorithms and validate the performance analysis results are presented

NOVEL TECHNIQUES FOR THE DETECTION AND ESTIMATION OF THREE-WAVE COUPLING WITH APPLICATION TO HUMAN BRAIN WAVES

Composite linear and quadratic systems produce three-wave coupling when stimulated by random-phase input sinusoids. Due to the non-linearity of the system the output frequencies are arithmetically related to the input. Using third order cumulant statistics and their associated bispectrum, techniques are devised based on phase-insensitive matrix structures for detection and frequency estimation of coupling frequencies. The separation of the third order cumulant series into symmetric and skew-symmetric portions allows us to exploit their characteristic eigendecompositions for frequency estimation. After symmetrization, biphases can be easily extracted as coefficients of the cumulant sequence. Using a generalized eigenvector representation, we can relate symmetric and skew-symmetric bases by a subspace rotation algorithm. Biphases can be estimated directly from generalized eigenvalues of the matrix pencil formed by symmetric and skew-symmetric matrices. The dimensionality of our matrices can be reduced through the use of cumulant projections which yield a slice of the bispectrum. The Radon transform procedure is related to bispectral processing through an isotropic radial slice Volterra filter. The compact third order Kronecker product matrix formulation and algorithms for coupling frequency estimation can also be converted for use in biphase estimation. Simulations showing the performance of the above procedures are also presented for both synthetic and biomedical time series. These include the detection and estimation of specific frequencies exhibiting nonlinearities in electroencephalographic (EEG) data