An overview of beamforming from a signal-processing perspective is provided, with an emphasis on recent research. Data-independent, statistically optimum, adaptive, and partially adaptive beamforming are discussed. Basic notation, terminology, and concepts are included. Several beamformer implementations are briefly described. >

Beamforming: a versatile approach to spatial filtering

High speed signal processing depends critically on parallel processor technology. In most applications, general-purpose parallel computers cannot offer satisfactory real-time processing speed due to severe system overhead. Therefore, for real-time digital signal processing (DSP) systems, special-purpose array processors have become the only appealing alternative. In designing or using such array Processors, most signal processing algorithms share the critical attributes of regularity, recursiveness, and local communication. These properties are effectively exploited in innovative systolic and wavefront array processors. These arrays maximize the strength of very large scale integration (VLSI) in terms of intensive and pipelined computing, and yet circumvent its main limitation on communication. The application domain of such array processors covers a very broad range, including digital filtering, spectrum estimation, adaptive array processing, image/vision processing, and seismic and tomographic signal processing, This article provides a general overview of VLSI array processors and a unified treatment from algorithm, architecture, and application perspectives.

VLSI Array processors

TRACKING, PREDICTION, AND SMOOTHING BASICS. g and g-h-k Filters. Kalman Filter. Practical Issues for Radar Tracking. LEAST-SQUARES FILTERING, VOLTAGE PROCESSING, ADAPTIVE ARRAY PROCESSING, AND EXTENDED KALMAN FILTER. Least-Squares and Minimum-Variance Estimates for Linear Time-Invariant Systems. Fixed-Memory Polynomial Filter. Expanding- Memory (Growing-Memory) Polynomial Filters. Fading-Memory (Discounted Least-Squares) Filter. General Form for Linear Time-Invariant System. General Recursive Minimum-Variance Growing-Memory Filter (Bayes and Kalman Filters without Target Process Noise). Voltage Least-Squares Algorithms Revisited. Givens Orthonormal Transformation. Householder Orthonormal Transformation. Gram--Schmidt Orthonormal Transformation. More on Voltage-Processing Techniques. Linear Time-Variant System. Nonlinear Observation Scheme and Dynamic Model (Extended Kalman Filter). Bayes Algorithm with Iterative Differential Correction for Nonlinear Systems. Kalman Filter Revisited. Appendix. Problems. Symbols and Acronyms. Solution to Selected Problems. References. Index.

https://astronu.jinr.ru/wiki/images/8/86/Brookner_Kalman.pdf

Tracking and Kalman Filtering Made Easy

Hyperspectral Data Processing: Algorithm Design and Analysis is a culmination of the research conducted in the Remote Sensing Signal and Image Processing Laboratory (RSSIPL) at the University of Maryland, Baltimore County. Specifically, it treats hyperspectral image processing and hyperspectral signal processing as separate subjects in two different categories. Most materials covered in this book can be used in conjunction with the author’s first book, Hyperspectral Imaging: Techniques for Spectral Detection and Classification, without much overlap.

Hyperspectral Data Processing: Algorithm Design and Analysis

A computer implemented method and system for gesture category recognition and training. Generally, a gesture is a hand or body initiated movement of a cursor directing device to outline a particular pattern in particular directions done in particular periods of time. The present invention allows a computer system to accept input data, originating from a user, in the form gesture data that are made using the cursor directing device. In one embodiment, a mouse device is used, but the present invention is equally well suited for use with other cursor directing devices (e.g., a track ball, a finger pad, an electronic stylus, etc.). In one embodiment, gesture data is accepted by pressing a key on the keyboard and then moving the mouse (with mouse button pressed) to trace out the gesture. Mouse position information and time stamps are recorded. The present invention then determines a multi-dimensional feature vector based on the gesture data. The feature vector is then passed through a gesture category recognition engine that, in one implementation, uses a radial basis function neural network to associate the feature vector to a pre-existing gesture category. Once identified, a set of user commands that are associated with the gesture category are applied to the computer system. The user commands can originate from an automatic process that extracts commands that are associated with the menu items of a particular application program. The present invention also allows user training so that user-defined gestures, and the computer commands associated therewith, can be programmed into the computer system.

Method and system for gesture category recognition and training using a feature vector

A novel algorithm and architecture are described which have specific application to high performance, digital, adaptive beamforming. It is shown how a simple, linearly constrained adaptive combiner forms the basis for a wide range of adaptive antenna subsystems. The function of such an adaptive combiner is formulated as a recursive least squares minimization operation and the corresponding weight vector is obtained by means of the Q-R decomposition algorithm using Givens rotations. An efficient pipelined architecture to implement this algorithm is also described. It takes the form of a triangular systolic/wavefront array and has many desirable features for very large scale integration (VLSI) system design.

A novel algorithm and architecture for adaptive digital beamforming

The development of a wavefront array processor for recursive least-squares minimization is described. It comprises a triangular array of processors each of which emulates the INMOS transputer chip. The array is programmed in occam - an associated high level language also developed by INMOS Ltd. Preliminary experiments have been carried out to compare the performance of the wavefront array with that of the associated systolic array. The results are presented.

A practical comparison of the systolic and wavefront array processing architectures

A fully systolic network is proposed for rapid and efficient multidimensional interpolation using radial basis functions (RBFs). The resulting processor, which constitutes a form of nonlinear adaptive filter, resembles a neural network based on the nonlinear, feedforward, multilayer perceptron model.

Systolic array for nonlinear multidimensional interpolation using radial basis functions

A fully systolic network is proposed for rapid and efficient multidimensional fitting and interpolation using radial basis functions. The resulting processor, which constitutes a form of nonlinear adaptive filter, behaves like a neural network based on the multilayer, feedforward perception model. One application of such a network is as a pattern classifier. >

A systolic array for nonlinear adaptive filtering and pattern recognition

A systolic array for multi-dimensional fitting and interpolation using (nonlinear) radial basis functions is proposed. The fit may be constrained very simply to ensure that the resulting surface takes a pre-determined value at one or more specific points. The processor, which constitutes a form of nonlinear adaptive filter, behaves like a neural network based on the multi-layer, feed-forward perceptron model. One obvious application of such a network is as a pattern classifier, the constraints being used to ensure the correct classification of selected patterns.

J.G. McWhirter

Papers

A novel algorithm and architecture for adaptive digital beamforming

A practical comparison of the systolic and wavefront array processing architectures

Systolic array for nonlinear multidimensional interpolation using radial basis functions

A systolic array for nonlinear adaptive filtering and pattern recognition

A systolic array for nonlinear adaptive filtering and pattern recognition