Array processing involves manipulation of signals induced on various antenna elements. Its capabilities of steering nulls to reduce cochannel interferences and pointing independent beams toward various mobiles, as well as its ability to provide estimates of directions of radiating sources, make it attractive to a mobile communications system designer. Array processing is expected to play an important role in fulfilling the increased demands of various mobile communications services. Part I of this paper showed how an array could be utilized in different configurations to improve the performance of mobile communications systems, with references to various studies where feasibility of apt array system for mobile communications is considered. This paper provides a comprehensive and detailed treatment of different beam-forming schemes, adaptive algorithms to adjust the required weighting on antennas, direction-of-arrival estimation methods-including their performance comparison-and effects of errors on the performance of an array system, as well as schemes to alleviate them. This paper brings together almost all aspects of array signal processing.

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Application of antenna arrays to mobile communications. II. Beam-forming and direction-of-arrival considerations

Active noise control (ANC) is achieved by introducing a cancelling "antinoise" wave through an appropriate array of secondary sources. These secondary sources are interconnected through an electronic system using a specific signal processing algorithm for the particular cancellation scheme. ANC has application to a wide variety of problems in manufacturing, industrial operations, and consumer products. The emphasis of this paper is on the practical aspects of ANC systems in terms of adaptive signal processing and digital signal processing (DSP) implementation for real-world applications. In this paper, the basic adaptive algorithm for ANC is developed and analyzed based on single-channel broad-band feedforward control. This algorithm is then modified for narrow-band feedforward and adaptive feedback control. In turn, these single-channel ANC algorithms are expanded to multiple-channel cases. Various online secondary-path modeling techniques and special adaptive algorithms, such as lattice, frequency-domain, subband, and recursive-least-squares, are also introduced. Applications of these techniques to actual problems are highlighted by several examples.

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Active noise control: a tutorial review

http://www2.math.umd.edu/~rvbalan/PAPERS/MyPapers/AbsValFrame_ACHAarticle.pdf

On signal reconstruction without phase

The first subject of the paper is the estimation of a high resolution directional field of fingerprints. Traditional methods are discussed and a method, based on principal component analysis, is proposed. The method not only computes the direction in any pixel location, but its coherence as well. It is proven that this method provides exactly the same results as the "averaged square-gradient method" that is known from literature. Undoubtedly, the existence of a completely different equivalent solution increases the insight into the problem's nature. The second subject of the paper is singular point detection. A very efficient algorithm is proposed that extracts singular points from the high-resolution directional field. The algorithm is based on the Poincare index and provides a consistent binary decision that is not based on postprocessing steps like applying a threshold on a continuous resemblance measure for singular points. Furthermore, a method is presented to estimate the orientation of the extracted singular points. The accuracy of the methods is illustrated by experiments on a live-scanned fingerprint database.

Systematic methods for the computation of the directional fields and singular points of fingerprints

Adaptive filtering algorithms fall into four main groups: recursive least squares (RLS) algorithms and the corresponding fast versions; QR- and inverse QR-least squares algorithms; least squares lattice (LSL) and QR decomposition-based least squares lattice (QRD-LSL) algorithms; and gradient-based algorithms such as the least-mean square (LMS) algorithm. Our purpose in this article is to present yet another approach, for the sake of achieving two important goals. The first one is to show how several different variants of the recursive least-squares algorithm can be directly related to the widely studied Kalman filtering problem of estimation and control. Our second important goal is to present all the different versions of the RLS algorithm in computationally convenient square-root forms: a prearray of numbers has to be triangularized by a rotation, or a sequence of elementary rotations, in order to yield a postarray of numbers. The quantities needed to form the next prearray can then be read off from the entries of the postarray, and the procedure can be repeated; the explicit forms of the rotation matrices are not needed in most cases. >

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A state-space approach to adaptive RLS filtering

The behavior of the delayed least-mean-square (DLMS) algorithm is studied. It is found that the step size in the coefficient update plays a key role in the convergence and stability of the algorithm. An upper bound for the step size is derived that ensures the stability of the DLMS. The relationship between the step size and the convergence speed, and the effect of the delay on the convergence speed, are also studied. The analytical results are supported by computer simulations. >

The LMS algorithm with delayed coefficient adaptation

Advanced Digital Signal Processing

1. Introduction. Characterization of Signals. Characterization of Linear Time-Invariant Systems. Sampling of Signals. Linear Filtering Methods Based on the DFT. The Cepstrum. Summary and References. Problems. 2. Algorithms for Convolution and DFT. Modulo Polynomials. Circular Convolution as Polynomial Multiplication mod un- 1. A Continued Fraction of Polynomials. Chinese Remainder Theorem for Polynomials. Algorithms for Short Circular Convolutions. How We Count Multiplications. Cyclotomic Polynomials. Elementary Number Theory. Convolution Length and Dimension. The DFT as a Circular Convolution. Winograd's DFT Algorithm. Number-Theoretic Analogy of DFT. Number-Theoretic Transform. Split-Radix FFT. Autogen Technique. Summary and References. Problems. 3. Linear Prediction and Optimum Linear Filters. Innovations Representation of a Stationary Random Process. Forward and Backward Linear Prediction. Solution of the Normal Equations. Properties of the Linear Prediction-Error Filters. AR Lattice and ARMA Lattice-Ladder Filters. Wiener Filters for Filtering and Prediction. Summary and References. Problems. 4. Least-Squares Methods for System Modeling and Filter Design. System Modeling and Identification. Lease-Squares Filter Design for Prediction and Deconvolution. Solution of Least-Squares Estimation Problems. Summary and References. Problems. 5. Adaptive Filters. Applications of Adaptive Filters. Adaptive Direct-Form FIR Filters. Adaptive Lattice-Ladder Filters. Summary and References. Problems. 6. Recursive Least-Squares Algorithms for Array Signal Processing. QR Decomposition for Least-Squares Estimation. Gram-Schmidt Orthogonalization for Least-Squares Estimation. Givens Algorithm for Time-Recursive Least-Squares Estimation. Recursive Least-Squares Estimation Based on the Householder Transformation. Order-Recursive Least-Squares Estimation Algorithms. Summary and References. Problems. 7. QRD-Based Fast Adaptive Filter Algorithms. Background. QRD Lattice. Multichannel Lattice. Fast QR Algorithm. Multichannel Fast QR Algorithm. Summary and References. Problems. 8. Power Spectrum Estimation. Estimation of Spectra from Finite-Duration Observations of Signals. Nonparametric Methods for Power Spectrum Estimation. Parametric Methods for Power Spectrum Estimation. Minimum-Variance Spectral Estimation. Eigenanalysis Algorithms for Spectrum Estimation. Summary and References. Problems. 9. Signal Analysis with Higher-Order Spectra. Use of Higher-Order Spectra in Signal Processing. Definition and Properties of Higher-Order Spectra. Conventional Estimators for Higher-Order Spectra. Parametric Methods for Higher-Order Spectrum Estimation. Cepstra of Higher-Order Spectra. Phase and Magnitude Retrieval from the Bispectrum. Summary and References. Problems. References. Index.

Algorithms for Statistical Signal Processing

This paper presents a recursive form of the modified Gram-Schmidt algorithm (RMGS). This new recursive least-squares (RLS) estimation algorithm has a computational complexity similar to the conventional RLS algorithm, but is more robust to roundoff errors and has a highly modular structure, suitable for VLSI implementation. Its properties and features are discussed and compared to other LS estimation algorithms.

A recursive modified Gram-Schmidt algorithm for least- squares estimation

New time-recursive equations are derived for the reflection coefficients and the ladder gains in the a priori and a posteriori forms of the exact least-squares (LS) lattice-ladder filtering algorithms. The numerical accuracy of the LS lattice-ladder algorithms obtained by use of these new direct time update equations is analyzed and compared to the accuracy resulting from the conventional LS lattice-ladder algorithms. The analysis and a number of simulation results which are presented lead us to conclude that the new a priori and a posteriori forms of the LS lattice-ladder algorithms yield superior performance.

Fuyun Ling

Papers

The LMS algorithm with delayed coefficient adaptation

Advanced Digital Signal Processing

Algorithms for Statistical Signal Processing

A recursive modified Gram-Schmidt algorithm for least- squares estimation

Numerically robust least-squares lattice-ladder algorithms with direct updating of the reflection coefficients