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

Following the idea of using first-order time derivatives, this paper presents a general recurrent neural network (RNN) model for online inversion of time-varying matrices. Different kinds of activation functions are investigated to guarantee the global exponential convergence of the neural model to the exact inverse of a given time-varying matrix. The robustness of the proposed neural model is also studied with respect to different activation functions and various implementation errors. Simulation results, including the application to kinematic control of redundant manipulators, substantiate the theoretical analysis and demonstrate the efficacy of the neural model on time-varying matrix inversion, especially when using a power-sigmoid activation function.

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Design and analysis of a general recurrent neural network model for time-varying matrix inversion

An iterative technique is developed to rigorously compute the electromagnetic time- and frequency-domain scattering problems. The method is based upon a wave-function expansion technique (this also includes the integral-representation techniques), in which the electromagnetic field equations and causality conditions are satisfied analytically, while the boundary conditions or the constitutive relations have to be satisfied in a computational manner. The latter is accomplished by an iterative minimization of the integrated square error. For the solution of an integral equation, it is shown how to obtain optimum convergence. Some numerical results pertaining to a number of representative problems illustrate the numerical advantages and disadvantages of the iterative method.

Iterative computational techniques in scattering based upon the integrated square error criterion

This technical note presents theoretical analysis and simulation results on the performance of a classic gradient neural network (GNN), which was designed originally for constant matrix inversion but is now exploited for time-varying matrix inversion. Compared to the constant matrix-inversion case, the gradient neural network inverting a time-varying matrix could only approximately approach its time-varying theoretical inverse, instead of converging exactly. In other words, the steady-state error between the GNN solution and the theoretical/exact inverse does not vanish to zero. In this technical note, the upper bound of such an error is estimated firstly. The global exponential convergence rate is then analyzed for such a Hopfield-type neural network when approaching the bound error. Computer-simulation results finally substantiate the performance analysis of this gradient neural network exploited to invert online time-varying matrices.

Performance Analysis of Gradient Neural Network Exploited for Online Time-Varying Matrix Inversion

Different from gradient-based neural networks, a special kind of recurrent neural network (RNN) has recently been proposed by Zhang for online matrix inversion. Such an RNN is designed based on a matrix-valued error function instead of a scalar-valued error function. In addition, it was depicted in an implicit dynamics instead of an explicit dynamics. In this paper, we develop and investigate a discrete-time model of Zhang neural network (termed as such and abbreviated as ZNN for presentation convenience), which is depicted by a system of difference equations. Comparing with Newton iteration for matrix inversion, we find that the discrete-time ZNN model incorporates Newton iteration as its special case. Noticing this relation, we perform numerical comparisons on different situations of using ZNN and Newton iteration for matrix inversion. Different kinds of activation functions and different step-size values are examined for superior convergence and better stability of ZNN. Numerical examples demonstrate the efficacy of both ZNN and Newton iteration for online matrix inversion.

From Zhang Neural Network to Newton Iteration for Matrix Inversion

Many of the popular methods for the solution of large matrix equations are surveyed with the hope of finding an efficient method suitable for both electromagnetic scattering and radiation problems and system identification problems.

R. Stratton

Papers

Survey of numerical methods for solution of large systems of linear equations for electromagnetic field problems