A summary of many of the new techniques developed in the last two decades for spectrum analysis of discrete time series is presented in this tutorial. An examination of the underlying time series model assumed by each technique serves as the common basis for understanding the differences among the various spectrum analysis approaches. Techniques discussed include the classical periodogram, classical Blackman-Tukey, autoregressive (maximum entropy), moving average, autotegressive-moving average, maximum likelihood, Prony, and Pisarenko methods. A summary table in the text provides a concise overview for all methods, including key references and appropriate equations for computation of each spectral estimate.

Spectrum analysis&#8212;A modern perspective

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.

/pdf/application-of-antenna-arrays-to-mobile-communications-ii-52fds1c81j.pdf

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

A fuzzy logic system (FLS) is unique in that it is able to simultaneously handle numerical data and linguistic knowledge. It is a nonlinear mapping of an input data (feature) vector into a scalar output, i.e., it maps numbers into numbers. Fuzzy set theory and fuzzy logic establish the specifics of the nonlinear mapping. This tutorial paper provides a guided tour through those aspects of fuzzy sets and fuzzy logic that are necessary to synthesize an FLS. It does this by starting with crisp set theory and dual logic and demonstrating how both can be extended to their fuzzy counterparts. Because engineering systems are, for the most part, causal, we impose causality as a constraint on the development of the FLS. After synthesizing a FLS, we demonstrate that it can be expressed mathematically as a linear combination of fuzzy basis functions, and is a nonlinear universal function approximator, a property that it shares with feedforward neural networks. The fuzzy basis function expansion is very powerful because its basis functions can be derived from either numerical data or linguistic knowledge, both of which can be cast into the forms of IF-THEN rules. >

Fuzzy logic systems for engineering: a tutorial

Chaotic time series data are observed routinely in experiments on physical systems and in observations in the field. The authors review developments in the extraction of information of physical importance from such measurements. They discuss methods for (1) separating the signal of physical interest from contamination ("noise reduction"), (2) constructing an appropriate state space or phase space for the data in which the full structure of the strange attractor associated with the chaotic observations is unfolded, (3) evaluating invariant properties of the dynamics such as dimensions, Lyapunov exponents, and topological characteristics, and (4) model making, local and global, for prediction and other goals. They briefly touch on the effects of linearly filtering data before analyzing it as a chaotic time series. Controlling chaotic physical systems and using them to synchronize and possibly communicate between source and receiver is considered. Finally, chaos in space-time systems, that is, the dynamics of fields, is briefly considered. While much is now known about the analysis of observed temporal chaos, spatio-temporal chaotic systems pose new challenges. The emphasis throughout the review is on the tools one now has for the realistic study of measured data in laboratory and field settings. It is the goal of this review to bring these tools into general use among physicists who study classical and semiclassical systems. Much of the progress in studying chaotic systems has rested on computational tools with some underlying rigorous mathematics. Heuristic and intuitive analysis tools guided by this mathematics and realizable on existing computers constitute the core of this review.

The analysis of observed chaotic data in physical systems

A multilayer neural-net (NN) controller for a general serial-link rigid robot arm is developed. The structure of the NN controller is derived using a filtered error/passivity approach. No off-line learning phase is needed for the proposed NN controller and the weights are easily initialized. The nonlinear nature of the NN, plus NN functional reconstruction inaccuracies and robot disturbances, mean that the standard delta rule using backpropagation tuning does not suffice for closed-loop dynamic control. Novel online weight tuning algorithms, including correction terms to the delta rule plus an added robust signal, guarantee bounded tracking errors as well as bounded NN weights. Specific bounds are determined, and the tracking error bound can be made arbitrarily small by increasing a certain feedback gain. The correction terms involve a second-order forward-propagated wave in the backpropagation network. New NN properties including the notions of a passive NN, a dissipative NN, and a robust NN are introduced.

Multilayer neural-net robot controller with guaranteed tracking performance

A novel real-time learning algorithm for a multilayered neural network is derived from the extended Kalman filter (EKF). Since this EKF-based learning algorithm approximately gives the minimum variance estimate of the linkweights, the convergence performance is improved in comparison with the backwards error propagation algorithm using the steepest descent techniques. Furthermore, tuning parameters which crucially govern the convergence properties are not included, which makes its application easier. Simulation results for the XOR and parity problems are provided. >

A real-time learning algorithm for a multilayered neural network based on the extended Kalman filter

The authors present a novel nonlinear regulator design method that integrates linear optimal control techniques and nonlinear neural network learning methods. Multilayered neural networks are used to add nonlinear effects to the linear optimal regulator (LOR). The regulator can compensate for nonlinear system uncertainties that are not considered in the LOR design and can tolerate a wider range of uncertainties than the LOR alone. The salient feature of the regulator is that the control performance is much improved by using a priori knowledge of the plant dynamics as the system equation and the corresponding LOR. Computer simulations are performed to show the applicability and the limitations of the regulator. >

A nonlinear regulator design in the presence of system uncertainties using multilayered neural network

We derive autocorrelations of a chaos arising from a simple nonlinear deterministic difference equation. The resulting autocorrelations are identical with those of a stochastic first-order autoregressive process.

Autocorrelations of a certain chaos

Recently, Pagano has found a one-to-one relationship between multivariate autoregression and scalar periodic autoregressions, and derived a set of fundamental Yule-Walker (YW) type equations for estimating the parameters of the periodic autoregressions. In this paper, we first obtain a Levinson-type recursive algorithm for solving the above mentioned YW equations. Then using this recursion we show a circular lattice structure of the process. This enables us to obtain a Burg-type algorithm which guarantees the filter stability. Lastly, we modify it to an adaptive form for on-line computation. This circular lattice filter simultaneously performs whitening and orthogonalization of the components of multivariate input samples. The most salient feature of the algorithm is that it consists of calculations of scalar quantities, thus completely avoiding matrix manipulations accompanying usual multivariate processing methods.

https://ieeexplore.ieee.org/iel6/29/26169/01163874.pdf

Circular lattice filtering using Pagano's method

We propose generic relay and subcarrier allocation schemes for multicarrier (MC) system with amplify-and-forward (AF) relays. The outage probability bounds are derived analytically for each scheme. Simulation results show that these bounds are very tight and better than the bounds obtained straightforwardly from the analysis in the Single-Carrier (SC) case. This is because in our analysis we reckon with the increased degree of freedom brought by the parallel channels. One of the proposed schemes, the Average Best Relay Selection scheme, is best suited for practical implementation since it approaches the best performance while minimizing the required amount of signaling.

Hideaki Sakai

Papers

A real-time learning algorithm for a multilayered neural network based on the extended Kalman filter

A nonlinear regulator design in the presence of system uncertainties using multilayered neural network

Autocorrelations of a certain chaos

Circular lattice filtering using Pagano's method

Amplify-and-Forward Cooperative Diversity Schemes for Multi-Carrier Systems