Detection of stochastic processes

This paper reviews two streams of development, from the 1940's to the present, in signal detection theory: the structure of the likelihood ratio for detecting signals in noise and the role of dynamic optimization in detection problems involving either very large signal sets or the joint optimization of observation time and performance. This treatment deals exclusively with basic results developed for the situation in which the observations are modeled as continuous-time stochastic processes. The mathematics and intuition behind such developments as the matched filter, the RAKE receiver, the estimator-correlator, maximum-likelihood sequence detectors, multiuser detectors, sequential probability ratio tests, and cumulative-sum quickest detectors, are described     

Locally connected VLSI architectures for the Viterbi algorithm

The Viterbi algorithm is a well-established technique for channel and source decoding in high-performance digital communication systems. Implementations of the Viterbi algorithm on three types of locally connected processor arrays are described. The restriction is motivated by the fact that both the cost and performance metrics of VLSI favour architectures in which on-chip interprocessor communication is localized. Each of the structures presented can accommodate arbitrary alphabet sizes and algorithm memory lengths     

A contribution to optimal lamp design in rapid thermal processing

Recent studies of wafer temperature control in rapid thermal processing systems have indicated that a multiring circularly symmetric lamp configuration with independent (multivariable) control of the power applied to each ring is likely to be more successful than the earlier lamp design approaches. An important issue in such multiring lamp systems is the optimal shaping of the output heat flux profile (HFP) of each ring to provide maximum controllability of the wafer temperature. In this paper we seek to optimize the ring HFP's via the lamp design parameters: ring positions and widths. We start by determining the heat loss profiles over the wafer surface for a variety of temperature setpoints and processing conditions. In order to maintain temperature uniformity across the wafer at a given setpoint, the lamp system should provide a compensating HFP. The total lamp HFP is the sum of the individual ring HFPs weighted by their respective applied powers. The HFP's are, in turn, functionally dependent on the lamp design parameters and this dependence can be measured through a calibration process. Therefore, the resulting optimization problem reduces to determining the lamp design parameters that result in lamp HFP's which best approximates the collection of the wafer heat loss profiles. Our method provides a practical technique for determining the optimal lamp design parameters     

High-resolution spectral analysis using multiple-interval adaptive prediction

The problem of adaptively detecting two sinusoids corrupted by noise is considered, with emphasis on resolution properties. The approach is to form a spectral estimate from the coefficients of a Δ-step-ahead adaptive predictor. A theoretical analysis reveals that attention to the choice of the prediction horizon Δ gives a distinct improvement in the spectral estimate and in the resolution of the signals. The theoretical results are illustrated with numerical examples. Comparisons with previously suggested techniques are also made.     

Supplement to “a survey of data smoothing”

Some additions and clarifications are presented as a supplement to a recent survey in this journal of smoothing for linear and nonlinear dynamic systems.     

An innovations approach to least-squares estimation--Part V: Innovations representations and recursive estimation in colored noise

We show that least-squares filtered and smoothed estimates of a random process given observations of another colored noise process can be expressed as certain linear combinations of the state vector of the so-called innovations representation (IR) of the observed process. The IR of a process is a representation of it as the response of a causal and causally invertible linear filter to a white-noise "innovations" process. For nonstationary colored noise processes, the IR may not always exist and a major part of this paper is devoted to the problem of identifying a proper class of such processes and of giving effective recursive algorithms for their determination. The IR can be expressed either in terms of the parameters of a known lumped model for the process or in terms of its covariance function. In the first case, our results on estimation encompass most of those found in the previous literature on the subject; in the second case, there seems to be no prior literature. Finally, we may note that our proofs rely on, and exploit in both directions, the intimate relation that exists between least-squares estimation and the innovations representation.     

Estimability and regulability of linear systems

A linear state-space system is said to be estimable if in estimating its state from its output the posterior error covariance matrix is strictly smaller than the prior covariance matrix. It is said to be regulatable if the quadratic cost of the state feedback control is strictly smaller than the cost when no feedback is used. Estimability and regulability are shown to be dual properties, equivalent to the nonreducibility of the Kalman filter and of the optimal linear quadratic regulator, respectively     

Obtaining schedules for digital systems

A systematic technique is presented to derive correct schedules for a synchronous digital system, given a signal flow graph for an algorithm. It is also shown how to use this technique to derive designs that are optimal in having the lowest latency, the highest throughput, or the smallest number of registers. The same technique can also be used to verify digital systems that have already been designed