Charles E. Rohrs

Impulse response shortening for discrete multitone transceivers

In discrete multitone (DMT) transceivers an intelligent guard time sequence, called a cyclic prefix (CP), is inserted between symbols to ensure that samples from one symbol do not interfere with the samples of another symbol. The length of the CP is determined by the length of the impulse response of the effective physical channel. Using a long CP reduces the throughput of the transceiver, To avoid using a long CP, a short time-domain finite impulse response (FIR) filter is used to shorten the effective channels impulse response. This paper explores various methods of determining the coefficients for this time-domain filter. An optimal shortening and a least-squares (LS) approach are developed for shortening the channels impulse response. To provide a computationally efficient algorithm a variation of the LS approach is explored. In full-duplex transceivers the length of the effective echo path impacts the computational requirements of the transceiver. A new paradigm of joint shortening is introduced and three methods are developed to jointly shorten the channel and the echo impulse responses in order to reduce the length of the CP and reduce computational requirements for the echo canceller.

Paper: Some design guidelines for discrete-time adaptive controllers

There have been many algorithms proposed for adaptive control which will provide globally asymptotically stable controllers if some stringent conditions on the plant are met. The conditions on the plant cannot be met in practice as all plants will contain high frequency unmodeled dynamics. This paper uses a linearization analysis of a nonlinear adaptive controller to demonstrate analytically some design guidelines which alleviate some of the problems associated with adaptive control in the presence of unmodeled dynamics. The points made are further demonstrated by simulation results.

The composite regressor algorithm for IIR adaptive systems

An adaptive IIR algorithm called the composite regressor algorithm (CRA) is developed. The algorithm is a generalization of the common equation error, a priori output error, and a posteriori output error adaptive IIR algorithms. The CRA is analyzed for convergence in a noiseless environment and for bias in a stochastic setting. It is determined that, by using a parameter called the regressor composition parameter, a tradeoff can be obtained between the automatic convergence but large bias results of the equation error algorithm and the difficult convergence condition but small bias results of the output error algorithms. In proving results for the CRA, it is shown that the a posteriori output error algorithm produces estimates with nonzero bias when the adaptive gain is small but bounded away from zero. A convergence condition for the a priori output error algorithm is derived for the first time. >

Identification with nonparametric uncertainty

The authors present an identification technique that is robust to nonparametric uncertainty (i.e., model mismatch). The identifier produces both a parameter set estimate and a frequency response set estimate. The estimates result from the inclusion of a model of the nonparametric uncertainty in the plant model. The frequency response set estimate is shown to always contain the frequency response of the plant as long as certain modeling conditions are met. This type of identifier would be useful in applications such as control where a property such as stability or performance level must be achieved in the face of low-order modeling and its associated nonparametric uncertainty.<<ETX>>

The composite regressor algorithm

A relation between equation error and output-error adaptive algorithms is presented. It leads to a clarified view of output-error bias and stability. It is shown that a tradeoff between desirable stability and bias characteristics can be achieved in output error by manipulation of the adaptive gain. The composite regressor algorithm (CRA) is introduced as a means of affecting this tradeoff, independent of the gain. Output error is shown to a special case of CRA. A stability constraint for CRA is developed in a theorem, and the bias properties of this algorithm are discussed.<<ETX>>

A neural network solutions for routing in three stage interconnection networks

A neural network solution to the problem of routing calls through a three-stage interconnection network is presented. The neural network is shown, via a theorem with proof, to select an open path through the interconnection network if one exists. The solution uses a Hopfield network with a binary threshold rather than a sigmoidal function. The weights of the neural network are fixed for all time, and thus are independent of the current state of the interconnection network. It is possible to implement various routing strategies through selection of inputs to the neural network, again independently of the weights. The convergence proof is based on a hypercube analysis technique that defines and locates all local minima of the neural network energy function. When one or more open paths exist, it is shown that all local minima correspond to such paths, and therefore convergence to a minimum is equivalent to selection of an open path. When no such path is available, the energy function is unimodal and the neural network converges to a null state indicating that the interconnection network is blocked.<<ETX>>

A Practical Robustness Theorem for Adaptive Control

In this paper, two theorems are quoted which, when applied together, provide much information about the robustness of adaptive control schemes. From these two theorems, another theorem is developed which can explain why adaptive controllers can perform robustly in certain practical situations, while possibly failing in other situations. In particular, if the bandwidth constraints on a control systems are lenient enough to allow the use of a sampling frequency which is smaller than the frequency at which unstructured uncertainty becomes significant, an adaptive controller can behave robustly. Many, if not all, of the applications of adaptive control which have been successful employ relatively slow sampling of the process. Thus, the results of this paper provide a theoretical explanation of how certain adaptive controllers are performing robustly in practice. In addition, the final theorem is of a form which provides insight into what a priori knowledge is required to achieve robust adaptive control and how this knowledge say be used.

Bias analysis of a combined output error-equation error algorithm

An analysis is presented of the bias produced in the composite regressor algorithm. This study contains what the authors believe is the first analytical demonstration that there is bias in the output error algorithm when the algorithm is used with a small but nonvanishing adaptation step size. The analysis provides insight into general bias properties of infinite-impulse-response adaptive filtering algorithms.<<ETX>>

A frequency selective adaptive controller

It has been established that currently available adaptive control algorithms may become unstable in the presence of high frequency unmodeled dynamics and additive sinuosidal disturbances [1]-[3]. It is argued here that these problems can be overcome by using a controller which is adaptive for some frequency range but fixed for another frequency range which includes high frequencies. One candidate for such a frequency selective adaptive controller is presented and tested by simulation.

How the paper 'Robustness of model-reference adaptive control systems with unmodelled dynamics' misrepresents the results of Rohrs and his coworkers†

Errors made in Chen and Cook (1984) in their discussion of Rohrs et al. (1982) are exposed. It is shown that these errors result from a lack of understanding of the concepts of Rohrs el al. (1982) and from a general lack of careful research. The approach and results of Rohrs et al. (1982) are further clarified as they relate to the results of Chen and Cook (1984).