Absfracf-We present a study of a matrix pencil method for estimating parameters (frequencies and damping factors) of exponentially damped and/or undamped sinusoids in noise. Comparison of this method to a polynomial method (SVD-Prony method) shows that the matrix pencil method and the polynomial method are two special cases of a matrix prediction approach but the pencil method is more efficient in computation and less restrictive about signal poles. I t is found through perturbation analysis and simulation that, for signals with unknown damping factors, the pencil method is less sensitive to noise than the polynomial method. I n Appendix A, a new expression of the Cramer-Ran bound for the exponential signals i s presented.

The approximation of a hnction by a sum of complex exponentials is a problem that is at least two centuries old. Fundamentally, all techniques discussed in this article proceed from using the same sequence of data samples and vary only, but importantly, in how those samples are used in achieving the parameter estimation. All of these techniques, in other words, seek the same quantitative parameters to represent the sampled data, but use different routes to get there. The techniques for estimating the parameters are either linear or nonlinear. The linear techniques are emphasized in this presentation. In particular, the Matrix Pencil Method is described, which is more robust to noise in the sampled data. The Matrix Pencil approach has a lower variance of the estimates of the parameters of interest than a polynomial-type method (Prony's method belongs to this category), and is also computationally more efficient. A bandpass version of the Matrix Pencil can be implemented in hardware, utilizing an AT&T DSP32C chip operating in real time. A copy of the computer program implementing the Matrix Pencil technique is given in Appendix.

In order to estimate the signal parameters accurately for mobile systems, it is necessary to estimate a system's propagation characteristics through a medium. Propagation analysis provides a good initial estimate of the signal characteristics. The ability to accurately predict radio-propagation behavior for wireless personal communication systems, such as cellular mobile radio, is becoming crucial to system design. Since site measurements are costly, propagation models have been developed as a suitable, low-cost, and convenient alternative. Channel modeling is required to predict path loss and to characterize the impulse response of the propagating channel. The path loss is associated with the design of base stations, as this tells us how much a transmitter needs to radiate to service a given region. Channel characterization, on the other hand, deals with the fidelity of the received signals, and has to do with the nature of the waveform received at a receiver. The objective here is to design a suitable receiver that will receive the transmitted signal, distorted.due to the multipath and dispersion effects of the channel, and that will decode the transmitted signal. An understanding of the various propagation models can. actually address both problems. This paper begins with a review of the information available on the various propagation models for both indoor and outdoor environments. .The existing models can be classified into two major classes: statistical models and site-specific models. The main characteristics of the radio channelsuch as path loss, fading, and time-delay spreadare discussed. Currently, a third alternative, which includes many new numerical methods, is being introduced to propagation prediction. The advantages and disadvantages of some of these methods are summarized. In'addition, an impulse-response characterization for the propagation path is also presented, including models for small-scale fading. Finally, it is shown that when two-way communication ports can be defined for a mobile system, it is possible to use reciprocity to focus the energy along the direction of an intended user without any explicit knowledge of the electromagnetic environment in which the system is operating, or knowledge of the spatial locations of the transmitter and the receiver.

A generalized pencil-of-function (GPOF) method for extracting the poles of an EM system from its transient response is developed. The GPOF method needs the solution of a generalized eigenvalue problem to find the poles. This is in contrast to the conventional Prony and pencil-of-function methods which yield the solution in two steps, namely, the solution of an ill-conditioned matrix equation and finding the roots of a polynomial. Subspace decomposition is also used to optimize the performance of the GPOF method. The GPOF method has advantages over the Prony method in both computation and noise sensitivity, and approaches the Cramer-Rao bound when the signal-to-noise ratio (SNR) is above threshold. An application of the GPOF method to a thin-wire target is also presented.

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