Masters Theses


Philip T. Tai


“In recent years communication engineers have given increased attention to the study of communication through random media. The name random is used to describe a medium the properties of which are stated only in a statistical sense. For example the impulsive response of a certain medium may only be known as one of an ensemble of possible impulsive responses; the particular member of interest being drawn up according to some statistical rule. In other words there exists some "uncertainty" concerning the characteristic description of the medium. Significant work on these problems has been done by Price and Turin. Related work has been done by Green, Root and Pitcher, R.C. Davis, Middleton, Kailath, and others.

Also considerable attention has recently been given to statistical decision theory in so far as its application to communications is concerned. While the formal beginning of statistical decision theory is generally attributed to Wald, the application of this theory to communications problems seems to have stemmed from the work of Middleton and Van Meter. The bulk of the work in statistical communications which deals with decision theory has been concerned with the detection of signals in noise and the estimation of signal parameters. Considerable attention has been focused on the estimation of linear (signal) parameters. (By a linear parameter is meant a signal parameter which can be extracted by a linear operation on the signal).

In this paper we wish to apply the techniques of statistical decision theory to the problem of finding an optimum receiver. In order to describe an optimal receiver, it is necessary to provide certain defining statements and adopt pertinent terminology. The terminology adopted here is essentially that of Middleton. To begin with, statistical reception is considered synonymous with statistical estimation. Estimation is performed by examining received data, the data being an additive combination of signal and noise. In general, the estimation process is divided into two categories: the first category, called detection, has only to do with a decision concerning the presence or absence of one or more signals. The second category called extraction, has to do with decisions concerning the estimation of one or more information bearing feature of the signal or signals. It is with the latter category that the present report is concerned.

The problem of interest here is depicted in Fig. 1. A known signal s(t) of finite duration is transmitted through a random linear channel, C, resulting in a waveform, say x(t), which is further corrupted by additive noise, n(t), before becoming available to the receiver. The final received signal is called r(t). Let T denote the duration, or the interval of observation, of r(t). For the present purposes, the optimum receiver is defined in the sense of Woodward as being the one that computes the set of a posteriori probabilities p(s(t)|r(t) )"--Introduction, pages 4-5.


Betten, J. Robert

Committee Member(s)

Pagano, Sylvester J., 1924-2006
Antle, Charles E.
Harden, Richard C.


Electrical and Computer Engineering

Degree Name

M.S. in Electrical Engineering


Five pages with figures are not numbered in the manuscript.


University of Missouri at Rolla

Publication Date



35 pages

Note about bibliography

Includes bibliographical references (pages 32-34).


© 1964 Philip T. Tai, All rights reserved.

Document Type

Thesis - Open Access

File Type




Thesis Number

T 1550

Print OCLC #