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# Accession Number:

## AD0466441

# Title:

## SIGNAL DETECTION USING A NOISY REFERENCE SIGNAL.

# Descriptive Note:

## Interim technical rept.,

# Corporate Author:

## HARVARD UNIV CAMBRIDGE MA CRUFT LAB

# Report Date:

## 1965-04-29

# Pagination or Media Count:

##
34.0

# Abstract:

## In digital communications, one is frequently confronted with the problem of signal discrimination under the added uncertainty of imprecise knowledge of the signaling waveforms. This added uncertainty is usually caused by the channel over which the signaling waveforms are transmitted. In this report, we consider the problem of discriminating among M signal waveforms which are of the form vtsjt theta nt, 0 less than or equal to t less than or equal to T, j 1,2,..., M where theta is a set of n unknown constant parameters and nt is gaussian noise. The receiver for detecting the signals is designed on the basis of an estimate theta estimate of the signal parameters which is derived from prior received waveforms of signal plus noise. Our major effort is devoted to the derivation of the estimate theta estimate which turns out to be an approximation to the maximum likelihood estimate of theta. This estimate is compared with three alternate estimators for theta that have been considered. For the specific case in which the unknown parameter is the signal phase phi, the effect of the four different estimates for phi on the performance of a binary and a quaternary communications system is evaluated by means of a Monte Carlo simulation of the systems on a digital computer. The error rates that resulted from the simulation are summarized in tabular form. Author

# Distribution Statement:

## APPROVED FOR PUBLIC RELEASE

#