Mathematical analysis and detailed study of generic model for coherent receiver has demonstrated that nonlinear coherence between given biphase-modulated input signal and supplied reference signal can be used in receivers to improve telecommunication systems

Lindsey, W. C.

Simon, M. K.

English

NASA Technical Reports Server

March 1973	 B78-10144 
NASA TECH BRIEF 
NASA Pasadena Office	 -4r 
NASA Tech Briefs announce new technology derived from the U.S. space program. They are issued to encourage 
commercial application. Tech Briefs are available on a subscription basis from the National Technical Information 
Service, Springfield, Virginia 22151. Requests for individual copies or questions relating to the Tech Brief program may 
be directed to the Technology Utilization Office, NASA, Code KT, Washington, D.C. 20546. 
A Nonlinear-Coherence Receiver 
Mathematical analysis and detailed study of a ge-
neric model for a coherent receiver has demonstrated 
that the nonlinear coherence between a given biphase-
modulated input signal and a supplied reference sig-
nal can be used advantageously in present-day re-
ceivers to improve telecommunication systems. There 
are many special cases of the general structure, but 
the only two that have been explored thus far (the 
data-aided and hybrid carrier tracking loops) have 
provided significant improvement in performance over 
the present-day phase-coherent tracking, telemetry, 
S
and command systems which utilize PCM/PSK/PM 
modulation. 
The usual method for examining the mutual power 
between two signals at an arbitrary frequency is 
through the use of a cross-spectrum, that is, the spec-
tral density of power that is mutually shared in a 
phase-coherent manner. It is important to note that 
each signal can have power in a common frequency 
band without there being cross-spectral power in that 
band; the existence of common frequency-components 
does not imply mutually coherent power. 
In a nonlinear system, it is possible to have coher-
ency between a signal at one frequency and another 
signal at some multiple of that frequency. For ex-
ample, when the generic model includes a squaring 
loop, an input signal with energy centered at a nom-
inal frequency is squared (nonlinear operation) to 
produce a signal that is centered at twice the nominal 
frequency and is phase-coherent with the suppressed 
carrier signal. The signal at the higher frequency is 
tracked by a conventional phase-lock loop with an 
oscillator of the same nominal frequency.
The results of detailed mathematical analyses of 
the generic model also demonstrate that nonlinear 
coherence receivers operated in a multiple loop conflg-
uration can very readily be made to provide improved 
signal-to-noise figures inasmuch as phase—time rela-
toinships within desired signals are not common with 
noise signals. Moreover, with telemetry signals which 
can have constant phase errors over several symbol 
intervals, appropriate delay elements can be intro-
duced into the generic model in order to exploit side-
band power in much the same manner as is done in 
differentially coherent detection or time diversity re-
ception; mathematical expressions for the signal and 
noise components of voltages appearing at various 
points in the generic model are tabulated in the report 
which summarizes the results of the study. 
Note: 
Requests for further information may be directed 
to:
Technology Utilization Officer 
NASA Pasadena Office 
4800 Oak Grove Drive 
Pasadena, California 91103 
Reference: TSP73-10144 
Source: Marvin K. Simon of 
Caltech/JPL
and William C. Lindsey of
University of Southern California 
under contract to 
NASA Pasadena Office 
(NPO-11921) 
Category 02 
This document was prepared under the sponsorship of the National 	 Government assumes any liability resulting from the use of the 
Aeronautics and Space Administration. Neither the United States 	 information contained in this document, or warrants that such use 
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A nonlinear-coherence receiver

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