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Characterization of Randomly Time-Variant Linear
Channels
Abstract—This paper is concerned with various aspects of the characterization of randomly
time-variant linear channels. At the outset it is demonstrated that time-varying linear
channels (or filters) may be characterized in an interesting symmetrical manner in time and
frequency variables by arranging system functions in (time- frequency) dual pairs.
Following this a statistical characterization of randomly time-variant linear channels is
carried out in terms of correlation functions for the various system functions. These results
are specialized by considering three classes of practically interesting channels. These are the
wide-sense stationary (WSS) channel, the uncorrelated scattering (US) channel, and the
wide-sense stationary uncorrelated scattering (WSSUS) channel. The WSS and US channels
are shown to be (time-frequency) duals. Previous discussions of channel correlation
functions and their relationships have dealt exclusively with the WSSUS channel. The point
of view presented here of dealing with the dually related system functions and starting with
the unrestricted linear channels is considerably more general and places in proper
perspective previous results on the WSSUS channel. Some attention is given to the problem
of characterizing radio channels. A model called the Quasi-WSSUS channel is presented to
model the behavior of such channels.
INTRODUCTION
D
URING RECENT YEARS there has been an increasing amount of attention given to the
study of randomly time-variant linear channels. This attention has been motivated to
a large extent by the advent of troposcatter, ionoscatter, chaff and moon
communication links and radar astronomy systems. The determination of optimum
modulation and demodulation techniques and the analytical determination of the efficacy
of optimum and suboptimum communication (or radar) techniques for such channels
depends heavily upon a satisfactory characterization of the transmission channel. Thus, the
characterization of randomly time- variant linear channels is of some interest.
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Architecture Diagram:
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