On the measurement and use of time-varying communication channels

Abstract

In radio, radar, sonar, and seismic signal detection there is often the problem of processing received signals which have been distorted by a linear operation in the process of being transmitted. Examples are scattering and multiple-path propagation of radio waves. Usually the nature of this linear operation cannot be known very precisely in advance, and it often is changing in time, so that in order to carry out effective processing of the received signals it is necessary repeatedly to test and measure the mode of transmission, or channel as it will be called.In this paper the beginnings of a theory are established concerning time-varying and random linear channels with the intent of characterizing classes of channels which can be determined exactly or approximately by measurement, showing how the measurements can be made, analyzing the errors, and applying the results to the theory of signal detection.The notion of a determinable class of channels is defined and general examples are given. These include classes of channels that are time-invariant, periodic, and which vary with a known trend. The measurement of slowly-varying channels by approximation by time-invariant ones belonging to a known determinable class is discussed. Relation between almost-time-invariance of a channel and the correlation properties of a kind of stationary random channel are developed and tied-in with the channel measurement theory. An application is made to the problem of detecting sure signals in noise when the channel is slowly-varying.