On the Measurement and Use of Time-Varying Communication Channels

In radio, radar , sonar, and seismic signal de tec t ion there is of ten the problem of processing received signals which have been distor ted by a l inear operat ion in the process of being t r ansmi t t ed . Examples are sca t te r ing and mul t ip le -pa th propaga t ion of radio waves. Usual ly the na tu re of th is l inear operat ion cannot be known very precisely in advance, and i t often is changing in time, so t h a t in order to carry out effective processing of the received signals i t is necessary repeatedly to tes t and measure the mode of t ransmiss ion, or channel as i t will be called. In th is paper the beginnings of a theory are es tabl ished concerning t ime-vary ing and random l inear channels wi th the i n t e n t of character iz ing classes of channels which can be de termined exact]y or approx imate ly by measurement , showing how the measurements can be made, ana lyz ing the errors, and applying the resul ts to the theory of signal detect ion. The not ion of a de te rminab le class of channels is defined and general examples are given. These include classes of channels t h a t are t imeinvar ian t , periodic, and which va ry wi th a known trend. The measurement of s lowly-varying channels by approximat ion by t imeinva r i an t ones belonging to a known de te rminable class is discussed. Re la t ion be tween a lmos t t imeinvar ianee of a channel and the corre la t ion proper t ies of a k ind ef s t a t iona ry random channel are developed and t iedin wi th the ehanne! measurement theory. An appl ica t ion is made to the problem of de tec t ing sure signals in noise when the channel is slowly-varying.