XCII. A theory of radar information

Abstract

The theoretical accuracy and certainty with which range may be determined by radar is obtained quantitatively by applying the principle of inverse probability. In agreement with experience, the theory yields two fundamental criteria for satisfactory radar reception. First, the total received signal energy must always be larger than the effective noise power per unit bandwidth. Secondly, there is a more stringent threshold of unambiguous reception which depends not only on the quantity of received energy but also on the bandwidth of the transmitted waveform, for as this is increased the minimum energy required for the certain detection of an echo also increases. The quantity of information obtainable at the receiver, as measured by reduction of entropy, is evaluated for comparison with that given by Shannon's general theory of communication (Shannon 1948). It is found that as the time of observation and hence the received energy increases, information is initially obtained at a roughly uniform rate which is not far removed from the absolute limit for an ideal communication system, but that after crossing the threshold of unambiguous reception, additional received energy contributes little further information.