Time-varying propagation circuits, description and applications

Abstract

In radio/radar observations of natural targets, such as planets, satellites, asteroids and comets, the Earth's surface or the ionosphere, the troposphere and the stratosphere the response of the target to a signal can often be thought of as the response of a time-varying circuit. In recent investigations of the mesosphere, troposphere and stratosphere the measurement of the coherence between returns obtained in response to gated sine wave transmissions at adjacent frequencies has been used to increase the range resolution. In atmospheric radar applications this procedure has been referred to as frequency domain interferometry. The frequency correlation concept was previously introduced into radar astronomy, and was worked into the general concept of description of a time varying random propagation circuit. In such a circuit the properties can be described by a function of two parameters, the time delay τ and the frequency offset from the transmitter frequency Δ f. Integrating the function over frequency offsets one obtains the square of the mean impulse response as a function of delay, and integrating over all time delays one relating to the power spectrum of the circuit time variation irrespective of time delay. The time delay and frequency pair, ( τ,Δ f), can be used for the circuit description, but there are three more ways of describing the circuit in statistical terms, two of them involving the frequency separation Δ f as in frequency-domain interferometry. The different statistical descriptions and their interrelations are explained. Methods are indicated whereby estimates of the different statistical parameters of the circuit can be determined. In some cases the statistical properties may be definite functions of the pair of parameters, and in such cases special methods may be devised to derive the circuit properties and optimize detectability.