Propagation from a Point Source in a Randomly Refracting Medium

For analysis of a detection or communication system which processes signals from an array of sensors, a convenient postulate is that the signal field in the vicinity of the array is a plane wave (or perhaps a finite collection of plane waves in the multipath case). Under such a postulate, coherent addition of the sensor outputs can yield array gain and directivity in the presence of ambient noise. However, there is always some disparity between the predicted performance and the performance realized in practice. In part, the disparity can be attributed to shortcomings in the signal model, the field not being a time-invariant plane wave in the vicinity of the array. The output of a single sensor may not be constant in time but instead is apt to 1129 1130 THE BELL SYSTEM TECHNICAL JOURNAL, M A Y - J U N E 1969 fade. Moreover, the outputs of different sensors do not fade "in step"; that is, after the array is steered, the signals do not fade with the unity correlation predicted by a fading-plane-wave model. Instead, the signals fade with correlation less than unity. The origin of these fading phenomena is the subject of this paper. A simplified model of fading is considered within the framework of the following assumptions. For a short period of time, the transmission properties of a propagation path are constant; then they undergo small deviations to attain another constant configuration for the next short period of time. These short-term deviations are relative to some nominal or average configuration, as opposed to representing a slow gross trend of the overall path properties.