Scattering statistics of Doppler faded acoustic signals using speckle noise models

Understanding scattering multipath channels that fade randomly with respect to time, frequency, and space is very crucial for the accurate detection of objects and the study of their scattering characteristics when mapped by active radar or sonar systems. In this paper, we derive stochastic models for the probability density function (pdf) of the shift in the carrier frequency caused by the Doppler effect on the received illuminating signal. Our derivation is based on single- and multi-look partially developed speckle noise models, which are in perfect agreement with the Doppler spread in the Clarke´s model. Finally, we study the problem of object detection in randomly faded channels by analogy to optimal detection of binary phase shift keying signals in digital communication.