Generalized ambiguity function of signals with compression in the case of the scattering of waves by bodies of complex shape

An analytical expression is derived for the generalized ambiguity function (GAF) for a body of complex shape which scatters as an ensemble of point reflectors, randomly oscillating as a single entity. This expression is used to investigate the compression and resolution of signals scattered by such a body and to determine losses in resolution and signal level connected with the finite spatial extent of the body and variations of the location of local regions of reflection as the body moves. It is shown that, for linear-FM signals with a Gaussian envelope, the expression for the GAF can be written in elementary functions.