Medium Inhomogeneities and Instabilities: Effects on Spatial and Temporal Processing

Abstract

Effects on signal processing (temporal and spatial) of the instabilities and inhomogeneities of the propagation medium are considered from different aspects:

• The first part “Characterization of a time-frequency-space variant channel” introduces the mathematical tools for describing the acoustic channel, in a way which is suitable for treating most of the signal processing problems.

• The “performance degradations of linear processors with imperfectly coherent signals” is treated in the second part. The linear or conventional processor is a filter, operating in one or several dimensions, which is matched with the original signal as if it was a perfectly coherent one. General expressions for computing the “gain degradation factor” are given. The method is applied to the one-dimension case of a line-array which is longer than the spatial correlation distance of the medium.

• Linear processing, however, is not optimum for an incoherent signal. In the third part “Optimum processing of an imperfectly coherent signal” it is shown that a substantial reduction of the gain degradation factor (about one half if the losses are expressed in dB) can be obtained, at the price of a relatively minor increase in the complexity of the processor.