Detection and estimation in antenna processing: applications

The processing of sensor array antennas is addressed here within the framework of decision theory applied to vector signals. The methodology introduced in Part I is applied. . However, to do this, preliminary modeling work is required, firstly to clarify the relationships between physical parameters and measurements, and secondly to provide the theory with observation probability densities that can be used in practice (sampling technique).

Decision theory is not really indispensable for introducing the basic concepts of antenna processing (ambiguity function and antenna gain, for example), but it does provide the appropriate framework for describing the performance of a method or for judging its optimality. Without decision theory, antenna processing would consist in proposing algebraic inversion methods that would be highly insensitive to computational errors, additive noise and modeling errors.

Nevertheless, this article is not just an exercise in the application of decision theory. The vector signal studied here has the particularity of having been generated by the sensors of an antenna immersed in a medium traversed by propagating waves. This gives a particular form to the results obtained and requires a description that gives antenna processing its specificity.

In short, readers with a particular interest in antenna processing will find here the main classical results in the field, such as the adaptive antenna or the adaptive goniometer, as well as the usual tools for describing it, such as the antenna variety.

For the more decision-theoretic reader, we have tried to show the intimate relationship between decision criteria and physics, such as the Cramer-Rao bound and the ambiguity function. The most significant point we wanted to develop is that the same problem can give rise to very different results, depending on how it is modelled.