On the Design of Optimal Measurements for Antenna Near-Field Imaging Problems

摘要

A mathematical framework is introduced for optimization of antenna near-field imaging problems, based on the multipole expansion of the electromagnetic field, the Fisher information to quantify the quality of data and use of modern interior point convex optimization techniques. We consider the general problem of optimizing the measurement sensor allocation for parameter estimation in distributed systems, and in particular the problem of optimizing the measurement set-up for antenna near-field estimation. As an application example for antenna near-field imaging, we consider a relevant measurement set-up using cylindrical probing coordinates. The convex optimization problem is examined using duality theory, and it is shown that several structural properties of the optimal measurement problem can be exploited in developing an efficient interior point optimization method. In particular, we show that the cylindrical measurement set-up yields a Fisher information matrix with block diagonal structure, a feature which can be directly exploited in the optimization algorithm by reducing the number of dual decision variables.