On the Sampling of the Electromagnetic Field Radiated by Sparse Sources

The aim of this paper is to discuss the effectiveness of random sampling of the electromagnetic field in problems involving sparse radiating sources. The method adopted in this paper uses an intuitive geometrical approach based on the Johnson-Linderstrauss lemma applied to the ε-net of the set of the fields radiated by the sparse source. The paper shows that a proper Non Uniform Random Sampling (NURS) using some a-priori information on the problem allows a significant reduction in the cardinality of the set of the measured data compared to uniform random sampling and to random sampling from a λ/2 equispaced set of data. It is also shown that there is a limiting number of data after which random sampling is not convenient. In this case a deterministic sampling strategy, called Modified Non Uniform Sampling (MNUS), is proposed. Numerical results on linear sparse arrays confirm the effectiveness of NURS and MNUS.