An effective approach for sparse arrays design with the minimum number of sensors

In this paper the antenna synthesis problem by involving the minimum number of sensors is considered from a new and interesting perspective, based on the compressive sensing theory. The Compressive Sensing (CS) theory asserts that one can recover certain signals from fewer samples than the traditional methods. To get such a result, the CS relies on two important principles: sparsity, which pertains to the signals to reconstruct, and incoherence, which pertains to the sensing modality. In other words, compressive sampling exploits the fact that many natural signals are sparse or compressible in the sense that they have concise representations when expressed in the proper basis. In the antenna synthesis problem if the location, amplitude and phase distribution of all the involved sensors can be obtained in the sparsest representation, then the aim of synthesizing a desired radiation pattern with the minimum antenna elements is achieved. In particular the complex weights distribution on the array support (which is a line in the case of linear array) is intrinsically sparse because it is a superposition of spikes (located in the element positions). Accordingly, it can be exactly recovered by solving a convex minimization problem.