Synthesis of clustered linear arrays through a total variation compressive sensing approach

In this work the problem of synthesizing the excitations of a linear array, clustered into contiguous sub-arrays of irregular length, is addressed. By suitably exploiting the behavior of clustered array aperture distributions (i.e., step-wise discrete functions), the problem has been formulated as the minimization of the total variation (TV) of the excitations, satisfying a matching condition on a predefined reference pattern. In virtue of the sparse nature of the unknowns, the minimization problem has been solved by means of an efficient total variation compressive sensing (TV-CS) optimization approach. A simple example validating the proposed technique is finally reported.