  The design of a conical phased array antenna for air traffic control (ATC)
radar systems is addressed in this work. The array, characterized by a fully
digital beam-forming (DBF) architecture, is composed of equal vertical modules
consisting of linear sparse arrays able to generate on receive multiple
instantaneous beams pointing along different elevation directions. The
synthesis problem is cast in the Compressive Sensing (CS) framework to achieve
the best trade-off between the antenna complexity (i.e., minimum number of
array elements and/or radio frequency components) and radiation performance
(i.e., matching of a set of reference patterns). Towards this aim, the
positions of the array elements and the set of complex element excitations of
each beam are jointly defined through a customized CS-based optimization tool.
Representative numerical results, concerned with ideal as well as real antenna
models, are reported and discussed to validate the proposed design strategy and
point out the features of the deigned modular sparse arrays also in comparison
with those obtained from conventional arrays with uniformly spaced elements.
