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.
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