This is the pre-peer reviewed version of the following article: A. F. Morabito, A. Massa, P. Rocca and T. Isernia, “An Effective Approach to the Synthesis of Phase- Only Reconfigurable Linear Arrays,” IEEE Transactions on Antennas and Propagation, vol. 60, no. 8, pp. 3622-3631, 2012. Article has been published in final form at: ieeexplore.ieee.org/document/6204059. DOI: 10.1109/TAP.2012.2201099. 0018-926X © 2012 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works.” Abstract—We present an effective approach to the optimal mask-constrained power pattern synthesis of uniformly spaced array antennas able to dynamically reconfigure their radiation pattern by modifying only the excitation phases. The proposed approach results in a design procedure having a very low computational burden and, by exploiting at best the knowledge available in the separate synthesis of each pattern, is able to solve the underlying combinatorial optimization problem and to achieve solutions close (or equivalent) to the global optimum. A set of representative examples are reported in order to validate the proposed approach. Some extensions of the developed theory to cases other than linear arrays are also outlined. Index Terms—Array antennas, reconfigurable arrays, phase- only control, antenna synthesis. I. INTRODUCTION FFECTIVE design of single antennas able to radiate more than one pattern is a very long standing subject in Electromagnetics, with contributions dating back to the seventies of the last century. Recently, the interest in the topic is due to the extraordinary large number of possible applications, ranging from remote sensing and radars to telecommunications, including wireless local area networks, base-transceiver stations for mobile communications, and satellite communications [1]-[16]. Among the different kinds of adopted radiating systems, phased array antennas have a relevant role, as they can be controlled by means of completely electronic techniques which increase the flexibility and speed of the reconfiguration [1]. In order to get a Beam Forming Network (BFN) as simple as possible, and thus to reduce costs while still guaranteeing the generation of different patterns, several architectures have been proposed. These include suitable sub-arraying strategies in order to modify excitations while not duplicating the BFN [4],[14], or arrays having common excitations when reconfiguring the pattern from a sum to a difference pattern [3],[14],[15], or even the exploitation of parasitic elements [16]. Amongst the different possibilities, architectures based on phase-only control, where the excitation sets corresponding to the various patterns differ only in their phase distributions, are by far the ones which have received the largest attention [2],[5]-[13]. Such a circumstance is due to the fact that the use of a single power-divider network makes the solutions cheaper and more efficient than those which dynamically modify the amplitude of the weight coefficients. Furthermore, because of scanning requirements, radar antennas based on electronic steering require a phase shifter for each element of the array so that a phase-only reconfigurability of the pattern shape does not actually require any additional hardware. The main drawback concerns the intrinsic difficulty in solving the corresponding synthesis problem in an optimal fashion, i.e., in fulfilling given design goals by exploiting the minimum number of elements or optimize given performances for a fixed number of elements. Indeed, the ‘common amplitude’ requirement on the excitations results in non-linear and non-convex constraints, which imply considerable additional difficulties in the development of effective synthesis procedures. In the literature, the problem has been approached both using the so-called ‘alternating projections’ technique [2],[6],[10] and exploiting global optimization strategies [5],[7]-[9],[11],[12]. Notably, both approaches are extremely flexible, as they allow one to take into account in an easy fashion not only the common amplitude requirement, but also other constraints such as Dynamic Range Ratio (DRR) of excitations, near-field behaviour, and the like. However, because of the non-linear constraints and the arising non-convex sets involved in the alternating projection technique, the optimization procedure can be trapped into local minima far from the actual optimal solution [2],[10]. As a consequence, ‘sub-optimal’ solutions will be found. Differently, ‘global optimization’ procedures, by definition, are not sensitive to such a problem. However, the computational cost of global optimization algorithms rapidly increases with the problem size [21],[22] and this, in practice, can prevent the attainment of the global optimum [18],[23]. In this paper, a new convenient perspective is introduced which allows one to define a novel procedure for the synthesis An Effective Approach to the Synthesis of Phase-Only Reconfigurable Linear Arrays A. F. Morabito, A. Massa, P. Rocca, and T. Isernia E